diff --git a/Project/AboutForm.cpp b/Project/AboutForm.cpp
index 619c6c15..2fea1ecd 100644
--- a/Project/AboutForm.cpp
+++ b/Project/AboutForm.cpp
@@ -22,7 +22,7 @@ AboutForm::~AboutForm() {}
 void AboutForm::Init()
 {
     // Set program version. Format: (Alpha/Beta/Release) (YEAR)w(WEEK)(a/b/c/...)
-    m_staticTextVersion->SetLabel("2020w28a-beta");
+    m_staticTextVersion->SetLabel("2020w31a-beta");
     
     // Create developers table
     m_gridCredits->EnableGridLines(false);
diff --git a/Project/MainFrame.cpp b/Project/MainFrame.cpp
index 1a9c9a97..178e2ebb 100644
--- a/Project/MainFrame.cpp
+++ b/Project/MainFrame.cpp
@@ -387,7 +387,10 @@ void MainFrame::OnOpenClick(wxRibbonButtonBarEvent& event)
     }
 }
 
-void MainFrame::OnPSPGuideClick(wxRibbonButtonBarEvent& event) {}
+void MainFrame::OnPSPGuideClick(wxRibbonButtonBarEvent& event)
+{
+    wxLaunchDefaultBrowser("https://thales1330.github.io/PSP/docs/");
+}
 void MainFrame::OnPasteClick(wxRibbonButtonBarEvent& event) {}
 void MainFrame::OnPowerFlowClick(wxRibbonButtonBarEvent& event)
 {
@@ -459,8 +462,10 @@ void MainFrame::OnAddElementsClick(wxCommandEvent& event)
     if (workspace) {
         if (workspace->GetWorkspaceMode() != Workspace::WorkspaceMode::MODE_INSERT) {
             auto elementList = workspace->GetElementList();
+            auto textList = workspace->GetTextList();
             wxString statusBarText = "";
             bool newElement = false;
+            bool isText = false;
 
             switch (event.GetId()) {
             case ID_ADDMENU_BUS: {
@@ -541,10 +546,21 @@ void MainFrame::OnAddElementsClick(wxCommandEvent& event)
                 statusBarText = _("Insert Synchronous Condenser: Click on a buses, ESC to cancel.");
                 newElement = true;
             } break;
+            case ID_ADDMENU_TEXT: {
+                Text* newText = new Text();
+                textList.push_back(newText);
+                statusBarText = _("Insert Text: Click to insert, ESC to cancel.");
+                newElement = true;
+                isText = true;
+            } break;
             }
             if (newElement) {
                 workspace->SetElementList(elementList);
-                workspace->SetWorkspaceMode(Workspace::WorkspaceMode::MODE_INSERT);
+                workspace->SetTextList(textList);
+                if(!isText)
+                    workspace->SetWorkspaceMode(Workspace::WorkspaceMode::MODE_INSERT);
+                else
+                    workspace->SetWorkspaceMode(Workspace::WorkspaceMode::MODE_INSERT_TEXT);
                 workspace->SetStatusBarText(statusBarText);
                 workspace->Redraw();
             }
diff --git a/Project/OpenGLText.cpp b/Project/OpenGLText.cpp
index f877afa4..a72af7f0 100644
--- a/Project/OpenGLText.cpp
+++ b/Project/OpenGLText.cpp
@@ -188,9 +188,13 @@ OpenGLText* OpenGLText::GetCopy()
 {
     OpenGLText* copy = new OpenGLText();
     *copy = *this;
+    copy->m_textCoord = nullptr;
+    copy->Init();
+
     copy->m_textureID = nullptr;
     copy->m_bitmapSize = wxSize(0, 0);
     copy->m_bitmap = wxNullBitmap;
+
     copy->SetText(copy->m_text);
     return copy;
 }
diff --git a/docs/01a85c17.0a6ca1f8.js b/docs/01a85c17.ec0de5b7.js
similarity index 86%
rename from docs/01a85c17.0a6ca1f8.js
rename to docs/01a85c17.ec0de5b7.js
index 5e0b0254..88ea72a5 100644
--- a/docs/01a85c17.0a6ca1f8.js
+++ b/docs/01a85c17.ec0de5b7.js
@@ -1 +1 @@
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diff --git a/docs/08185850.135a38bd.js b/docs/08185850.b523173f.js
similarity index 99%
rename from docs/08185850.135a38bd.js
rename to docs/08185850.b523173f.js
index c0e42f29..5581d46a 100644
--- a/docs/08185850.135a38bd.js
+++ b/docs/08185850.b523173f.js
@@ -1 +1 @@
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diminuem a corre\xe7\xe3o."),Object(m.b)("div",{className:"admonition admonition-info alert alert--info"},Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(m.b)("h5",{parentName:"div"},Object(m.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(m.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"14",height:"16",viewBox:"0 0 14 16"}),Object(m.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"})))),"Informa\xe7\xe3o")),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"Valores menores que ",Object(m.b)("span",Object(s.a)({parentName:"p"},{className:"math 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",Object(m.b)("em",{parentName:"p"},"podem")," auxiliar na converg\xeancia, por\xe9m aumentam o n\xfamero de itera\xe7\xf5es e consequentemente o tempo de processamento do m\xe9todo."))),Object(m.b)("p",null,"Essa op\xe7\xe3o \xe9 habilitada somente para o m\xe9todo de ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerFlow#newton-raphson"}),"Newton-Raphson"),"."),Object(m.b)("h4",{id:"toler\xe2ncia-do-gauss"},"Toler\xe2ncia do Gauss"),Object(m.b)("p",null,"Define a toler\xe2ncia do Gauss-Seidel para o m\xe9todo h\xedbrido. 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Ao solt\xe1-lo todos os objetos que intercederem o ret\xe2ngulo ser\xe3o selecionados."),Object(n.b)("p",null,"Mantendo pressionado a tecla Control (Ctrl) do teclado pode-se manter sele\xe7\xf5es anteriores enquanto novos elementos s\xe3o selecionados."),Object(n.b)("p",null,"Para desmarcar todos os objetos basta clicar em uma \xe1rea sem objetos."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,playsInline:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/select.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/select.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"mover"},"Mover"),Object(n.b)("p",null,"Um elemento poder\xe1 ser movido para qualquer local por meio da a\xe7\xe3o ",Object(n.b)("em",{parentName:"p"},"drag-and-drop")," (clicando e arrastando) ou pela ferramenta mover."),Object(n.b)("p",null,"Ao habilitar o \u201cmodo mover\u201d, movendo todos os componentes selecionados \xe0 medida que a posi\xe7\xe3o do mouse \xe9 alterada. 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O elemento tamb\xe9m pode ser rotacionado pelo ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"submenu Ferramentas")," ou ao acessar o menu de contexto clicando com o bot\xe3o direito sobre o elemento."),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(t.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(t.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(t.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"O menu de contexto somente ser\xe1 exibido se o elemento estiver selecionado."))),Object(n.b)("p",null,"Ao utilizar essa ferramenta os objetos ir\xe3o girar 45\xba a partir do seu ponto de origem. Para atingir a angula\xe7\xe3o pretendida basta repetir o processo de rota\xe7\xe3o."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,playsInline:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/rotate.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/rotate.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"arrastar"},"Arrastar"),Object(n.b)("p",null,"Tr\xeas ferramentas muito \xfateis na navega\xe7\xe3o do circuito, principalmente em grandes redes, s\xe3o: arrastar, zoom e encaixar."),Object(n.b)("p",null,"A ferramenta arrastar possibilita mover todo o circuito ",Object(n.b)("strong",{parentName:"p"},"preservando as posi\xe7\xf5es relativas entre os elementos"),". Esta ferramenta pode ser acessada pelo submenu \u201cFerramentas\u201d ou ",Object(n.b)("strong",{parentName:"p"},"mantendo pressionada o ",Object(n.b)("em",{parentName:"strong"},"scroll")," do mouse"),", ativando assim o \u201cmodo arrastar\u201d. Ao ativ\xe1-lo todo o circuito ser\xe1 movido clicando e arrastando na dire\xe7\xe3o desejada."),Object(n.b)("p",null,"Para sair do \u201cmodo arrastar\u201d basta pressionar a tecla Escape do teclado."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,playsInline:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/drag.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/drag.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"zoom"},"Zoom"),Object(n.b)("p",null,"O zoom ser\xe1 aplicado ao utilizar o ",Object(n.b)("strong",{parentName:"p"},"scroll do mouse")," para mais ou menos zoom. A ferramenta zoom ir\xe1 aproximar ou distanciar o circuito a partir da posi\xe7\xe3o do ponteiro do mouse na tela para encontrar objetos ou destaca-los."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,playsInline:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/zoom.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/zoom.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"encaixar"},"Encaixar"),Object(n.b)("p",null,"A ferramenta encaixar ir\xe1 mover o circuito e aplicar o zoom necess\xe1rio para que todos os componentes da rede sejam exibidos na tela. Esta ferramenta pode ser acessada atrav\xe9s do submenu \u201cFerramentas\u201d ou pela combina\xe7\xe3o de teclas \u201cShift + F\u201d."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,playsInline:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/fit.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/fit.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"copiar-e-colar"},"Copiar e Colar"),Object(n.b)("p",null,"Duas ferramentas importantes durante o processo de cria\xe7\xe3o da rede el\xe9trica de pot\xeancia no ",Object(n.b)("em",{parentName:"p"},"software")," s\xe3o copiar e colar. Qualquer circuito criado no PSP-UFU poder\xe1 ser duplicado completamente ou parcialmente no mesmo projeto ou em m\xfaltiplos atrav\xe9s dessas ferramentas."),Object(n.b)("p",null,"Para copiar basta selecionar os elementos que se deseja duplicar e acessar a ferramenta no submenu \u201cFerramentas\u201d ou pressionando a combina\xe7\xe3o das teclas \u201cCtrl + C\u201d, ent\xe3o os dados do circuito ser\xe3o copiados para a \xe1rea de transfer\xeancia. Ao copiar um circuito ele poder\xe1 ser colado no mesmo projeto ou em um projeto distinto, utilizando o mesmo submenu ou pressionando a combina\xe7\xe3o das teclas \u201cCtrl + V\u201d."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,playsInline:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/copyPaste.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/copyPaste.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"excluir"},"Excluir"),Object(n.b)("p",null,"Qualquer objeto poder\xe1 ser exclu\xeddo do projeto por meio da ferramenta deletar, presente no menu Ribbon, pela tecla de atalho Delete ou pelo acesso ao menu de contexto clicando com o bot\xe3o direito sobre o elemento selecionado."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,playsInline:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/delete.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/delete.webm"),type:"video/webm"})),Object(n.b)("h2",{id:"personaliza\xe7\xe3o-gr\xe1fica-os-elementos"},"Personaliza\xe7\xe3o gr\xe1fica os elementos"),Object(n.b)("p",null,"Alguns elementos permitem sua personaliza\xe7\xe3o gr\xe1fica, como as barras e linhas."),Object(n.b)("h3",{id:"barra"},"Barra"),Object(n.b)("p",null,"No caso dos barramentos, pode-se alterar o ",Object(n.b)("strong",{parentName:"p"},"comprimento da barra")," clicando e arrastando no ",Object(n.b)("em",{parentName:"p"},"pickbox")," exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado."),Object(n.b)("h3",{id:"linha"},"Linha"),Object(n.b)("p",null,"As linhas podem ser inseridas com ",Object(n.b)("strong",{parentName:"p"},'"n\xf3s" (pontos de ancoragem)'),", personalizando a disposi\xe7\xe3o das linhas no diagrama unifilar. Esses n\xf3s s\xe3o inseridos durante o processo de cria\xe7\xe3o do elemento, anteriormente \xe0 sele\xe7\xe3o da segunda barra."),Object(n.b)("p",null,"Ap\xf3s a sua inser\xe7\xe3o, novos n\xf3s podem ser anexados pelo menu de contexto acessado ao clicar com o bot\xe3o direito sobre a linha selecionada. Sua remo\xe7\xe3o tamb\xe9m \xe9 alcan\xe7ada por uma op\xe7\xe3o do menu de contexto."),Object(n.b)("p",null,"Assim como nos barramentos, a altera\xe7\xe3o da posi\xe7\xe3o dos n\xf3s \xe9 obtida clicando e arrastando o ",Object(n.b)("em",{parentName:"p"},"pickbox")," exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,playsInline:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/graphicPropsChange.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/graphicPropsChange.webm"),type:"video/webm"})),Object(n.b)("h2",{id:"conex\xe3o-e-desconex\xe3o-de-elemetos-na-barra"},"Conex\xe3o e desconex\xe3o de elemetos na barra"),Object(n.b)("p",null,"Os elementos podem ser desconectados e reconectados \xe0s barras ap\xf3s sua inser\xe7\xe3o somente pela ferramenta ",Object(n.b)("em",{parentName:"p"},"drag-and-drop"),". Para isso, o elemento deve ser selecionado e o seu n\xf3 de conex\xe3o deve ser arrastado para o local requerido."),Object(n.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(t.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(t.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(n.b)("path",Object(t.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado!")),Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"O elemento a ser desconectado/reconectado ",Object(n.b)("strong",{parentName:"p"},"deve ser previamente selecionado")," para efetuar a opera\xe7\xe3o. Caso contr\xe1rio a barra ser\xe1 movida ou nenhuma opera\xe7\xe3o ser\xe1 realizada."))),Object(n.b)("p",null,"No caso de desconex\xe3o, o elemento ser\xe1 automaticamente removido da simula\xe7\xe3o, sendo indicado pela sua cor (o elemento passa a ter cor ",Object(n.b)(d,{color:"#7f7f7f",mdxType:"Highlight"},"cinza"),")."),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(t.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(t.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(t.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Ao reconectar o elemento ao circuito, deve-se ",Object(n.b)("strong",{parentName:"p"},'atentar para estado do seu "disjuntor"'),", indicado por um quadrado pr\xf3ximo ao seu n\xf3 de conex\xe3o. 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",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Desenho_assistido_por_computador"}),"Wikipedia"))),Object(n.b)("h2",{id:"ferramentas-do-menu"},"Ferramentas do menu"),Object(n.b)("p",null,"Todos os objetos criados cont\xeam v\xe1rios atributos gr\xe1ficos, como: posi\xe7\xe3o, orienta\xe7\xe3o, cor, tamanho, etc. Para modific\xe1-los foram inseridas algumas ferramentas intuitivas e de f\xe1cil utiliza\xe7\xe3o, as quais s\xe3o: ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#selecionar"}),Object(n.b)("strong",{parentName:"a"},"selecionar")),", ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#mover"}),Object(n.b)("strong",{parentName:"a"},"mover")),", ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#girar"}),Object(n.b)("strong",{parentName:"a"},"girar")),", ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#arrastar"}),Object(n.b)("strong",{parentName:"a"},"arrastar")),", ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#zoom"}),Object(n.b)("strong",{parentName:"a"},"zoom")),", ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#encaixar"}),Object(n.b)("strong",{parentName:"a"},"encaixar")),", ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#copiar-e-colar"}),Object(n.b)("strong",{parentName:"a"},"copiar, colar"))," e ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"cadTools#excluir"}),Object(n.b)("strong",{parentName:"a"},"excluir")),"."),Object(n.b)("p",null,"Essas ferramentas podem ser acessadas por suas teclas de atalho assim como pelo ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"submenu Ferramentas"),"."),Object(n.b)("p",null,"Tais ferramentas permitem a ",Object(n.b)("strong",{parentName:"p"},"personaliza\xe7\xe3o"),", ",Object(n.b)("strong",{parentName:"p"},"navega\xe7\xe3o")," e auxiliam a ",Object(n.b)("strong",{parentName:"p"},"cria\xe7\xe3o")," de redes el\xe9tricas de pot\xeancia, assim como diagramas de controle na plataforma."),Object(n.b)("h3",{id:"selecionar"},"Selecionar"),Object(n.b)("p",null,"A sele\xe7\xe3o de um \xfanico objeto \xe9 realizada clicando com o bot\xe3o esquerdo do mouse sobre o elemento, que ser\xe1 identificado pelo contorno em ",Object(n.b)(d,{color:"#80bfff",mdxType:"Highlight"},"azul")," do objeto."),Object(n.b)("p",null,"Para a sele\xe7\xe3o de v\xe1rios objetos simultaneamente \xe9 necess\xe1rio clicar com o bot\xe3o esquerdo do mouse em um local vazio da tela e arrast\xe1-lo, criando assim um ",Object(n.b)("strong",{parentName:"p"},"ret\xe2ngulo de sele\xe7\xe3o")," que ir\xe1 acompanhar o ponteiro do mouse enquanto o bot\xe3o esquerdo estiver pressionado. Ao solt\xe1-lo todos os objetos que intercederem o ret\xe2ngulo ser\xe3o selecionados."),Object(n.b)("p",null,"Mantendo pressionado a tecla Control (Ctrl) do teclado pode-se manter sele\xe7\xf5es anteriores enquanto novos elementos s\xe3o selecionados."),Object(n.b)("p",null,"Para desmarcar todos os objetos basta clicar em uma \xe1rea sem objetos."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/select.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/select.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"mover"},"Mover"),Object(n.b)("p",null,"Um elemento poder\xe1 ser movido para qualquer local por meio da a\xe7\xe3o ",Object(n.b)("em",{parentName:"p"},"drag-and-drop")," (clicando e arrastando) ou pela ferramenta mover."),Object(n.b)("p",null,"Ao habilitar o \u201cmodo mover\u201d, movendo todos os componentes selecionados \xe0 medida que a posi\xe7\xe3o do mouse \xe9 alterada. Para desabilitar esse modo basta pressionar a tecla Escape do teclado."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/move.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/move.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"girar"},"Girar"),Object(n.b)("p",null,"Alguns objetos poder\xe3o ser rotacionados atrav\xe9s da ferramenta girar, acessado pela tecla de atalho \u201cR\u201d, girando o objeto no sentido hor\xe1rio, ou \u201cShift + R\u201d, para o sentido anti-hor\xe1rio (essa op\xe7\xe3o ir\xe1 afetar todos os objetos selecionados). O elemento tamb\xe9m pode ser rotacionado pelo ",Object(n.b)("a",Object(t.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"submenu Ferramentas")," ou ao acessar o menu de contexto clicando com o bot\xe3o direito sobre o elemento."),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(t.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(t.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(t.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"O menu de contexto somente ser\xe1 exibido se o elemento estiver selecionado."))),Object(n.b)("p",null,"Ao utilizar essa ferramenta os objetos ir\xe3o girar 45\xba a partir do seu ponto de origem. Para atingir a angula\xe7\xe3o pretendida basta repetir o processo de rota\xe7\xe3o."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/rotate.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/rotate.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"arrastar"},"Arrastar"),Object(n.b)("p",null,"Tr\xeas ferramentas muito \xfateis na navega\xe7\xe3o do circuito, principalmente em grandes redes, s\xe3o: arrastar, zoom e encaixar."),Object(n.b)("p",null,"A ferramenta arrastar possibilita mover todo o circuito ",Object(n.b)("strong",{parentName:"p"},"preservando as posi\xe7\xf5es relativas entre os elementos"),". Esta ferramenta pode ser acessada pelo submenu \u201cFerramentas\u201d ou ",Object(n.b)("strong",{parentName:"p"},"mantendo pressionada o ",Object(n.b)("em",{parentName:"strong"},"scroll")," do mouse"),", ativando assim o \u201cmodo arrastar\u201d. Ao ativ\xe1-lo todo o circuito ser\xe1 movido clicando e arrastando na dire\xe7\xe3o desejada."),Object(n.b)("p",null,"Para sair do \u201cmodo arrastar\u201d basta pressionar a tecla Escape do teclado."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/drag.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/drag.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"zoom"},"Zoom"),Object(n.b)("p",null,"O zoom ser\xe1 aplicado ao utilizar o ",Object(n.b)("strong",{parentName:"p"},"scroll do mouse")," para mais ou menos zoom. A ferramenta zoom ir\xe1 aproximar ou distanciar o circuito a partir da posi\xe7\xe3o do ponteiro do mouse na tela para encontrar objetos ou destaca-los."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/zoom.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/zoom.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"encaixar"},"Encaixar"),Object(n.b)("p",null,"A ferramenta encaixar ir\xe1 mover o circuito e aplicar o zoom necess\xe1rio para que todos os componentes da rede sejam exibidos na tela. Esta ferramenta pode ser acessada atrav\xe9s do submenu \u201cFerramentas\u201d ou pela combina\xe7\xe3o de teclas \u201cShift + F\u201d."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/fit.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/fit.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"copiar-e-colar"},"Copiar e Colar"),Object(n.b)("p",null,"Duas ferramentas importantes durante o processo de cria\xe7\xe3o da rede el\xe9trica de pot\xeancia no ",Object(n.b)("em",{parentName:"p"},"software")," s\xe3o copiar e colar. Qualquer circuito criado no PSP-UFU poder\xe1 ser duplicado completamente ou parcialmente no mesmo projeto ou em m\xfaltiplos atrav\xe9s dessas ferramentas."),Object(n.b)("p",null,"Para copiar basta selecionar os elementos que se deseja duplicar e acessar a ferramenta no submenu \u201cFerramentas\u201d ou pressionando a combina\xe7\xe3o das teclas \u201cCtrl + C\u201d, ent\xe3o os dados do circuito ser\xe3o copiados para a \xe1rea de transfer\xeancia. Ao copiar um circuito ele poder\xe1 ser colado no mesmo projeto ou em um projeto distinto, utilizando o mesmo submenu ou pressionando a combina\xe7\xe3o das teclas \u201cCtrl + V\u201d."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/copyPaste.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/copyPaste.webm"),type:"video/webm"})),Object(n.b)("h3",{id:"excluir"},"Excluir"),Object(n.b)("p",null,"Qualquer objeto poder\xe1 ser exclu\xeddo do projeto por meio da ferramenta deletar, presente no menu Ribbon, pela tecla de atalho Delete ou pelo acesso ao menu de contexto clicando com o bot\xe3o direito sobre o elemento selecionado."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/delete.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/delete.webm"),type:"video/webm"})),Object(n.b)("h2",{id:"personaliza\xe7\xe3o-gr\xe1fica-os-elementos"},"Personaliza\xe7\xe3o gr\xe1fica os elementos"),Object(n.b)("p",null,"Alguns elementos permitem sua personaliza\xe7\xe3o gr\xe1fica, como as barras e linhas."),Object(n.b)("h3",{id:"barra"},"Barra"),Object(n.b)("p",null,"No caso dos barramentos, pode-se alterar o ",Object(n.b)("strong",{parentName:"p"},"comprimento da barra")," clicando e arrastando no ",Object(n.b)("em",{parentName:"p"},"pickbox")," exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado."),Object(n.b)("h3",{id:"linha"},"Linha"),Object(n.b)("p",null,"As linhas podem ser inseridas com ",Object(n.b)("strong",{parentName:"p"},'"n\xf3s" (pontos de ancoragem)'),", personalizando a disposi\xe7\xe3o das linhas no diagrama unifilar. Esses n\xf3s s\xe3o inseridos durante o processo de cria\xe7\xe3o do elemento, anteriormente \xe0 sele\xe7\xe3o da segunda barra."),Object(n.b)("p",null,"Ap\xf3s a sua inser\xe7\xe3o, novos n\xf3s podem ser anexados pelo menu de contexto acessado ao clicar com o bot\xe3o direito sobre a linha selecionada. Sua remo\xe7\xe3o tamb\xe9m \xe9 alcan\xe7ada por uma op\xe7\xe3o do menu de contexto."),Object(n.b)("p",null,"Assim como nos barramentos, a altera\xe7\xe3o da posi\xe7\xe3o dos n\xf3s \xe9 obtida clicando e arrastando o ",Object(n.b)("em",{parentName:"p"},"pickbox")," exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado."),Object(n.b)("video",{autoPlay:!0,loop:!0,muted:!0,controls:!0},Object(n.b)("source",{src:Object(s.a)("videos/graphicPropsChange.mp4"),type:"video/mp4"}),Object(n.b)("source",{src:Object(s.a)("videos/graphicPropsChange.webm"),type:"video/webm"})),Object(n.b)("h2",{id:"conex\xe3o-e-desconex\xe3o-de-elemetos-na-barra"},"Conex\xe3o e desconex\xe3o de elemetos na barra"),Object(n.b)("p",null,"Os elementos podem ser desconectados e reconectados \xe0s barras ap\xf3s sua inser\xe7\xe3o somente pela ferramenta ",Object(n.b)("em",{parentName:"p"},"drag-and-drop"),". Para isso, o elemento deve ser selecionado e o seu n\xf3 de conex\xe3o deve ser arrastado para o local requerido."),Object(n.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(t.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(t.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(n.b)("path",Object(t.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado!")),Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"O elemento a ser desconectado/reconectado ",Object(n.b)("strong",{parentName:"p"},"deve ser previamente selecionado")," para efetuar a opera\xe7\xe3o. Caso contr\xe1rio a barra ser\xe1 movida ou nenhuma opera\xe7\xe3o ser\xe1 realizada."))),Object(n.b)("p",null,"No caso de desconex\xe3o, o elemento ser\xe1 automaticamente removido da simula\xe7\xe3o, sendo indicado pela sua cor (o elemento passa a ter cor ",Object(n.b)(d,{color:"#7f7f7f",mdxType:"Highlight"},"cinza"),")."),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(t.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(t.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(t.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(n.b)("div",Object(t.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Ao reconectar o elemento ao circuito, deve-se ",Object(n.b)("strong",{parentName:"p"},'atentar para estado do seu "disjuntor"'),", indicado por um quadrado pr\xf3ximo ao seu n\xf3 de conex\xe3o. 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diff --git a/docs/1.63a834da.js b/docs/1.c48a090e.js
similarity index 93%
rename from docs/1.63a834da.js
rename to docs/1.c48a090e.js
index 411a6a07..029445bc 100644
--- a/docs/1.63a834da.js
+++ b/docs/1.c48a090e.js
@@ -1 +1 @@
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similarity index 93%
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Em contrapartida, caso as vari\xe1veis de estado dos elementos do sistema oscilem ap\xf3s uma perturba\xe7\xe3o e se estabele\xe7am em um novo ponto de opera\xe7\xe3o, mesmo que distinto dos valores iniciais, o sistema \xe9 considerado ",Object(m.b)("strong",{parentName:"p"},"est\xe1vel"),"."),Object(m.b)("h2",{id:"execu\xe7\xe3o-do-estudo-de-estabilidade-no-psp-ufu"},"Execu\xe7\xe3o do estudo de estabilidade no PSP-UFU"),Object(m.b)("p",null,"Ap\xf3s a constru\xe7\xe3o do diagrama unifilar no ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"editor de pot\xeancia"),", assim como os ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"controlEditor"}),"controles")," das ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator"}),"m\xe1quinas s\xedncronas"),", a execu\xe7\xe3o da estabilidade \xe9 realizada no ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"menu Simula\xe7\xe3o")," clicando no \xedcone do bot\xe3o ",Object(m.b)("strong",{parentName:"p"},"Executar Estabilidade"),'. Ao clicar na parte inferior do bot\xe3o "Executar Estabilidade" ser\xe1 exibido um menu suspenso com a op\xe7\xe3o ',Object(m.b)("strong",{parentName:"p"},"Lista de eventos de estabilidade"),"."),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(r.a)("images/menuSimulationStability.svg"),alt:"Menu Simula\xe7\xe3o",title:"Menu Simula\xe7\xe3o"}))),Object(m.b)("p",null,"Ao executar o c\xe1lculo de estabilidade, uma caixa com o status do processo de simula\xe7\xe3o ser\xe1 exibida, indicando primeiramente a inicializa\xe7\xe3o do estudo e posteriormente o tempo de simula\xe7\xe3o calculado."),Object(m.b)("p",null,"Ao clicar na lista de eventos de estabilidade, ser\xe1 exibida uma janela com a descri\xe7\xe3o dos eventos de estabilidade inseridos."),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(r.a)("images/stabList.png"),alt:"Lista de eventos de estabilidade",title:"Lista de eventos de estabilidade"}))),Object(m.b)("h3",{id:"inserindo-um-evento-de-estabilidade"},"Inserindo um evento de estabilidade"),Object(m.b)("p",null,"Os dist\xfarbios mais comuns aplicados em estudos de estabilidade transit\xf3ria s\xe3o faltas e chaveamentos. Tais opera\xe7\xf5es s\xe3o facilmente realizadas no PSP-UFU:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Faltas"),": Curtos-circuitos trif\xe1sicos podem ser inseridos nos ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"bus"}),"barramentos")," do sistema por meio da inclus\xe3o da imped\xe2ncia de falta na matriz admit\xe2ncia de barras da mesma maneira realizada em um elemento ",Object(m.b)("em",{parentName:"p"},"shunt"),". Tal valor \xe9 definido pelo usu\xe1rio e caso seja um curto-circuito franco, um valor n\xe3o nulo, mas suficientemente pr\xf3ximo de zero, \xe9 aplicado, de forma que a tens\xe3o no barramento \xe9 levada a zero durante o dist\xfarbio.")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Chaveamento de ramo"),": Da mesma forma que as faltas, o chaveamento de ramos \xe9 realizado por meio da altera\xe7\xe3o na matriz admit\xe2ncia, removendo ou inserindo os par\xe2metros do elemento a ser chaveado.\nCada ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"elemento de pot\xeancia"),' possui um bot\xe3o de "Chaveamento" ou "Estabilidade", em que pode ser inserido os tempos de remo\xe7\xe3o e/ou inser\xe7\xe3o do componente.')),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Chaveamento de m\xe1quinas"),": A remo\xe7\xe3o de uma m\xe1quina s\xedncrona \xe9 efetivada com a retirada de sua participa\xe7\xe3o no vetor de correntes, al\xe9m da remo\xe7\xe3o de sua admit\xe2ncia fict\xedcia.\nAssim como os ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"elementos de pot\xeancia"),", as ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator"}),"m\xe1quinas s\xedncronas"),' possui um bot\xe3o "Chaveamento", em que pode ser inserido os tempos de remo\xe7\xe3o e/ou inser\xe7\xe3o do componente.'),Object(m.b)("div",Object(s.a)({parentName:"li"},{className:"admonition admonition-caution alert alert--warning"}),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(m.b)("h5",{parentName:"div"},Object(m.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(m.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(m.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"Mesmo que removida da barra, os par\xe2metros das ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator"}),"m\xe1quinas s\xedncronas")," continuam a ser calculados com a corrente do estator nula, podendo fornecer resultados em uma eventual reconex\xe3o."))))),Object(m.b)("div",{className:"admonition admonition-tip alert alert--success"},Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(m.b)("h5",{parentName:"div"},Object(m.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(m.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(m.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"})))),"Dica")),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"Eventos nos ",Object(m.b)("strong",{parentName:"p"},"sistemas de controle")," podem ser facilmente introduzidos com o bloco de ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"mathExpression"}),"express\xe3o matem\xe1tica"),". Nesse caso, tais eventos ",Object(m.b)("strong",{parentName:"p"},"n\xe3o")," ser\xe3o exibidos na lista de eventos de estabilidade."))),Object(m.b)("h3",{id:"erros-comuns-na-execu\xe7\xe3o-do-estudo-de-estabilidade"},"Erros comuns na execu\xe7\xe3o do estudo de estabilidade"),Object(m.b)("p",null,"A seguir s\xe3o apresentados os erros mais comuns relacionados ao estudo de estabilidade."),Object(m.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-n\xe3o-foi-poss\xedvel-construir-a-matriz-admit\xe2ncia"},'A seguinte mensagem de erro \xe9 exibida: "N\xe3o foi poss\xedvel construir a matriz admit\xe2ncia"'),Object(m.b)("p",null,"Essa mensagem de erro \xe9 exibida quando n\xe3o \xe9 poss\xedvel construir a matriz admit\xe2ncia de barras. As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Os par\xe2metros do circuito est\xe3o incorretos"),". Caso par\xe2metros muito fora dos valores padr\xe3o dos elementos el\xe9tricos sejam inseridos, o c\xe1lculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Algum barramento est\xe1 isolado"),". Esse erro \xe9 bastante comum e pode ocorrer ao inserir um barramento sem conect\xe1-lo ao sistema ou ao remover os elementos de ramo que conectam uma barra ao sistema. A solu\xe7\xe3o \xe9 eliminar essa barra do diagrama."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Algum elemento possui par\xe2metros discrepantes dos demais"),". Caso um dos elementos inseridos possua um valor de imped\xe2ncia muito distinto dos demais, como por exemplo uma linha com imped\xe2ncia muito elevada ou uma carga muito pequena, pode levar \xe0 diverg\xeancia do m\xe9todo num\xe9rico. Nesse caso, reconsidere a necessidade de representa\xe7\xe3o desses elementos no circuito e alterne entre os m\xe9todos num\xe9ricos de solu\xe7\xe3o dispon\xedveis.")),Object(m.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-erro-ao-inicializar-os-valores-de-satura\xe7\xe3o-do"},'A seguinte mensagem de erro \xe9 exibida: "Erro ao inicializar os valores de satura\xe7\xe3o do..."'),Object(m.b)("p",null,"Essa mensagem de erro \xe9 exibida quando n\xe3o \xe9 poss\xedvel calcular os fatores de satura\xe7\xe3o da ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator"}),"m\xe1quina s\xedncrona"),". As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"O fator de satura\xe7\xe3o \xe9 menor que 1,2"),". Esse valor deve ser maior que 1,2, ou ir\xe1 gerar erros na simula\xe7\xe3o. Caso n\xe3o seja informado, a satura\xe7\xe3o da m\xe1quina n\xe3o \xe9 considerada nos c\xe1lculos."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Os par\xe2metros da m\xe1quina s\xedncrona est\xe3o incorretos"),". Caso par\xe2metros muito fora dos valores padr\xe3o das m\xe1quinas s\xedncronas sejam inseridos, o c\xe1lculo dos fatores de satura\xe7\xe3o pode divergir. Verifique se os dados foram inseridos corretamente.")),Object(m.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-erro-ao-inicializar-o-avr--regulador-de-velocidade"},'A seguinte mensagem de erro \xe9 exibida: "Erro ao inicializar o AVR / regulador de velocidade..."'),Object(m.b)("p",null,"Essa mensagem de erro \xe9 exibida quando n\xe3o \xe9 poss\xedvel ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"controlEditor#inicializa%C3%A7%C3%A3o-do-sistema-de-controle"}),"inicializar o sistema de controle")," de uma ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator"}),"m\xe1quina s\xedncrona"),". As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"O sistema de controle est\xe1 vazio"),". Caso esteja habilitado o AVR e/ou o regulador de velocidade e o controle n\xe3o foi inserido, esse erro pode ser acionado. Insira o controle da m\xe1quina ou desmarque a op\xe7\xe3o de utiliza\xe7\xe3o do AVR e/ou regulador de velocidade."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"O sistema de controle n\xe3o possui ao menos uma entrada e uma sa\xedda"),". O sistema de controle deve ter ao menos uma ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"io"}),"entrada e uma sa\xedda"),", caso contr\xe1rio apresentar\xe1 erro de execu\xe7\xe3o."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"O passo de integra\xe7\xe3o est\xe1 muito pequeno"),". Caso o passo de integra\xe7\xe3o esteja muito pequeno, os c\xe1lculos gerar\xe3o erros e ir\xe3o divergir. Reduza o passo de integra\xe7\xe3o nas ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),".")),Object(m.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-imposs\xedvel-resolver-as-m\xe1quinas-do-sistema"},'A seguinte mensagem de erro \xe9 exibida: "Imposs\xedvel resolver as m\xe1quinas do sistema"'),Object(m.b)("p",null,"Essa mensagem de erro \xe9 exibida quando n\xe3o \xe9 poss\xedvel resolver as EADs das m\xe1quinas s\xedncronas inseridas no sistemas. As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Os par\xe2metros da m\xe1quina s\xedncrona est\xe3o incorretos"),". Caso par\xe2metros muito fora dos valores padr\xe3o das m\xe1quinas s\xedncronas sejam inseridos, o c\xe1lculo das EADs pode se tornar imposs\xedvel. Verifique se os dados foram inseridos corretamente."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"O passo de integra\xe7\xe3o est\xe1 muito pequeno"),". Caso o passo de integra\xe7\xe3o esteja muito pequeno, os c\xe1lculos gerar\xe3o erros e ir\xe3o divergir. Reduza o passo de integra\xe7\xe3o nas ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),"."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Os par\xe2metros do circuito est\xe3o incorretos"),". Caso par\xe2metros muito fora dos valores padr\xe3o dos elementos el\xe9tricos sejam inseridos, o c\xe1lculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Algum barramento est\xe1 isolado"),". Esse erro \xe9 bastante comum e pode ocorrer ao inserir um barramento sem conect\xe1-lo ao sistema ou ao remover os elementos de ramo que conectam uma barra ao sistema. A solu\xe7\xe3o \xe9 eliminar essa barra do diagrama."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Algum elemento possui par\xe2metros discrepantes dos demais"),". Caso um dos elementos inseridos possua um valor de imped\xe2ncia muito distinto dos demais, como por exemplo uma linha com imped\xe2ncia muito elevada ou uma carga muito pequena, pode levar \xe0 diverg\xeancia do m\xe9todo num\xe9rico. Nesse caso, reconsidere a necessidade de representa\xe7\xe3o desses elementos no circuito e alterne entre os m\xe9todos num\xe9ricos de solu\xe7\xe3o dispon\xedveis.")),Object(m.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-erro-ao-inicializar-o-escorregamento-do-motor"},'A seguinte mensagem de erro \xe9 exibida: "Erro ao inicializar o escorregamento do motor..."'),Object(m.b)("p",null,"Essa mensagem de erro \xe9 exibida quando n\xe3o \xe9 poss\xedvel calcular o valor de escorregamento inicial do motor de indu\xe7\xe3o. As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Os par\xe2metros de estabilidade do motor est\xe3o incorretos"),". Caso par\xe2metros muito fora dos valores padr\xe3o dos motores de indu\xe7\xe3o sejam inseridos, o c\xe1lculo do escorregamento pode se tornar imposs\xedvel. Verifique se os dados foram inseridos corretamente.")),Object(m.b)("h2",{id:"estrutura-da-ferramenta-de-estabilidade"},"Estrutura da ferramenta de estabilidade"),Object(m.b)("p",null,"A estabilidade de um SEP \xe9 um problema din\xe2mico e necessita de modelos mais elaborados de elementos de pot\xeancia comparados \xe0queles apresentados nos outros estudos. Esses modelos s\xe3o descritos individualmente, com destaque \xe0s ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator#gerador-s%C3%ADncrono-no-estudo-de-estabilidade"}),"m\xe1quinas s\xedncronas"),", ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"load#carga-no-estudo-de-estabilidade"}),"cargas ZIP")," e ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"indMotor#motor-de-indu%C3%A7%C3%A3o-trif%C3%A1sico-no-estudo-de-estabilidade"}),"motores de indu\xe7\xe3o"),"."),Object(m.b)("p",null,"A representa\xe7\xe3o dos demais componentes do sistema el\xe9trico: ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"line"}),"linhas de transmiss\xe3o"),", ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"transformer"}),"transformadores")," e elementos ",Object(m.b)("em",{parentName:"p"},"shunt")," (com exce\xe7\xe3o de cargas ZIP), que formam a rede de transmiss\xe3o ou distribui\xe7\xe3o balanceada, \xe9 realizada utilizando os mesmos modelos do ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerFlow"}),"fluxo de carga"),"."),Object(m.b)("p",null,"Os modelos din\xe2micos para a an\xe1lise no dom\xednio do tempo s\xe3o na forma de um sistema de equa\xe7\xf5es alg\xe9brico-diferenciais (EADs), descritas a seguir:"),Object(m.b)("div",{className:"math 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estado"),Object(m.b)("li",{parentName:"ul"},Object(m.b)("span",Object(s.a)({parentName:"li"},{className:"math math-inline"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mi",{parentName:"mrow"},"y")),Object(m.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"y")))),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord 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permanecem constantes durante todo o processo de c\xe1lculo. Para o problema de estabilidade, as vari\xe1veis alg\xe9bricas iniciais correspondem \xe0s tens\xf5es e \xe2ngulos das barras calculadas no ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerFlow"}),"fluxo de carga"),". As vari\xe1veis de estado iniciais s\xe3o estimadas ap\xf3s a converg\xeancia do fluxo de pot\xeancia (inicializa\xe7\xe3o dos elementos din\xe2micos)."),Object(m.b)("p",null,"Na sequ\xeancia \xe9 apresentado, na forma de fluxogramas, a estrutura do m\xf3dulo de estabilidade implementado no PSP-UFU. O fluxograma abaixo mostra a estrutura geral da ferramenta de estabilidade."),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(r.a)("images/stabGeneral.svg"),alt:"Estrutura geral da ferramenta de estabilidade",title:"Estrutura geral da ferramenta de estabilidade"}))),Object(m.b)("p",null,"A inicializa\xe7\xe3o da rede el\xe9trica e dos elementos din\xe2micos, assim como o precesso iterativo para solu\xe7\xe3o das EADs s\xe3o apresentados nos dois fluxogramas conseguintes."),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(r.a)("images/stabInit.svg"),alt:"Inicializa\xe7\xe3o da ferramenta de estabilidade",title:"Inicializa\xe7\xe3o da ferramenta de estabilidade"}))),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(r.a)("images/stabIterative.svg"),alt:"Processo iterativo para c\xe1lculo dos elementos din\xe2micos",title:"Estrutura geral da ferramenta de estabilidade"}))),Object(m.b)("h3",{id:"integra\xe7\xe3o-num\xe9rica"},"Integra\xe7\xe3o num\xe9rica"),Object(m.b)("p",null,"Para resolver as equa\xe7\xf5es diferenciais da m\xe1quina \xe9 necess\xe1rio um m\xe9todo de integra\xe7\xe3o num\xe9rica. Tais m\xe9todos s\xe3o classificados em dois grupos: m\xe9todos expl\xedcitos e m\xe9todos impl\xedcitos. Os m\xe9todos expl\xedcitos, devido \xe0 sua formula\xe7\xe3o, calculam diretamente o estado do sistema em um instante de tempo posterior, enquanto m\xe9todos impl\xedcitos envolvem estados atuais e posteriores em suas equa\xe7\xf5es, exigindo, portanto, um processo iterativo."),Object(m.b)("p",null,"As constantes de tempo presentes no estudo de estabilidade t\xeam uma grande varia\xe7\xe3o em seu valor (podem variar de ",Object(m.b)("span",Object(s.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mn",{parentName:"mrow"},"1"),Object(m.b)("msup",{parentName:"mrow"},Object(m.b)("mn",{parentName:"msup"},"0"),Object(m.b)("mrow",{parentName:"msup"},Object(m.b)("mo",{parentName:"mrow"},"\u2212"),Object(m.b)("mn",{parentName:"mrow"},"3"))),Object(m.b)("mtext",{parentName:"mrow"},"\xa0"),Object(m.b)("mi",{parentName:"mrow"},"s")),Object(m.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"10^{-3}~s")))),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"0.8141079999999999em",verticalAlign:"0em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"1"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"0"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"msupsub"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-t"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-r"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"vlist",style:{height:"0.8141079999999999em"}}),Object(m.b)("span",Object(s.a)({parentName:"span"},{style:{top:"-3.063em",marginRight:"0.05em"}}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"pstrut",style:{height:"2.7em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"sizing reset-size6 size3 mtight"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mtight"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mtight"}),"\u2212"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mtight"}),"3"))))))))),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mspace nobreak"}),"\xa0"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"s")))))," a ",Object(m.b)("span",Object(s.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mn",{parentName:"mrow"},"10"),Object(m.b)("mtext",{parentName:"mrow"},"\xa0"),Object(m.b)("mi",{parentName:"mrow"},"s")),Object(m.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"10~s")))),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"0.64444em",verticalAlign:"0em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"1"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"0"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mspace nobreak"}),"\xa0"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"s"))))),"). Isso torna o sistema de equa\xe7\xf5es diferenciais da m\xe1quina s\xedncrona como um sistema r\xedgido (",Object(m.b)("em",{parentName:"p"},Object(m.b)("a",Object(s.a)({parentName:"em"},{href:"https://en.wikipedia.org/wiki/Stiff_equation"}),"stiff equation")),"). Caso a an\xe1lise da estabilidade num\xe9rica tanto das equa\xe7\xf5es diferenciais r\xedgidas quanto do m\xe9todo de integra\xe7\xe3o obtenham o mesmo comportamento, o m\xe9todo \xe9 chamado de absolutamente est\xe1vel, ou A-est\xe1vel."),Object(m.b)("p",null,"M\xe9todos de integra\xe7\xe3o num\xe9rica expl\xedcitos, como por exemplo o ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods"}),"Runge-Kutta")," de quarta ordem, n\xe3o podem ser A-est\xe1veis e, portanto, normalmente possuem comportamento ruim em problemas com equa\xe7\xf5es diferenciais r\xedgidas. Por outro lado, m\xe9todos impl\xedcitos podem ser A-est\xe1veis. Um m\xe9todo impl\xedcito adequado para solu\xe7\xe3o do comportamento din\xe2mico de sistemas el\xe9tricos \xe9 o ",Object(m.b)("strong",{parentName:"p"},"Trapezoidal Impl\xedcito"),", por possuir as seguintes vantagens:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},"\xc9 numericamente est\xe1vel (A-est\xe1vel);"),Object(m.b)("li",{parentName:"ul"},"\xc9 bastante r\xe1pida;"),Object(m.b)("li",{parentName:"ul"},"Possui boa precis\xe3o (dependendo somente do passo de integra\xe7\xe3o utilizado).")),Object(m.b)("p",null,"Tal m\xe9todo foi implementado no PSP-UFU tanto para solu\xe7\xe3o das equa\xe7\xf5es diferenciais da m\xe1quina s\xedncrona quanto nas ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"transferFunction"}),"fun\xe7\xf5es transfer\xeancia")," do ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"controlEditor"}),"sistema de controle"),". 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AIEE Transactions, v. 48, n. 3, jul 1929. doi: ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1109/T-AIEE.1929.5055275"}),"https://doi.org/10.1109/T-AIEE.1929.5055275")),Object(m.b)("li",{parentName:"ol"},"ANDERSON, P. M.; FOUAD, A. A. Power System Control and Stability. Wiley-IEEE Press, New York, 2002. doi: ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1109/9780470545577"}),"https://doi.org/10.1109/9780470545577")),Object(m.b)("li",{parentName:"ol"},"SAUER, P. W.; PAI, M. A. Power System Dynamics and Stability. Pretience Hall, Upper Saddle River, 1998."),Object(m.b)("li",{parentName:"ol"},"KUNDUR, P. Power System Stability and Control. McGraw-Hill, New York, 1994."),Object(m.b)("li",{parentName:"ol"},"DOMMEL, H. W.; SATO, N. Fast Transient Stability Solutions. IEEE Transactions on Power Aparatus and Systems, v. 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A estabilidade \xe9 reconhecida como um importante problema para a seguran\xe7a da opera\xe7\xe3o desde a d\xe9cada de 1920. Muitos ",Object(m.b)("em",{parentName:"p"},"blackouts")," de grande porte causados pela instabilidade do SEP t\xeam ilustrado a import\xe2ncia desse fen\xf4meno."),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(r.a)("images/stability.svg"),alt:"Estabilidade",title:"Estabilidade"}))),Object(m.b)("p",null,"Normalmente s\xe3o realizados dois tipos de estudos de estabilidade (uma classifica\xe7\xe3o mais aprofundada pode ser observada ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"https://doi.org/10.1109/TPWRS.2004.825981"}),"nesse artigo"),"). A recupera\xe7\xe3o de uma r\xe1pida e brusca perturba\xe7\xe3o \xe9 chamada de ",Object(m.b)("strong",{parentName:"p"},"estabilidade transit\xf3ria"),", e sua solu\xe7\xe3o \xe9 geralmente obtida no dom\xednio do tempo. 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Em contrapartida, caso as vari\xe1veis de estado dos elementos do sistema oscilem ap\xf3s uma perturba\xe7\xe3o e se estabele\xe7am em um novo ponto de opera\xe7\xe3o, mesmo que distinto dos valores iniciais, o sistema \xe9 considerado ",Object(m.b)("strong",{parentName:"p"},"est\xe1vel"),"."),Object(m.b)("h2",{id:"execu\xe7\xe3o-do-estudo-de-estabilidade-no-psp-ufu"},"Execu\xe7\xe3o do estudo de estabilidade no PSP-UFU"),Object(m.b)("p",null,"Ap\xf3s a constru\xe7\xe3o do diagrama unifilar no ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"editor de pot\xeancia"),", assim como os ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"controlEditor"}),"controles")," das ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator"}),"m\xe1quinas s\xedncronas"),", a execu\xe7\xe3o da estabilidade \xe9 realizada no ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"menu Simula\xe7\xe3o")," clicando no \xedcone do bot\xe3o ",Object(m.b)("strong",{parentName:"p"},"Executar Estabilidade"),'. Ao clicar na parte inferior do bot\xe3o "Executar Estabilidade" ser\xe1 exibido um menu suspenso com a op\xe7\xe3o ',Object(m.b)("strong",{parentName:"p"},"Lista de eventos de estabilidade"),"."),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(r.a)("images/menuSimulationStability.svg"),alt:"Menu Simula\xe7\xe3o",title:"Menu Simula\xe7\xe3o"}))),Object(m.b)("p",null,"Ao executar o c\xe1lculo de estabilidade, uma caixa com o status do processo de simula\xe7\xe3o ser\xe1 exibida, indicando primeiramente a inicializa\xe7\xe3o do estudo e posteriormente o tempo de simula\xe7\xe3o calculado."),Object(m.b)("p",null,"Ao clicar na lista de eventos de estabilidade, ser\xe1 exibida uma janela com a descri\xe7\xe3o dos eventos de estabilidade inseridos."),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(r.a)("images/stabList.png"),alt:"Lista de eventos de estabilidade",title:"Lista de eventos de estabilidade"}))),Object(m.b)("h3",{id:"inserindo-um-evento-de-estabilidade"},"Inserindo um evento de estabilidade"),Object(m.b)("p",null,"Os dist\xfarbios mais comuns aplicados em estudos de estabilidade transit\xf3ria s\xe3o faltas e chaveamentos. Tais opera\xe7\xf5es s\xe3o facilmente realizadas no PSP-UFU:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Faltas"),": Curtos-circuitos trif\xe1sicos podem ser inseridos nos ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"bus"}),"barramentos")," do sistema por meio da inclus\xe3o da imped\xe2ncia de falta na matriz admit\xe2ncia de barras da mesma maneira realizada em um elemento ",Object(m.b)("em",{parentName:"p"},"shunt"),". Tal valor \xe9 definido pelo usu\xe1rio e caso seja um curto-circuito franco, um valor n\xe3o nulo, mas suficientemente pr\xf3ximo de zero, \xe9 aplicado, de forma que a tens\xe3o no barramento \xe9 levada a zero durante o dist\xfarbio.")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Chaveamento de ramo"),": Da mesma forma que as faltas, o chaveamento de ramos \xe9 realizado por meio da altera\xe7\xe3o na matriz admit\xe2ncia, removendo ou inserindo os par\xe2metros do elemento a ser chaveado.\nCada ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"elemento de pot\xeancia"),' possui um bot\xe3o de "Chaveamento" ou "Estabilidade", em que pode ser inserido os tempos de remo\xe7\xe3o e/ou inser\xe7\xe3o do componente.')),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Chaveamento de m\xe1quinas"),": A remo\xe7\xe3o de uma m\xe1quina s\xedncrona \xe9 efetivada com a retirada de sua participa\xe7\xe3o no vetor de correntes, al\xe9m da remo\xe7\xe3o de sua admit\xe2ncia fict\xedcia.\nAssim como os ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"elementos de pot\xeancia"),", as ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator"}),"m\xe1quinas s\xedncronas"),' possui um bot\xe3o "Chaveamento", em que pode ser inserido os tempos de remo\xe7\xe3o e/ou inser\xe7\xe3o do componente.'),Object(m.b)("div",Object(s.a)({parentName:"li"},{className:"admonition admonition-caution alert alert--warning"}),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(m.b)("h5",{parentName:"div"},Object(m.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(m.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(m.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"Mesmo que removida da barra, os par\xe2metros das ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator"}),"m\xe1quinas s\xedncronas")," continuam a ser calculados com a corrente do estator nula, podendo fornecer resultados em uma eventual reconex\xe3o."))))),Object(m.b)("div",{className:"admonition admonition-tip alert alert--success"},Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(m.b)("h5",{parentName:"div"},Object(m.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(m.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(m.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"})))),"Dica")),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"Eventos nos ",Object(m.b)("strong",{parentName:"p"},"sistemas de controle")," podem ser facilmente introduzidos com o bloco de ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"mathExpression"}),"express\xe3o matem\xe1tica"),". Nesse caso, tais eventos ",Object(m.b)("strong",{parentName:"p"},"n\xe3o")," ser\xe3o exibidos na lista de eventos de estabilidade."))),Object(m.b)("h3",{id:"erros-comuns-na-execu\xe7\xe3o-do-estudo-de-estabilidade"},"Erros comuns na execu\xe7\xe3o do estudo de estabilidade"),Object(m.b)("p",null,"A seguir s\xe3o apresentados os erros mais comuns relacionados ao estudo de estabilidade."),Object(m.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-n\xe3o-foi-poss\xedvel-construir-a-matriz-admit\xe2ncia"},'A seguinte mensagem de erro \xe9 exibida: "N\xe3o foi poss\xedvel construir a matriz admit\xe2ncia"'),Object(m.b)("p",null,"Essa mensagem de erro \xe9 exibida quando n\xe3o \xe9 poss\xedvel construir a matriz admit\xe2ncia de barras. As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Os par\xe2metros do circuito est\xe3o incorretos"),". Caso par\xe2metros muito fora dos valores padr\xe3o dos elementos el\xe9tricos sejam inseridos, o c\xe1lculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Algum barramento est\xe1 isolado"),". Esse erro \xe9 bastante comum e pode ocorrer ao inserir um barramento sem conect\xe1-lo ao sistema ou ao remover os elementos de ramo que conectam uma barra ao sistema. A solu\xe7\xe3o \xe9 eliminar essa barra do diagrama."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Algum elemento possui par\xe2metros discrepantes dos demais"),". Caso um dos elementos inseridos possua um valor de imped\xe2ncia muito distinto dos demais, como por exemplo uma linha com imped\xe2ncia muito elevada ou uma carga muito pequena, pode levar \xe0 diverg\xeancia do m\xe9todo num\xe9rico. Nesse caso, reconsidere a necessidade de representa\xe7\xe3o desses elementos no circuito e alterne entre os m\xe9todos num\xe9ricos de solu\xe7\xe3o dispon\xedveis.")),Object(m.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-erro-ao-inicializar-os-valores-de-satura\xe7\xe3o-do"},'A seguinte mensagem de erro \xe9 exibida: "Erro ao inicializar os valores de satura\xe7\xe3o do..."'),Object(m.b)("p",null,"Essa mensagem de erro \xe9 exibida quando n\xe3o \xe9 poss\xedvel calcular os fatores de satura\xe7\xe3o da ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator"}),"m\xe1quina s\xedncrona"),". As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"O fator de satura\xe7\xe3o \xe9 menor que 1,2"),". Esse valor deve ser maior que 1,2, ou ir\xe1 gerar erros na simula\xe7\xe3o. Caso n\xe3o seja informado, a satura\xe7\xe3o da m\xe1quina n\xe3o \xe9 considerada nos c\xe1lculos."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Os par\xe2metros da m\xe1quina s\xedncrona est\xe3o incorretos"),". Caso par\xe2metros muito fora dos valores padr\xe3o das m\xe1quinas s\xedncronas sejam inseridos, o c\xe1lculo dos fatores de satura\xe7\xe3o pode divergir. Verifique se os dados foram inseridos corretamente.")),Object(m.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-erro-ao-inicializar-o-avr--regulador-de-velocidade"},'A seguinte mensagem de erro \xe9 exibida: "Erro ao inicializar o AVR / regulador de velocidade..."'),Object(m.b)("p",null,"Essa mensagem de erro \xe9 exibida quando n\xe3o \xe9 poss\xedvel ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"controlEditor#inicializa%C3%A7%C3%A3o-do-sistema-de-controle"}),"inicializar o sistema de controle")," de uma ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator"}),"m\xe1quina s\xedncrona"),". As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"O sistema de controle est\xe1 vazio"),". Caso esteja habilitado o AVR e/ou o regulador de velocidade e o controle n\xe3o foi inserido, esse erro pode ser acionado. Insira o controle da m\xe1quina ou desmarque a op\xe7\xe3o de utiliza\xe7\xe3o do AVR e/ou regulador de velocidade."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"O sistema de controle n\xe3o possui ao menos uma entrada e uma sa\xedda"),". O sistema de controle deve ter ao menos uma ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"io"}),"entrada e uma sa\xedda"),", caso contr\xe1rio apresentar\xe1 erro de execu\xe7\xe3o."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"O passo de integra\xe7\xe3o est\xe1 muito pequeno"),". Caso o passo de integra\xe7\xe3o esteja muito pequeno, os c\xe1lculos gerar\xe3o erros e ir\xe3o divergir. Reduza o passo de integra\xe7\xe3o nas ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),".")),Object(m.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-imposs\xedvel-resolver-as-m\xe1quinas-do-sistema"},'A seguinte mensagem de erro \xe9 exibida: "Imposs\xedvel resolver as m\xe1quinas do sistema"'),Object(m.b)("p",null,"Essa mensagem de erro \xe9 exibida quando n\xe3o \xe9 poss\xedvel resolver as EADs das m\xe1quinas s\xedncronas inseridas no sistemas. As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Os par\xe2metros da m\xe1quina s\xedncrona est\xe3o incorretos"),". Caso par\xe2metros muito fora dos valores padr\xe3o das m\xe1quinas s\xedncronas sejam inseridos, o c\xe1lculo das EADs pode se tornar imposs\xedvel. Verifique se os dados foram inseridos corretamente."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"O passo de integra\xe7\xe3o est\xe1 muito pequeno"),". Caso o passo de integra\xe7\xe3o esteja muito pequeno, os c\xe1lculos gerar\xe3o erros e ir\xe3o divergir. Reduza o passo de integra\xe7\xe3o nas ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),"."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Os par\xe2metros do circuito est\xe3o incorretos"),". Caso par\xe2metros muito fora dos valores padr\xe3o dos elementos el\xe9tricos sejam inseridos, o c\xe1lculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Algum barramento est\xe1 isolado"),". Esse erro \xe9 bastante comum e pode ocorrer ao inserir um barramento sem conect\xe1-lo ao sistema ou ao remover os elementos de ramo que conectam uma barra ao sistema. A solu\xe7\xe3o \xe9 eliminar essa barra do diagrama."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Algum elemento possui par\xe2metros discrepantes dos demais"),". Caso um dos elementos inseridos possua um valor de imped\xe2ncia muito distinto dos demais, como por exemplo uma linha com imped\xe2ncia muito elevada ou uma carga muito pequena, pode levar \xe0 diverg\xeancia do m\xe9todo num\xe9rico. Nesse caso, reconsidere a necessidade de representa\xe7\xe3o desses elementos no circuito e alterne entre os m\xe9todos num\xe9ricos de solu\xe7\xe3o dispon\xedveis.")),Object(m.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-erro-ao-inicializar-o-escorregamento-do-motor"},'A seguinte mensagem de erro \xe9 exibida: "Erro ao inicializar o escorregamento do motor..."'),Object(m.b)("p",null,"Essa mensagem de erro \xe9 exibida quando n\xe3o \xe9 poss\xedvel calcular o valor de escorregamento inicial do motor de indu\xe7\xe3o. As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Os par\xe2metros de estabilidade do motor est\xe3o incorretos"),". Caso par\xe2metros muito fora dos valores padr\xe3o dos motores de indu\xe7\xe3o sejam inseridos, o c\xe1lculo do escorregamento pode se tornar imposs\xedvel. Verifique se os dados foram inseridos corretamente.")),Object(m.b)("h2",{id:"estrutura-da-ferramenta-de-estabilidade"},"Estrutura da ferramenta de estabilidade"),Object(m.b)("p",null,"A estabilidade de um SEP \xe9 um problema din\xe2mico e necessita de modelos mais elaborados de elementos de pot\xeancia comparados \xe0queles apresentados nos outros estudos. Esses modelos s\xe3o descritos individualmente, com destaque \xe0s ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator#gerador-s%C3%ADncrono-no-estudo-de-estabilidade"}),"m\xe1quinas s\xedncronas"),", ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"load#carga-no-estudo-de-estabilidade"}),"cargas ZIP")," e ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"indMotor#motor-de-indu%C3%A7%C3%A3o-trif%C3%A1sico-no-estudo-de-estabilidade"}),"motores de indu\xe7\xe3o"),"."),Object(m.b)("p",null,"A representa\xe7\xe3o dos demais componentes do sistema el\xe9trico: ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"line"}),"linhas de transmiss\xe3o"),", ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"transformer"}),"transformadores")," e elementos ",Object(m.b)("em",{parentName:"p"},"shunt")," (com exce\xe7\xe3o de cargas ZIP), que formam a rede de transmiss\xe3o ou distribui\xe7\xe3o balanceada, \xe9 realizada utilizando os mesmos modelos do ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerFlow"}),"fluxo de carga"),"."),Object(m.b)("p",null,"Os modelos din\xe2micos para a an\xe1lise no dom\xednio do tempo s\xe3o na forma de um sistema de equa\xe7\xf5es alg\xe9brico-diferenciais (EADs), descritas a seguir:"),Object(m.b)("div",{className:"math 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Isso torna o sistema de equa\xe7\xf5es diferenciais da m\xe1quina s\xedncrona como um sistema r\xedgido (",Object(m.b)("em",{parentName:"p"},Object(m.b)("a",Object(s.a)({parentName:"em"},{href:"https://en.wikipedia.org/wiki/Stiff_equation"}),"stiff equation")),"). Caso a an\xe1lise da estabilidade num\xe9rica tanto das equa\xe7\xf5es diferenciais r\xedgidas quanto do m\xe9todo de integra\xe7\xe3o obtenham o mesmo comportamento, o m\xe9todo \xe9 chamado de absolutamente est\xe1vel, ou A-est\xe1vel."),Object(m.b)("p",null,"M\xe9todos de integra\xe7\xe3o num\xe9rica expl\xedcitos, como por exemplo o ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods"}),"Runge-Kutta")," de quarta ordem, n\xe3o podem ser A-est\xe1veis e, portanto, normalmente possuem comportamento ruim em problemas com equa\xe7\xf5es diferenciais r\xedgidas. Por outro lado, m\xe9todos impl\xedcitos podem ser A-est\xe1veis. Um m\xe9todo impl\xedcito adequado para solu\xe7\xe3o do comportamento din\xe2mico de sistemas el\xe9tricos \xe9 o ",Object(m.b)("strong",{parentName:"p"},"Trapezoidal Impl\xedcito"),", por possuir as seguintes vantagens:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},"\xc9 numericamente est\xe1vel (A-est\xe1vel);"),Object(m.b)("li",{parentName:"ul"},"\xc9 bastante r\xe1pida;"),Object(m.b)("li",{parentName:"ul"},"Possui boa precis\xe3o (dependendo somente do passo de integra\xe7\xe3o utilizado).")),Object(m.b)("p",null,"Tal m\xe9todo foi implementado no PSP-UFU tanto para solu\xe7\xe3o das equa\xe7\xf5es diferenciais da m\xe1quina s\xedncrona quanto nas ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"transferFunction"}),"fun\xe7\xf5es transfer\xeancia")," do ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"controlEditor"}),"sistema de controle"),". 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AIEE Transactions, v. 48, n. 3, jul 1929. doi: ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1109/T-AIEE.1929.5055275"}),"https://doi.org/10.1109/T-AIEE.1929.5055275")),Object(m.b)("li",{parentName:"ol"},"ANDERSON, P. M.; FOUAD, A. A. Power System Control and Stability. Wiley-IEEE Press, New York, 2002. doi: ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1109/9780470545577"}),"https://doi.org/10.1109/9780470545577")),Object(m.b)("li",{parentName:"ol"},"SAUER, P. W.; PAI, M. A. Power System Dynamics and Stability. Pretience Hall, Upper Saddle River, 1998."),Object(m.b)("li",{parentName:"ol"},"KUNDUR, P. Power System Stability and Control. McGraw-Hill, New York, 1994."),Object(m.b)("li",{parentName:"ol"},"DOMMEL, H. W.; SATO, N. Fast Transient Stability Solutions. IEEE Transactions on Power Aparatus and Systems, v. PAS-91, n. 4, jul 1972, p. 1643-1650. doi: ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1109/TPAS.1972.293341"}),"https://doi.org/10.1109/TPAS.1972.293341"))))}i.isMDXComponent=!0}}]);
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Retorna o \xe2ngulo em radianos.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"sinh(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Mesmo que ",Object(b.b)("inlineCode",{parentName:"td"},"sin()"),", mas para seno hiperb\xf3lico.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"sqrt(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Raiz quadrada de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"tan(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Tangente de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". 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Retorna o n\xfamero inteiro de ",Object(b.b)("inlineCode",{parentName:"td"},"A")," sem a parcela fracionada.")))),Object(b.b)("p",null,"\xc9 poss\xedvel atribuir novas vari\xe1veis utilizando a seguinte sintaxe: "),Object(b.b)("pre",null,Object(b.b)("code",Object(n.a)({parentName:"pre"},{className:"language-cpp"}),"<nome da vari\xe1vel> := <express\xe3o>; <fun\xe7\xe3o>\n")),Object(b.b)("p",null,"Por exemplo:"),Object(b.b)("pre",null,Object(b.b)("code",Object(n.a)({parentName:"pre"},{className:"language-cpp"}),"comprimento := sqrt(x*x+y*y); 2*comprimento*sin(comprimento)\n")),Object(b.b)("div",{className:"admonition admonition-tip alert alert--success"},Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(b.b)("h5",{parentName:"div"},Object(b.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(b.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(b.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"})))),"Dica")),Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(b.b)("p",{parentName:"div"},"O caractere de espa\xe7o e de nova linha s\xe3o ignorados na interpreta\xe7\xe3o da express\xe3o, portanto para maior organiza\xe7\xe3o, o c\xf3digo anterior pode ser escrito da seguinte forma:"),Object(b.b)("pre",{parentName:"div"},Object(b.b)("code",Object(n.a)({parentName:"pre"},{className:"language-cpp"}),"comprimento := sqrt(x*x+y*y);\n2*comprimento*sin(comprimento)\n")))),Object(b.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(b.b)("h5",{parentName:"div"},Object(b.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(b.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(b.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado!")),Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(b.b)("p",{parentName:"div"},"Note que a express\xe3o que determina o valor de sa\xedda do bloco ",Object(b.b)("strong",{parentName:"p"},"n\xe3o possui")," o caractere ",Object(b.b)("inlineCode",{parentName:"p"},";")," em seu final."))),Object(b.b)("h2",{id:"formul\xe1rio-de-edi\xe7\xe3o-de-dados-do-bloco-de-express\xe3o-matem\xe1tica"},"Formul\xe1rio de edi\xe7\xe3o de dados do bloco de Express\xe3o Matem\xe1tica"),Object(b.b)("p",null,"O formul\xe1rio de inser\xe7\xe3o e edi\xe7\xe3o das entradas do bloco e da express\xe3o matem\xe1tica gen\xe9rica, assim como ferramentas de aux\xedlio de sua constru\xe7\xe3o \xe9 apresentado na figura abaixo."),Object(b.b)("div",null,Object(b.b)("center",null,Object(b.b)("img",{src:Object(m.a)("images/mathExpressionForm.png"),alt:"Formul\xe1rio de edi\xe7\xe3o de dados do bloco de express\xe3o matem\xe1tica no PSP-UFU",title:"Formul\xe1rio de edi\xe7\xe3o de dados do bloco de express\xe3o matem\xe1tica no PSP-UFU"}))),Object(b.b)("p",null,"No campo de \u201cVari\xe1veis de entrada\u201d \xe9 inserida uma lista com os nomes das entradas separados por espa\xe7os. Um n\xfamero qualquer de entrada pode ser definido nessa lista esses nomes s\xe3o apresentados no \xedcone gr\xe1fico presente no editor de controle, al\xe9m de serem destacados na express\xe3o inserida pelo usu\xe1rio. O n\xfamero de entradas e sa\xeddas se comporta de forma semelhante aos ",Object(b.b)("a",Object(n.a)({parentName:"p"},{href:"sum"}),"blocos somadores"),"."),Object(b.b)("p",null,"Abaixo do campo das vari\xe1veis de entrada est\xe1 presente o local para inser\xe7\xe3o da express\xe3o matem\xe1tica. A sintaxe da express\xe3o inserida pelo usu\xe1rio possui realce (por meio de diferentes formas e cores da fonte) para n\xfameros, operadores, vari\xe1veis de entrada, fun\xe7\xf5es e constantes, facilitando a cria\xe7\xe3o, manipula\xe7\xe3o e identifica\xe7\xe3o de erros de digita\xe7\xe3o e l\xf3gica."),Object(b.b)("div",{className:"admonition admonition-info alert alert--info"},Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(b.b)("h5",{parentName:"div"},Object(b.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(b.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"14",height:"16",viewBox:"0 0 14 16"}),Object(b.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"})))),"Informa\xe7\xe3o")),Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(b.b)("p",{parentName:"div"},"Como ferramenta de aux\xedlio ao usu\xe1rio foi desenvolvida uma verifica\xe7\xe3o da express\xe3o inserida."))),Object(b.b)("p",null,"Tal ferramenta ir\xe1 encontrar erros e indicar\xe1 ao usu\xe1rio qual o tipo do erro, al\xe9m da sua localiza\xe7\xe3o, destacando-o. A figura anterior exemplifica a identifica\xe7\xe3o autom\xe1tica do erro pelo PSP-UFU, assim como sua posi\xe7\xe3o na express\xe3o inserida."),Object(b.b)("h2",{id:"exemplo-de-express\xe3o-matem\xe1tica"},"Exemplo de Express\xe3o Matem\xe1tica"),Object(b.b)("p",null,"A corrente de campo em ",Object(b.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(b.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(b.b)("semantics",{parentName:"math"},Object(b.b)("mrow",{parentName:"semantics"},Object(b.b)("mi",{parentName:"mrow"},"p"),Object(b.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(b.b)("mi",{parentName:"mrow"},"u"),Object(b.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(b.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),".")))))," pode ser estimada de forma aproximada utilizando as pot\xeancias ativa (",Object(b.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(b.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(b.b)("semantics",{parentName:"math"},Object(b.b)("mrow",{parentName:"semantics"},Object(b.b)("mi",{parentName:"mrow"},"P")),Object(b.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"P")))),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.68333em",verticalAlign:"0em"}})),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.13889em"}}),"P"))))),") e reativa (",Object(b.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(b.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(b.b)("semantics",{parentName:"math"},Object(b.b)("mrow",{parentName:"semantics"},Object(b.b)("mi",{parentName:"mrow"},"Q")),Object(b.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"Q")))),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.8777699999999999em",verticalAlign:"-0.19444em"}})),Object(b.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"Q"))))),"), assim como as reat\xe2ncias transit\xf3rias de eixo direto 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A.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"max(A,B)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Se ",Object(b.b)("inlineCode",{parentName:"td"},"A>B"),", o resultado \xe9 ",Object(b.b)("inlineCode",{parentName:"td"},"A"),", sen\xe3o \xe9 ",Object(b.b)("inlineCode",{parentName:"td"},"B"),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"min(A,B)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Se ",Object(b.b)("inlineCode",{parentName:"td"},"A<B"),", o resultado \xe9 ",Object(b.b)("inlineCode",{parentName:"td"},"A"),", sen\xe3o \xe9 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",Object(b.b)("inlineCode",{parentName:"td"},"B"),")")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"real(A,B)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Retorna a parte real do n\xfamero complexo ",Object(b.b)("inlineCode",{parentName:"td"},"A"),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"sec(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Secante de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"sin(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Seno de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". Retorna o \xe2ngulo em radianos.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"sinh(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Mesmo que ",Object(b.b)("inlineCode",{parentName:"td"},"sin()"),", mas para seno hiperb\xf3lico.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"sqrt(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Raiz quadrada de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),".")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"tan(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Tangente de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". Retorna o \xe2ngulo em radianos.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"tanh(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Mesmo que ",Object(b.b)("inlineCode",{parentName:"td"},"tan()"),", mas para tangente hiperb\xf3lica.")),Object(b.b)("tr",{parentName:"tbody"},Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),Object(b.b)("inlineCode",{parentName:"td"},"trunc(A)")),Object(b.b)("td",Object(n.a)({parentName:"tr"},{align:null}),"Valor truncado de ",Object(b.b)("inlineCode",{parentName:"td"},"A"),". Retorna o n\xfamero inteiro de ",Object(b.b)("inlineCode",{parentName:"td"},"A")," sem a parcela fracionada.")))),Object(b.b)("p",null,"\xc9 poss\xedvel atribuir novas vari\xe1veis utilizando a seguinte sintaxe: "),Object(b.b)("pre",null,Object(b.b)("code",Object(n.a)({parentName:"pre"},{className:"language-cpp"}),"<nome da vari\xe1vel> := <express\xe3o>; <fun\xe7\xe3o>\n")),Object(b.b)("p",null,"Por exemplo:"),Object(b.b)("pre",null,Object(b.b)("code",Object(n.a)({parentName:"pre"},{className:"language-cpp"}),"comprimento := sqrt(x*x+y*y); 2*comprimento*sin(comprimento)\n")),Object(b.b)("div",{className:"admonition admonition-tip alert alert--success"},Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(b.b)("h5",{parentName:"div"},Object(b.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(b.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(b.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"})))),"Dica")),Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(b.b)("p",{parentName:"div"},"O caractere de espa\xe7o e de nova linha s\xe3o ignorados na interpreta\xe7\xe3o da express\xe3o, portanto para maior organiza\xe7\xe3o, o c\xf3digo anterior pode ser escrito da seguinte forma:"),Object(b.b)("pre",{parentName:"div"},Object(b.b)("code",Object(n.a)({parentName:"pre"},{className:"language-cpp"}),"comprimento := sqrt(x*x+y*y);\n2*comprimento*sin(comprimento)\n")))),Object(b.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(b.b)("h5",{parentName:"div"},Object(b.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(b.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(b.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado!")),Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(b.b)("p",{parentName:"div"},"Note que a express\xe3o que determina o valor de sa\xedda do bloco ",Object(b.b)("strong",{parentName:"p"},"n\xe3o possui")," o caractere ",Object(b.b)("inlineCode",{parentName:"p"},";")," em seu final."))),Object(b.b)("h2",{id:"formul\xe1rio-de-edi\xe7\xe3o-de-dados-do-bloco-de-express\xe3o-matem\xe1tica"},"Formul\xe1rio de edi\xe7\xe3o de dados do bloco de Express\xe3o Matem\xe1tica"),Object(b.b)("p",null,"O formul\xe1rio de inser\xe7\xe3o e edi\xe7\xe3o das entradas do bloco e da express\xe3o matem\xe1tica gen\xe9rica, assim como ferramentas de aux\xedlio de sua constru\xe7\xe3o \xe9 apresentado na figura abaixo."),Object(b.b)("div",null,Object(b.b)("center",null,Object(b.b)("img",{src:Object(m.a)("images/mathExpressionForm.png"),alt:"Formul\xe1rio de edi\xe7\xe3o de dados do bloco de express\xe3o matem\xe1tica no PSP-UFU",title:"Formul\xe1rio de edi\xe7\xe3o de dados do bloco de express\xe3o matem\xe1tica no PSP-UFU"}))),Object(b.b)("p",null,"No campo de \u201cVari\xe1veis de entrada\u201d \xe9 inserida uma lista com os nomes das entradas separados por espa\xe7os. Um n\xfamero qualquer de entrada pode ser definido nessa lista esses nomes s\xe3o apresentados no \xedcone gr\xe1fico presente no editor de controle, al\xe9m de serem destacados na express\xe3o inserida pelo usu\xe1rio. O n\xfamero de entradas e sa\xeddas se comporta de forma semelhante aos ",Object(b.b)("a",Object(n.a)({parentName:"p"},{href:"sum"}),"blocos somadores"),"."),Object(b.b)("p",null,"Abaixo do campo das vari\xe1veis de entrada est\xe1 presente o local para inser\xe7\xe3o da express\xe3o matem\xe1tica. A sintaxe da express\xe3o inserida pelo usu\xe1rio possui realce (por meio de diferentes formas e cores da fonte) para n\xfameros, operadores, vari\xe1veis de entrada, fun\xe7\xf5es e constantes, facilitando a cria\xe7\xe3o, manipula\xe7\xe3o e identifica\xe7\xe3o de erros de digita\xe7\xe3o e l\xf3gica."),Object(b.b)("div",{className:"admonition admonition-info alert alert--info"},Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(b.b)("h5",{parentName:"div"},Object(b.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(b.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"14",height:"16",viewBox:"0 0 14 16"}),Object(b.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"})))),"Informa\xe7\xe3o")),Object(b.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(b.b)("p",{parentName:"div"},"Como ferramenta de aux\xedlio ao usu\xe1rio foi desenvolvida uma verifica\xe7\xe3o da express\xe3o inserida."))),Object(b.b)("p",null,"Tal ferramenta ir\xe1 encontrar erros e indicar\xe1 ao usu\xe1rio qual o tipo do erro, al\xe9m da sua localiza\xe7\xe3o, destacando-o. A figura anterior exemplifica a identifica\xe7\xe3o autom\xe1tica do erro pelo PSP-UFU, assim como sua posi\xe7\xe3o na express\xe3o inserida."),Object(b.b)("h2",{id:"exemplo-de-express\xe3o-matem\xe1tica"},"Exemplo de Express\xe3o Matem\xe1tica"),Object(b.b)("p",null,"A corrente de campo em ",Object(b.b)("span",Object(n.a)({parentName:"p"},{className:"math 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a[e]=r({},a[e]),a[e][t]?(a[e][t]=a[e][t].slice(),a[e][t].push(i)):a[e][t]=[i],this.setQueryParameters({numericRefinements:a})},getConjunctiveRefinements:function(e){return this.isConjunctiveFacet(e)&&this.facetsRefinements[e]||[]},getDisjunctiveRefinements:function(e){return this.isDisjunctiveFacet(e)&&this.disjunctiveFacetsRefinements[e]||[]},getHierarchicalRefinement:function(e){return this.hierarchicalFacetsRefinements[e]||[]},getExcludeRefinements:function(e){return this.isConjunctiveFacet(e)&&this.facetsExcludes[e]||[]},removeNumericRefinement:function(e,t,n){return void 0!==n?this.isNumericRefined(e,t,n)?this.setQueryParameters({numericRefinements:this._clearNumericRefinements((function(r,i){return i===e&&r.op===t&&h(r.val,c(n))}))}):this:void 0!==t?this.isNumericRefined(e,t)?this.setQueryParameters({numericRefinements:this._clearNumericRefinements((function(n,r){return r===e&&n.op===t}))}):this:this.isNumericRefined(e)?this.setQueryParameters({numericRefinements:this._clearNumericRefinements((function(t,n){return n===e}))}):this},getNumericRefinements:function(e){return this.numericRefinements[e]||{}},getNumericRefinement:function(e,t){return this.numericRefinements[e]&&this.numericRefinements[e][t]},_clearNumericRefinements:function(e){if(void 0===e)return o(this.numericRefinements)?{}:this.numericRefinements;if("string"==typeof e)return o(this.numericRefinements[e])?u(this.numericRefinements,[e]):this.numericRefinements;if("function"==typeof e){var t=!1,n=this.numericRefinements,r=Object.keys(n).reduce((function(r,i){var a=n[i],s={};return a=a||{},Object.keys(a).forEach((function(n){var r=a[n]||[],c=[];r.forEach((function(t){e({val:t,op:n},i,"numeric")||c.push(t)})),c.length!==r.length&&(t=!0),s[n]=c})),r[i]=s,r}),{});return t?r:this.numericRefinements}},addFacet:function(e){return this.isConjunctiveFacet(e)?this:this.setQueryParameters({facets:this.facets.concat([e])})},addDisjunctiveFacet:function(e){return this.isDisjunctiveFacet(e)?this:this.setQueryParameters({disjunctiveFacets:this.disjunctiveFacets.concat([e])})},addHierarchicalFacet:function(e){if(this.isHierarchicalFacet(e.name))throw new Error("Cannot declare two hierarchical facets with the same name: `"+e.name+"`");return this.setQueryParameters({hierarchicalFacets:this.hierarchicalFacets.concat([e])})},addFacetRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the facets attribute of the helper configuration");return f.isRefined(this.facetsRefinements,e,t)?this:this.setQueryParameters({facetsRefinements:f.addRefinement(this.facetsRefinements,e,t)})},addExcludeRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the facets attribute of the helper configuration");return 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t!==e}))}):this},removeHierarchicalFacet:function(e){return this.isHierarchicalFacet(e)?this.clearRefinements(e).setQueryParameters({hierarchicalFacets:this.hierarchicalFacets.filter((function(t){return t.name!==e}))}):this},removeFacetRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the facets attribute of the helper configuration");return f.isRefined(this.facetsRefinements,e,t)?this.setQueryParameters({facetsRefinements:f.removeRefinement(this.facetsRefinements,e,t)}):this},removeExcludeRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the facets attribute of the helper configuration");return f.isRefined(this.facetsExcludes,e,t)?this.setQueryParameters({facetsExcludes:f.removeRefinement(this.facetsExcludes,e,t)}):this},removeDisjunctiveFacetRefinement:function(e,t){if(!this.isDisjunctiveFacet(e))throw new Error(e+" is not defined in the disjunctiveFacets attribute of the helper configuration");return f.isRefined(this.disjunctiveFacetsRefinements,e,t)?this.setQueryParameters({disjunctiveFacetsRefinements:f.removeRefinement(this.disjunctiveFacetsRefinements,e,t)}):this},removeTagRefinement:function(e){if(!this.isTagRefined(e))return this;var t={tagRefinements:this.tagRefinements.filter((function(t){return t!==e}))};return this.setQueryParameters(t)},toggleRefinement:function(e,t){return this.toggleFacetRefinement(e,t)},toggleFacetRefinement:function(e,t){if(this.isHierarchicalFacet(e))return this.toggleHierarchicalFacetRefinement(e,t);if(this.isConjunctiveFacet(e))return this.toggleConjunctiveFacetRefinement(e,t);if(this.isDisjunctiveFacet(e))return this.toggleDisjunctiveFacetRefinement(e,t);throw new Error("Cannot refine the undeclared facet "+e+"; it should be added to the helper options facets, disjunctiveFacets or hierarchicalFacets")},toggleConjunctiveFacetRefinement:function(e,t){if(!this.isConjunctiveFacet(e))throw new Error(e+" is not defined in the 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0===this.page?this:this.setPage(0)},_getHierarchicalFacetSortBy:function(e){return e.sortBy||["isRefined:desc","name:asc"]},_getHierarchicalFacetSeparator:function(e){return e.separator||" > "},_getHierarchicalRootPath:function(e){return e.rootPath||null},_getHierarchicalShowParentLevel:function(e){return"boolean"!=typeof e.showParentLevel||e.showParentLevel},getHierarchicalFacetByName:function(e){return s(this.hierarchicalFacets,(function(t){return t.name===e}))},getHierarchicalFacetBreadcrumb:function(e){if(!this.isHierarchicalFacet(e))return[];var t=this.getHierarchicalRefinement(e)[0];if(!t)return[];var n=this._getHierarchicalFacetSeparator(this.getHierarchicalFacetByName(e));return t.split(n).map((function(e){return e.trim()}))},toString:function(){return JSON.stringify(this,null,2)}},e.exports=l},154:function(e,t,n){"use strict";e.exports=function(e,t){if(null===e)return{};var n,r,i={},a=Object.keys(e);for(r=0;r<a.length;r++)n=a[r],t.indexOf(n)>=0||(i[n]=e[n]);return i}},155:function(e,t,n){"use strict";var r=n(138),i=n(139),a=n(156),s=n(176),c=n(135),u=n(177),o=n(157),f=n(178);function h(e){var t={};return e.forEach((function(e,n){t[e]=n})),t}function l(e,t,n){t&&t[n]&&(e.stats=t[n])}function m(e,t){var n=t[0];this._rawResults=t;var a=this;Object.keys(n).forEach((function(e){a[e]=n[e]})),this.processingTimeMS=t.reduce((function(e,t){return void 0===t.processingTimeMS?e:e+t.processingTimeMS}),0),this.disjunctiveFacets=[],this.hierarchicalFacets=e.hierarchicalFacets.map((function(){return[]})),this.facets=[];var o=e.getRefinedDisjunctiveFacets(),m=h(e.facets),d=h(e.disjunctiveFacets),v=1,p=n.facets||{};Object.keys(p).forEach((function(t){var r,i,s=p[t],o=(r=e.hierarchicalFacets,i=t,c(r,(function(e){return(e.attributes||[]).indexOf(i)>-1})));if(o){var f=o.attributes.indexOf(t),h=u(e.hierarchicalFacets,(function(e){return e.name===o.name}));a.hierarchicalFacets[h][f]={attribute:t,data:s,exhaustive:n.exhaustiveFacetsCount}}else{var 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m=c[0].split(s)[0];l[m]=a.hierarchicalFacets[o][h].data[m]}a.hierarchicalFacets[o][h].data=i(l,n,a.hierarchicalFacets[o][h].data)}})),v++}})),Object.keys(e.facetsExcludes).forEach((function(t){var r=e.facetsExcludes[t],i=m[t];a.facets[i]={name:t,data:n.facets[t],exhaustive:n.exhaustiveFacetsCount},r.forEach((function(e){a.facets[i]=a.facets[i]||{name:t},a.facets[i].data=a.facets[i].data||{},a.facets[i].data[e]=0}))})),this.hierarchicalFacets=this.hierarchicalFacets.map(f(e)),this.facets=s(this.facets),this.disjunctiveFacets=s(this.disjunctiveFacets),this._state=e}function d(e,t){if(!t.data||0===t.data.length)return t;var n=t.data.map((function(t){return d(e,t)})),i=e(n);return r({},t,{data:i})}function v(e,t){var n=c(e,(function(e){return e.name===t}));return n&&n.stats}function p(e,t,n,r,i){var a=c(i,(function(e){return 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r=i({},t,{sortBy:m.DEFAULT_SORT});if(Array.isArray(r.sortBy)){var s=o(r.sortBy,m.DEFAULT_SORT);return Array.isArray(n)?a(n,s[0],s[1]):d((function(e){return a(e,s[0],s[1])}),n)}if("function"==typeof r.sortBy)return Array.isArray(n)?n.sort(r.sortBy):d((function(e){return function(e,t){return t.sort(e)}(r.sortBy,e)}),n);throw new Error("options.sortBy is optional but if defined it must be either an array of string (predicates) or a sorting function")}},m.prototype.getFacetStats=function(e){return this._state.isConjunctiveFacet(e)?v(this.facets,e):this._state.isDisjunctiveFacet(e)?v(this.disjunctiveFacets,e):void 0},m.prototype.getRefinements=function(){var e=this._state,t=this,n=[];return Object.keys(e.facetsRefinements).forEach((function(r){e.facetsRefinements[r].forEach((function(i){n.push(p(e,"facet",r,i,t.facets))}))})),Object.keys(e.facetsExcludes).forEach((function(r){e.facetsExcludes[r].forEach((function(i){n.push(p(e,"exclude",r,i,t.facets))}))})),Object.keys(e.disjunctiveFacetsRefinements).forEach((function(r){e.disjunctiveFacetsRefinements[r].forEach((function(i){n.push(p(e,"disjunctive",r,i,t.disjunctiveFacets))}))})),Object.keys(e.hierarchicalFacetsRefinements).forEach((function(r){e.hierarchicalFacetsRefinements[r].forEach((function(i){n.push(function(e,t,n,r){var i=e.getHierarchicalFacetByName(t),a=e._getHierarchicalFacetSeparator(i),s=n.split(a),u=c(r,(function(e){return e.name===t})),o=s.reduce((function(e,t){var n=e&&c(e.data,(function(e){return e.name===t}));return void 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e.name===n})),s=a&&a.data&&a.data[r]?a.data[r]:0,u=a&&a.exhaustive||!1;return{type:t,attributeName:n,name:r,count:s,exhaustive:u}}m.prototype.getFacetByName=function(e){function t(t){return t.name===e}return c(this.facets,t)||c(this.disjunctiveFacets,t)||c(this.hierarchicalFacets,t)},m.DEFAULT_SORT=["isRefined:desc","count:desc","name:asc"],m.prototype.getFacetValues=function(e,t){var n=function(e,t){function n(e){return e.name===t}if(e._state.isConjunctiveFacet(t)){var r=c(e.facets,n);return r?Object.keys(r.data).map((function(n){return{name:n,count:r.data[n],isRefined:e._state.isFacetRefined(t,n),isExcluded:e._state.isExcludeRefined(t,n)}})):[]}if(e._state.isDisjunctiveFacet(t)){var i=c(e.disjunctiveFacets,n);return i?Object.keys(i.data).map((function(n){return{name:n,count:i.data[n],isRefined:e._state.isDisjunctiveFacetRefined(t,n)}})):[]}if(e._state.isHierarchicalFacet(t))return c(e.hierarchicalFacets,n)}(this,e);if(n){var r=i({},t,{sortBy:m.DEFAULT_SORT});if(Array.isArray(r.sortBy)){var s=o(r.sortBy,m.DEFAULT_SORT);return Array.isArray(n)?a(n,s[0],s[1]):d((function(e){return a(e,s[0],s[1])}),n)}if("function"==typeof r.sortBy)return Array.isArray(n)?n.sort(r.sortBy):d((function(e){return function(e,t){return t.sort(e)}(r.sortBy,e)}),n);throw new Error("options.sortBy is optional but if defined it must be either an array of string (predicates) or a sorting function")}},m.prototype.getFacetStats=function(e){return this._state.isConjunctiveFacet(e)?v(this.facets,e):this._state.isDisjunctiveFacet(e)?v(this.disjunctiveFacets,e):void 0},m.prototype.getRefinements=function(){var e=this._state,t=this,n=[];return Object.keys(e.facetsRefinements).forEach((function(r){e.facetsRefinements[r].forEach((function(i){n.push(p(e,"facet",r,i,t.facets))}))})),Object.keys(e.facetsExcludes).forEach((function(r){e.facetsExcludes[r].forEach((function(i){n.push(p(e,"exclude",r,i,t.facets))}))})),Object.keys(e.disjunctiveFacetsRefinements).forEach((function(r){e.disjunctiveFacetsRefinements[r].forEach((function(i){n.push(p(e,"disjunctive",r,i,t.disjunctiveFacets))}))})),Object.keys(e.hierarchicalFacetsRefinements).forEach((function(r){e.hierarchicalFacetsRefinements[r].forEach((function(i){n.push(function(e,t,n,r){var i=e.getHierarchicalFacetByName(t),a=e._getHierarchicalFacetSeparator(i),s=n.split(a),u=c(r,(function(e){return e.name===t})),o=s.reduce((function(e,t){var n=e&&c(e.data,(function(e){return e.name===t}));return void 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similarity index 97%
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index c94a7ba4..b1095961 100644
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Sua unidade pode ser selecionada, sendo expressa em V ou em kV."),Object(r.b)("p",null,"A modifica\xe7\xe3o desse par\xe2metro ir\xe1 alterar toda a tens\xe3o do trecho conectado por linhas el\xe9tricas, sendo emitido um alerta ao usu\xe1rio."),Object(r.b)("h4",{id:"tens\xe3o-controlada"},"Tens\xe3o controlada"),Object(r.b)("p",null,"Caracteriza o barramento como ",Object(r.b)("strong",{parentName:"p"},"barra de tens\xe3o controlada (",Object(r.b)("a",Object(n.a)({parentName:"strong"},{href:"powerFlow"}),"Barra PV"),")"),","),Object(r.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(r.b)("h5",{parentName:"div"},Object(r.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(r.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(r.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(r.b)("p",{parentName:"div"},"Essa op\xe7\xe3o \xe9 somente v\xe1lida caso alguma m\xe1quina s\xedncrona esteja conectado, caso contr\xe1rio esse valor ser\xe1 ignorado. Caso o limite de pot\xeancia reativa da m\xe1quina s\xedncrona conectada seja ultrapassado esse valor tamb\xe9m \xe9 ignorado."))),Object(r.b)("p",null,"O valor poder\xe1 ser inserido em p.u. ou em volts (ou kV caso a tens\xe3o nominal esteja nesta unidade)."),Object(r.b)("h4",{id:"barra-de-refer\xeancia"},"Barra de refer\xeancia"),Object(r.b)("p",null,"Caracteriza o barramento como ",Object(r.b)("strong",{parentName:"p"},"barra de refer\xeancia (",Object(r.b)("a",Object(n.a)({parentName:"strong"},{href:"powerFlow"}),"Barra de oscila\xe7\xe3o"),")"),". Essa op\xe7\xe3o \xe9 somente v\xe1lida caso esteja conectado um gerador s\xedncrono, caso contr\xe1rio uma mensagem de erro ser\xe1 exibida ao usu\xe1rio ao realizar algum dos c\xe1lculos do programa.")),Object(r.b)(b.a,{value:"fault",mdxType:"TabItem"},Object(r.b)("h4",{id:"inserir-falta"},"Inserir falta"),Object(r.b)("p",null,"Indica se existe um curto-circuito na barra nos estudos de ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"fault"}),"curto-circuito"),"."),Object(r.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(r.b)("h5",{parentName:"div"},Object(r.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(r.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(r.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado!")),Object(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(r.b)("p",{parentName:"div"},"Nota-se que essa op\xe7\xe3o ir\xe1 inserir uma falta no c\xe1lculo de ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"fault"}),"curto-circuito")," e ",Object(r.b)("strong",{parentName:"p"},"n\xe3o ser\xe1 considerado no estudo de estabilidade"),"."))),Object(r.b)("h4",{id:"tipo-de-falta"},"Tipo de falta"),Object(r.b)("p",null,"Seleciona o tipo de falha shunt da barra:"),Object(r.b)("ul",null,Object(r.b)("li",{parentName:"ul"},"trif\xe1sico para a terra"),Object(r.b)("li",{parentName:"ul"},"fase-fase"),Object(r.b)("li",{parentName:"ul"},"fase-fase-terra"),Object(r.b)("li",{parentName:"ul"},"fase-terra")),Object(r.b)("h4",{id:"local-da-falta"},"Local da falta"),Object(r.b)("p",null,"Seleciona a fase em que se situa a falta (ou combina\xe7\xe3o delas no caso de falha entre duas fases), sendo essa op\xe7\xe3o desabilitada para o tipo de falta trif\xe1sica."),Object(r.b)("h4",{id:"resist\xeancia-e-reat\xe2ncia-de-falta"},"Resist\xeancia e reat\xe2ncia de falta"),Object(r.b)("p",null,"Representam a imped\xe2ncia da falta. 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Os seguintes dados s\xe3o exibidos:"),Object(r.b)("ul",null,Object(r.b)("li",{parentName:"ul"},"m\xf3dulo da tens\xe3o do barramento"),Object(r.b)("li",{parentName:"ul"},"\xe2ngulo da tens\xe3o do barramento.")),Object(r.b)("h4",{id:"inserir-falta-1"},"Inserir falta"),Object(r.b)("p",null,"Insere uma falta trif\xe1sica na barra no c\xe1lculo de ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"stability"}),"estabilidade"),"."),Object(r.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(r.b)("h5",{parentName:"div"},Object(r.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(r.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(r.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado!")),Object(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(r.b)("p",{parentName:"div"},"Nota-se que essa op\xe7\xe3o ir\xe1 inserir uma falta no c\xe1lculo de ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"stability"}),"estabilidade")," e ",Object(r.b)("strong",{parentName:"p"},"n\xe3o ser\xe1 considerado no estudo de ",Object(r.b)("a",Object(n.a)({parentName:"strong"},{href:"fault"}),"curto-circuito")),"."))),Object(r.b)("h4",{id:"tempo"},"Tempo"),Object(r.b)("p",null,"Instante no tempo (",Object(r.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(r.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(r.b)("semantics",{parentName:"math"},Object(r.b)("mrow",{parentName:"semantics"},Object(r.b)("msub",{parentName:"mrow"},Object(r.b)("mi",{parentName:"msub"},"t"),Object(r.b)("mrow",{parentName:"msub"},Object(r.b)("mi",{parentName:"mrow"},"f"),Object(r.b)("mi",{parentName:"mrow"},"a"),Object(r.b)("mi",{parentName:"mrow"},"l"),Object(r.b)("mi",{parentName:"mrow"},"t"),Object(r.b)("mi",{parentName:"mrow"},"a")))),Object(r.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"t_{falta}")))),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.9011879999999999em",verticalAlign:"-0.286108em"}})),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"t"),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"msupsub"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-t vlist-t2"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-r"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"vlist",style:{height:"0.3361079999999999em"}}),Object(r.b)("span",Object(n.a)({parentName:"span"},{style:{top:"-2.5500000000000003em",marginLeft:"0em",marginRight:"0.05em"}}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"pstrut",style:{height:"2.7em"}})),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"sizing reset-size6 size3 mtight"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"mord mtight"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight",style:{marginRight:"0.10764em"}}),"f"),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight"}),"a"),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight",style:{marginRight:"0.01968em"}}),"l"),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight"}),"t"),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight"}),"a"))))),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-s"}),"\u200b")),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-r"}),Object(r.b)("span",Object(n.a)({parentName:"span"},{className:"vlist",style:{height:"0.286108em"}}),Object(r.b)("span",{parentName:"span"})))))))))),") em que ocorre a falta durante os estudos de ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"stability"}),"estabilidade"),". 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similarity index 94%
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Essa vari\xe1vel \xe9 normalmente utilizada no c\xe1lculo do erro da tens\xe3o de refer\xeancia do AVR;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Velocidade")," (",Object(m.b)("em",{parentName:"p"},"entrada: AVR e RV"),"): Velocidade da m\xe1quina s\xedncrona, em rad/s, vari\xe1vel no tempo. Normalmente utilizada no c\xe1lculo do erro de velocidade nos reguladores de velocidade, al\xe9m de entrada do PSS em AVRs;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Pot\xeancia ativa e reativa")," (",Object(m.b)("em",{parentName:"p"},"entrada: AVR"),"): Pot\xeancia ativa fornecida pela m\xe1quina s\xedncrona, em ",Object(m.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mi",{parentName:"mrow"},"p"),Object(m.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(m.b)("mi",{parentName:"mrow"},"u"),Object(m.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(m.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."))))),", vari\xe1vel no tempo. Normalmente utilizada como entrada do PSS (pot\xeancia ativa) e controle de sub e sobrecorrente de excita\xe7\xe3o nos AVRs;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Tens\xe3o terminal inicial")," (",Object(m.b)("em",{parentName:"p"},"entrada: AVR"),"): M\xf3dulo da tens\xe3o no barramento da m\xe1quina s\xedncrona pr\xe9via ao estudo din\xe2mico originado do fluxo de carga, em ",Object(m.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mi",{parentName:"mrow"},"p"),Object(m.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(m.b)("mi",{parentName:"mrow"},"u"),Object(m.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(m.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."))))),", fixo no tempo. Essa vari\xe1vel est\xe1 normalmente associada \xe0 refer\xeancia de tens\xe3o do AVR;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Velocidade inicial")," (",Object(m.b)("em",{parentName:"p"},"entrada: AVR e RV"),"): Velocidade do sistema (",Object(m.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mn",{parentName:"mrow"},"2"),Object(m.b)("mi",{parentName:"mrow"},"\u03c0"),Object(m.b)("msub",{parentName:"mrow"},Object(m.b)("mi",{parentName:"msub"},"f"),Object(m.b)("mrow",{parentName:"msub"},Object(m.b)("mi",{parentName:"mrow"},"r"),Object(m.b)("mi",{parentName:"mrow"},"e"),Object(m.b)("mi",{parentName:"mrow"},"f")))),Object(m.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"2 \\pi f_{ref}")))),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.980548em",verticalAlign:"-0.286108em"}})),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"2"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.03588em"}}),"\u03c0"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.10764em"}}),"f"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"msupsub"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-t vlist-t2"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-r"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"vlist",style:{height:"0.3361079999999999em"}}),Object(m.b)("span",Object(n.a)({parentName:"span"},{style:{top:"-2.5500000000000003em",marginLeft:"-0.10764em",marginRight:"0.05em"}}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"pstrut",style:{height:"2.7em"}})),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"sizing reset-size6 size3 mtight"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mtight"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight",style:{marginRight:"0.02778em"}}),"r"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight"}),"e"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight",style:{marginRight:"0.10764em"}}),"f"))))),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-s"}),"\u200b")),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-r"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"vlist",style:{height:"0.286108em"}}),Object(m.b)("span",{parentName:"span"})))))))))),"), definida nas ",Object(m.b)("a",Object(n.a)({parentName:"p"},{href:"simulationConfig"}),"op\xe7\xf5es de simula\xe7\xe3o"),", em rad/s, fixa no tempo. Normalmente utiliza-se essa vari\xe1vel como refer\xeancia de velocidade em RVs e normaliza\xe7\xe3o da velocidade;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Pot\xeancia mec\xe2nica inicial")," (",Object(m.b)("em",{parentName:"p"},"entrada: RV"),"): Pot\xeancia mec\xe2nica inicial, calculada ap\xf3s a inicializa\xe7\xe3o das m\xe1quinas s\xedncronas com os dados originados do fluxo de carga, em ",Object(m.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mi",{parentName:"mrow"},"p"),Object(m.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(m.b)("mi",{parentName:"mrow"},"u"),Object(m.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(m.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."))))),", fixa no tempo. Normalmente \xe9 utilizada como refer\xeancia de pot\xeancia mec\xe2nica nos reguladores de velocidade;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Varia\xe7\xe3o de velocidade e pot\xeancia ativa")," (",Object(m.b)("em",{parentName:"p"},"entrada: AVR"),"): C\xe1lculo da varia\xe7\xe3o dessas entradas entre os passos de integra\xe7\xe3o normalizada pelo passo de integra\xe7\xe3o, conforme a equa\xe7\xe3o:"),Object(m.b)("div",Object(n.a)({parentName:"li"},{className:"math 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Normalmente utilizada no c\xe1lculo do erro de velocidade nos reguladores de velocidade, al\xe9m de entrada do PSS em AVRs;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Pot\xeancia ativa e reativa")," (",Object(m.b)("em",{parentName:"p"},"entrada: AVR"),"): Pot\xeancia ativa fornecida pela m\xe1quina s\xedncrona, em ",Object(m.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mi",{parentName:"mrow"},"p"),Object(m.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(m.b)("mi",{parentName:"mrow"},"u"),Object(m.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(m.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."))))),", vari\xe1vel no tempo. Normalmente utilizada como entrada do PSS (pot\xeancia ativa) e controle de sub e sobrecorrente de excita\xe7\xe3o nos AVRs;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Tens\xe3o terminal inicial")," (",Object(m.b)("em",{parentName:"p"},"entrada: AVR"),"): M\xf3dulo da tens\xe3o no barramento da m\xe1quina s\xedncrona pr\xe9via ao estudo din\xe2mico originado do fluxo de carga, em ",Object(m.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mi",{parentName:"mrow"},"p"),Object(m.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(m.b)("mi",{parentName:"mrow"},"u"),Object(m.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(m.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."))))),", fixo no tempo. Essa vari\xe1vel est\xe1 normalmente associada \xe0 refer\xeancia de tens\xe3o do AVR;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Velocidade inicial")," (",Object(m.b)("em",{parentName:"p"},"entrada: AVR e RV"),"): Velocidade do sistema (",Object(m.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mn",{parentName:"mrow"},"2"),Object(m.b)("mi",{parentName:"mrow"},"\u03c0"),Object(m.b)("msub",{parentName:"mrow"},Object(m.b)("mi",{parentName:"msub"},"f"),Object(m.b)("mrow",{parentName:"msub"},Object(m.b)("mi",{parentName:"mrow"},"r"),Object(m.b)("mi",{parentName:"mrow"},"e"),Object(m.b)("mi",{parentName:"mrow"},"f")))),Object(m.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"2 \\pi f_{ref}")))),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.980548em",verticalAlign:"-0.286108em"}})),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"2"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.03588em"}}),"\u03c0"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.10764em"}}),"f"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"msupsub"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-t vlist-t2"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-r"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"vlist",style:{height:"0.3361079999999999em"}}),Object(m.b)("span",Object(n.a)({parentName:"span"},{style:{top:"-2.5500000000000003em",marginLeft:"-0.10764em",marginRight:"0.05em"}}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"pstrut",style:{height:"2.7em"}})),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"sizing reset-size6 size3 mtight"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mtight"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight",style:{marginRight:"0.02778em"}}),"r"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight"}),"e"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault mtight",style:{marginRight:"0.10764em"}}),"f"))))),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-s"}),"\u200b")),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"vlist-r"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"vlist",style:{height:"0.286108em"}}),Object(m.b)("span",{parentName:"span"})))))))))),"), definida nas ",Object(m.b)("a",Object(n.a)({parentName:"p"},{href:"simulationConfig"}),"op\xe7\xf5es de simula\xe7\xe3o"),", em rad/s, fixa no tempo. Normalmente utiliza-se essa vari\xe1vel como refer\xeancia de velocidade em RVs e normaliza\xe7\xe3o da velocidade;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Pot\xeancia mec\xe2nica inicial")," (",Object(m.b)("em",{parentName:"p"},"entrada: RV"),"): Pot\xeancia mec\xe2nica inicial, calculada ap\xf3s a inicializa\xe7\xe3o das m\xe1quinas s\xedncronas com os dados originados do fluxo de carga, em ",Object(m.b)("span",Object(n.a)({parentName:"p"},{className:"math math-inline"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mi",{parentName:"mrow"},"p"),Object(m.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(m.b)("mi",{parentName:"mrow"},"u"),Object(m.b)("mi",Object(n.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(m.b)("annotation",Object(n.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"p.u.")))),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"strut",style:{height:"0.625em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(m.b)("span",Object(n.a)({parentName:"span"},{className:"mord"}),"."))))),", fixa no tempo. Normalmente \xe9 utilizada como refer\xeancia de pot\xeancia mec\xe2nica nos reguladores de velocidade;")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("p",{parentName:"li"},Object(m.b)("strong",{parentName:"p"},"Varia\xe7\xe3o de velocidade e pot\xeancia ativa")," (",Object(m.b)("em",{parentName:"p"},"entrada: AVR"),"): C\xe1lculo da varia\xe7\xe3o dessas entradas entre os passos de integra\xe7\xe3o normalizada pelo passo de integra\xe7\xe3o, conforme a equa\xe7\xe3o:"),Object(m.b)("div",Object(n.a)({parentName:"li"},{className:"math 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",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"https://twitter.com/PspUfu"}),"Twitter"),"."))),Object(r.b)("p",null,"Na sequ\xeancia s\xe3o apresentados o passo-a-passo para instala\xe7\xe3o dos SOs ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"installation#windows"}),"Windows")," e ",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"installation#linux"}),"Linux"),". 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O execut\xe1vel est\xe1 presente na pasta "',Object(r.b)("em",{parentName:"p"},"<local de instala\xe7\xe3o>/PSP-UFU/bin/PSP-UFU.exe"),'".'),Object(r.b)("h3",{id:"problemas-recorrentes-no-windows"},"Problemas recorrentes no Windows"),Object(r.b)("ul",null,Object(r.b)("li",{parentName:"ul"},"Ao baixar o navegador pode ",Object(r.b)("strong",{parentName:"li"},"falsamente"),' sinalizar que \xe9 um arquivo perigoso, basta clicar em "Manter arquivo";'),Object(r.b)("li",{parentName:"ul"},'Ao abrir o instalador, novamente o Windows sinaliza que o arquivo \xe9 perigoso, basta clicar em "Executar assim mesmo";'),Object(r.b)("li",{parentName:"ul"},"Ao abrir o programa e alterar o seu idioma, uma mensagem de erro \xe9 exibida. Para resolver esse problema basta executar o PSP-UFU como administrador (clicar com bot\xe3o direito no atalho do programa e posteriormente em executar como administrador). 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Reinicie o programa.')),Object(r.b)("h2",{id:"linux"},"Linux"),Object(r.b)("p",null,"A instala\xe7\xe3o no sistema Linux \xe9 facilmente realizado pelo pacote de instala\xe7\xe3o autom\xe1tico ",Object(r.b)("em",{parentName:"p"},".deb"),"."),Object(r.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(r.b)("h5",{parentName:"div"},Object(r.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(r.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(r.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 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",Object(r.b)("a",Object(n.a)({parentName:"p"},{href:"https://wiki.wxwidgets.org/Compiling_and_getting_started#Running_wxWidgets_projects"}),"diret\xf3rio das bibliotecas do wxWidgets")," nas vari\xe1veis de ambiente.\nPara isso, siga ",Object(r.b)("strong",{parentName:"p"},"UM")," dos m\xe9todos apresentados abaixo:"),Object(r.b)("h4",{id:"m\xe9todo-i-recomendado"},Object(r.b)("em",{parentName:"h4"},"M\xe9todo I (recomendado)")),Object(r.b)("p",null,"Insira o seguinte comando no arquivo ",Object(r.b)("strong",{parentName:"p"},"~/.bashrc"),":"),Object(r.b)("pre",null,Object(r.b)("code",Object(n.a)({parentName:"pre"},{className:"language-shell"}),'echo "export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib" >> ~/.bashrc\n')),Object(r.b)("h4",{id:"m\xe9todo-ii-n\xe3o-recomendado"},Object(r.b)("em",{parentName:"h4"},"M\xe9todo II (n\xe3o recomendado)")),Object(r.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(r.b)("h5",{parentName:"div"},Object(r.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(r.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(r.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado!")),Object(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-content"}),Object(r.b)("p",{parentName:"div"},"Utilizando esse m\xe9todo os passos abaixo devem ser executados ",Object(r.b)("strong",{parentName:"p"},"todas as vezes")," que voc\xea quiser abrir o PSP-UFU."))),Object(r.b)("ol",null,Object(r.b)("li",{parentName:"ol"},"Abra o terminal e acesse o diret\xf3rio onde est\xe1 instalado o PSP-UFU:")),Object(r.b)("pre",null,Object(r.b)("code",Object(n.a)({parentName:"pre"},{className:"language-shell"}),"cd /usr/local/bin\n")),Object(r.b)("ol",{start:2},Object(r.b)("li",{parentName:"ol"},"Insira as bibliotecas compartilhadas do wxWidgets nas vari\xe1veis de ambiente:")),Object(r.b)("pre",null,Object(r.b)("code",Object(n.a)({parentName:"pre"},{className:"language-shell"}),"export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib\n")),Object(r.b)("ol",{start:3},Object(r.b)("li",{parentName:"ol"},"Ent\xe3o, execute o PSP-UFU na ",Object(r.b)("strong",{parentName:"li"},"mesma se\xe7\xe3o")," do terminal:")),Object(r.b)("pre",null,Object(r.b)("code",Object(n.a)({parentName:"pre"},{className:"language-shell"}),"./PSP-UFU\n")),Object(r.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(r.b)("div",Object(n.a)({parentName:"div"},{className:"admonition-heading"}),Object(r.b)("h5",{parentName:"div"},Object(r.b)("span",Object(n.a)({parentName:"h5"},{className:"admonition-icon"}),Object(r.b)("svg",Object(n.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(r.b)("path",Object(n.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 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similarity index 58%
rename from docs/7c02804c.3db30e62.js
rename to docs/7c02804c.f5417704.js
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",Object(o.b)("a",Object(r.a)({parentName:"p"},{href:"http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=601-02-04"}),Object(o.b)("em",{parentName:"a"},"tradu\xe7\xe3o livre")," - IEC 60050"),".")),Object(o.b)("div",{className:"admonition admonition-info alert alert--info"},Object(o.b)("div",Object(r.a)({parentName:"div"},{className:"admonition-heading"}),Object(o.b)("h5",{parentName:"div"},Object(o.b)("span",Object(r.a)({parentName:"h5"},{className:"admonition-icon"}),Object(o.b)("svg",Object(r.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"14",height:"16",viewBox:"0 0 14 16"}),Object(o.b)("path",Object(r.a)({parentName:"svg"},{fillRule:"evenodd",d:"M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"})))),"Informa\xe7\xe3o")),Object(o.b)("div",Object(r.a)({parentName:"div"},{className:"admonition-content"}),Object(o.b)("p",{parentName:"div"},"Todos os elementos inseridos pode ser manipulados e editados utilizando as ",Object(o.b)("a",Object(r.a)({parentName:"p"},{href:"cadTools"}),"Ferramentas CAD"),"."))),Object(o.b)("h2",{id:"novo-projeto"},"Novo projeto"),Object(o.b)("p",null,"A cria\xe7\xe3o de um novo projeto \xe9 realizada clicando no item ",Object(o.b)("strong",{parentName:"p"},"Novo projeto")," no ",Object(o.b)("a",Object(r.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"submenu ",Object(o.b)("strong",{parentName:"a"},"Arquivo")),". Essa a\xe7\xe3o cria um sistema em branco na \xe1rea de trabalho, local onde \xe9 poss\xedvel inserir os elementos el\xe9tricos por meio do ",Object(o.b)("a",Object(r.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"submenu ",Object(o.b)("strong",{parentName:"a"},"Ferramentas"))," ou pelas ",Object(o.b)("a",Object(r.a)({parentName:"p"},{href:"powerEditor#teclas-de-atalho"}),"teclas de atalho"),"."),Object(o.b)("p",null,"Abaixo s\xe3o apresentados os elementos el\xe9tricos de pot\xeancia que podem ser inseridos no PSP-UFU:"),Object(o.b)("ul",null,Object(o.b)("li",{parentName:"ul"},Object(o.b)("a",Object(r.a)({parentName:"li"},{href:"bus"}),"Barramento")),Object(o.b)("li",{parentName:"ul"},"Elementos de ramo",Object(o.b)("ul",{parentName:"li"},Object(o.b)("li",{parentName:"ul"},Object(o.b)("a",Object(r.a)({parentName:"li"},{href:"line"}),"Linha")),Object(o.b)("li",{parentName:"ul"},Object(o.b)("a",Object(r.a)({parentName:"li"},{href:"transformer"}),"Transformador")))),Object(o.b)("li",{parentName:"ul"},"Elementos Shunt",Object(o.b)("ul",{parentName:"li"},Object(o.b)("li",{parentName:"ul"},Object(o.b)("a",Object(r.a)({parentName:"li"},{href:"load"}),"Carga")),Object(o.b)("li",{parentName:"ul"},Object(o.b)("a",Object(r.a)({parentName:"li"},{href:"capacitor"}),"Capacitor")),Object(o.b)("li",{parentName:"ul"},Object(o.b)("a",Object(r.a)({parentName:"li"},{href:"inductor"}),"Indutor")),Object(o.b)("li",{parentName:"ul"},Object(o.b)("a",Object(r.a)({parentName:"li"},{href:"harmSource"}),"Fonte de Corrente Harm\xf4nica")))),Object(o.b)("li",{parentName:"ul"},"M\xe1quinas",Object(o.b)("ul",{parentName:"li"},Object(o.b)("li",{parentName:"ul"},Object(o.b)("a",Object(r.a)({parentName:"li"},{href:"syncGenerator"}),"Gerador S\xedncrono")),Object(o.b)("li",{parentName:"ul"},Object(o.b)("a",Object(r.a)({parentName:"li"},{href:"syncMotor"}),"Compensador S\xedncrono")),Object(o.b)("li",{parentName:"ul"},Object(o.b)("a",Object(r.a)({parentName:"li"},{href:"indMotor"}),"Motor de Indu\xe7\xe3o"))))),Object(o.b)("div",null,Object(o.b)("center",null,Object(o.b)("img",{src:Object(c.a)("images/powerElements.svg"),alt:"Elementos de pot\xeancia",title:"Elementos de pot\xeancia"}))),Object(o.b)("h2",{id:"inserindo-elementos"},"Inserindo elementos"),Object(o.b)("p",null,"Por meio do submenu ",Object(o.b)("strong",{parentName:"p"},"Ferramentas")," pode-se inserir os elementos de pot\xeancia, como \xe9 apresentado na imagem abaixo."),Object(o.b)("div",null,Object(o.b)("center",null,Object(o.b)("img",{src:Object(c.a)("images/addPowerElements.png"),alt:"Adicionar elementos de pot\xeancia",title:"Adicionar elementos de pot\xeancia"}))),Object(o.b)("p",null,"No caso de inser\xe7\xe3o de um barramento, o usu\xe1rio deve apenas clicar na posi\xe7\xe3o desejada, j\xe1 para os outros componentes ser\xe1 solicitado que o usu\xe1rio selecione em uma ou duas barras, o qual o novo componente ser\xe1 conectado."),Object(o.b)("p",null,"Sempre que s\xe3o inseridos novos elementos, um formul\xe1rio de dados \xe9 exibido e pode-se editar os dados el\xe9tricos e acessar formul\xe1rios adicionais, como dados de estabilidade."),Object(o.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(o.b)("div",Object(r.a)({parentName:"div"},{className:"admonition-heading"}),Object(o.b)("h5",{parentName:"div"},Object(o.b)("span",Object(r.a)({parentName:"h5"},{className:"admonition-icon"}),Object(o.b)("svg",Object(r.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(o.b)("path",Object(r.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o")),Object(o.b)("div",Object(r.a)({parentName:"div"},{className:"admonition-content"}),Object(o.b)("p",{parentName:"div"},"O primeiro elemento que a ser inserido no projeto ",Object(o.b)("strong",{parentName:"p"},"deve")," ser um barramento. 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Para os demais elementos ",Object(o.b)("strong",{parentName:"p"},"deve-se clicar em uma mais barras")," para exibir o elemento inserido."),Object(o.b)("p",{parentName:"div"},Object(o.b)("strong",{parentName:"p"},"Sempre fique atento \xe0s instru\xe7\xf5es da ",Object(o.b)("a",Object(r.a)({parentName:"strong"},{href:"mainScreen#barra-de-status"}),"Barra de Status"),".")))),Object(o.b)("video",{autoPlay:!0,loop:!0,muted:!0,playsInline:!0,controls:!0},Object(o.b)("source",{src:"/PSP/videos/timelapseBuild.mp4",type:"video/mp4"})),Object(o.b)("h3",{id:"teclas-de-atalho"},"Teclas de atalho"),Object(o.b)("p",null,"\xc9 poss\xedvel inserir todos os elementos de pot\xeancia por meio de teclas de atalho, facilitando e agilizando a cria\xe7\xe3o dos diagramas unifilares no PSP-UFU. 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Todos os dados podem ser ",Object(o.b)("strong",{parentName:"p"},"alterados")," ao ",Object(o.b)("strong",{parentName:"p"},"clicar duas vezes sobre o elemento")," ou por op\xe7\xe3o do ",Object(o.b)("strong",{parentName:"p"},"menu de contexto")," exibido ao clicar com o bot\xe3o direito sobre o elemento."),Object(o.b)("p",null,"Cada formul\xe1rio de edi\xe7\xe3o de dados el\xe9tricos dos elementos possuem suas particularidades e s\xe3o descritos em documenta\xe7\xe3o espec\xedfica: ",Object(o.b)("a",Object(r.a)({parentName:"p"},{href:"bus"}),"Barramento"),", ",Object(o.b)("a",Object(r.a)({parentName:"p"},{href:"line"}),"Linha"),", ",Object(o.b)("a",Object(r.a)({parentName:"p"},{href:"transformer"}),"Transformador"),", ",Object(o.b)("a",Object(r.a)({parentName:"p"},{href:"load"}),"Carga"),", ",Object(o.b)("a",Object(r.a)({parentName:"p"},{href:"capacitor"}),"Capacitor"),", ",Object(o.b)("a",Object(r.a)({parentName:"p"},{href:"inductor"}),"Indutor"),", ",Object(o.b)("a",Object(r.a)({parentName:"p"},{href:"harmSource"}),"Fonte de Corrente Harm\xf4nica"),", ",Object(o.b)("a",Object(r.a)({parentName:"p"},{href:"syncGenerator"}),"Gerador S\xedncrono"),", ",Object(o.b)("a",Object(r.a)({parentName:"p"},{href:"syncMotor"}),"Compensador S\xedncrono"),", ",Object(o.b)("a",Object(r.a)({parentName:"p"},{href:"indMotor"}),"Motor de Indu\xe7\xe3o"),"."))}d.isMDXComponent=!0}}]);
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6H6v2h2v-2z"})))),"Informa\xe7\xe3o")),Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"As ",Object(n.b)("strong",{parentName:"p"},"barras PQ")," geralmente s\xe3o representadas pelos barramentos de carga, os quais n\xe3o h\xe1 gera\xe7\xe3o e controle de tens\xe3o."),Object(n.b)("p",{parentName:"div"},"As ",Object(n.b)("strong",{parentName:"p"},"barras PV")," se caracterizam pelo controle de tens\xe3o mediante a inje\xe7\xe3o ou absor\xe7\xe3o de pot\xeancia reativa por meio do controle da excita\xe7\xe3o de uma m\xe1quina s\xedncrona."),Object(n.b)("p",{parentName:"div"},"A ",Object(n.b)("strong",{parentName:"p"},"barra de Refer\xeancia")," (ou de folga, de oscila\xe7\xe3o) tem como fun\xe7\xe3o, assim como o pr\xf3prio nome diz, servir de refer\xeancia de tens\xe3o e \xe2ngulo do sistema. Essa barra \xe9 necessariamente geradora, uma vez que ela \xe9 respons\xe1vel pelo equil\xedbrio do balan\xe7o de pot\xeancia do sistema."))),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"O tipo de barra deve ser definido no ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"bus"}),"elemento barramento"),"."),Object(n.b)("p",{parentName:"div"},"Note que ",Object(n.b)("strong",{parentName:"p"},"o sistema deve possuir somente uma barra de refer\xeancia"),"."))),Object(n.b)("p",null,"Como mencionado anteriormente, as equa\xe7\xf5es s\xe3o n\xe3o-lineares e a solu\xe7\xe3o anal\xedtica n\xe3o \xe9 pr\xe1tica. As solu\xe7\xf5es dessas equa\xe7\xf5es seguem ",Object(n.b)("strong",{parentName:"p"},Object(n.b)("a",Object(s.a)({parentName:"strong"},{href:"https://en.wikipedia.org/wiki/Iterative_method"}),"processos iterativos")),", em que s\xe3o atribu\xeddos valores estimados (ou iniciais) para as barras com tens\xf5es desconhecidas e, baseado na pot\xeancia ativa e reativa e m\xf3dulo da tens\xe3o especificados, calcula-se por meio das equa\xe7\xf5es previamente apresentadas as novas tens\xf5es complexas em cada n\xf3 do sistema."),Object(n.b)("p",null,"Na sequ\xeancia, esse conjunto de valores para as tens\xf5es em cada barra \xe9 utilizado para novamente calcular outro grupo de tens\xf5es. Cada c\xe1lculo de um novo conjunto de tens\xf5es \xe9 chamado itera\xe7\xe3o. O processo iterativo \xe9 repetido at\xe9 que as mudan\xe7as em todas as barras sejam menores do que um valor pr\xe9-estipulado, obtendo assim a converg\xeancia."),Object(n.b)("h2",{id:"execu\xe7\xe3o-do-fluxo-de-carga-no-psp-ufu"},"Execu\xe7\xe3o do fluxo de carga no PSP-UFU"),Object(n.b)("p",null,"Ap\xf3s a constru\xe7\xe3o do diagrama unifilar no ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"editor de pot\xeancia"),", a execu\xe7\xe3o do fluxo de carga \xe9 realizada no ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"menu Simula\xe7\xe3o")," clicando no bot\xe3o ",Object(n.b)("strong",{parentName:"p"},"Fluxo de carga"),"."),Object(n.b)("div",null,Object(n.b)("center",null,Object(n.b)("img",{src:Object(b.a)("images/menuSimulationPF.svg"),alt:"Menu Simula\xe7\xe3o",title:"Menu Simula\xe7\xe3o"}))),Object(n.b)("div",{className:"admonition admonition-tip alert alert--success"},Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(n.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"})))),"Dica")),Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Caso o fluxo de carga tenha sido executado com sucesso, as setas de pot\xeancia ser\xe3o exibidas, a barra de status indicar\xe1 sucesso na opera\xe7\xe3o e os ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"text"}),"elementos de texto")," ser\xe3o atualizados."))),Object(n.b)("p",null,Object(n.b)("strong",{parentName:"p"},"Outra possibilidade")," \xe9 a execu\xe7\xe3o por meio do c\xe1lculo cont\xednuo, tamb\xe9m presente no ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"menu Simula\xe7\xe3o")," e seu acionamento \xe9 realizado co clicar no bot\xe3o ",Object(n.b)("strong",{parentName:"p"},"Habilitar solu\xe7\xe3o"),". Com essa op\xe7\xe3o, os c\xe1lculos est\xe1ticos selecionados nas ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o")," s\xe3o automaticamente realizados ao modificar quaisquer par\xe2metros da rede, como dados el\xe9tricos e acionamento dos disjuntores dos elementos (remo\xe7\xe3o ou inser\xe7\xe3o)."),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Evite construir o circuito com o c\xe1lculo cont\xednuo habilitado, uma vez que configura\xe7\xf5es tempor\xe1rias podem levar a erros de execu\xe7\xe3o da simula\xe7\xe3o."),Object(n.b)("p",{parentName:"div"},"Para desabilitar o c\xe1lculo cont\xednuo clique no bot\xe3o ",Object(n.b)("strong",{parentName:"p"},"Desabilitar solu\xe7\xe3o"),"."))),Object(n.b)("p",null,"Os resultados do fluxo de carga s\xe3o exibidos nos ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"text"}),"elementos de texto vinculado"),", ao posicionar o mouse sobre os elementos e em ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"tabularReport"}),"relat\xf3rios tabulares"),"."),Object(n.b)("h3",{id:"erros-comuns-na-execu\xe7\xe3o-do-fluxo-de-carga"},"Erros comuns na execu\xe7\xe3o do fluxo de carga"),Object(n.b)("p",null,"A seguir s\xe3o apresentados os erros mais comuns relacionados ao fluxo de carga."),Object(n.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-o-n\xfamero-m\xe1ximo-de-itera\xe7\xf5es-foi-alcan\xe7ado"},'A seguinte mensagem de erro \xe9 exibida: "O n\xfamero m\xe1ximo de itera\xe7\xf5es foi alcan\xe7ado"'),Object(n.b)("p",null,"Essa mensagem de erro \xe9 exibida quando o m\xe9todo de solu\xe7\xe3o num\xe9rica selecionado nas ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o")," atinge o n\xfamero m\xe1ximo de itera\xe7\xf5es inserido. As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(n.b)("ul",null,Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Os par\xe2metros do circuito est\xe3o incorretos"),". caso par\xe2metros muito fora dos valores padr\xe3o dos elementos el\xe9tricos sejam inseridos, o c\xe1lculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Algum elemento possui par\xe2metros discrepantes dos demais"),". Caso um dos elementos inseridos possua um valor de imped\xe2ncia muito distinto dos demais, como por exemplo uma linha com imped\xe2ncia muito elevada ou uma carga muito pequena, pode levar \xe0 diverg\xeancia do m\xe9todo num\xe9rico. Nesse caso, reconsidere a necessidade de representa\xe7\xe3o desses elementos no circuito e alterne entre os m\xe9todos num\xe9ricos de solu\xe7\xe3o dispon\xedveis."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"O n\xfamero m\xe1ximo de itera\xe7\xf5es est\xe1 muito baixo"),". Alguns circuitos exigem um n\xfamero maior de itera\xe7\xf5es, portanto altere o valor do m\xe1ximo de itera\xe7\xf5es nas ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),". Tamb\xe9m tente alternar entre os m\xe9todos num\xe9ricos de solu\xe7\xe3o dispon\xedveis."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Os par\xe2metros de simula\xe7\xe3o est\xe3o inadequados"),". Caso um par\xe2metro do m\xe9todo de solu\xe7\xe3o esteja inadequado, como fator de acelera\xe7\xe3o ou toler\xe2ncia, o c\xe1lculo pode n\xe3o alcan\xe7ar a converg\xeancia. Altere esses par\xe2metros nas ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),".")),Object(n.b)("h4",{id:"os-dados-de-sa\xedda-s\xe3o-exibidos-como-nan-ou-nan"},'Os dados de sa\xedda s\xe3o exibidos como "NaN" ou "nan"'),Object(n.b)("p",null,'Isso ocorre devido a erros de opera\xe7\xf5es matem\xe1ticas nos c\xe1lculos de fluxo de carga. "NaN" significa ',Object(n.b)("em",{parentName:"p"},"Not a Number"),"."),Object(n.b)("ul",null,Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Algum barramento est\xe1 isolado"),". Esse erro \xe9 bastante comum e pode ocorrer ao inserir um barramento sem conect\xe1-lo ao sistema ou ao remover os elementos de ramo que conectam uma barra ao sistema. A solu\xe7\xe3o \xe9 eliminar essa barra do diagrama."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Os par\xe2metros do circuito est\xe3o incorretos"),". caso par\xe2metros muito fora dos valores padr\xe3o dos elementos el\xe9tricos sejam inseridos, o c\xe1lculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Algum elemento possui par\xe2metros discrepantes dos demais"),". Caso um dos elementos inseridos possua um valor de imped\xe2ncia muito distinto dos demais, como por exemplo uma linha com imped\xe2ncia muito elevada ou uma carga muito pequena, pode levar \xe0 diverg\xeancia do m\xe9todo num\xe9rico. Nesse caso, reconsidere a necessidade de representa\xe7\xe3o desses elementos no circuito e alterne entre os m\xe9todos num\xe9ricos de solu\xe7\xe3o dispon\xedveis.")),Object(n.b)("h2",{id:"m\xe9todos-de-solu\xe7\xe3o-num\xe9rica-do-fluxo-de-carga-no-psp-ufu"},"M\xe9todos de solu\xe7\xe3o num\xe9rica do fluxo de carga no PSP-UFU"),Object(n.b)("p",null,"Os m\xe9todos implementados no programa para solu\xe7\xe3o do problema de fluxo de carga no PSP-UFU s\xe3o ",Object(n.b)("strong",{parentName:"p"},"Gauss-Seidel (GS)")," e ",Object(n.b)("strong",{parentName:"p"},"Newton-Raphson (NR)"),". 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Atualmente, restri\xe7\xf5es computacionais s\xe3o menos problem\xe1ticas e outros m\xe9todos s\xe3o normalmente escolhidos, por\xe9m o Gauss-Seidel ainda possui valor did\xe1tico e, visto que o PSP-UFU tamb\xe9m possui fins educacionais, optou-se pela implementa\xe7\xe3o desse m\xe9todo."),Object(n.b)("p",null,"Para iniciar as itera\xe7\xf5es do m\xe9todo s\xe3o necess\xe1rios valores iniciais para as tens\xf5es (",Object(n.b)("span",Object(s.a)({parentName:"p"},{className:"math math-inline"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(n.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(n.b)("semantics",{parentName:"math"},Object(n.b)("mrow",{parentName:"semantics"},Object(n.b)("msubsup",{parentName:"mrow"},Object(n.b)("mover",Object(s.a)({parentName:"msubsup"},{accent:"true"}),Object(n.b)("mi",{parentName:"mover"},"V"),Object(n.b)("mo",{parentName:"mover"},"\u02d9")),Object(n.b)("mi",{parentName:"msubsup"},"i"),Object(n.b)("mn",{parentName:"msubsup"},"0"))),Object(n.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"\\dot{V}_i^0")))),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"1.178854em",verticalAlign:"-0.258664em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord accent"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-t"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-r"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist",style:{height:"0.9201900000000001em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{style:{top:"-3em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"pstrut",style:{height:"3em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.22222em"}}),"V"))),Object(n.b)("span",Object(s.a)({parentName:"span"},{style:{top:"-3.25233em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"pstrut",style:{height:"3em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"accent-body",style:{left:"-0.13889em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"\u02d9"))))))),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"msupsub"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-t vlist-t2"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-r"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist",style:{height:"0.8141079999999999em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{style:{top:"-2.441336em",marginRight:"0.05em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"pstrut",style:{height:"2.7em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"sizing reset-size6 size3 mtight"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault mtight"}),"i"))),Object(n.b)("span",Object(s.a)({parentName:"span"},{style:{top:"-3.063em",marginRight:"0.05em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"pstrut",style:{height:"2.7em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"sizing reset-size6 size3 mtight"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mtight"}),"0")))),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-s"}),"\u200b")),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-r"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist",style:{height:"0.258664em"}}),Object(n.b)("span",{parentName:"span"})))))))))),") que devem ser calculadas. 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tens\xe3o deixa de ser controlada partir de ent\xe3o."),Object(n.b)("p",null,"A verifica\xe7\xe3o de viola\xe7\xe3o e troca de tipo de barra pode ser realizada a cada itera\xe7\xe3o ou ao final da converg\xeancia do c\xe1lculo. No PSP-UFU foi implementada a \xfaltima estrat\xe9gia, uma vez que separa os conceitos de c\xe1lculo e de verifica\xe7\xe3o de limites, tornando mais f\xe1cil o desenvolvimento de novos m\xe9todos num\xe9ricos e limites. Nessa abordagem, ao ajustar o sistema para a nova situa\xe7\xe3o n\xe3o violadora o c\xe1lculo iterativo deve ser retomado at\xe9 que obtenha novamente a converg\xeancia."),Object(n.b)("h2",{id:"refer\xeancias"},"Refer\xeancias"),Object(n.b)("ol",null,Object(n.b)("li",{parentName:"ol"},"MONTICELLI, A. J. Fluxo de Carga em Redes de Energia El\xe9trica. S\xe3o Paulo: Edgar Bl\xfccher, 1983."),Object(n.b)("li",{parentName:"ol"},"STEVENSON JR.; WILLIAN, D. Elementos de An\xe1lise de Sistemas de Pot\xeancia. 2\xaa ed. S\xe3o Paulo: McGraw-Hill, 1986."),Object(n.b)("li",{parentName:"ol"},"MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1007/978-3-642-13669-6"}),"https://doi.org/10.1007/978-3-642-13669-6")),Object(n.b)("li",{parentName:"ol"},"ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley & Sons, New York, 2001. doi: ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1002/9781118878286"}),"https://doi.org/10.1002/9781118878286")),Object(n.b)("li",{parentName:"ol"},"TINNEY, W. F.; HART, C. E. Power Flow Solution by Newton\u2019s Method. IEEE Transaction on Power Apparatus and Systems, v. PAS-86, n. 11, nov. 1967. doi: ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1109/TPAS.1967.291823"}),"https://doi.org/10.1109/TPAS.1967.291823"))))}j.isMDXComponent=!0}}]);
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Essa barra \xe9 necessariamente geradora, uma vez que ela \xe9 respons\xe1vel pelo equil\xedbrio do balan\xe7o de pot\xeancia do sistema."))),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"O tipo de barra deve ser definido no ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"bus"}),"elemento barramento"),"."),Object(n.b)("p",{parentName:"div"},"Note que ",Object(n.b)("strong",{parentName:"p"},"o sistema deve possuir somente uma barra de refer\xeancia"),"."))),Object(n.b)("p",null,"Como mencionado anteriormente, as equa\xe7\xf5es s\xe3o n\xe3o-lineares e a solu\xe7\xe3o anal\xedtica n\xe3o \xe9 pr\xe1tica. As solu\xe7\xf5es dessas equa\xe7\xf5es seguem ",Object(n.b)("strong",{parentName:"p"},Object(n.b)("a",Object(s.a)({parentName:"strong"},{href:"https://en.wikipedia.org/wiki/Iterative_method"}),"processos iterativos")),", em que s\xe3o atribu\xeddos valores estimados (ou iniciais) para as barras com tens\xf5es desconhecidas e, baseado na pot\xeancia ativa e reativa e m\xf3dulo da tens\xe3o especificados, calcula-se por meio das equa\xe7\xf5es previamente apresentadas as novas tens\xf5es complexas em cada n\xf3 do sistema."),Object(n.b)("p",null,"Na sequ\xeancia, esse conjunto de valores para as tens\xf5es em cada barra \xe9 utilizado para novamente calcular outro grupo de tens\xf5es. Cada c\xe1lculo de um novo conjunto de tens\xf5es \xe9 chamado itera\xe7\xe3o. O processo iterativo \xe9 repetido at\xe9 que as mudan\xe7as em todas as barras sejam menores do que um valor pr\xe9-estipulado, obtendo assim a converg\xeancia."),Object(n.b)("h2",{id:"execu\xe7\xe3o-do-fluxo-de-carga-no-psp-ufu"},"Execu\xe7\xe3o do fluxo de carga no PSP-UFU"),Object(n.b)("p",null,"Ap\xf3s a constru\xe7\xe3o do diagrama unifilar no ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"editor de pot\xeancia"),", a execu\xe7\xe3o do fluxo de carga \xe9 realizada no ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"menu Simula\xe7\xe3o")," clicando no bot\xe3o ",Object(n.b)("strong",{parentName:"p"},"Fluxo de carga"),"."),Object(n.b)("div",null,Object(n.b)("center",null,Object(n.b)("img",{src:Object(b.a)("images/menuSimulationPF.svg"),alt:"Menu Simula\xe7\xe3o",title:"Menu Simula\xe7\xe3o"}))),Object(n.b)("div",{className:"admonition admonition-tip alert alert--success"},Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(n.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"})))),"Dica")),Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Caso o fluxo de carga tenha sido executado com sucesso, as setas de pot\xeancia ser\xe3o exibidas, a barra de status indicar\xe1 sucesso na opera\xe7\xe3o e os ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"text"}),"elementos de texto")," ser\xe3o atualizados."))),Object(n.b)("p",null,Object(n.b)("strong",{parentName:"p"},"Outra possibilidade")," \xe9 a execu\xe7\xe3o por meio do c\xe1lculo cont\xednuo, tamb\xe9m presente no ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"menu Simula\xe7\xe3o")," e seu acionamento \xe9 realizado co clicar no bot\xe3o ",Object(n.b)("strong",{parentName:"p"},"Habilitar solu\xe7\xe3o"),". Com essa op\xe7\xe3o, os c\xe1lculos est\xe1ticos selecionados nas ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o")," s\xe3o automaticamente realizados ao modificar quaisquer par\xe2metros da rede, como dados el\xe9tricos e acionamento dos disjuntores dos elementos (remo\xe7\xe3o ou inser\xe7\xe3o)."),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Evite construir o circuito com o c\xe1lculo cont\xednuo habilitado, uma vez que configura\xe7\xf5es tempor\xe1rias podem levar a erros de execu\xe7\xe3o da simula\xe7\xe3o."),Object(n.b)("p",{parentName:"div"},"Para desabilitar o c\xe1lculo cont\xednuo clique no bot\xe3o ",Object(n.b)("strong",{parentName:"p"},"Desabilitar solu\xe7\xe3o"),"."))),Object(n.b)("p",null,"Os resultados do fluxo de carga s\xe3o exibidos nos ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"text"}),"elementos de texto vinculado"),", ao posicionar o mouse sobre os elementos e em ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"tabularReport"}),"relat\xf3rios tabulares"),"."),Object(n.b)("h3",{id:"erros-comuns-na-execu\xe7\xe3o-do-fluxo-de-carga"},"Erros comuns na execu\xe7\xe3o do fluxo de carga"),Object(n.b)("p",null,"A seguir s\xe3o apresentados os erros mais comuns relacionados ao fluxo de carga."),Object(n.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-o-n\xfamero-m\xe1ximo-de-itera\xe7\xf5es-foi-alcan\xe7ado"},'A seguinte mensagem de erro \xe9 exibida: "O n\xfamero m\xe1ximo de itera\xe7\xf5es foi alcan\xe7ado"'),Object(n.b)("p",null,"Essa mensagem de erro \xe9 exibida quando o m\xe9todo de solu\xe7\xe3o num\xe9rica selecionado nas ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o")," atinge o n\xfamero m\xe1ximo de itera\xe7\xf5es inserido. As seguintes situa\xe7\xf5es podem ocasionar esse erro:"),Object(n.b)("ul",null,Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Os par\xe2metros do circuito est\xe3o incorretos"),". caso par\xe2metros muito fora dos valores padr\xe3o dos elementos el\xe9tricos sejam inseridos, o c\xe1lculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Algum elemento possui par\xe2metros discrepantes dos demais"),". Caso um dos elementos inseridos possua um valor de imped\xe2ncia muito distinto dos demais, como por exemplo uma linha com imped\xe2ncia muito elevada ou uma carga muito pequena, pode levar \xe0 diverg\xeancia do m\xe9todo num\xe9rico. Nesse caso, reconsidere a necessidade de representa\xe7\xe3o desses elementos no circuito e alterne entre os m\xe9todos num\xe9ricos de solu\xe7\xe3o dispon\xedveis."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"O n\xfamero m\xe1ximo de itera\xe7\xf5es est\xe1 muito baixo"),". Alguns circuitos exigem um n\xfamero maior de itera\xe7\xf5es, portanto altere o valor do m\xe1ximo de itera\xe7\xf5es nas ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),". Tamb\xe9m tente alternar entre os m\xe9todos num\xe9ricos de solu\xe7\xe3o dispon\xedveis."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Os par\xe2metros de simula\xe7\xe3o est\xe3o inadequados"),". Caso um par\xe2metro do m\xe9todo de solu\xe7\xe3o esteja inadequado, como fator de acelera\xe7\xe3o ou toler\xe2ncia, o c\xe1lculo pode n\xe3o alcan\xe7ar a converg\xeancia. Altere esses par\xe2metros nas ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),".")),Object(n.b)("h4",{id:"os-dados-de-sa\xedda-s\xe3o-exibidos-como-nan-ou-nan"},'Os dados de sa\xedda s\xe3o exibidos como "NaN" ou "nan"'),Object(n.b)("p",null,'Isso ocorre devido a erros de opera\xe7\xf5es matem\xe1ticas nos c\xe1lculos de fluxo de carga. "NaN" significa ',Object(n.b)("em",{parentName:"p"},"Not a Number"),"."),Object(n.b)("ul",null,Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Algum barramento est\xe1 isolado"),". Esse erro \xe9 bastante comum e pode ocorrer ao inserir um barramento sem conect\xe1-lo ao sistema ou ao remover os elementos de ramo que conectam uma barra ao sistema. A solu\xe7\xe3o \xe9 eliminar essa barra do diagrama."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Os par\xe2metros do circuito est\xe3o incorretos"),". caso par\xe2metros muito fora dos valores padr\xe3o dos elementos el\xe9tricos sejam inseridos, o c\xe1lculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente."),Object(n.b)("li",{parentName:"ul"},Object(n.b)("strong",{parentName:"li"},"Algum elemento possui par\xe2metros discrepantes dos demais"),". Caso um dos elementos inseridos possua um valor de imped\xe2ncia muito distinto dos demais, como por exemplo uma linha com imped\xe2ncia muito elevada ou uma carga muito pequena, pode levar \xe0 diverg\xeancia do m\xe9todo num\xe9rico. Nesse caso, reconsidere a necessidade de representa\xe7\xe3o desses elementos no circuito e alterne entre os m\xe9todos num\xe9ricos de solu\xe7\xe3o dispon\xedveis.")),Object(n.b)("h2",{id:"m\xe9todos-de-solu\xe7\xe3o-num\xe9rica-do-fluxo-de-carga-no-psp-ufu"},"M\xe9todos de solu\xe7\xe3o num\xe9rica do fluxo de carga no PSP-UFU"),Object(n.b)("p",null,"Os m\xe9todos implementados no programa para solu\xe7\xe3o do problema de fluxo de carga no PSP-UFU s\xe3o ",Object(n.b)("strong",{parentName:"p"},"Gauss-Seidel (GS)")," e ",Object(n.b)("strong",{parentName:"p"},"Newton-Raphson (NR)"),". Al\xe9m desses m\xe9todos cl\xe1ssicos, um m\xe9todo h\xedbrido pode ser utilizado (definido nas ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),"), em que \xe9 utilizado inicialmente o GS e na sequ\xeancia o NR, aumentando a chance de converg\xeancia do NR."),Object(n.b)("h3",{id:"gauss-seidel"},"Gauss-Seidel"),Object(n.b)("p",null,"O m\xe9todo de Gauss-Seidel tem sido bastante utilizado nas \xfaltimas d\xe9cadas para solu\xe7\xe3o do problema de fluxo de carga, uma vez que n\xe3o h\xe1 a necessidade de fatorar a matrizes, reduzindo o esfor\xe7o computacional. Atualmente, restri\xe7\xf5es computacionais s\xe3o menos problem\xe1ticas e outros m\xe9todos s\xe3o normalmente escolhidos, por\xe9m o Gauss-Seidel ainda possui valor did\xe1tico e, visto que o PSP-UFU tamb\xe9m possui fins educacionais, optou-se pela implementa\xe7\xe3o desse m\xe9todo."),Object(n.b)("p",null,"Para iniciar as itera\xe7\xf5es do m\xe9todo s\xe3o necess\xe1rios valores iniciais para as tens\xf5es (",Object(n.b)("span",Object(s.a)({parentName:"p"},{className:"math math-inline"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(n.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(n.b)("semantics",{parentName:"math"},Object(n.b)("mrow",{parentName:"semantics"},Object(n.b)("msubsup",{parentName:"mrow"},Object(n.b)("mover",Object(s.a)({parentName:"msubsup"},{accent:"true"}),Object(n.b)("mi",{parentName:"mover"},"V"),Object(n.b)("mo",{parentName:"mover"},"\u02d9")),Object(n.b)("mi",{parentName:"msubsup"},"i"),Object(n.b)("mn",{parentName:"msubsup"},"0"))),Object(n.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"\\dot{V}_i^0")))),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"1.178854em",verticalAlign:"-0.258664em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord accent"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-t"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-r"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist",style:{height:"0.9201900000000001em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{style:{top:"-3em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"pstrut",style:{height:"3em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.22222em"}}),"V"))),Object(n.b)("span",Object(s.a)({parentName:"span"},{style:{top:"-3.25233em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"pstrut",style:{height:"3em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"accent-body",style:{left:"-0.13889em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"\u02d9"))))))),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"msupsub"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-t vlist-t2"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-r"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist",style:{height:"0.8141079999999999em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{style:{top:"-2.441336em",marginRight:"0.05em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"pstrut",style:{height:"2.7em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"sizing reset-size6 size3 mtight"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault mtight"}),"i"))),Object(n.b)("span",Object(s.a)({parentName:"span"},{style:{top:"-3.063em",marginRight:"0.05em"}}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"pstrut",style:{height:"2.7em"}})),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"sizing reset-size6 size3 mtight"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"mord mtight"}),"0")))),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-s"}),"\u200b")),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist-r"}),Object(n.b)("span",Object(s.a)({parentName:"span"},{className:"vlist",style:{height:"0.258664em"}}),Object(n.b)("span",{parentName:"span"})))))))))),") que devem ser calculadas. 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tens\xe3o deixa de ser controlada partir de ent\xe3o."),Object(n.b)("p",null,"A verifica\xe7\xe3o de viola\xe7\xe3o e troca de tipo de barra pode ser realizada a cada itera\xe7\xe3o ou ao final da converg\xeancia do c\xe1lculo. No PSP-UFU foi implementada a \xfaltima estrat\xe9gia, uma vez que separa os conceitos de c\xe1lculo e de verifica\xe7\xe3o de limites, tornando mais f\xe1cil o desenvolvimento de novos m\xe9todos num\xe9ricos e limites. Nessa abordagem, ao ajustar o sistema para a nova situa\xe7\xe3o n\xe3o violadora o c\xe1lculo iterativo deve ser retomado at\xe9 que obtenha novamente a converg\xeancia."),Object(n.b)("h2",{id:"refer\xeancias"},"Refer\xeancias"),Object(n.b)("ol",null,Object(n.b)("li",{parentName:"ol"},"MONTICELLI, A. J. Fluxo de Carga em Redes de Energia El\xe9trica. S\xe3o Paulo: Edgar Bl\xfccher, 1983."),Object(n.b)("li",{parentName:"ol"},"STEVENSON JR.; WILLIAN, D. Elementos de An\xe1lise de Sistemas de Pot\xeancia. 2\xaa ed. S\xe3o Paulo: McGraw-Hill, 1986."),Object(n.b)("li",{parentName:"ol"},"MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1007/978-3-642-13669-6"}),"https://doi.org/10.1007/978-3-642-13669-6")),Object(n.b)("li",{parentName:"ol"},"ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley & Sons, New York, 2001. doi: ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1002/9781118878286"}),"https://doi.org/10.1002/9781118878286")),Object(n.b)("li",{parentName:"ol"},"TINNEY, W. F.; HART, C. E. Power Flow Solution by Newton\u2019s Method. IEEE Transaction on Power Apparatus and Systems, v. PAS-86, n. 11, nov. 1967. doi: ",Object(n.b)("a",Object(s.a)({parentName:"li"},{href:"https://doi.org/10.1109/TPAS.1967.291823"}),"https://doi.org/10.1109/TPAS.1967.291823"))))}j.isMDXComponent=!0}}]);
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diff --git a/docs/99b37ce5.4b5eaab3.js b/docs/99b37ce5.8192d2cc.js
similarity index 94%
rename from docs/99b37ce5.4b5eaab3.js
rename to docs/99b37ce5.8192d2cc.js
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Podem ser inseridos quaisquer n\xfameros de caracteres no padr\xe3o ",Object(r.b)("a",Object(o.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Unicode"}),"Unicode"),"."),Object(r.b)("p",null,"Todos os componentes de pot\xeancia do PSP-UFU possuem esse campo."),Object(r.b)("h4",{id:"pot\xeancia-nominal"},"Pot\xeancia nominal"),Object(r.b)("p",null,"Pot\xeancia nominal do compensador, inserida em MVA, kVA ou VA."),Object(r.b)("p",null,'Esse campo \xe9 especialmente importante caso a op\xe7\xe3o "Utilizar a pot\xeancia nominal como base" esteja marcada.'),Object(r.b)("h4",{id:"pot\xeancias-ativa-e-reativa"},"Pot\xeancias ativa e reativa"),Object(r.b)("p",null,"Pot\xeancias ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do compensador."),Object(r.b)("p",null,"Caso a barra conectada seja PV o valor de pot\xeancia reativa ser\xe1 ignorado e caso seja de refer\xeancia ambos os valores inseridos ser\xe3o desprezados."),Object(r.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(r.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-heading"}),Object(r.b)("h5",{parentName:"div"},Object(r.b)("span",Object(o.a)({parentName:"h5"},{className:"admonition-icon"}),Object(r.b)("svg",Object(o.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(r.b)("path",Object(o.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(r.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-content"}),Object(r.b)("p",{parentName:"div"},"Caso mais de um compensador esteja conectado na mesma barra, os valores de pot\xeancia reativa (nas barras de refer\xeancia e PV) e ativa (nas barras de refer\xeancia) s\xe3o igualmente distribu\xeddas, respeitando os limites individuais de pot\xeancia reativa."))),Object(r.b)("h4",{id:"pot\xeancias-reativas-m\xe1xima-e-m\xednima"},"Pot\xeancias reativas m\xe1xima e m\xednima"),Object(r.b)("p",null,"Limites de pot\xeancia reativa m\xe1xima e m\xednima do compensador para controle de tens\xe3o em barras PV. 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Esses dados s\xe3o obtidos por meio do estudo de ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerFlow"}),"fluxo de carga"),"."),Object(m.b)("div",{className:"admonition admonition-info alert alert--info"},Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(m.b)("h5",{parentName:"div"},Object(m.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(m.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"14",height:"16",viewBox:"0 0 14 16"}),Object(m.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"})))),"Informa\xe7\xe3o")),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"Atualmente, o PSP-UFU fornece resultado para os seguintes tipos de falta:"),Object(m.b)("ul",{parentName:"div"},Object(m.b)("li",{parentName:"ul"},"Falta Trif\xe1sica (3F-T);"),Object(m.b)("li",{parentName:"ul"},"Falta Fase-Terra (F-T);"),Object(m.b)("li",{parentName:"ul"},"Falta Fase-Fase (F-F);"),Object(m.b)("li",{parentName:"ul"},"Falta Fase-Fase-Terra (F-F-T).")))),Object(m.b)("p",null,"Os modelos dos elementos el\xe9tricos que constituem um sistema de pot\xeancia para o estudo de curto-circuito s\xe3o semelhantes aos do fluxo de carga, apresentando algumas diverg\xeancias para as faltas desbalanceadas (F-T, F-F e F-F-T)."),Object(m.b)("p",null,"As faltas que ocorrem com maior frequ\xeancia em sistemas de pot\xeancia s\xe3o assim\xe9tricas. Como qualquer falta assim\xe9trica provoca fluxo de corrente desequilibrada \xe9 necess\xe1rio empregar o m\xe9todo das componentes sim\xe9tricas. Esse m\xe9todo permite o estudo de sistemas balanceados em conjunto cargas desbalanceadas."),Object(m.b)("h2",{id:"execu\xe7\xe3o-do-c\xe1lculo-de-curto-circuito-no-psp-ufu"},"Execu\xe7\xe3o do c\xe1lculo de curto-circuito no PSP-UFU"),Object(m.b)("p",null,"Existem duas formas de se calcular o curto-circuito no PSP-UFU:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Falta"),": Calcula a falta inserida nas ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"bus"}),"barras"),". Nesse tipo de c\xe1lculo \xe9 poss\xedvel calcular faltas ",Object(m.b)("em",{parentName:"li"},"shunt")," nos ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"bus"}),"barramentos")," balanceadas e desbalanceadas."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"N\xedvel de curto-circuito"),": Calcula o n\xedvel de curto-circuito (falta trif\xe1sica) em todos ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"bus"}),"barramentos")," do sistema.")),Object(m.b)("p",null,"Ap\xf3s a constru\xe7\xe3o do diagrama unifilar no ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"editor de pot\xeancia"),", a execu\xe7\xe3o do c\xe1lculo de curto-circuito \xe9 realizada no ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"menu Simula\xe7\xe3o")," clicando no bot\xe3o ",Object(m.b)("strong",{parentName:"p"},"Falta"),". Para calcular o n\xedvel de curto-circuito (falta trif\xe1sica) em todos ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"bus"}),"barramentos")," do sistema, basta clicar no bot\xe3o ",Object(m.b)("strong",{parentName:"p"},"N\xedvel de curto-circuito"),"."),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(b.a)("images/menuSimulationFaulta.svg"),alt:"Execu\xe7\xe3o dos c\xe1lculos de curto-circuito",title:"Execu\xe7\xe3o dos c\xe1lculos de curto-circuito"}))),Object(m.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(m.b)("h5",{parentName:"div"},Object(m.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(m.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(m.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o")),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"\xc9 poss\xedvel calcular as faltas sem a execu\xe7\xe3o do ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerFlow"}),"fluxo de carga"),", por\xe9m ",Object(m.b)("strong",{parentName:"p"},"n\xe3o \xe9 recomend\xe1vel"),", visto que os valores das correntes de falta s\xe3o significativamente alteradas."))),Object(m.b)("p",null,Object(m.b)("strong",{parentName:"p"},"Outra possibilidade")," \xe9 a execu\xe7\xe3o por meio do c\xe1lculo cont\xednuo, tamb\xe9m presente no ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"menu Simula\xe7\xe3o")," e seu acionamento \xe9 realizado co clicar no bot\xe3o ",Object(m.b)("strong",{parentName:"p"},"Habilitar solu\xe7\xe3o"),". Com essa op\xe7\xe3o, os c\xe1lculos est\xe1ticos selecionados nas ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o")," s\xe3o automaticamente realizados ao modificar quaisquer par\xe2metros da rede, como dados el\xe9tricos e acionamento dos disjuntores dos elementos (remo\xe7\xe3o ou inser\xe7\xe3o)."),Object(m.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(m.b)("h5",{parentName:"div"},Object(m.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(m.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(m.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado!")),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"Os c\xe1lculos de curtos-circuitos n\xe3o s\xe3o habilitados por padr\xe3o no c\xe1lculo cont\xednuo e devem ser inseridos nas ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),"."))),Object(m.b)("p",null,"Os resultados do c\xe1lculo de curto-circuito s\xe3o exibidos nos ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"text"}),"elementos de texto vinculado"),", ao posicionar o mouse sobre os barramentos e em ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"tabularReport"}),"relat\xf3rios tabulares"),"."),Object(m.b)("h3",{id:"erros-comuns-na-execu\xe7\xe3o-do-c\xe1lculo-de-curto-circuito"},"Erros comuns na execu\xe7\xe3o do c\xe1lculo de curto-circuito"),Object(m.b)("p",null,"A seguir s\xe3o apresentados os erros mais comuns relacionados ao calculo de curto-circuito."),Object(m.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-falha-ao-inverter-a-matriz-admit\xe2ncia-de-sequ\xeancia-zero"},'A seguinte mensagem de erro \xe9 exibida: "Falha ao inverter a matriz admit\xe2ncia de sequ\xeancia zero"'),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Impossibilidade de circula\xe7\xe3o da corrente de sequ\xeancia zero"),". Caso o gerador n\xe3o seja aterrado, n\xe3o circular\xe1 corrente de sequ\xeancia zero por ele. Nesse caso, dependendo da conex\xe3o do transformador pr\xf3ximo ao gerador sem aterramento, a matriz admit\xe2ncia de sequ\xeancia zero \xe9 singular. Para contornar esse problema escolha uma das duas solu\xe7\xf5es abaixo:",Object(m.b)("ul",{parentName:"li"},Object(m.b)("li",{parentName:"ul"},'Marque a op\xe7\xe3o "Neutro aterrado" e insira um alto valor de reat\xe2ncia de aterramento (',Object(m.b)("span",Object(s.a)({parentName:"li"},{className:"math math-inline"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mi",{parentName:"mrow"},"j"),Object(m.b)("mn",{parentName:"mrow"},"9999"),Object(m.b)("mtext",{parentName:"mrow"},"\xa0"),Object(m.b)("mi",{parentName:"mrow"},"p"),Object(m.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(m.b)("mi",{parentName:"mrow"},"u"),Object(m.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(m.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"j9999~p.u.")))),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"0.85396em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.05724em"}}),"j"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"9"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"9"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"9"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"9"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mspace nobreak"}),"\xa0"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"."),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"."))))),", por exemplo);"),Object(m.b)("li",{parentName:"ul"},"Ou, na barra do gerador, insira um reator de baixo valor de pot\xeancia reativa (",Object(m.b)("span",Object(s.a)({parentName:"li"},{className:"math math-inline"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mn",{parentName:"mrow"},"1"),Object(m.b)("mo",Object(s.a)({parentName:"mrow"},{separator:"true",lspace:"0em",rspace:"0em"}),","),Object(m.b)("mn",{parentName:"mrow"},"0"),Object(m.b)("mtext",{parentName:"mrow"},"\xa0"),Object(m.b)("mi",{parentName:"mrow"},"v"),Object(m.b)("mi",{parentName:"mrow"},"a"),Object(m.b)("mi",{parentName:"mrow"},"r")),Object(m.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"1{,}0~var")))),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"0.8388800000000001em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"1"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mpunct"}),",")),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"0"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mspace nobreak"}),"\xa0"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.03588em"}}),"v"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"a"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.02778em"}}),"r"))))),", por exemplo).")))),Object(m.b)("h2",{id:"o-c\xe1lculo-de-curto-circuito"},"O c\xe1lculo de curto-circuito"),Object(m.b)("p",null,"Como j\xe1 foi apresentado anteriormente, as faltas que ocorrem com maior frequ\xeancia em sistemas de pot\xeancia s\xe3o assim\xe9tricas. Como qualquer falta assim\xe9trica provoca fluxo de corrente desequilibrada \xe9 necess\xe1rio empregar o m\xe9todo das componentes sim\xe9tricas. Esse m\xe9todo permite o estudo de sistemas balanceados com cargas desbalanceadas."),Object(m.b)("h3",{id:"m\xe9todo-das-componentes-sim\xe9tricas"},"M\xe9todo das componentes sim\xe9tricas"),Object(m.b)("p",null,"Esse m\xe9todo proposto por C. L. Fortescue, permite definir um sistema de n fasores desbalanceados em n \u2013 1 sistemas de n fases balanceados e um sistema de fase zero. O sistema de fase zero \xe9 definido por todas as fases de mesmo m\xf3dulo e \xe2ngulo.\nPara um sistema trif\xe1sico pode-se definir tr\xeas componentes de sequ\xeancia:"),Object(m.b)("ol",null,Object(m.b)("li",{parentName:"ol"},"Componentes de sequ\xeancia positiva, constituindo em tr\xeas fasores iguais em m\xf3dulo, 120\xba defasados entre si, e tendo a mesma sequ\xeancia de fase que os fasores originais;"),Object(m.b)("li",{parentName:"ol"},"Componentes de sequ\xeancia negativa, constituindo em tr\xeas fasores iguais em m\xf3dulo, 120\xba defasados entre si, e tendo a sequ\xeancia de fase oposta \xe0 dos fasores originais."),Object(m.b)("li",{parentName:"ol"},"Componentes de sequ\xeancia zero, constituindo em tr\xeas fasores iguais em m\xf3dulo e com defasagem nula entre si.")),Object(m.b)("p",null,"Com isso pode-se decompor as tens\xf5es de fase em componentes sim\xe9tricas pelas seguintes equa\xe7\xf5es:"),Object(m.b)("div",{className:"math 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Como qualquer falta assim\xe9trica provoca fluxo de corrente desequilibrada \xe9 necess\xe1rio empregar o m\xe9todo das componentes sim\xe9tricas. Esse m\xe9todo permite o estudo de sistemas balanceados em conjunto cargas desbalanceadas."),Object(m.b)("h2",{id:"execu\xe7\xe3o-do-c\xe1lculo-de-curto-circuito-no-psp-ufu"},"Execu\xe7\xe3o do c\xe1lculo de curto-circuito no PSP-UFU"),Object(m.b)("p",null,"Existem duas formas de se calcular o curto-circuito no PSP-UFU:"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Falta"),": Calcula a falta inserida nas ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"bus"}),"barras"),". Nesse tipo de c\xe1lculo \xe9 poss\xedvel calcular faltas ",Object(m.b)("em",{parentName:"li"},"shunt")," nos ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"bus"}),"barramentos")," balanceadas e desbalanceadas."),Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"N\xedvel de curto-circuito"),": Calcula o n\xedvel de curto-circuito (falta trif\xe1sica) em todos ",Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"bus"}),"barramentos")," do sistema.")),Object(m.b)("p",null,"Ap\xf3s a constru\xe7\xe3o do diagrama unifilar no ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"editor de pot\xeancia"),", a execu\xe7\xe3o do c\xe1lculo de curto-circuito \xe9 realizada no ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"menu Simula\xe7\xe3o")," clicando no bot\xe3o ",Object(m.b)("strong",{parentName:"p"},"Falta"),". Para calcular o n\xedvel de curto-circuito (falta trif\xe1sica) em todos ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"bus"}),"barramentos")," do sistema, basta clicar no bot\xe3o ",Object(m.b)("strong",{parentName:"p"},"N\xedvel de curto-circuito"),"."),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(b.a)("images/menuSimulationFaulta.svg"),alt:"Execu\xe7\xe3o dos c\xe1lculos de curto-circuito",title:"Execu\xe7\xe3o dos c\xe1lculos de curto-circuito"}))),Object(m.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(m.b)("h5",{parentName:"div"},Object(m.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(m.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(m.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o")),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"\xc9 poss\xedvel calcular as faltas sem a execu\xe7\xe3o do ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerFlow"}),"fluxo de carga"),", por\xe9m ",Object(m.b)("strong",{parentName:"p"},"n\xe3o \xe9 recomend\xe1vel"),", visto que os valores das correntes de falta s\xe3o significativamente alteradas."))),Object(m.b)("p",null,Object(m.b)("strong",{parentName:"p"},"Outra possibilidade")," \xe9 a execu\xe7\xe3o por meio do c\xe1lculo cont\xednuo, tamb\xe9m presente no ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"menu Simula\xe7\xe3o")," e seu acionamento \xe9 realizado co clicar no bot\xe3o ",Object(m.b)("strong",{parentName:"p"},"Habilitar solu\xe7\xe3o"),". Com essa op\xe7\xe3o, os c\xe1lculos est\xe1ticos selecionados nas ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o")," s\xe3o automaticamente realizados ao modificar quaisquer par\xe2metros da rede, como dados el\xe9tricos e acionamento dos disjuntores dos elementos (remo\xe7\xe3o ou inser\xe7\xe3o)."),Object(m.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(m.b)("h5",{parentName:"div"},Object(m.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(m.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(m.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado!")),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"Os c\xe1lculos de curtos-circuitos n\xe3o s\xe3o habilitados por padr\xe3o no c\xe1lculo cont\xednuo e devem ser inseridos nas ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"simulationConfig"}),"configura\xe7\xf5es de simula\xe7\xe3o"),"."))),Object(m.b)("p",null,"Os resultados do c\xe1lculo de curto-circuito s\xe3o exibidos nos ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"text"}),"elementos de texto vinculado"),", ao posicionar o mouse sobre os barramentos e em ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"tabularReport"}),"relat\xf3rios tabulares"),"."),Object(m.b)("h3",{id:"erros-comuns-na-execu\xe7\xe3o-do-c\xe1lculo-de-curto-circuito"},"Erros comuns na execu\xe7\xe3o do c\xe1lculo de curto-circuito"),Object(m.b)("p",null,"A seguir s\xe3o apresentados os erros mais comuns relacionados ao calculo de curto-circuito."),Object(m.b)("h4",{id:"a-seguinte-mensagem-de-erro-\xe9-exibida-falha-ao-inverter-a-matriz-admit\xe2ncia-de-sequ\xeancia-zero"},'A seguinte mensagem de erro \xe9 exibida: "Falha ao inverter a matriz admit\xe2ncia de sequ\xeancia zero"'),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("strong",{parentName:"li"},"Impossibilidade de circula\xe7\xe3o da corrente de sequ\xeancia zero"),". Caso o gerador n\xe3o seja aterrado, n\xe3o circular\xe1 corrente de sequ\xeancia zero por ele. Nesse caso, dependendo da conex\xe3o do transformador pr\xf3ximo ao gerador sem aterramento, a matriz admit\xe2ncia de sequ\xeancia zero \xe9 singular. Para contornar esse problema escolha uma das duas solu\xe7\xf5es abaixo:",Object(m.b)("ul",{parentName:"li"},Object(m.b)("li",{parentName:"ul"},'Marque a op\xe7\xe3o "Neutro aterrado" e insira um alto valor de reat\xe2ncia de aterramento (',Object(m.b)("span",Object(s.a)({parentName:"li"},{className:"math math-inline"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mi",{parentName:"mrow"},"j"),Object(m.b)("mn",{parentName:"mrow"},"9999"),Object(m.b)("mtext",{parentName:"mrow"},"\xa0"),Object(m.b)("mi",{parentName:"mrow"},"p"),Object(m.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),"."),Object(m.b)("mi",{parentName:"mrow"},"u"),Object(m.b)("mi",Object(s.a)({parentName:"mrow"},{mathvariant:"normal"}),".")),Object(m.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"j9999~p.u.")))),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"0.85396em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.05724em"}}),"j"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"9"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"9"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"9"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"9"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mspace nobreak"}),"\xa0"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"p"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"."),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"u"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"."))))),", por exemplo);"),Object(m.b)("li",{parentName:"ul"},"Ou, na barra do gerador, insira um reator de baixo valor de pot\xeancia reativa (",Object(m.b)("span",Object(s.a)({parentName:"li"},{className:"math math-inline"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-mathml"}),Object(m.b)("math",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/1998/Math/MathML"}),Object(m.b)("semantics",{parentName:"math"},Object(m.b)("mrow",{parentName:"semantics"},Object(m.b)("mn",{parentName:"mrow"},"1"),Object(m.b)("mo",Object(s.a)({parentName:"mrow"},{separator:"true",lspace:"0em",rspace:"0em"}),","),Object(m.b)("mn",{parentName:"mrow"},"0"),Object(m.b)("mtext",{parentName:"mrow"},"\xa0"),Object(m.b)("mi",{parentName:"mrow"},"v"),Object(m.b)("mi",{parentName:"mrow"},"a"),Object(m.b)("mi",{parentName:"mrow"},"r")),Object(m.b)("annotation",Object(s.a)({parentName:"semantics"},{encoding:"application/x-tex"}),"1{,}0~var")))),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"katex-html","aria-hidden":"true"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"base"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"strut",style:{height:"0.8388800000000001em",verticalAlign:"-0.19444em"}})),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"1"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mpunct"}),",")),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord"}),"0"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mspace nobreak"}),"\xa0"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.03588em"}}),"v"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault"}),"a"),Object(m.b)("span",Object(s.a)({parentName:"span"},{className:"mord mathdefault",style:{marginRight:"0.02778em"}}),"r"))))),", por exemplo).")))),Object(m.b)("h2",{id:"o-c\xe1lculo-de-curto-circuito"},"O c\xe1lculo de curto-circuito"),Object(m.b)("p",null,"Como j\xe1 foi apresentado anteriormente, as faltas que ocorrem com maior frequ\xeancia em sistemas de pot\xeancia s\xe3o assim\xe9tricas. Como qualquer falta assim\xe9trica provoca fluxo de corrente desequilibrada \xe9 necess\xe1rio empregar o m\xe9todo das componentes sim\xe9tricas. Esse m\xe9todo permite o estudo de sistemas balanceados com cargas desbalanceadas."),Object(m.b)("h3",{id:"m\xe9todo-das-componentes-sim\xe9tricas"},"M\xe9todo das componentes sim\xe9tricas"),Object(m.b)("p",null,"Esse m\xe9todo proposto por C. L. Fortescue, permite definir um sistema de n fasores desbalanceados em n \u2013 1 sistemas de n fases balanceados e um sistema de fase zero. O sistema de fase zero \xe9 definido por todas as fases de mesmo m\xf3dulo e \xe2ngulo.\nPara um sistema trif\xe1sico pode-se definir tr\xeas componentes de sequ\xeancia:"),Object(m.b)("ol",null,Object(m.b)("li",{parentName:"ol"},"Componentes de sequ\xeancia positiva, constituindo em tr\xeas fasores iguais em m\xf3dulo, 120\xba defasados entre si, e tendo a mesma sequ\xeancia de fase que os fasores originais;"),Object(m.b)("li",{parentName:"ol"},"Componentes de sequ\xeancia negativa, constituindo em tr\xeas fasores iguais em m\xf3dulo, 120\xba defasados entre si, e tendo a sequ\xeancia de fase oposta \xe0 dos fasores originais."),Object(m.b)("li",{parentName:"ol"},"Componentes de sequ\xeancia zero, constituindo em tr\xeas fasores iguais em m\xf3dulo e com defasagem nula entre si.")),Object(m.b)("p",null,"Com isso pode-se decompor as tens\xf5es de fase em componentes sim\xe9tricas pelas seguintes equa\xe7\xf5es:"),Object(m.b)("div",{className:"math 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Essas configura\xe7\xf5es s\xe3o aplicadas para todos os projetos e permanecem gravadas no disco."),Object(n.b)("div",null,Object(n.b)("center",null,Object(n.b)("img",{src:Object(i.a)("images/generalSettings.png"),alt:"Configura\xe7\xf5es gerais",title:"Configura\xe7\xf5es gerais"}))),Object(n.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(o.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(o.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(n.b)("path",Object(o.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado")),Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Algumas configura\xe7\xf5es de seguran\xe7a do seu computador (principalmente em sistemas Windows) podem gerar uma mensagem de erro ao confirmar as altera\xe7\xf5es das configura\xe7\xf5es gerais."),Object(n.b)("p",{parentName:"div"},"Para resolver esse problema basta ",Object(n.b)("strong",{parentName:"p"},"executar o PSP-UFU como administrador")," (clicar com bot\xe3o direito no atalho do programa e posteriormente em executar como administrador). Altere novamente as configura\xe7\xf5es e reinicie o programa."))),Object(n.b)("h3",{id:"idioma"},"Idioma"),Object(n.b)("p",null,"Atualmente os seguintes idiomas est\xe3o dispon\xedveis no PSP-UFU:"),Object(n.b)("ul",null,Object(n.b)("li",{parentName:"ul"},"Ingl\xeas"),Object(n.b)("li",{parentName:"ul"},"Portugu\xeas")),Object(n.b)("div",{className:"admonition admonition-info alert alert--info"},Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(o.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(o.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"14",height:"16",viewBox:"0 0 14 16"}),Object(n.b)("path",Object(o.a)({parentName:"svg"},{fillRule:"evenodd",d:"M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"})))),"Informa\xe7\xe3o")),Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"O programa deve ser reiniciado para surtir efeito da altera\xe7\xe3o do idioma."))),Object(n.b)("h3",{id:"renderiza\xe7\xe3o"},"Renderiza\xe7\xe3o"),Object(n.b)("p",null,"Define como os elementos gr\xe1ficos do ",Object(n.b)("a",Object(o.a)({parentName:"p"},{href:"powerEditor"}),"editor de pot\xeancia")," e do ",Object(n.b)("a",Object(o.a)({parentName:"p"},{href:"controlEditor"}),"editor de controle")," s\xe3o desenhados na tela. Atualmente duas op\xe7\xf5es est\xe3o dispon\xedveis:"),Object(n.b)("ul",null,Object(n.b)("li",{parentName:"ul"},Object(n.b)("a",Object(o.a)({parentName:"li"},{href:"https://www.opengl.org/about/"}),"OpenGL")),Object(n.b)("li",{parentName:"ul"},Object(n.b)("a",Object(o.a)({parentName:"li"},{href:"https://docs.wxwidgets.org/3.0/classwx_graphics_context.html"}),"Device Context"))),Object(n.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(o.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(o.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(n.b)("path",Object(o.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado!")),Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},'o OpenGL pode n\xe3o ser suportado pelo seu computador. Nesse caso, ao criar um novo projeto a tela de trabalho n\xe3o \xe9 exibida ou \xe9 exibida uma tela preta. A solu\xe7\xe3o \xe9 alterar o renderizador para "Device Context". '),Object(n.b)("p",{parentName:"div"},"Caso apare\xe7a uma mensagem de erro, execute o programa como administrador e repita o processo."))),Object(n.b)("div",{className:"admonition admonition-info alert alert--info"},Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(o.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(o.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"14",height:"16",viewBox:"0 0 14 16"}),Object(n.b)("path",Object(o.a)({parentName:"svg"},{fillRule:"evenodd",d:"M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"})))),"Informa\xe7\xe3o")),Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"O programa deve ser reiniciado para surtir efeito de altera\xe7\xe3o do renderizador."))),Object(n.b)("h2",{id:"arquivos-de-projeto-do-psp-ufu"},"Arquivos de projeto do PSP-UFU"),Object(n.b)("p",null,"As op\xe7\xf5es de cria\xe7\xe3o, grava\xe7\xe3o e abertura de projetos no disco, assim como importa\xe7\xe3o de arquivos de outros programas est\xe3o presentes no submenu Ribbon ",Object(n.b)("strong",{parentName:"p"},"Arquivo"),"."),Object(n.b)("h3",{id:"novo-projeto"},"Novo projeto"),Object(n.b)("p",null,"A cria\xe7\xe3o de um novo projeto \xe9 realizada clicando no bot\xe3o ",Object(n.b)("strong",{parentName:"p"},"Novo projeto")," no ",Object(n.b)("a",Object(o.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"submenu ",Object(n.b)("strong",{parentName:"a"},"Arquivo")),". Essa a\xe7\xe3o cria um sistema em branco na \xe1rea de trabalho, local onde \xe9 poss\xedvel inserir os elementos el\xe9tricos por meio do ",Object(n.b)("a",Object(o.a)({parentName:"p"},{href:"mainScreen#menu-ribbon"}),"submenu ",Object(n.b)("strong",{parentName:"a"},"Ferramentas"))," ou pelas ",Object(n.b)("a",Object(o.a)({parentName:"p"},{href:"powerEditor#teclas-de-atalho"}),"teclas de atalho"),"."),Object(n.b)("p",null,"Esse sistema em branco pode ser ciado utilizando o ",Object(n.b)("a",Object(o.a)({parentName:"p"},{href:"powerEditor"}),"Editor de Pot\xeancia"),"."),Object(n.b)("h3",{id:"salvar-e-salvar-como"},"Salvar e Salvar como..."),Object(n.b)("p",null,'A op\xe7\xe3o "Salvar" sobrep\xf5e as altera\xe7\xf5es realizadas no projeto aberto e grava no disco. A op\xe7\xe3o "Salvar como..." cria um novo arquivo e grava o projeto no disco com o aux\xedlio de uma janela de sele\xe7\xe3o de pasta (e defini\xe7\xe3o do nome do arquivo).'),Object(n.b)("div",{className:"admonition admonition-info alert alert--info"},Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(o.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(o.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"14",height:"16",viewBox:"0 0 14 16"}),Object(n.b)("path",Object(o.a)({parentName:"svg"},{fillRule:"evenodd",d:"M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"})))),"Informa\xe7\xe3o")),Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},'Para projetos que est\xe3o sendo gravados pela primeira vez a op\xe7\xe3o "Salvar" se comporta de forma id\xeantica \xe0 op\xe7\xe3o "Salvar como...".'))),Object(n.b)("div",{className:"admonition admonition-tip alert alert--success"},Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(o.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(o.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(n.b)("path",Object(o.a)({parentName:"svg"},{fillRule:"evenodd",d:"M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"})))),"Dica")),Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"O PSP-UFU grava os arquivos com a extens\xe3o ",Object(n.b)("em",{parentName:"p"},".psp"),". Esses arquivos nada mais s\xe3o que arquivos de texto utilizando a ",Object(n.b)("a",Object(o.a)({parentName:"p"},{href:"https://en.wikipedia.org/wiki/Markup_language"}),"linguagem de marca\xe7\xe3o")," XML (",Object(n.b)("a",Object(o.a)({parentName:"p"},{href:"https://en.wikipedia.org/wiki/XML"}),"eXtensible Markup Language"),"), que define uma s\xe9rie de regras de formata\xe7\xe3o dos dados de forma que eles s\xe3o tanto leg\xedveis por humanos quanto por m\xe1quinas."),Object(n.b)("p",{parentName:"div"},"Portanto, os dados el\xe9tricos contidos neles podem ser facilmente identificados e alterados, caso necess\xe1rio."))),Object(n.b)("h3",{id:"abrir-projeto"},"Abrir projeto"),Object(n.b)("p",null,"Essa op\xe7\xe3o abre os projetos gravados no disco por meio com o aux\xedlio de uma janela de sele\xe7\xe3o de arquivos. "),Object(n.b)("h3",{id:"importar-projeto"},"Importar projeto"),Object(n.b)("p",null,"O PSP-UFU permite a importa\xe7\xe3o de arquivos dos seguintes programas:"),Object(n.b)("ul",null,Object(n.b)("li",{parentName:"ul"},Object(n.b)("a",Object(o.a)({parentName:"li"},{href:"http://www.cepel.br/pt_br/produtos/programas-computacionais-por-categoria/menu/anarede-analise-de-redes-eletricas.htm"}),"ANAREDE")),Object(n.b)("li",{parentName:"ul"},Object(n.b)("a",Object(o.a)({parentName:"li"},{href:"https://matpower.org/"}),"Matpower"))),Object(n.b)("p",null,"Para importa\xe7\xe3o dos arquivos do ",Object(n.b)("strong",{parentName:"p"},"ANAREDE")," s\xe3o utilizados tanto o arquivo de dados el\xe9tricos (",Object(n.b)("em",{parentName:"p"},".pwf"),") quanto de dados gr\xe1ficos dos elementos (",Object(n.b)("em",{parentName:"p"},".lst"),")."),Object(n.b)("p",null,"Uma vez que o arquivo do ",Object(n.b)("strong",{parentName:"p"},"Matpower")," (",Object(n.b)("em",{parentName:"p"},".m"),") n\xe3o possui dados gr\xe1ficos dos elementos el\xe9tricos, o diagrama unifilar \xe9 automaticamente gerado pelo PSP-UFU ao import\xe1-lo."),Object(n.b)("h4",{id:"gera\xe7\xe3o-autom\xe1tica-do-layout-de-diagramas-unifilares"},"Gera\xe7\xe3o autom\xe1tica do ",Object(n.b)("em",{parentName:"h4"},"layout")," de diagramas unifilares"),Object(n.b)("p",null,"Para criar o ",Object(n.b)("em",{parentName:"p"},"layout")," autom\xe1tico, utilizou-se a teoria dos grafos baseada no posicionamento direcionado \xe0 for\xe7a e aplica\xe7\xe3o de grafos com arestas ponderadas. De acordo com a teoria dos grafos, o sistema \xe9 modelado como v\xe9rtices e arestas. Nesse contexto, os barramentos s\xe3o os v\xe9rtices e os ramos do sistema (linhas e transformadores) s\xe3o as arestas. As localiza\xe7\xf5es de elementos de deriva\xe7\xe3o, assim como os n\xf3s dos elementos, s\xe3o automaticamente controladas pelo PSP-UFU."),Object(n.b)("p",null,"A ferramenta de ",Object(n.b)("em",{parentName:"p"},"layout")," autom\xe1tico \xe9 composta por um processo iterativo e os resultados s\xe3o mais refinados com um n\xfamero maior de itera\xe7\xf5es. Os melhores resultados s\xe3o obtidos utilizando o n\xfamero de itera\xe7\xf5es igual ou superior a cinco vezes o n\xfamero de barramentos do sistema."),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(o.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(o.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(o.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"O ",Object(n.b)("em",{parentName:"p"},"layout")," autom\xe1tico ainda est\xe1 em desenvolvimento e algumas melhorias podem ser feitas para evitar cruzamentos e sobreposi\xe7\xf5es, por\xe9m, em seu estado atual, \xe9 totalmente funcional e satisfat\xf3rio."))),Object(n.b)("div",{className:"admonition admonition-tip alert alert--success"},Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(o.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(o.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(n.b)("path",Object(o.a)({parentName:"svg"},{fillRule:"evenodd",d:"M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"})))),"Dica")),Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Uma vez que o Matpower pode converter os formatos CDF (",Object(n.b)("em",{parentName:"p"},"Common Data Format"),") e PSS/E RAW para arquivos ",Object(n.b)("em",{parentName:"p"},".m"),", estes podem ser importados de forma indireta para o PSP-UFU."))))}m.isMDXComponent=!0}}]);
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Caso tenha alguma d\xfavida siga as instru\xe7\xf5es apresentadas nesse componente."))),Object(n.b)("h2",{id:"configura\xe7\xf5es-gerais"},"Configura\xe7\xf5es gerais"),Object(n.b)("p",null,"As configura\xe7\xf5es gerais do programa s\xe3o acessadas no submenu Ribbon ",Object(n.b)("strong",{parentName:"p"},"Arquivo"),". Essas configura\xe7\xf5es s\xe3o aplicadas para todos os projetos e permanecem gravadas no disco."),Object(n.b)("div",null,Object(n.b)("center",null,Object(n.b)("img",{src:Object(i.a)("images/generalSettings.png"),alt:"Configura\xe7\xf5es gerais",title:"Configura\xe7\xf5es gerais"}))),Object(n.b)("div",{className:"admonition admonition-warning alert alert--danger"},Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(o.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(o.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"12",height:"16",viewBox:"0 0 12 16"}),Object(n.b)("path",Object(o.a)({parentName:"svg"},{fillRule:"evenodd",d:"M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"})))),"Cuidado")),Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Algumas configura\xe7\xf5es de seguran\xe7a do seu computador (principalmente em sistemas Windows) podem gerar uma mensagem de erro ao confirmar as altera\xe7\xf5es das configura\xe7\xf5es gerais."),Object(n.b)("p",{parentName:"div"},"Para resolver esse problema basta ",Object(n.b)("strong",{parentName:"p"},"executar o PSP-UFU como administrador")," (clicar com bot\xe3o direito no atalho do programa e posteriormente em executar como administrador). Altere novamente as configura\xe7\xf5es e reinicie o programa."))),Object(n.b)("h3",{id:"idioma"},"Idioma"),Object(n.b)("p",null,"Atualmente os seguintes idiomas est\xe3o dispon\xedveis no PSP-UFU:"),Object(n.b)("ul",null,Object(n.b)("li",{parentName:"ul"},"Ingl\xeas"),Object(n.b)("li",{parentName:"ul"},"Portugu\xeas")),Object(n.b)("div",{className:"admonition admonition-info alert alert--info"},Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(o.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(o.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"14",height:"16",viewBox:"0 0 14 16"}),Object(n.b)("path",Object(o.a)({parentName:"svg"},{fillRule:"evenodd",d:"M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"})))),"Informa\xe7\xe3o")),Object(n.b)("div",Object(o.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"O programa deve ser reiniciado para surtir efeito da altera\xe7\xe3o do idioma."))),Object(n.b)("h3",{id:"renderiza\xe7\xe3o"},"Renderiza\xe7\xe3o"),Object(n.b)("p",null,"Define como os elementos gr\xe1ficos do ",Object(n.b)("a",Object(o.a)({parentName:"p"},{href:"powerEditor"}),"editor de pot\xeancia")," e do ",Object(n.b)("a",Object(o.a)({parentName:"p"},{href:"controlEditor"}),"editor de controle")," s\xe3o desenhados na tela. 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col--offset-2"><article><header><h1 class="margin-bottom--sm blogPostTitle_1mse">2019w42a-beta</h1><div class="margin-vert--md"><time datetime="2019-10-13T00:00:00.000Z" class="blogPostDate_3bQP">October 13, 2019  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Harmonic study implemented;</li><li>Autolayout from importation implemented;</li><li>Importation of Matpower files;</li><li>Several minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a 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class="DocSearch-Button-Key">⌘</span><span class="DocSearch-Button-Key">K</span></button></div></div><div role="presentation" class="navbar-sidebar__backdrop"></div><div class="navbar-sidebar"><div class="navbar-sidebar__brand"><a class="navbar__brand" href="/PSP/"><img class="navbar__logo" src="/PSP/img/logo.svg" alt="PSP-UFU logo"><strong class="navbar__title">PSP-UFU</strong></a></div><div class="navbar-sidebar__items"><div class="menu"><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" href="/PSP/docs/">User Guide</a></li><li class="menu__list-item"><a aria-current="page" class="menu__link navbar__link--active" href="/PSP/blog">Changelog</a></li><li class="menu__list-item"><a href="https://github.com/Thales1330/PSP" target="_blank" rel="noopener noreferrer" class="menu__link">PSP-UFU Source Code</a></li></ul></div></div></div></nav><div class="main-wrapper"><div class="container margin-vert--lg"><div class="row"><div class="col col--8 col--offset-2"><article><header><h1 class="margin-bottom--sm blogPostTitle_1mse">22019w44a-beta</h1><div class="margin-vert--md"><time datetime="2019-11-01T00:00:00.000Z" class="blogPostDate_3bQP">November 1, 2019  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Minor changes to 32bit MSW version for compatibility;</li><li>Travis CI (Continuous Integration) implemented (Linux).</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><div><a href="https://github.com/Thales1330/PSP/tree/master/docs/blog/2019-11-01-2019w44a-beta.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div><div class="margin-vert--xl"><nav class="pagination-nav" aria-label="Blog post page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/blog/2020w24a-beta"><div class="pagination-nav__sublabel">Newer Post</div><div class="pagination-nav__label">« 2020w24a-beta</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/blog/2019w42a-beta"><div 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class="DocSearch-Button-Key">⌘</span><span class="DocSearch-Button-Key">K</span></button></div></div><div role="presentation" class="navbar-sidebar__backdrop"></div><div class="navbar-sidebar"><div class="navbar-sidebar__brand"><a class="navbar__brand" href="/PSP/"><img class="navbar__logo" src="/PSP/img/logo.svg" alt="PSP-UFU logo"><strong class="navbar__title">PSP-UFU</strong></a></div><div class="navbar-sidebar__items"><div class="menu"><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" href="/PSP/docs/">User Guide</a></li><li class="menu__list-item"><a aria-current="page" class="menu__link navbar__link--active" href="/PSP/blog">Changelog</a></li><li class="menu__list-item"><a href="https://github.com/Thales1330/PSP" target="_blank" rel="noopener noreferrer" class="menu__link">PSP-UFU Source Code</a></li></ul></div></div></div></nav><div class="main-wrapper"><div class="container margin-vert--lg"><div class="row"><div class="col col--8 col--offset-2"><article><header><h1 class="margin-bottom--sm blogPostTitle_1mse">22019w44a-beta</h1><div class="margin-vert--md"><time datetime="2019-11-01T00:00:00.000Z" class="blogPostDate_3bQP">November 1, 2019  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>✔️ Minor changes to 32bit MSW version for compatibility;</li><li>✔️ Travis CI (Continuous Integration) implemented (Linux).</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><div><a href="https://github.com/Thales1330/PSP/tree/master/docs/blog/2019-11-01-2019w44a-beta.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div><div class="margin-vert--xl"><nav class="pagination-nav" aria-label="Blog post page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/blog/2020w24a-beta"><div class="pagination-nav__sublabel">Newer Post</div><div class="pagination-nav__label">« 2020w24a-beta</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/blog/2019w42a-beta"><div 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index d42f57c7..e870976f 100644
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some machines can&#x27;t use it properly);</li><li>Added Visual Studio solution to the GitHub project;</li><li>Several major and minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><div><a href="https://github.com/Thales1330/PSP/tree/master/docs/blog/2020-06-13-2020w24a-beta.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div><div class="margin-vert--xl"><nav class="pagination-nav" aria-label="Blog post page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/blog/2020w28a-beta"><div class="pagination-nav__sublabel">Newer Post</div><div class="pagination-nav__label">« 2020w28a-beta</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/blog/2019w44a-beta"><div class="pagination-nav__sublabel">Older Post</div><div class="pagination-nav__label">22019w44a-beta »</div></a></div></nav></div></div></div></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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some machines can&#x27;t use it properly);</li><li>✔️ Added Visual Studio solution to the GitHub project;</li><li>🐛 Several major and minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><div><a href="https://github.com/Thales1330/PSP/tree/master/docs/blog/2020-06-13-2020w24a-beta.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div><div class="margin-vert--xl"><nav class="pagination-nav" aria-label="Blog post page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/blog/2020w28a-beta"><div class="pagination-nav__sublabel">Newer Post</div><div class="pagination-nav__label">« 2020w28a-beta</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/blog/2019w44a-beta"><div class="pagination-nav__sublabel">Older Post</div><div class="pagination-nav__label">22019w44a-beta »</div></a></div></nav></div></div></div></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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col--offset-2"><article><header><h1 class="margin-bottom--sm blogPostTitle_1mse">2020w28a-beta</h1><div class="margin-vert--md"><time datetime="2020-07-09T00:00:00.000Z" class="blogPostDate_3bQP">July 9, 2020  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Voltage heatmap implemented (OpenGL enabled);</li><li>Several major and minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><div><a href="https://github.com/Thales1330/PSP/tree/master/docs/blog/2020-07-09-2020w28a-beta.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div><div class="margin-vert--xl"><nav class="pagination-nav" aria-label="Blog post page navigation"><div class="pagination-nav__item"></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/blog/2020w24a-beta"><div class="pagination-nav__sublabel">Older Post</div><div class="pagination-nav__label">2020w24a-beta »</div></a></div></nav></div></div></div></div></div><footer class="footer 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href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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col--offset-2"><article><header><h1 class="margin-bottom--sm blogPostTitle_1mse">2020w28a-beta</h1><div class="margin-vert--md"><time datetime="2020-07-09T00:00:00.000Z" class="blogPostDate_3bQP">July 9, 2020  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>🔥 Voltage heatmap implemented (OpenGL enabled);</li><li>🐛 Several major and minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><div><a href="https://github.com/Thales1330/PSP/tree/master/docs/blog/2020-07-09-2020w28a-beta.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div><div class="margin-vert--xl"><nav class="pagination-nav" aria-label="Blog post page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/blog/2020w31a-beta"><div class="pagination-nav__sublabel">Newer Post</div><div class="pagination-nav__label">« 2020w31a-beta</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/blog/2020w24a-beta"><div 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diff --git a/docs/blog/2020w31a-beta/index.html b/docs/blog/2020w31a-beta/index.html
new file mode 100644
index 00000000..5c3cf638
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Code</a><div class="react-toggle react-toggle--disabled displayOnlyInLargeViewport_2aTZ"><div class="react-toggle-track"><div class="react-toggle-track-check"><span class="toggle_BsTx"></span></div><div class="react-toggle-track-x"><span class="toggle_BsTx"></span></div></div><div class="react-toggle-thumb"></div><input type="checkbox" disabled="" aria-label="Dark mode toggle" class="react-toggle-screenreader-only"></div><button type="button" class="DocSearch DocSearch-Button" aria-label="Search"><svg width="20" height="20" class="DocSearch-Search-Icon" viewBox="0 0 20 20"><path d="M14.386 14.386l4.0877 4.0877-4.0877-4.0877c-2.9418 2.9419-7.7115 2.9419-10.6533 0-2.9419-2.9418-2.9419-7.7115 0-10.6533 2.9418-2.9419 7.7115-2.9419 10.6533 0 2.9419 2.9418 2.9419 7.7115 0 10.6533z" stroke="currentColor" fill="none" fill-rule="evenodd" stroke-linecap="round" stroke-linejoin="round"></path></svg><span class="DocSearch-Button-Placeholder">Search</span><span class="DocSearch-Button-Key">⌘</span><span class="DocSearch-Button-Key">K</span></button></div></div><div role="presentation" class="navbar-sidebar__backdrop"></div><div class="navbar-sidebar"><div class="navbar-sidebar__brand"><a class="navbar__brand" href="/PSP/"><img class="navbar__logo" src="/PSP/img/logo.svg" alt="PSP-UFU logo"><strong class="navbar__title">PSP-UFU</strong></a></div><div class="navbar-sidebar__items"><div class="menu"><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" href="/PSP/docs/">User Guide</a></li><li class="menu__list-item"><a aria-current="page" class="menu__link navbar__link--active" href="/PSP/blog">Changelog</a></li><li class="menu__list-item"><a href="https://github.com/Thales1330/PSP" target="_blank" rel="noopener noreferrer" class="menu__link">PSP-UFU Source Code</a></li></ul></div></div></div></nav><div class="main-wrapper"><div class="container margin-vert--lg"><div class="row"><div class="col col--8 col--offset-2"><article><header><h1 class="margin-bottom--sm blogPostTitle_1mse">2020w31a-beta</h1><div class="margin-vert--md"><time datetime="2020-08-01T00:00:00.000Z" class="blogPostDate_3bQP">August 1, 2020  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>🔥 PSP-UFU online user guide finally written (only in Brazilian Portuguese, if you want to help me translate this guide, contact-me on <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> or <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>);</li><li>✔️ New fancy <a href="https://thales1330.github.io/PSP/" target="_blank" rel="noopener noreferrer">PSP-UFU website</a> and <a href="https://thales1330.github.io/PSP/blog" target="_blank" rel="noopener noreferrer">changelog</a> using <a href="https://v2.docusaurus.io/" target="_blank" rel="noopener noreferrer">docusaurus</a>;</li><li>✔️ Text element performance improved for OpenGL render;</li><li>🐛 Several major and minor bug fixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><div><a href="https://github.com/Thales1330/PSP/tree/master/docs/blog/2020-08-01-2020w31a-beta.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div><div class="margin-vert--xl"><nav class="pagination-nav" aria-label="Blog post page navigation"><div class="pagination-nav__item"></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/blog/2020w28a-beta"><div class="pagination-nav__sublabel">Older Post</div><div class="pagination-nav__label">2020w28a-beta »</div></a></div></nav></div></div></div></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a 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some machines can&#x27;t use it properly);</li><li>Added Visual Studio solution to the GitHub project;</li><li>Several major and minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_1mse"><a href="/PSP/blog/2019w44a-beta">22019w44a-beta</a></h2><div class="margin-vert--md"><time datetime="2019-11-01T00:00:00.000Z" class="blogPostDate_3bQP">November 1, 2019  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Minor changes to 32bit MSW version for compatibility;</li><li>Travis CI (Continuous Integration) implemented (Linux).</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_1mse"><a href="/PSP/blog/2019w42a-beta">2019w42a-beta</a></h2><div class="margin-vert--md"><time datetime="2019-10-13T00:00:00.000Z" class="blogPostDate_3bQP">October 13, 2019  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Harmonic study implemented;</li><li>Autolayout from importation implemented;</li><li>Importation of Matpower files;</li><li>Several minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"></div><div class="pagination-nav__item pagination-nav__item--next"></div></nav></main></div></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_1mse"><a href="/PSP/blog/2020w31a-beta">2020w31a-beta</a></h2><div class="margin-vert--md"><time datetime="2020-08-01T00:00:00.000Z" class="blogPostDate_3bQP">August 1, 2020  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>🔥 PSP-UFU online user guide finally written (only in Brazilian Portuguese, if you want to help me translate this guide, contact-me on <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> or <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>);</li><li>✔️ New fancy <a href="https://thales1330.github.io/PSP/" target="_blank" rel="noopener noreferrer">PSP-UFU website</a> and <a href="https://thales1330.github.io/PSP/blog" target="_blank" rel="noopener noreferrer">changelog</a> using <a href="https://v2.docusaurus.io/" target="_blank" rel="noopener noreferrer">docusaurus</a>;</li><li>✔️ Text element performance improved for OpenGL render;</li><li>🐛 Several major and minor bug fixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_1mse"><a href="/PSP/blog/2020w28a-beta">2020w28a-beta</a></h2><div class="margin-vert--md"><time datetime="2020-07-09T00:00:00.000Z" class="blogPostDate_3bQP">July 9, 2020  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>🔥 Voltage heatmap implemented (OpenGL enabled);</li><li>🐛 Several major and minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_1mse"><a href="/PSP/blog/2020w24a-beta">2020w24a-beta</a></h2><div class="margin-vert--md"><time datetime="2020-06-13T00:00:00.000Z" class="blogPostDate_3bQP">June 13, 2020  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>✔️ Device context render implemented (to avoid use OpenGL - some machines can&#x27;t use it properly);</li><li>✔️ Added Visual Studio solution to the GitHub project;</li><li>🐛 Several major and minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_1mse"><a href="/PSP/blog/2019w44a-beta">22019w44a-beta</a></h2><div class="margin-vert--md"><time datetime="2019-11-01T00:00:00.000Z" class="blogPostDate_3bQP">November 1, 2019  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>✔️ Minor changes to 32bit MSW version for compatibility;</li><li>✔️ Travis CI (Continuous Integration) implemented (Linux).</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_1mse"><a href="/PSP/blog/2019w42a-beta">2019w42a-beta</a></h2><div class="margin-vert--md"><time datetime="2019-10-13T00:00:00.000Z" class="blogPostDate_3bQP">October 13, 2019  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>🔥 Harmonic study implemented;</li><li>🔥 Autolayout from importation implemented;</li><li>🔥 Importation of Matpower files;</li><li>🐛 Several minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div></footer></article><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"></div><div class="pagination-nav__item pagination-nav__item--next"></div></nav></main></div></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code 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-<nav class="navbar navbar--light navbar--fixed-top"><div class="navbar__inner"><div class="navbar__items"><div aria-label="Navigation bar toggle" class="navbar__toggle" role="button" tabindex="0"><svg xmlns="http://www.w3.org/2000/svg" width="30" height="30" viewBox="0 0 30 30" role="img" focusable="false"><title>Menu</title><path stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" stroke-width="2" d="M4 7h22M4 15h22M4 23h22"></path></svg></div><a class="navbar__brand" href="/PSP/"><img class="navbar__logo" src="/PSP/img/logo.svg" alt="PSP-UFU logo"><strong class="navbar__title">PSP-UFU</strong></a><a class="navbar__item navbar__link" href="/PSP/docs/">User Guide</a><a aria-current="page" class="navbar__item navbar__link navbar__link--active" href="/PSP/blog">Changelog</a></div><div class="navbar__items navbar__items--right"><a href="https://github.com/Thales1330/PSP" target="_blank" rel="noopener noreferrer" class="navbar__item navbar__link">PSP-UFU Source 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class="DocSearch-Button-Key">⌘</span><span class="DocSearch-Button-Key">K</span></button></div></div><div role="presentation" class="navbar-sidebar__backdrop"></div><div class="navbar-sidebar"><div class="navbar-sidebar__brand"><a class="navbar__brand" href="/PSP/"><img class="navbar__logo" src="/PSP/img/logo.svg" alt="PSP-UFU logo"><strong class="navbar__title">PSP-UFU</strong></a></div><div class="navbar-sidebar__items"><div class="menu"><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" href="/PSP/docs/">User Guide</a></li><li class="menu__list-item"><a aria-current="page" class="menu__link navbar__link--active" href="/PSP/blog">Changelog</a></li><li class="menu__list-item"><a href="https://github.com/Thales1330/PSP" target="_blank" rel="noopener noreferrer" class="menu__link">PSP-UFU Source Code</a></li></ul></div></div></div></nav><div class="main-wrapper"><div class="container margin-vert--lg"><div class="row"><main class="col col--8 col--offset-2"><h1>4 posts tagged with &quot;psp-ufu&quot;</h1><a href="/PSP/blog/tags">View All Tags</a><div class="margin-vert--xl"><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_1mse"><a href="/PSP/blog/2020w28a-beta">2020w28a-beta</a></h2><div class="margin-vert--md"><time datetime="2020-07-09T00:00:00.000Z" class="blogPostDate_3bQP">July 9, 2020  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Voltage heatmap implemented (OpenGL enabled);</li><li>Several major and minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div><div class="col text--right"><a aria-label="Read more about 2020w28a-beta" href="/PSP/blog/2020w28a-beta"><strong>Read More</strong></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_1mse"><a href="/PSP/blog/2020w24a-beta">2020w24a-beta</a></h2><div class="margin-vert--md"><time datetime="2020-06-13T00:00:00.000Z" class="blogPostDate_3bQP">June 13, 2020  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Device context render implemented (to avoid use OpenGL - some machines can&#x27;t use it properly);</li><li>Added Visual Studio solution to the GitHub project;</li><li>Several major and minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div><div class="col text--right"><a aria-label="Read more about 2020w24a-beta" href="/PSP/blog/2020w24a-beta"><strong>Read More</strong></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_1mse"><a href="/PSP/blog/2019w44a-beta">22019w44a-beta</a></h2><div class="margin-vert--md"><time datetime="2019-11-01T00:00:00.000Z" class="blogPostDate_3bQP">November 1, 2019  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Minor changes to 32bit MSW version for compatibility;</li><li>Travis CI (Continuous Integration) implemented (Linux).</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div><div class="col text--right"><a aria-label="Read more about 22019w44a-beta" href="/PSP/blog/2019w44a-beta"><strong>Read More</strong></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_1mse"><a href="/PSP/blog/2019w42a-beta">2019w42a-beta</a></h2><div class="margin-vert--md"><time datetime="2019-10-13T00:00:00.000Z" class="blogPostDate_3bQP">October 13, 2019  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>Harmonic study implemented;</li><li>Autolayout from importation implemented;</li><li>Importation of Matpower files;</li><li>Several minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div><div class="col text--right"><a aria-label="Read more about 2019w42a-beta" href="/PSP/blog/2019w42a-beta"><strong>Read More</strong></a></div></footer></article></div></main></div></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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Code</a><div class="react-toggle react-toggle--disabled displayOnlyInLargeViewport_2aTZ"><div class="react-toggle-track"><div class="react-toggle-track-check"><span class="toggle_BsTx"></span></div><div class="react-toggle-track-x"><span class="toggle_BsTx"></span></div></div><div class="react-toggle-thumb"></div><input type="checkbox" disabled="" aria-label="Dark mode toggle" class="react-toggle-screenreader-only"></div><button type="button" class="DocSearch DocSearch-Button" aria-label="Search"><svg width="20" height="20" class="DocSearch-Search-Icon" viewBox="0 0 20 20"><path d="M14.386 14.386l4.0877 4.0877-4.0877-4.0877c-2.9418 2.9419-7.7115 2.9419-10.6533 0-2.9419-2.9418-2.9419-7.7115 0-10.6533 2.9418-2.9419 7.7115-2.9419 10.6533 0 2.9419 2.9418 2.9419 7.7115 0 10.6533z" stroke="currentColor" fill="none" fill-rule="evenodd" stroke-linecap="round" stroke-linejoin="round"></path></svg><span class="DocSearch-Button-Placeholder">Search</span><span class="DocSearch-Button-Key">⌘</span><span class="DocSearch-Button-Key">K</span></button></div></div><div role="presentation" class="navbar-sidebar__backdrop"></div><div class="navbar-sidebar"><div class="navbar-sidebar__brand"><a class="navbar__brand" href="/PSP/"><img class="navbar__logo" src="/PSP/img/logo.svg" alt="PSP-UFU logo"><strong class="navbar__title">PSP-UFU</strong></a></div><div class="navbar-sidebar__items"><div class="menu"><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" href="/PSP/docs/">User Guide</a></li><li class="menu__list-item"><a aria-current="page" class="menu__link navbar__link--active" href="/PSP/blog">Changelog</a></li><li class="menu__list-item"><a href="https://github.com/Thales1330/PSP" target="_blank" rel="noopener noreferrer" class="menu__link">PSP-UFU Source Code</a></li></ul></div></div></div></nav><div class="main-wrapper"><div class="container margin-vert--lg"><div class="row"><main class="col col--8 col--offset-2"><h1>5 posts tagged with &quot;psp-ufu&quot;</h1><a href="/PSP/blog/tags">View All Tags</a><div class="margin-vert--xl"><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_1mse"><a href="/PSP/blog/2020w31a-beta">2020w31a-beta</a></h2><div class="margin-vert--md"><time datetime="2020-08-01T00:00:00.000Z" class="blogPostDate_3bQP">August 1, 2020  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>🔥 PSP-UFU online user guide finally written (only in Brazilian Portuguese, if you want to help me translate this guide, contact-me on <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> or <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>);</li><li>✔️ New fancy <a href="https://thales1330.github.io/PSP/" target="_blank" rel="noopener noreferrer">PSP-UFU website</a> and <a href="https://thales1330.github.io/PSP/blog" target="_blank" rel="noopener noreferrer">changelog</a> using <a href="https://v2.docusaurus.io/" target="_blank" rel="noopener noreferrer">docusaurus</a>;</li><li>✔️ Text element performance improved for OpenGL render;</li><li>🐛 Several major and minor bug fixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div><div class="col text--right"><a aria-label="Read more about 2020w31a-beta" href="/PSP/blog/2020w31a-beta"><strong>Read More</strong></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_1mse"><a href="/PSP/blog/2020w28a-beta">2020w28a-beta</a></h2><div class="margin-vert--md"><time datetime="2020-07-09T00:00:00.000Z" class="blogPostDate_3bQP">July 9, 2020  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>🔥 Voltage heatmap implemented (OpenGL enabled);</li><li>🐛 Several major and minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div><div class="col text--right"><a aria-label="Read more about 2020w28a-beta" href="/PSP/blog/2020w28a-beta"><strong>Read More</strong></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_1mse"><a href="/PSP/blog/2020w24a-beta">2020w24a-beta</a></h2><div class="margin-vert--md"><time datetime="2020-06-13T00:00:00.000Z" class="blogPostDate_3bQP">June 13, 2020  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>✔️ Device context render implemented (to avoid use OpenGL - some machines can&#x27;t use it properly);</li><li>✔️ Added Visual Studio solution to the GitHub project;</li><li>🐛 Several major and minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div><div class="col text--right"><a aria-label="Read more about 2020w24a-beta" href="/PSP/blog/2020w24a-beta"><strong>Read More</strong></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_1mse"><a href="/PSP/blog/2019w44a-beta">22019w44a-beta</a></h2><div class="margin-vert--md"><time datetime="2019-11-01T00:00:00.000Z" class="blogPostDate_3bQP">November 1, 2019  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>✔️ Minor changes to 32bit MSW version for compatibility;</li><li>✔️ Travis CI (Continuous Integration) implemented (Linux).</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div><div class="col text--right"><a aria-label="Read more about 22019w44a-beta" href="/PSP/blog/2019w44a-beta"><strong>Read More</strong></a></div></footer></article><article class="margin-bottom--xl"><header><h2 class="margin-bottom--sm blogPostTitle_1mse"><a href="/PSP/blog/2019w42a-beta">2019w42a-beta</a></h2><div class="margin-vert--md"><time datetime="2019-10-13T00:00:00.000Z" class="blogPostDate_3bQP">October 13, 2019  · 1 min read</time></div><div class="avatar margin-vert--md"><a class="avatar__photo-link avatar__photo" href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener"><img src="https://avatars0.githubusercontent.com/u/16141330?s=460&amp;v=4" alt="Thales"></a><div class="avatar__intro"><h4 class="avatar__name"><a href="https://github.com/thales1330" target="_blank" rel="noreferrer noopener">Thales</a></h4><small class="avatar__subtitle">PhD</small></div></div></header><section class="markdown"><ul><li>🔥 Harmonic study implemented;</li><li>🔥 Autolayout from importation implemented;</li><li>🔥 Importation of Matpower files;</li><li>🐛 Several minor bugfixes.</li></ul></section><footer class="row margin-vert--lg"><div class="col"><strong>Tags:</strong><a class="margin-horiz--sm" href="/PSP/blog/tags/psp-ufu">psp-ufu</a></div><div class="col text--right"><a aria-label="Read more about 2019w42a-beta" href="/PSP/blog/2019w42a-beta"><strong>Read More</strong></a></div></footer></article></div></main></div></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. Built with Docusaurus.</div></div></div></footer></div>
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index b6304a8f..ddc683fb 100644
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+(window.webpackJsonp=window.webpackJsonp||[]).push([[46],{103:function(e,a,t){"use strict";t.r(a),t.d(a,"frontMatter",(function(){return b})),t.d(a,"metadata",(function(){return p})),t.d(a,"rightToc",(function(){return r})),t.d(a,"default",(function(){return l}));var s=t(2),n=t(6),m=(t(0),t(124)),c=t(125),b={id:"controlEditor",title:"Editor de Controle",sidebar_label:"Editor de Controle"},p={unversionedId:"controlEditor",id:"controlEditor",isDocsHomePage:!1,title:"Editor de Controle",description:"Os controles das m\xe1quinas s\xedncronas s\xe3o criados, modificados, importados e exportados em um editor distinto dos elementos de pot\xeancia, apresentado na figura abaixo.",source:"@site/docs\\controlEditor.md",permalink:"/PSP/docs/controlEditor",editUrl:"https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/controlEditor.md",sidebar_label:"Editor de Controle",sidebar:"docs",previous:{title:"Motor de Indu\xe7\xe3o",permalink:"/PSP/docs/indMotor"},next:{title:"Entrada / Sa\xedda",permalink:"/PSP/docs/io"}},r=[{value:"Elementos de Controle",id:"elementos-de-controle",children:[]},{value:"Inicializa\xe7\xe3o do sistema de controle",id:"inicializa\xe7\xe3o-do-sistema-de-controle",children:[]},{value:"Teste do diagrama de controle",id:"teste-do-diagrama-de-controle",children:[]}],i={rightToc:r};function l(e){var a=e.components,t=Object(n.a)(e,["components"]);return Object(m.b)("wrapper",Object(s.a)({},i,t,{components:a,mdxType:"MDXLayout"}),Object(m.b)("link",{rel:"stylesheet",href:Object(c.a)("katex/katex.min.css")}),Object(m.b)("p",null,"Os controles das ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator"}),"m\xe1quinas s\xedncronas")," s\xe3o criados, modificados, importados e exportados em um editor distinto dos elementos de pot\xeancia, apresentado na figura abaixo."),Object(m.b)("div",null,Object(m.b)("center",null,Object(m.b)("img",{src:Object(c.a)("images/controlEditor.png"),alt:"Editor de elementos de controle do PSP-UFU",title:"Editor de elementos de controle do PSP-UFU"}))),Object(m.b)("p",null,"O acesso ao editor \xe9 realizado por meio de dois bot\xf5es presentes no ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"syncGenerator#formul%C3%A1rio-de-edi%C3%A7%C3%A3o-dos-geradores-s%C3%ADncronos"}),"formul\xe1rio de edi\xe7\xe3o dos dados de estabilidade dos geradores s\xedncronos"),":"),Object(m.b)("ul",null,Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"syncGenerator#utilizar-avr-e-regulador-de-velocidade"}),"Editar AVR")),Object(m.b)("li",{parentName:"ul"},Object(m.b)("a",Object(s.a)({parentName:"li"},{href:"syncGenerator#utilizar-avr-e-regulador-de-velocidade"}),"Editar regulador de velocidade"))),Object(m.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(m.b)("h5",{parentName:"div"},Object(m.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(m.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(m.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"No PSP-UFU a op\xe7\xe3o de editar o ",Object(m.b)("strong",{parentName:"p"},"AVR")," engloba mais que somente o controle de tens\xe3o da m\xe1quina. 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Os elementos s\xe3o ent\xe3o conectados por \u201clinhas de conex\xe3o\u201d inseridas ao clicar nos n\xf3s dos componentes previamente adicionados, permitindo a constru\xe7\xe3o da rede de controle gen\xe9rica."),Object(m.b)("p",null,"As ferramentas de manipula\xe7\xe3o e navega\xe7\xe3o, como arrastar, mover e excluir s\xe3o ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"cadTools"}),"herdadas")," do ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"editor de elementos de pot\xeancia"),", possuindo comportamento id\xeantico. 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Nessa op\xe7\xe3o ",Object(m.b)("strong",{parentName:"p"},"deve")," ser inserida ao menos a malha de controle da regula\xe7\xe3o prim\xe1ria de velocidade, assim como o ",Object(m.b)("strong",{parentName:"p"},"modelo da turbina"),". Estrat\xe9gias opcionais de controle da velocidade tamb\xe9m s\xe3o inseridas nessa op\xe7\xe3o."))),Object(m.b)("h2",{id:"elementos-de-controle"},"Elementos de Controle"),Object(m.b)("p",null,"O acesso aos elementos de controle \xe9 realizado em uma janela (remov\xedvel e encaix\xe1vel) por meio de \xedcones relacionados."),Object(m.b)("p",null,"Uma vez que o usu\xe1rio clicar no \xedcone desejado, o elemento de controle acompanhar\xe1 o ponteiro do mouse at\xe9 ser efetivamente inserido na posi\xe7\xe3o desejada ao clicar novamente na \xe1rea de trabalho. Os elementos s\xe3o ent\xe3o conectados por \u201clinhas de conex\xe3o\u201d inseridas ao clicar nos n\xf3s dos componentes previamente adicionados, permitindo a constru\xe7\xe3o da rede de controle gen\xe9rica."),Object(m.b)("p",null,"As ferramentas de manipula\xe7\xe3o e navega\xe7\xe3o, como arrastar, mover e excluir s\xe3o ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"cadTools"}),"herdadas")," do ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"powerEditor"}),"editor de elementos de pot\xeancia"),", possuindo comportamento id\xeantico. 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Tal procedimento \xe9 realizado por meio da solu\xe7\xe3o de toda rede de controle at\xe9 que se obtenha sua converg\xeancia, ou seja, a diferen\xe7a absoluta entre as mesmas sa\xeddas de uma solu\xe7\xe3o anterior e uma atual deve ser nula ou muito pr\xf3xima de zero."),Object(m.b)("div",{className:"admonition admonition-info alert alert--info"},Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(m.b)("h5",{parentName:"div"},Object(m.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(m.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"14",height:"16",viewBox:"0 0 14 16"}),Object(m.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"})))),"info")),Object(m.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(m.b)("p",{parentName:"div"},"O processo de ",Object(m.b)("strong",{parentName:"p"},"inicializa\xe7\xe3o \xe9 realizada automaticamente")," pelo PSP-UFU."),Object(m.b)("p",{parentName:"div"},"Uma vez que a inicializa\xe7\xe3o \xe9 imposta pelas ",Object(m.b)("a",Object(s.a)({parentName:"p"},{href:"io"}),"entradas")," do controle, erros de converg\xeancia podem ocorrer devido \xe0 m\xe1 parametriza\xe7\xe3o dos elementos dos sistemas de ",Object(m.b)("strong",{parentName:"p"},"pot\xeancia e controle"),"."))),Object(m.b)("p",null,"Para otimizar e melhorar a estabilidade do processo de inicializa\xe7\xe3o utilizou-se um passo de integra\xe7\xe3o vari\xe1vel dentro de limites, de forma que o passo aumenta em condi\xe7\xf5es de diferen\xe7as menores entre as solu\xe7\xf5es do sistema de controle e diminui caso essa diferen\xe7a se torne elevada. 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Nele \xe9 poss\xedvel tamb\xe9m acessar aos controles das m\xe1quinas s\xedncronas manipulados pelo ',Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"controlEditor"}),"editor de controle"),"."),Object(n.b)("div",null,Object(n.b)("center",null,Object(n.b)("img",{src:Object(b.a)("images/syncGeneratorStabForm.png"),alt:"Formul\xe1rio de estabilidade dos geradores s\xedncronos no PSP-UFU",title:"Formul\xe1rio de estabilidade dos geradores s\xedncronos no PSP-UFU"}))),Object(n.b)("p",null,'No formul\xe1rio de estabilidade pode ser observado o bot\xe3o "Chaveamento" na parte inferior esquerda do formul\xe1rio. 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Podem ser inseridos quaisquer n\xfameros de caracteres no padr\xe3o ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Unicode"}),"Unicode"),"."),Object(n.b)("p",null,"Todos os componentes de pot\xeancia do PSP-UFU possuem esse campo."),Object(n.b)("h4",{id:"pot\xeancia-nominal"},"Pot\xeancia nominal"),Object(n.b)("p",null,"Pot\xeancia nominal do gerador, inserida em MVA, kVA ou VA."),Object(n.b)("p",null,'Esse campo \xe9 especialmente importante caso a op\xe7\xe3o "Utilizar a pot\xeancia nominal como base" esteja marcada.'),Object(n.b)("h4",{id:"pot\xeancias-ativa-e-reativa"},"Pot\xeancias ativa e reativa"),Object(n.b)("p",null,"Pot\xeancias ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do gerador."),Object(n.b)("p",null,"Caso a barra conectada seja PV o valor de pot\xeancia reativa ser\xe1 ignorado e caso seja de refer\xeancia ambos os valores inseridos ser\xe3o desprezados."),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Caso mais de um gerador esteja conectado na mesma barra, os valores de pot\xeancia reativa (nas barras de refer\xeancia e PV) e ativa (nas barras de refer\xeancia) s\xe3o igualmente distribu\xeddas, respeitando os limites individuais de pot\xeancia reativa."))),Object(n.b)("h4",{id:"pot\xeancias-reativas-m\xe1xima-e-m\xednima"},"Pot\xeancias reativas m\xe1xima e m\xednima"),Object(n.b)("p",null,"Limites de pot\xeancia reativa m\xe1xima e m\xednima do gerador para controle de tens\xe3o em barras PV. 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Nele \xe9 poss\xedvel tamb\xe9m acessar aos controles das m\xe1quinas s\xedncronas manipulados pelo ',Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"controlEditor"}),"editor de controle"),"."),Object(n.b)("div",null,Object(n.b)("center",null,Object(n.b)("img",{src:Object(b.a)("images/syncGeneratorStabForm.png"),alt:"Formul\xe1rio de estabilidade dos geradores s\xedncronos no PSP-UFU",title:"Formul\xe1rio de estabilidade dos geradores s\xedncronos no PSP-UFU"}))),Object(n.b)("p",null,'No formul\xe1rio de estabilidade pode ser observado o bot\xe3o "Chaveamento" na parte inferior esquerda do formul\xe1rio. 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Podem ser inseridos quaisquer n\xfameros de caracteres no padr\xe3o ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Unicode"}),"Unicode"),"."),Object(n.b)("p",null,"Todos os componentes de pot\xeancia do PSP-UFU possuem esse campo."),Object(n.b)("h4",{id:"pot\xeancia-nominal"},"Pot\xeancia nominal"),Object(n.b)("p",null,"Pot\xeancia nominal do gerador, inserida em MVA, kVA ou VA."),Object(n.b)("p",null,'Esse campo \xe9 especialmente importante caso a op\xe7\xe3o "Utilizar a pot\xeancia nominal como base" esteja marcada.'),Object(n.b)("h4",{id:"pot\xeancias-ativa-e-reativa"},"Pot\xeancias ativa e reativa"),Object(n.b)("p",null,"Pot\xeancias ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do gerador."),Object(n.b)("p",null,"Caso a barra conectada seja PV o valor de pot\xeancia reativa ser\xe1 ignorado e caso seja de refer\xeancia ambos os valores inseridos ser\xe3o desprezados."),Object(n.b)("div",{className:"admonition admonition-caution alert alert--warning"},Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-heading"}),Object(n.b)("h5",{parentName:"div"},Object(n.b)("span",Object(s.a)({parentName:"h5"},{className:"admonition-icon"}),Object(n.b)("svg",Object(s.a)({parentName:"span"},{xmlns:"http://www.w3.org/2000/svg",width:"16",height:"16",viewBox:"0 0 16 16"}),Object(n.b)("path",Object(s.a)({parentName:"svg"},{fillRule:"evenodd",d:"M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"})))),"Aten\xe7\xe3o!")),Object(n.b)("div",Object(s.a)({parentName:"div"},{className:"admonition-content"}),Object(n.b)("p",{parentName:"div"},"Caso mais de um gerador esteja conectado na mesma barra, os valores de pot\xeancia reativa (nas barras de refer\xeancia e PV) e ativa (nas barras de refer\xeancia) s\xe3o igualmente distribu\xeddas, respeitando os limites individuais de pot\xeancia reativa."))),Object(n.b)("h4",{id:"pot\xeancias-reativas-m\xe1xima-e-m\xednima"},"Pot\xeancias reativas m\xe1xima e m\xednima"),Object(n.b)("p",null,"Limites de pot\xeancia reativa m\xe1xima e m\xednima do gerador para controle de tens\xe3o em barras PV. 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New York: Wiley-IEEE Press, 1995.")))}l.isMDXComponent=!0},123:function(a,e,t){"use strict";var s=t(0),m=t(20);e.a=function(){const a=Object(s.useContext)(m.a);if(null===a)throw new Error("Docusaurus context not provided");return a}},124:function(a,e,t){"use strict";t.d(e,"a",(function(){return j})),t.d(e,"b",(function(){return i}));var s=t(0),m=t.n(s);function n(a,e,t){return e in a?Object.defineProperty(a,e,{value:t,enumerable:!0,configurable:!0,writable:!0}):a[e]=t,a}function b(a,e){var t=Object.keys(a);if(Object.getOwnPropertySymbols){var s=Object.getOwnPropertySymbols(a);e&&(s=s.filter((function(e){return Object.getOwnPropertyDescriptor(a,e).enumerable}))),t.push.apply(t,s)}return t}function p(a){for(var e=1;e<arguments.length;e++){var 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Barramento</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Condutor de baixa impedância ao qual vários circuitos elétricos podem ser conectados em pontos separados.
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class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Barramento</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Condutor de baixa impedância ao qual vários circuitos elétricos podem ser conectados em pontos separados.
 Nota - Em muitos casos, o barramento consiste em uma barra. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=151-12-30" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="barramento-no-psp-ufu"></a>Barramento no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#barramento-no-psp-ufu" title="Direct link to heading">#</a></h2><p>O elemento <strong>barramento</strong>, ou simplesmente <strong>barra</strong>, é um conector ou nó do diagrama unifilar do PSP-UFU. Essa barra pode representar um PAC (Ponto de Acoplamento Comum), um poste de distribuição, uma subestação, um barramento da subestação, entre inúmeros outros tipos pontos de análise e conexão entre elementos.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-dos-barramentos"></a>Formulário de edição dos barramentos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-barramentos" title="Direct link to heading">#</a></h2><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>O barramento deve ser o <strong>primeiro elemento elétrico a ser inserido no diagrama de potência</strong>, uma vez que os demais componentes de potência são conectados nele.</p></div></div><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados das barras:</p><div><center><img src="/PSP/images/busForm.png" alt="Formulário dos barramentos no PSP-UFU" title="Formulário dos barramentos no PSP-UFU"></center></div><p>Esse formulário é subdividido em quatro contextos distintos:</p><ul><li><strong>Geral</strong>: no qual são inseridas informações gerais da barra e informações do fluxo de carga;</li><li><strong>Falta</strong>: local onde o curto-circuito <em>shunt</em> deve ser inserido;</li><li><strong>Estabilidade</strong>: contendo opções de visualização de dados da barra em gráficos no tempo e inserção de faltas trifásicas no cálculo de estabilidade transitória;</li><li><strong>Qualidade de energia</strong>: contém a opção de de visualização da impedância harmônica vista pela barra.</li></ul><hr><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_1w39 tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Falta</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Estabilidade</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Qualidade de energia</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="tensão-nominal"></a>Tensão nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tensão-nominal" title="Direct link to heading">#</a></h4><p>Utilizado para cálculo da impedância base de alguns elementos conectados, além do cálculo da relação de transformação dos transformadores conectados entre barras. Sua unidade pode ser selecionada, sendo expressa em V ou em kV.</p><p>A modificação desse parâmetro irá alterar toda a tensão do trecho conectado por linhas elétricas, sendo emitido um alerta ao usuário.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="tensão-controlada"></a>Tensão controlada<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tensão-controlada" title="Direct link to heading">#</a></h4><p>Caracteriza o barramento como <strong>barra de tensão controlada (<a href="/PSP/docs/powerFlow">Barra PV</a>)</strong>,</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Essa opção é somente válida caso alguma máquina síncrona esteja conectado, caso contrário esse valor será ignorado. Caso o limite de potência reativa da máquina síncrona conectada seja ultrapassado esse valor também é ignorado.</p></div></div><p>O valor poderá ser inserido em p.u. ou em volts (ou kV caso a tensão nominal esteja nesta unidade).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="barra-de-referência"></a>Barra de referência<a aria-hidden="true" tabindex="-1" class="hash-link" href="#barra-de-referência" title="Direct link to heading">#</a></h4><p>Caracteriza o barramento como <strong>barra de referência (<a href="/PSP/docs/powerFlow">Barra de oscilação</a>)</strong>. Essa opção é somente válida caso esteja conectado um gerador síncrono, caso contrário uma mensagem de erro será exibida ao usuário ao realizar algum dos cálculos do programa.</p></div></div></div><hr><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Resumo de como definir o tipo de barra:</p><ul><li>Para definir o barramento como sendo uma <strong><a href="/PSP/docs/powerFlow">Barra PQ</a></strong>, as opções &quot;Barra de referência&quot; e &quot;Tensão controlada&quot; devem estar <strong>desmarcadas</strong>; </li><li>Para definir o barramento como sendo uma <strong><a href="/PSP/docs/powerFlow">Barra PV</a></strong>, deve-se <strong>marcar somente</strong> a opção &quot;Tensão controlada&quot;, mantendo a opção &quot;Barra de referência&quot; desmarcada;</li><li>Para definir o barramento como sendo uma <strong><a href="/PSP/docs/powerFlow">Barra de Referência</a></strong>, deve-se marcar a opção &quot;Barra de referência&quot;. Caso a opção &quot;Tensão controlada&quot; esteja desmarcada será admitido um valor de tensão controlada de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>0</mn><mtext> </mtext><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">1{,}0~p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span><span class="mspace nobreak"> </span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></li></ul></div></div><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p><strong>O sistema deve possuir somente uma barra de referência</strong>.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/bus.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/powerEditor"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Editor de Potência</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/line"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Linha »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#barramento-no-psp-ufu" class="table-of-contents__link">Barramento no PSP-UFU</a></li><li><a href="#formulário-de-edição-dos-barramentos" class="table-of-contents__link">Formulário de edição dos barramentos</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Ferramentas CAD</h1></header><div class="markdown"><blockquote><p>Desenho assistido por computador (DAC; em inglês: <em>computer aided design</em> - CAD) é o nome genérico de sistemas computacionais (<em>software</em>) utilizados pela engenharia, geologia, geografia, arquitetura e design para facilitar o projeto e desenho técnicos. No caso do <em>design</em>, este pode estar ligado especificamente a todas as suas vertentes (produtos como vestuário, eletroeletrônicos, automobilísticos, etc.), de modo que os jargões de cada especialidade são incorporados na interface de cada programa. <a href="https://pt.wikipedia.org/wiki/Desenho_assistido_por_computador" target="_blank" rel="noopener noreferrer">Wikipedia</a></p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="ferramentas-do-menu"></a>Ferramentas do menu<a aria-hidden="true" tabindex="-1" class="hash-link" href="#ferramentas-do-menu" title="Direct link to heading">#</a></h2><p>Todos os objetos criados contêm vários atributos gráficos, como: posição, orientação, cor, tamanho, etc. Para modificá-los foram inseridas algumas ferramentas intuitivas e de fácil utilização, as quais são: <a href="/PSP/docs/cadTools#selecionar"><strong>selecionar</strong></a>, <a href="/PSP/docs/cadTools#mover"><strong>mover</strong></a>, <a href="/PSP/docs/cadTools#girar"><strong>girar</strong></a>, <a href="/PSP/docs/cadTools#arrastar"><strong>arrastar</strong></a>, <a href="/PSP/docs/cadTools#zoom"><strong>zoom</strong></a>, <a href="/PSP/docs/cadTools#encaixar"><strong>encaixar</strong></a>, <a href="/PSP/docs/cadTools#copiar-e-colar"><strong>copiar, colar</strong></a> e <a href="/PSP/docs/cadTools#excluir"><strong>excluir</strong></a>.</p><p>Essas ferramentas podem ser acessadas por suas teclas de atalho assim como pelo <a href="/PSP/docs/mainScreen#menu-ribbon">submenu Ferramentas</a>.</p><p>Tais ferramentas permitem a <strong>personalização</strong>, <strong>navegação</strong> e auxiliam a <strong>criação</strong> de redes elétricas de potência, assim como diagramas de controle na plataforma.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="selecionar"></a>Selecionar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#selecionar" title="Direct link to heading">#</a></h3><p>A seleção de um único objeto é realizada clicando com o botão esquerdo do mouse sobre o elemento, que será identificado pelo contorno em <span style="background-color:#80bfff;border-radius:2px;color:#000;padding:0.2rem">azul</span> do objeto.</p><p>Para a seleção de vários objetos simultaneamente é necessário clicar com o botão esquerdo do mouse em um local vazio da tela e arrastá-lo, criando assim um <strong>retângulo de seleção</strong> que irá acompanhar o ponteiro do mouse enquanto o botão esquerdo estiver pressionado. Ao soltá-lo todos os objetos que intercederem o retângulo serão selecionados.</p><p>Mantendo pressionado a tecla Control (Ctrl) do teclado pode-se manter seleções anteriores enquanto novos elementos são selecionados.</p><p>Para desmarcar todos os objetos basta clicar em uma área sem objetos.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/select.mp4" type="video/mp4"><source src="/PSP/videos/select.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="mover"></a>Mover<a aria-hidden="true" tabindex="-1" class="hash-link" href="#mover" title="Direct link to heading">#</a></h3><p>Um elemento poderá ser movido para qualquer local por meio da ação <em>drag-and-drop</em> (clicando e arrastando) ou pela ferramenta mover.</p><p>Ao habilitar o “modo mover”, movendo todos os componentes selecionados à medida que a posição do mouse é alterada. Para desabilitar esse modo basta pressionar a tecla Escape do teclado.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/move.mp4" type="video/mp4"><source src="/PSP/videos/move.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="girar"></a>Girar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#girar" title="Direct link to heading">#</a></h3><p>Alguns objetos poderão ser rotacionados através da ferramenta girar, acessado pela tecla de atalho “R”, girando o objeto no sentido horário, ou “Shift + R”, para o sentido anti-horário (essa opção irá afetar todos os objetos selecionados). O elemento também pode ser rotacionado pelo <a href="/PSP/docs/mainScreen#menu-ribbon">submenu Ferramentas</a> ou ao acessar o menu de contexto clicando com o botão direito sobre o elemento.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>O menu de contexto somente será exibido se o elemento estiver selecionado.</p></div></div><p>Ao utilizar essa ferramenta os objetos irão girar 45º a partir do seu ponto de origem. Para atingir a angulação pretendida basta repetir o processo de rotação.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/rotate.mp4" type="video/mp4"><source src="/PSP/videos/rotate.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="arrastar"></a>Arrastar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#arrastar" title="Direct link to heading">#</a></h3><p>Três ferramentas muito úteis na navegação do circuito, principalmente em grandes redes, são: arrastar, zoom e encaixar.</p><p>A ferramenta arrastar possibilita mover todo o circuito <strong>preservando as posições relativas entre os elementos</strong>. Esta ferramenta pode ser acessada pelo submenu “Ferramentas” ou <strong>mantendo pressionada o <em>scroll</em> do mouse</strong>, ativando assim o “modo arrastar”. Ao ativá-lo todo o circuito será movido clicando e arrastando na direção desejada.</p><p>Para sair do “modo arrastar” basta pressionar a tecla Escape do teclado.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/drag.mp4" type="video/mp4"><source src="/PSP/videos/drag.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="zoom"></a>Zoom<a aria-hidden="true" tabindex="-1" class="hash-link" href="#zoom" title="Direct link to heading">#</a></h3><p>O zoom será aplicado ao utilizar o <strong>scroll do mouse</strong> para mais ou menos zoom. A ferramenta zoom irá aproximar ou distanciar o circuito a partir da posição do ponteiro do mouse na tela para encontrar objetos ou destaca-los.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/zoom.mp4" type="video/mp4"><source src="/PSP/videos/zoom.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="encaixar"></a>Encaixar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#encaixar" title="Direct link to heading">#</a></h3><p>A ferramenta encaixar irá mover o circuito e aplicar o zoom necessário para que todos os componentes da rede sejam exibidos na tela. Esta ferramenta pode ser acessada através do submenu “Ferramentas” ou pela combinação de teclas “Shift + F”.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/fit.mp4" type="video/mp4"><source src="/PSP/videos/fit.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="copiar-e-colar"></a>Copiar e Colar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#copiar-e-colar" title="Direct link to heading">#</a></h3><p>Duas ferramentas importantes durante o processo de criação da rede elétrica de potência no <em>software</em> são copiar e colar. Qualquer circuito criado no PSP-UFU poderá ser duplicado completamente ou parcialmente no mesmo projeto ou em múltiplos através dessas ferramentas.</p><p>Para copiar basta selecionar os elementos que se deseja duplicar e acessar a ferramenta no submenu “Ferramentas” ou pressionando a combinação das teclas “Ctrl + C”, então os dados do circuito serão copiados para a área de transferência. Ao copiar um circuito ele poderá ser colado no mesmo projeto ou em um projeto distinto, utilizando o mesmo submenu ou pressionando a combinação das teclas “Ctrl + V”.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/copyPaste.mp4" type="video/mp4"><source src="/PSP/videos/copyPaste.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="excluir"></a>Excluir<a aria-hidden="true" tabindex="-1" class="hash-link" href="#excluir" title="Direct link to heading">#</a></h3><p>Qualquer objeto poderá ser excluído do projeto por meio da ferramenta deletar, presente no menu Ribbon, pela tecla de atalho Delete ou pelo acesso ao menu de contexto clicando com o botão direito sobre o elemento selecionado.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/delete.mp4" type="video/mp4"><source src="/PSP/videos/delete.webm" type="video/webm"></video><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="personalização-gráfica-os-elementos"></a>Personalização gráfica os elementos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#personalização-gráfica-os-elementos" title="Direct link to heading">#</a></h2><p>Alguns elementos permitem sua personalização gráfica, como as barras e linhas.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="barra"></a>Barra<a aria-hidden="true" tabindex="-1" class="hash-link" href="#barra" title="Direct link to heading">#</a></h3><p>No caso dos barramentos, pode-se alterar o <strong>comprimento da barra</strong> clicando e arrastando no <em>pickbox</em> exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="linha"></a>Linha<a aria-hidden="true" tabindex="-1" class="hash-link" href="#linha" title="Direct link to heading">#</a></h3><p>As linhas podem ser inseridas com <strong>&quot;nós&quot; (pontos de ancoragem)</strong>, personalizando a disposição das linhas no diagrama unifilar. Esses nós são inseridos durante o processo de criação do elemento, anteriormente à seleção da segunda barra.</p><p>Após a sua inserção, novos nós podem ser anexados pelo menu de contexto acessado ao clicar com o botão direito sobre a linha selecionada. Sua remoção também é alcançada por uma opção do menu de contexto.</p><p>Assim como nos barramentos, a alteração da posição dos nós é obtida clicando e arrastando o <em>pickbox</em> exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/graphicPropsChange.mp4" type="video/mp4"><source src="/PSP/videos/graphicPropsChange.webm" type="video/webm"></video><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="conexão-e-desconexão-de-elemetos-na-barra"></a>Conexão e desconexão de elemetos na barra<a aria-hidden="true" tabindex="-1" class="hash-link" href="#conexão-e-desconexão-de-elemetos-na-barra" title="Direct link to heading">#</a></h2><p>Os elementos podem ser desconectados e reconectados às barras após sua inserção somente pela ferramenta <em>drag-and-drop</em>. Para isso, o elemento deve ser selecionado e o seu nó de conexão deve ser arrastado para o local requerido.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>O elemento a ser desconectado/reconectado <strong>deve ser previamente selecionado</strong> para efetuar a operação. Caso contrário a barra será movida ou nenhuma operação será realizada.</p></div></div><p>No caso de desconexão, o elemento será automaticamente removido da simulação, sendo indicado pela sua cor (o elemento passa a ter cor <span style="background-color:#7f7f7f;border-radius:2px;color:#000;padding:0.2rem">cinza</span>).</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Ao reconectar o elemento ao circuito, deve-se <strong>atentar para estado do seu &quot;disjuntor&quot;</strong>, indicado por um quadrado próximo ao seu nó de conexão. Um elemento reconectado volta ao circuito com seu disjuntor aberto (<span style="background-color:#ff1919;border-radius:2px;color:#000;padding:0.2rem">vermelho</span>), sendo necessário clicar sobre o mesmo a fim de inserir o elemento no circuito.</p></div></div><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/disconnect.mp4" type="video/mp4"><source src="/PSP/videos/disconnect.webm" type="video/webm"></video></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/cadTools.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/mainScreen"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Tela Principal</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/powerEditor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Editor de Potência »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#ferramentas-do-menu" class="table-of-contents__link">Ferramentas do menu</a><ul><li><a href="#selecionar" class="table-of-contents__link">Selecionar</a></li><li><a href="#mover" class="table-of-contents__link">Mover</a></li><li><a href="#girar" class="table-of-contents__link">Girar</a></li><li><a href="#arrastar" class="table-of-contents__link">Arrastar</a></li><li><a href="#zoom" class="table-of-contents__link">Zoom</a></li><li><a href="#encaixar" class="table-of-contents__link">Encaixar</a></li><li><a href="#copiar-e-colar" class="table-of-contents__link">Copiar e Colar</a></li><li><a href="#excluir" class="table-of-contents__link">Excluir</a></li></ul></li><li><a href="#personalização-gráfica-os-elementos" class="table-of-contents__link">Personalização gráfica os elementos</a><ul><li><a href="#barra" class="table-of-contents__link">Barra</a></li><li><a href="#linha" class="table-of-contents__link">Linha</a></li></ul></li><li><a href="#conexão-e-desconexão-de-elemetos-na-barra" class="table-of-contents__link">Conexão e desconexão de elemetos na barra</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Ferramentas CAD</h1></header><div class="markdown"><blockquote><p>Desenho assistido por computador (DAC; em inglês: <em>computer aided design</em> - CAD) é o nome genérico de sistemas computacionais (<em>software</em>) utilizados pela engenharia, geologia, geografia, arquitetura e design para facilitar o projeto e desenho técnicos. No caso do <em>design</em>, este pode estar ligado especificamente a todas as suas vertentes (produtos como vestuário, eletroeletrônicos, automobilísticos, etc.), de modo que os jargões de cada especialidade são incorporados na interface de cada programa. <a href="https://pt.wikipedia.org/wiki/Desenho_assistido_por_computador" target="_blank" rel="noopener noreferrer">Wikipedia</a></p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="ferramentas-do-menu"></a>Ferramentas do menu<a aria-hidden="true" tabindex="-1" class="hash-link" href="#ferramentas-do-menu" title="Direct link to heading">#</a></h2><p>Todos os objetos criados contêm vários atributos gráficos, como: posição, orientação, cor, tamanho, etc. Para modificá-los foram inseridas algumas ferramentas intuitivas e de fácil utilização, as quais são: <a href="/PSP/docs/cadTools#selecionar"><strong>selecionar</strong></a>, <a href="/PSP/docs/cadTools#mover"><strong>mover</strong></a>, <a href="/PSP/docs/cadTools#girar"><strong>girar</strong></a>, <a href="/PSP/docs/cadTools#arrastar"><strong>arrastar</strong></a>, <a href="/PSP/docs/cadTools#zoom"><strong>zoom</strong></a>, <a href="/PSP/docs/cadTools#encaixar"><strong>encaixar</strong></a>, <a href="/PSP/docs/cadTools#copiar-e-colar"><strong>copiar, colar</strong></a> e <a href="/PSP/docs/cadTools#excluir"><strong>excluir</strong></a>.</p><p>Essas ferramentas podem ser acessadas por suas teclas de atalho assim como pelo <a href="/PSP/docs/mainScreen#menu-ribbon">submenu Ferramentas</a>.</p><p>Tais ferramentas permitem a <strong>personalização</strong>, <strong>navegação</strong> e auxiliam a <strong>criação</strong> de redes elétricas de potência, assim como diagramas de controle na plataforma.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="selecionar"></a>Selecionar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#selecionar" title="Direct link to heading">#</a></h3><p>A seleção de um único objeto é realizada clicando com o botão esquerdo do mouse sobre o elemento, que será identificado pelo contorno em <span style="background-color:#80bfff;border-radius:2px;color:#000;padding:0.2rem">azul</span> do objeto.</p><p>Para a seleção de vários objetos simultaneamente é necessário clicar com o botão esquerdo do mouse em um local vazio da tela e arrastá-lo, criando assim um <strong>retângulo de seleção</strong> que irá acompanhar o ponteiro do mouse enquanto o botão esquerdo estiver pressionado. Ao soltá-lo todos os objetos que intercederem o retângulo serão selecionados.</p><p>Mantendo pressionado a tecla Control (Ctrl) do teclado pode-se manter seleções anteriores enquanto novos elementos são selecionados.</p><p>Para desmarcar todos os objetos basta clicar em uma área sem objetos.</p><video autoplay="" loop="" muted="" playsinline="" controls=""><source src="/PSP/videos/select.mp4" type="video/mp4"><source src="/PSP/videos/select.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="mover"></a>Mover<a aria-hidden="true" tabindex="-1" class="hash-link" href="#mover" title="Direct link to heading">#</a></h3><p>Um elemento poderá ser movido para qualquer local por meio da ação <em>drag-and-drop</em> (clicando e arrastando) ou pela ferramenta mover.</p><p>Ao habilitar o “modo mover”, movendo todos os componentes selecionados à medida que a posição do mouse é alterada. Para desabilitar esse modo basta pressionar a tecla Escape do teclado.</p><video autoplay="" loop="" muted="" playsinline="" controls=""><source src="/PSP/videos/move.mp4" type="video/mp4"><source src="/PSP/videos/move.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="girar"></a>Girar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#girar" title="Direct link to heading">#</a></h3><p>Alguns objetos poderão ser rotacionados através da ferramenta girar, acessado pela tecla de atalho “R”, girando o objeto no sentido horário, ou “Shift + R”, para o sentido anti-horário (essa opção irá afetar todos os objetos selecionados). O elemento também pode ser rotacionado pelo <a href="/PSP/docs/mainScreen#menu-ribbon">submenu Ferramentas</a> ou ao acessar o menu de contexto clicando com o botão direito sobre o elemento.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>O menu de contexto somente será exibido se o elemento estiver selecionado.</p></div></div><p>Ao utilizar essa ferramenta os objetos irão girar 45º a partir do seu ponto de origem. Para atingir a angulação pretendida basta repetir o processo de rotação.</p><video autoplay="" loop="" muted="" playsinline="" controls=""><source src="/PSP/videos/rotate.mp4" type="video/mp4"><source src="/PSP/videos/rotate.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="arrastar"></a>Arrastar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#arrastar" title="Direct link to heading">#</a></h3><p>Três ferramentas muito úteis na navegação do circuito, principalmente em grandes redes, são: arrastar, zoom e encaixar.</p><p>A ferramenta arrastar possibilita mover todo o circuito <strong>preservando as posições relativas entre os elementos</strong>. Esta ferramenta pode ser acessada pelo submenu “Ferramentas” ou <strong>mantendo pressionada o <em>scroll</em> do mouse</strong>, ativando assim o “modo arrastar”. Ao ativá-lo todo o circuito será movido clicando e arrastando na direção desejada.</p><p>Para sair do “modo arrastar” basta pressionar a tecla Escape do teclado.</p><video autoplay="" loop="" muted="" playsinline="" controls=""><source src="/PSP/videos/drag.mp4" type="video/mp4"><source src="/PSP/videos/drag.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="zoom"></a>Zoom<a aria-hidden="true" tabindex="-1" class="hash-link" href="#zoom" title="Direct link to heading">#</a></h3><p>O zoom será aplicado ao utilizar o <strong>scroll do mouse</strong> para mais ou menos zoom. A ferramenta zoom irá aproximar ou distanciar o circuito a partir da posição do ponteiro do mouse na tela para encontrar objetos ou destaca-los.</p><video autoplay="" loop="" muted="" playsinline="" controls=""><source src="/PSP/videos/zoom.mp4" type="video/mp4"><source src="/PSP/videos/zoom.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="encaixar"></a>Encaixar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#encaixar" title="Direct link to heading">#</a></h3><p>A ferramenta encaixar irá mover o circuito e aplicar o zoom necessário para que todos os componentes da rede sejam exibidos na tela. Esta ferramenta pode ser acessada através do submenu “Ferramentas” ou pela combinação de teclas “Shift + F”.</p><video autoplay="" loop="" muted="" playsinline="" controls=""><source src="/PSP/videos/fit.mp4" type="video/mp4"><source src="/PSP/videos/fit.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="copiar-e-colar"></a>Copiar e Colar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#copiar-e-colar" title="Direct link to heading">#</a></h3><p>Duas ferramentas importantes durante o processo de criação da rede elétrica de potência no <em>software</em> são copiar e colar. Qualquer circuito criado no PSP-UFU poderá ser duplicado completamente ou parcialmente no mesmo projeto ou em múltiplos através dessas ferramentas.</p><p>Para copiar basta selecionar os elementos que se deseja duplicar e acessar a ferramenta no submenu “Ferramentas” ou pressionando a combinação das teclas “Ctrl + C”, então os dados do circuito serão copiados para a área de transferência. Ao copiar um circuito ele poderá ser colado no mesmo projeto ou em um projeto distinto, utilizando o mesmo submenu ou pressionando a combinação das teclas “Ctrl + V”.</p><video autoplay="" loop="" muted="" playsinline="" controls=""><source src="/PSP/videos/copyPaste.mp4" type="video/mp4"><source src="/PSP/videos/copyPaste.webm" type="video/webm"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="excluir"></a>Excluir<a aria-hidden="true" tabindex="-1" class="hash-link" href="#excluir" title="Direct link to heading">#</a></h3><p>Qualquer objeto poderá ser excluído do projeto por meio da ferramenta deletar, presente no menu Ribbon, pela tecla de atalho Delete ou pelo acesso ao menu de contexto clicando com o botão direito sobre o elemento selecionado.</p><video autoplay="" loop="" muted="" playsinline="" controls=""><source src="/PSP/videos/delete.mp4" type="video/mp4"><source src="/PSP/videos/delete.webm" type="video/webm"></video><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="personalização-gráfica-os-elementos"></a>Personalização gráfica os elementos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#personalização-gráfica-os-elementos" title="Direct link to heading">#</a></h2><p>Alguns elementos permitem sua personalização gráfica, como as barras e linhas.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="barra"></a>Barra<a aria-hidden="true" tabindex="-1" class="hash-link" href="#barra" title="Direct link to heading">#</a></h3><p>No caso dos barramentos, pode-se alterar o <strong>comprimento da barra</strong> clicando e arrastando no <em>pickbox</em> exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="linha"></a>Linha<a aria-hidden="true" tabindex="-1" class="hash-link" href="#linha" title="Direct link to heading">#</a></h3><p>As linhas podem ser inseridas com <strong>&quot;nós&quot; (pontos de ancoragem)</strong>, personalizando a disposição das linhas no diagrama unifilar. Esses nós são inseridos durante o processo de criação do elemento, anteriormente à seleção da segunda barra.</p><p>Após a sua inserção, novos nós podem ser anexados pelo menu de contexto acessado ao clicar com o botão direito sobre a linha selecionada. Sua remoção também é alcançada por uma opção do menu de contexto.</p><p>Assim como nos barramentos, a alteração da posição dos nós é obtida clicando e arrastando o <em>pickbox</em> exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado.</p><video autoplay="" loop="" muted="" playsinline="" controls=""><source src="/PSP/videos/graphicPropsChange.mp4" type="video/mp4"><source src="/PSP/videos/graphicPropsChange.webm" type="video/webm"></video><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="conexão-e-desconexão-de-elemetos-na-barra"></a>Conexão e desconexão de elemetos na barra<a aria-hidden="true" tabindex="-1" class="hash-link" href="#conexão-e-desconexão-de-elemetos-na-barra" title="Direct link to heading">#</a></h2><p>Os elementos podem ser desconectados e reconectados às barras após sua inserção somente pela ferramenta <em>drag-and-drop</em>. Para isso, o elemento deve ser selecionado e o seu nó de conexão deve ser arrastado para o local requerido.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>O elemento a ser desconectado/reconectado <strong>deve ser previamente selecionado</strong> para efetuar a operação. Caso contrário a barra será movida ou nenhuma operação será realizada.</p></div></div><p>No caso de desconexão, o elemento será automaticamente removido da simulação, sendo indicado pela sua cor (o elemento passa a ter cor <span style="background-color:#7f7f7f;border-radius:2px;color:#000;padding:0.2rem">cinza</span>).</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Ao reconectar o elemento ao circuito, deve-se <strong>atentar para estado do seu &quot;disjuntor&quot;</strong>, indicado por um quadrado próximo ao seu nó de conexão. Um elemento reconectado volta ao circuito com seu disjuntor aberto (<span style="background-color:#ff1919;border-radius:2px;color:#000;padding:0.2rem">vermelho</span>), sendo necessário clicar sobre o mesmo a fim de inserir o elemento no circuito.</p></div></div><video autoplay="" loop="" muted="" playsinline="" controls=""><source src="/PSP/videos/disconnect.mp4" type="video/mp4"><source src="/PSP/videos/disconnect.webm" type="video/webm"></video></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/cadTools.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/mainScreen"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Tela Principal</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/powerEditor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Editor de Potência »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#ferramentas-do-menu" class="table-of-contents__link">Ferramentas do menu</a><ul><li><a href="#selecionar" class="table-of-contents__link">Selecionar</a></li><li><a href="#mover" class="table-of-contents__link">Mover</a></li><li><a href="#girar" class="table-of-contents__link">Girar</a></li><li><a href="#arrastar" class="table-of-contents__link">Arrastar</a></li><li><a href="#zoom" class="table-of-contents__link">Zoom</a></li><li><a href="#encaixar" class="table-of-contents__link">Encaixar</a></li><li><a href="#copiar-e-colar" class="table-of-contents__link">Copiar e Colar</a></li><li><a href="#excluir" class="table-of-contents__link">Excluir</a></li></ul></li><li><a href="#personalização-gráfica-os-elementos" class="table-of-contents__link">Personalização gráfica os elementos</a><ul><li><a href="#barra" class="table-of-contents__link">Barra</a></li><li><a href="#linha" class="table-of-contents__link">Linha</a></li></ul></li><li><a href="#conexão-e-desconexão-de-elemetos-na-barra" class="table-of-contents__link">Conexão e desconexão de elemetos na barra</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Capacitor</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Um dispositivo constituído essencialmente por dois eletrodos separados por um dielétrico. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=436-01-03" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="capacitor-no-psp-ufu"></a>Capacitor no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#capacitor-no-psp-ufu" title="Direct link to heading">#</a></h2><p>O elemento capacitor representa, geralmente, um banco de capacitores <em>shunt</em> no circuito do PSP-UFU.</p><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Um arranjo série de uma <a href="/PSP/docs/line">linha</a> sem as susceptâncias <em>shunt</em>, um <a href="/PSP/docs/bus">barramento</a> e um <a href="/PSP/docs/capacitor">capacitor</a> pode ser utilizado para fabricar um filtro passivo nos <a href="/PSP/docs/harmonics">estudos harmônicos</a>. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.</p></div></div><p>Os capacitores e reatores exigem somente sua potência reativa como parâmetro. Esses elementos passivos são somente inseridos na matriz admitância cuja impedância é calculada a partir de sua potência e tensão nominais.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-dos-capacitores"></a>Formulário de edição dos capacitores<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-capacitores" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos capacitores:</p><div><center><img src="/PSP/images/capacitorForm.png" alt="Formulário dos capacitores no PSP-UFU" title="Formulário dos capacitores no PSP-UFU"></center></div><p>Além do único contexto geral, pode ser observado o botão &quot;Estabilidade&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do capacitor durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/swCapacitor.png" alt="Formulário de chaveamento do capacitor" title="Formulário de chaveamento do capacitor"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_1w39 tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Botão Estabilidade</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-reativa"></a>Potência reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-reativa" title="Direct link to heading">#</a></h4><p>Os capacitores e reatores exigem somente sua potência reativa como parâmetro, inserida em Mvar, kvar, var ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> (na base de potência do sistema). </p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/capacitor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/load"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Carga</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/inductor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Indutor »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#capacitor-no-psp-ufu" class="table-of-contents__link">Capacitor no PSP-UFU</a></li><li><a href="#formulário-de-edição-dos-capacitores" class="table-of-contents__link">Formulário de edição dos capacitores</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Capacitor</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Um dispositivo constituído essencialmente por dois eletrodos separados por um dielétrico. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=436-01-03" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="capacitor-no-psp-ufu"></a>Capacitor no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#capacitor-no-psp-ufu" title="Direct link to heading">#</a></h2><p>O elemento capacitor representa, geralmente, um banco de capacitores <em>shunt</em> no circuito do PSP-UFU.</p><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Um arranjo série de uma <a href="/PSP/docs/line">linha</a> sem as susceptâncias <em>shunt</em>, um <a href="/PSP/docs/bus">barramento</a> e um <a href="/PSP/docs/capacitor">capacitor</a> pode ser utilizado para fabricar um filtro passivo nos <a href="/PSP/docs/harmonics">estudos harmônicos</a>. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.</p></div></div><p>Os capacitores e reatores exigem somente sua potência reativa como parâmetro. Esses elementos passivos são somente inseridos na matriz admitância cuja impedância é calculada a partir de sua potência e tensão nominais.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-dos-capacitores"></a>Formulário de edição dos capacitores<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-capacitores" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos capacitores:</p><div><center><img src="/PSP/images/capacitorForm.png" alt="Formulário dos capacitores no PSP-UFU" title="Formulário dos capacitores no PSP-UFU"></center></div><p>Além do único contexto geral, pode ser observado o botão &quot;Estabilidade&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do capacitor durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/swCapacitor.png" alt="Formulário de chaveamento do capacitor" title="Formulário de chaveamento do capacitor"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_1w39 tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Botão Estabilidade</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-reativa"></a>Potência reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-reativa" title="Direct link to heading">#</a></h4><p>Os capacitores e reatores exigem somente sua potência reativa como parâmetro, inserida em Mvar, kvar, var ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> (na base de potência do sistema). </p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/capacitor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/load"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Carga</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/inductor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Indutor »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#capacitor-no-psp-ufu" class="table-of-contents__link">Capacitor no PSP-UFU</a></li><li><a href="#formulário-de-edição-dos-capacitores" class="table-of-contents__link">Formulário de edição dos capacitores</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Constante</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>As constantes são valores numéricos reais que permanecem inalteradas em todo o período de simulação. Esses elementos possuem somente um nó de saída, o qual poderá ser conectado a qualquer outro nó de entrada dos elementos de controle.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Esse elemento pode, por exemplo, ser utilizado para definir valores alvos ou deslocamentos de sinal.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/const.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/rateLimiter"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Limitador de taxa</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/gain"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Ganho »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Editor de Controle</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Os controles das <a href="/PSP/docs/syncGenerator">máquinas síncronas</a> são criados, modificados, importados e exportados em um editor distinto dos elementos de potência, apresentado na figura abaixo.</p><div><center><img src="/PSP/images/controlEditor.png" alt="Editor de elementos de controle do PSP-UFU" title="Editor de elementos de controle do PSP-UFU"></center></div><p>O acesso ao editor é realizado por meio de dois botões presentes no <a href="/PSP/docs/syncGenerator#formul%C3%A1rio-de-edi%C3%A7%C3%A3o-dos-geradores-s%C3%ADncronos">formulário de edição dos dados de estabilidade dos geradores síncronos</a>:</p><ul><li><a href="/PSP/docs/syncGenerator#utilizar-avr-e-regulador-de-velocidade">Editar AVR</a></li><li><a href="/PSP/docs/syncGenerator#utilizar-avr-e-regulador-de-velocidade">Editar regulador de velocidade</a></li></ul><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>No PSP-UFU a opção de editar o <strong>AVR</strong> engloba mais que somente o controle de tensão da máquina. Nele <strong>deve</strong> ser inserida a malha de controle da máquina assim como a <strong>excitatriz da máquina síncrona</strong>. Outras estratégias de controle (opcionais), como PSS (<em>Power System Stabilizer</em>) e/ou controles de sobre e sub excitação, são também implementadas em conjunto (como apresentado na figura anterior).</p></div></div><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Assim como no AVR, o <strong>Regulador de Velocidade</strong> engloba mais que a regulação primária da máquina. Nessa opção <strong>deve</strong> ser inserida ao menos a malha de controle da regulação primária de velocidade, assim como o <strong>modelo da turbina</strong>. Estratégias opcionais de controle da velocidade também são inseridas nessa opção.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="elementos-de-controle"></a>Elementos de Controle<a aria-hidden="true" tabindex="-1" class="hash-link" href="#elementos-de-controle" title="Direct link to heading">#</a></h2><p>O acesso aos elementos de controle é realizado em uma janela (removível e encaixável) por meio de ícones relacionados.</p><p>Uma vez que o usuário clicar no ícone desejado, o elemento de controle acompanhará o ponteiro do mouse até ser efetivamente inserido na posição desejada ao clicar novamente na área de trabalho. Os elementos são então conectados por “linhas de conexão” inseridas ao clicar nos nós dos componentes previamente adicionados, permitindo a construção da rede de controle genérica.</p><p>As ferramentas de manipulação e navegação, como arrastar, mover e excluir são <a href="/PSP/docs/cadTools">herdadas</a> do <a href="/PSP/docs/powerEditor">editor de elementos de potência</a>, possuindo comportamento idêntico. A <strong>edição dos dados</strong> dos componentes inseridos também é realizada com <strong>duplo clique</strong> sobre o elemento inserido, exibindo um formulário de edição de dados.</p><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/timelapseControlEditor.mp4" type="video/mp4"><source src="/PSP/videos/timelapseControlEditor.webm" type="video/webm"></video><p>Os seguintes blocos de controle estão presentes no PSP-UFU:</p><ul><li><a href="/PSP/docs/io">Entrada e Saída</a></li><li><a href="/PSP/docs/transferFunction">Função Transferência</a></li><li>Matemática<ul><li><a href="/PSP/docs/sum">Somador</a></li><li><a href="/PSP/docs/multiplier">Multiplicador</a></li><li><a href="/PSP/docs/divider">Divisor</a></li><li><a href="/PSP/docs/exponential">Exponencial</a></li></ul></li><li>Limitadores<ul><li><a href="/PSP/docs/limiter">Limitador absoluto</a></li><li><a href="/PSP/docs/rateLimiter">Limitador de taxa</a></li></ul></li><li>Constantes<ul><li><a href="/PSP/docs/const">Constante</a></li><li><a href="/PSP/docs/gain">Ganho</a></li></ul></li><li><a href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="inicialização-do-sistema-de-controle"></a>Inicialização do sistema de controle<a aria-hidden="true" tabindex="-1" class="hash-link" href="#inicialização-do-sistema-de-controle" title="Direct link to heading">#</a></h2><p>Caso as entradas do sistema de controle apresentem valores diferentes de zero ou a primeira operação entre elas não resulte em uma saída nula, o sistema necessita de inicialização, de forma a adequar os valores de entradas e saída dos blocos elementares e dos vetores de estado das <a href="/PSP/docs/transferFunction">funções transferências</a> presentes. Tal procedimento é realizado por meio da solução de toda rede de controle até que se obtenha sua convergência, ou seja, a diferença absoluta entre as mesmas saídas de uma solução anterior e uma atual deve ser nula ou muito próxima de zero.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>info</h5></div><div class="admonition-content"><p>O processo de <strong>inicialização é realizada automaticamente</strong> pelo PSP-UFU.</p><p>Uma vez que a inicialização é imposta pelas <a href="/PSP/docs/io">entradas</a> do controle, erros de convergência podem ocorrer devido à má parametrização dos elementos dos sistemas de <strong>potência e controle</strong>.</p></div></div><p>Para otimizar e melhorar a estabilidade do processo de inicialização utilizou-se um passo de integração variável dentro de limites, de forma que o passo aumenta em condições de diferenças menores entre as soluções do sistema de controle e diminui caso essa diferença se torne elevada. A implementação dessa abordagem reduziu significativamente o encerramento do processo com erro causado pela instabilidade numérica, além de acelerar a inicialização.</p><p>O fluxograma abaixo evidencia o processo de inicialização implementado no PSP-UFU:</p><div><center><img src="/PSP/images/controlInit.png" alt="Estrutura da inicialização do sistema de controle" title="Estrutura da inicialização do sistema de controle"></center></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="teste-do-diagrama-de-controle"></a>Teste do diagrama de controle<a aria-hidden="true" tabindex="-1" class="hash-link" href="#teste-do-diagrama-de-controle" title="Direct link to heading">#</a></h2><p>Na parte inferior esquerda do Editor de Controle está presente o botão &quot;<strong>Testar Sistema...</strong>&quot;. O botão acessa o formulário de teste de controles, como é indicado na figura abaixo:</p><div><center><img src="/PSP/images/testControl.png" alt="Formulário de teste de controles" title="Formulário de teste de controles"></center></div><p>Nesse formulário é possível inserir o comportamento de <strong>todas as entradas do diagrama</strong>:</p><ul><li><strong>Tipo de entrada</strong>: Define um dos tipos de entradas possíveis no PSP-UFU: &quot;Passo (<em>Step</em>)&quot;, Rampa (<em>Ramp</em>) ou Quadrática (<em>Quadratic</em>);</li><li><strong>Tempo de início (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>t</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">t_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76508em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>)</strong>: Define o tempo de início na simulação da entrada definida. As entradas iniciais são sempre definidas como zero e assumem valores diferentes após o tempo de início;</li><li><strong>Inclinação (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>α</mi></mrow><annotation encoding="application/x-tex">\alpha</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.0037em">α</span></span></span></span></span>)</strong>: Valor relacionado ao tipo de entrada:<ul><li>Para entrada do tipo &quot;Passo&quot; - O valor da inclinação define o valor final do passo:<div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>&lt;</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>0</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>≥</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>α</mi></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} \text{Se~} t &lt; t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em"><span style="top:-3.69em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.0037em">α</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div></li><li>Para entrada do tipo &quot;Rampa&quot; - define o coeficiente de inclinação da reta:<div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>&lt;</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>0</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>≥</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>α</mi><mo>×</mo><mi>t</mi></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} \text{Se~} t &lt; t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \times t \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em"><span style="top:-3.69em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.0037em">α</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div></li><li>Para entrada do tipo &quot;Quadrática&quot; - define o coeficiente de crescimento da curva:<div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>&lt;</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>0</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>≥</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>α</mi><mo>×</mo><msup><mi>t</mi><mn>2</mn></msup></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} \text{Se~} t &lt; t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \times t^2 \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em"><span style="top:-3.69em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.0037em">α</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div></li></ul></li><li><strong>Passo de integração (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em"></span><span class="mord mathdefault">h</span></span></span></span></span>)</strong>: Passo do método de integração Trapezoidal Implícito;</li><li><strong>Tempo de simulação (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>t</mi><mi>f</mi></msub></mrow><annotation encoding="application/x-tex">t_f</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9011879999999999em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>)</strong>: Tempo total de simulação.</li></ul><p>Após a simulação os resultados são exibidos no <a href="/PSP/docs/graphViewer">visualizador de gráficos</a>.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>A mesma parametrização de entrada é aplicada em todos os blocos de <a href="/PSP/docs/io">entrada</a> do sistema.</p></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>É possível aplicar <strong>várias entradas distintas</strong> (inclusive com condicionais!) utilizando o bloco de <a href="/PSP/docs/mathExpression">expressão matemática</a>.</p></div></div><p>Utilizando o bloco de <a href="/PSP/docs/mathExpression">expressão matemática</a> é possível inserir entradas complexas, como por exemplo testar o diagrama de blocos (AVR DC1C + PSS1A - <a href="https://doi.org/10.1109/IEEESTD.2016.7553421" target="_blank" rel="noopener noreferrer">IEEE Std. 421.5-2016</a>) da figura abaixo:</p><div><center><img src="/PSP/images/exControl.svg" alt="Sistema de controle sob teste" title="Sistema de controle sob teste"></center></div><div><center><img src="/PSP/images/compControl.svg" alt="Comparação do sistema de controle sob teste" title="Comparação do sistema de controle sob teste"></center></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/controlEditor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/indMotor"><div 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class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Editor de Controle</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Os controles das <a href="/PSP/docs/syncGenerator">máquinas síncronas</a> são criados, modificados, importados e exportados em um editor distinto dos elementos de potência, apresentado na figura abaixo.</p><div><center><img src="/PSP/images/controlEditor.png" alt="Editor de elementos de controle do PSP-UFU" title="Editor de elementos de controle do PSP-UFU"></center></div><p>O acesso ao editor é realizado por meio de dois botões presentes no <a href="/PSP/docs/syncGenerator#formul%C3%A1rio-de-edi%C3%A7%C3%A3o-dos-geradores-s%C3%ADncronos">formulário de edição dos dados de estabilidade dos geradores síncronos</a>:</p><ul><li><a href="/PSP/docs/syncGenerator#utilizar-avr-e-regulador-de-velocidade">Editar AVR</a></li><li><a href="/PSP/docs/syncGenerator#utilizar-avr-e-regulador-de-velocidade">Editar regulador de velocidade</a></li></ul><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>No PSP-UFU a opção de editar o <strong>AVR</strong> engloba mais que somente o controle de tensão da máquina. Nele <strong>deve</strong> ser inserida a malha de controle da máquina assim como a <strong>excitatriz da máquina síncrona</strong>. Outras estratégias de controle (opcionais), como PSS (<em>Power System Stabilizer</em>) e/ou controles de sobre e sub excitação, são também implementadas em conjunto (como apresentado na figura anterior).</p></div></div><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Assim como no AVR, o <strong>Regulador de Velocidade</strong> engloba mais que a regulação primária da máquina. Nessa opção <strong>deve</strong> ser inserida ao menos a malha de controle da regulação primária de velocidade, assim como o <strong>modelo da turbina</strong>. Estratégias opcionais de controle da velocidade também são inseridas nessa opção.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="elementos-de-controle"></a>Elementos de Controle<a aria-hidden="true" tabindex="-1" class="hash-link" href="#elementos-de-controle" title="Direct link to heading">#</a></h2><p>O acesso aos elementos de controle é realizado em uma janela (removível e encaixável) por meio de ícones relacionados.</p><p>Uma vez que o usuário clicar no ícone desejado, o elemento de controle acompanhará o ponteiro do mouse até ser efetivamente inserido na posição desejada ao clicar novamente na área de trabalho. Os elementos são então conectados por “linhas de conexão” inseridas ao clicar nos nós dos componentes previamente adicionados, permitindo a construção da rede de controle genérica.</p><p>As ferramentas de manipulação e navegação, como arrastar, mover e excluir são <a href="/PSP/docs/cadTools">herdadas</a> do <a href="/PSP/docs/powerEditor">editor de elementos de potência</a>, possuindo comportamento idêntico. A <strong>edição dos dados</strong> dos componentes inseridos também é realizada com <strong>duplo clique</strong> sobre o elemento inserido, exibindo um formulário de edição de dados.</p><video autoplay="" loop="" muted="" playsinline="" controls=""><source src="/PSP/videos/timelapseControlEditor.mp4" type="video/mp4"><source src="/PSP/videos/timelapseControlEditor.webm" type="video/webm"></video><p>Os seguintes blocos de controle estão presentes no PSP-UFU:</p><ul><li><a href="/PSP/docs/io">Entrada e Saída</a></li><li><a href="/PSP/docs/transferFunction">Função Transferência</a></li><li>Matemática<ul><li><a href="/PSP/docs/sum">Somador</a></li><li><a href="/PSP/docs/multiplier">Multiplicador</a></li><li><a href="/PSP/docs/divider">Divisor</a></li><li><a href="/PSP/docs/exponential">Exponencial</a></li></ul></li><li>Limitadores<ul><li><a href="/PSP/docs/limiter">Limitador absoluto</a></li><li><a href="/PSP/docs/rateLimiter">Limitador de taxa</a></li></ul></li><li>Constantes<ul><li><a href="/PSP/docs/const">Constante</a></li><li><a href="/PSP/docs/gain">Ganho</a></li></ul></li><li><a href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="inicialização-do-sistema-de-controle"></a>Inicialização do sistema de controle<a aria-hidden="true" tabindex="-1" class="hash-link" href="#inicialização-do-sistema-de-controle" title="Direct link to heading">#</a></h2><p>Caso as entradas do sistema de controle apresentem valores diferentes de zero ou a primeira operação entre elas não resulte em uma saída nula, o sistema necessita de inicialização, de forma a adequar os valores de entradas e saída dos blocos elementares e dos vetores de estado das <a href="/PSP/docs/transferFunction">funções transferências</a> presentes. Tal procedimento é realizado por meio da solução de toda rede de controle até que se obtenha sua convergência, ou seja, a diferença absoluta entre as mesmas saídas de uma solução anterior e uma atual deve ser nula ou muito próxima de zero.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>info</h5></div><div class="admonition-content"><p>O processo de <strong>inicialização é realizada automaticamente</strong> pelo PSP-UFU.</p><p>Uma vez que a inicialização é imposta pelas <a href="/PSP/docs/io">entradas</a> do controle, erros de convergência podem ocorrer devido à má parametrização dos elementos dos sistemas de <strong>potência e controle</strong>.</p></div></div><p>Para otimizar e melhorar a estabilidade do processo de inicialização utilizou-se um passo de integração variável dentro de limites, de forma que o passo aumenta em condições de diferenças menores entre as soluções do sistema de controle e diminui caso essa diferença se torne elevada. A implementação dessa abordagem reduziu significativamente o encerramento do processo com erro causado pela instabilidade numérica, além de acelerar a inicialização.</p><p>O fluxograma abaixo evidencia o processo de inicialização implementado no PSP-UFU:</p><div><center><img src="/PSP/images/controlInit.png" alt="Estrutura da inicialização do sistema de controle" title="Estrutura da inicialização do sistema de controle"></center></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="teste-do-diagrama-de-controle"></a>Teste do diagrama de controle<a aria-hidden="true" tabindex="-1" class="hash-link" href="#teste-do-diagrama-de-controle" title="Direct link to heading">#</a></h2><p>Na parte inferior esquerda do Editor de Controle está presente o botão &quot;<strong>Testar Sistema...</strong>&quot;. O botão acessa o formulário de teste de controles, como é indicado na figura abaixo:</p><div><center><img src="/PSP/images/testControl.png" alt="Formulário de teste de controles" title="Formulário de teste de controles"></center></div><p>Nesse formulário é possível inserir o comportamento de <strong>todas as entradas do diagrama</strong>:</p><ul><li><strong>Tipo de entrada</strong>: Define um dos tipos de entradas possíveis no PSP-UFU: &quot;Passo (<em>Step</em>)&quot;, Rampa (<em>Ramp</em>) ou Quadrática (<em>Quadratic</em>);</li><li><strong>Tempo de início (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>t</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">t_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76508em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>)</strong>: Define o tempo de início na simulação da entrada definida. As entradas iniciais são sempre definidas como zero e assumem valores diferentes após o tempo de início;</li><li><strong>Inclinação (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>α</mi></mrow><annotation encoding="application/x-tex">\alpha</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.0037em">α</span></span></span></span></span>)</strong>: Valor relacionado ao tipo de entrada:<ul><li>Para entrada do tipo &quot;Passo&quot; - O valor da inclinação define o valor final do passo:<div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>&lt;</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>0</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>≥</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>α</mi></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} \text{Se~} t &lt; t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em"><span style="top:-3.69em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.0037em">α</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div></li><li>Para entrada do tipo &quot;Rampa&quot; - define o coeficiente de inclinação da reta:<div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>&lt;</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>0</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>≥</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>α</mi><mo>×</mo><mi>t</mi></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} \text{Se~} t &lt; t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \times t \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em"><span style="top:-3.69em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.0037em">α</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div></li><li>Para entrada do tipo &quot;Quadrática&quot; - define o coeficiente de crescimento da curva:<div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>&lt;</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>0</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>Se </mtext><mi>t</mi><mo>≥</mo><msub><mi>t</mi><mi>i</mi></msub><mo>→</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>α</mi><mo>×</mo><msup><mi>t</mi><mn>2</mn></msup></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} \text{Se~} t &lt; t_i \rightarrow f(t) = 0,0\\ \text{Se~} t \ge t_i \rightarrow f(t) = \alpha \times t^2 \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em"><span style="top:-3.69em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">Se</span><span class="mord nobreak"> </span></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.0037em">α</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div></li></ul></li><li><strong>Passo de integração (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em"></span><span class="mord mathdefault">h</span></span></span></span></span>)</strong>: Passo do método de integração Trapezoidal Implícito;</li><li><strong>Tempo de simulação (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>t</mi><mi>f</mi></msub></mrow><annotation encoding="application/x-tex">t_f</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9011879999999999em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>)</strong>: Tempo total de simulação.</li></ul><p>Após a simulação os resultados são exibidos no <a href="/PSP/docs/graphViewer">visualizador de gráficos</a>.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>A mesma parametrização de entrada é aplicada em todos os blocos de <a href="/PSP/docs/io">entrada</a> do sistema.</p></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>É possível aplicar <strong>várias entradas distintas</strong> (inclusive com condicionais!) utilizando o bloco de <a href="/PSP/docs/mathExpression">expressão matemática</a>.</p></div></div><p>Utilizando o bloco de <a href="/PSP/docs/mathExpression">expressão matemática</a> é possível inserir entradas complexas, como por exemplo testar o diagrama de blocos (AVR DC1C + PSS1A - <a href="https://doi.org/10.1109/IEEESTD.2016.7553421" target="_blank" rel="noopener noreferrer">IEEE Std. 421.5-2016</a>) da figura abaixo:</p><div><center><img src="/PSP/images/exControl.svg" alt="Sistema de controle sob teste" title="Sistema de controle sob teste"></center></div><div><center><img src="/PSP/images/compControl.svg" alt="Comparação do sistema de controle sob teste" title="Comparação do sistema de controle sob teste"></center></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/controlEditor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/indMotor"><div 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class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Divisor</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Esse elemento é bastante simples e cumpre com a função matemáticas de seu nome.</p><p>Possui duas entradas de valores reais e sua saída é computada na sequência do nó superior pelo inferior, ou seja, a saída será o valor presente no nó 1 dividido pelo nó 2.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Nós não conectados no divisor são considerados como valor nulo. Caso a divisão possua numerador zero, o valor da saída é definida como sendo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><msup><mn>0</mn><mn>15</mn></msup></mrow><annotation encoding="application/x-tex">10^{15}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141079999999999em;vertical-align:0em"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mord mtight">5</span></span></span></span></span></span></span></span></span></span></span></span></span>.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/divider.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/multiplier"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Multiplicador</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/exponential"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Exponencial »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Divisor</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Esse elemento é bastante simples e cumpre com a função matemáticas de seu nome.</p><p>Possui duas entradas de valores reais e sua saída é computada na sequência do nó superior pelo inferior, ou seja, a saída será o valor presente no nó 1 dividido pelo nó 2.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Nós não conectados no divisor são considerados como valor nulo. Caso a divisão possua numerador zero, o valor da saída é definida como sendo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><msup><mn>0</mn><mn>15</mn></msup></mrow><annotation encoding="application/x-tex">10^{15}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141079999999999em;vertical-align:0em"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mord mtight">5</span></span></span></span></span></span></span></span></span></span></span></span></span>.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/divider.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/multiplier"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Multiplicador</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/exponential"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Exponencial »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Exponencial</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>A função exponencial dos elementos de controle realiza essa operação com uma entrada real, obedecendo a expressão:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mi>n</mi></msub><mo>=</mo><mi mathvariant="bold">A</mi><msup><mi>e</mi><mrow><mi mathvariant="bold">B</mi><msub><mi>u</mi><mi>n</mi></msub></mrow></msup></mrow><annotation encoding="application/x-tex">y_n = \bold{A} e^{\bold{B} u_n}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.8932769999999999em;vertical-align:0em"></span><span class="mord"><span class="mord mathbf">A</span></span><span class="mord"><span class="mord mathdefault">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8932769999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathbf mtight">B</span></span><span class="mord mtight"><span class="mord mathdefault mtight">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.16454285714285719em"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">u_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">y_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	é a entrada e a saída do bloco exponencial, respectivamente;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold">A</mi></mrow><annotation encoding="application/x-tex">\bold{A}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68611em;vertical-align:0em"></span><span class="mord"><span class="mord mathbf">A</span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold">B</mi></mrow><annotation encoding="application/x-tex">\bold{B}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68611em;vertical-align:0em"></span><span class="mord"><span class="mord mathbf">B</span></span></span></span></span></span>	são constantes definidas pelo usuário.</li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-de-dados-do-bloco-exponencial"></a>Formulário de edição de dados do bloco Exponencial<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-de-dados-do-bloco-exponencial" title="Direct link to heading">#</a></h2><p>A figura abaixo apresenta o formulário de edição de dados do bloco exponencial.</p><div><center><img src="/PSP/images/expForm.png" alt="Formulário de edição de dados do bloco exponencial no PSP-UFU" title="Formulário de edição de dados do bloco exponencial no PSP-UFU"></center></div><p>Esse bloco não linear é definido pelas constantes A e B, inseridas pelo usuário.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Tais blocos são úteis na representação de não linearidades, como, por exemplo, modelagem da saturação de máquinas de corrente contínuas presentes em alguns reguladores automáticos de tensão.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/exponential.md" target="_blank" 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class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Exponencial</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>A função exponencial dos elementos de controle realiza essa operação com uma entrada real, obedecendo a expressão:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mi>n</mi></msub><mo>=</mo><mi mathvariant="bold">A</mi><msup><mi>e</mi><mrow><mi mathvariant="bold">B</mi><msub><mi>u</mi><mi>n</mi></msub></mrow></msup></mrow><annotation encoding="application/x-tex">y_n = \bold{A} e^{\bold{B} u_n}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.8932769999999999em;vertical-align:0em"></span><span class="mord"><span class="mord mathbf">A</span></span><span class="mord"><span class="mord mathdefault">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8932769999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathbf mtight">B</span></span><span class="mord mtight"><span class="mord mathdefault mtight">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.16454285714285719em"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">u_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">y_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	é a entrada e a saída do bloco exponencial, respectivamente;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold">A</mi></mrow><annotation encoding="application/x-tex">\bold{A}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68611em;vertical-align:0em"></span><span class="mord"><span class="mord mathbf">A</span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold">B</mi></mrow><annotation encoding="application/x-tex">\bold{B}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68611em;vertical-align:0em"></span><span class="mord"><span class="mord mathbf">B</span></span></span></span></span></span>	são constantes definidas pelo usuário.</li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-de-dados-do-bloco-exponencial"></a>Formulário de edição de dados do bloco Exponencial<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-de-dados-do-bloco-exponencial" title="Direct link to heading">#</a></h2><p>A figura abaixo apresenta o formulário de edição de dados do bloco exponencial.</p><div><center><img src="/PSP/images/expForm.png" alt="Formulário de edição de dados do bloco exponencial no PSP-UFU" title="Formulário de edição de dados do bloco exponencial no PSP-UFU"></center></div><p>Esse bloco não linear é definido pelas constantes A e B, inseridas pelo usuário.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Tais blocos são úteis na representação de não linearidades, como, por exemplo, modelagem da saturação de máquinas de corrente contínuas presentes em alguns reguladores automáticos de tensão.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/exponential.md" target="_blank" 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class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Curto-Circuito</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>O principal objetivo da análise de curto-circuito é o cálculo das correntes e tensões de falta para especificação de disjuntores, transformadores de corrente e a parametrização de relés de proteção. De 70 a 80% das faltas em linhas de transmissão são entre uma fase e terra, as quais ocorrem devido ao centelhamento de apenas uma fase da linha para a torre e então para a terra.O menor número de faltas, cerca de 5%, envolve todas as três fases, chamadas de faltas trifásicas. Os outros tipos de faltas envolvem duas fases e duas fases e a terra.</p><p>Todas essas falhas, exceto a trifásica, são assimétricas e causam desequilíbrio entre as fases.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="cálculo-de-curto-circuito-no-psp-ufu"></a>Cálculo de Curto-Circuito no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#cálculo-de-curto-circuito-no-psp-ufu" title="Direct link to heading">#</a></h2><p>O primeiro estágio do cálculo de curto-circuito é a determinação das tensões pré-falta, das potências de geração e cargas do sistema. Esses dados são obtidos por meio do estudo de <a href="/PSP/docs/powerFlow">fluxo de carga</a>.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Atualmente, o PSP-UFU fornece resultado para os seguintes tipos de falta:</p><ul><li>Falta Trifásica (3F-T);</li><li>Falta Fase-Terra (F-T);</li><li>Falta Fase-Fase (F-F);</li><li>Falta Fase-Fase-Terra (F-F-T).</li></ul></div></div><p>Os modelos dos elementos elétricos que constituem um sistema de potência para o estudo de curto-circuito são semelhantes aos do fluxo de carga, apresentando algumas divergências para as faltas desbalanceadas (F-T, F-F e F-F-T).</p><p>As faltas que ocorrem com maior frequência em sistemas de potência são assimétricas. Como qualquer falta assimétrica provoca fluxo de corrente desequilibrada é necessário empregar o método das componentes simétricas. Esse método permite o estudo de sistemas balanceados em conjunto cargas desbalanceadas.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="execução-do-cálculo-de-curto-circuito-no-psp-ufu"></a>Execução do cálculo de curto-circuito no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#execução-do-cálculo-de-curto-circuito-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Existem duas formas de se calcular o curto-circuito no PSP-UFU:</p><ul><li><strong>Falta</strong>: Calcula a falta inserida nas <a href="/PSP/docs/bus">barras</a>. Nesse tipo de cálculo é possível calcular faltas <em>shunt</em> nos <a href="/PSP/docs/bus">barramentos</a> balanceadas e desbalanceadas.</li><li><strong>Nível de curto-circuito</strong>: Calcula o nível de curto-circuito (falta trifásica) em todos <a href="/PSP/docs/bus">barramentos</a> do sistema.</li></ul><p>Após a construção do diagrama unifilar no <a href="/PSP/docs/powerEditor">editor de potência</a>, a execução do cálculo de curto-circuito é realizada no <a href="/PSP/docs/mainScreen#menu-ribbon">menu Simulação</a> clicando no botão <strong>Falta</strong>. Para calcular o nível de curto-circuito (falta trifásica) em todos <a href="/PSP/docs/bus">barramentos</a> do sistema, basta clicar no botão <strong>Nível de curto-circuito</strong>.</p><div><center><img src="/PSP/images/menuSimulationFaulta.svg" alt="Execução dos cálculos de curto-circuito" title="Execução dos cálculos de curto-circuito"></center></div><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>É possível calcular as faltas sem a execução do <a href="/PSP/docs/powerFlow">fluxo de carga</a>, porém <strong>não é recomendável</strong>, visto que os valores das correntes de falta são significativamente alteradas.</p></div></div><p><strong>Outra possibilidade</strong> é a execução por meio do cálculo contínuo, também presente no <a href="/PSP/docs/mainScreen#menu-ribbon">menu Simulação</a> e seu acionamento é realizado co clicar no botão <strong>Habilitar solução</strong>. Com essa opção, os cálculos estáticos selecionados nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a> são automaticamente realizados ao modificar quaisquer parâmetros da rede, como dados elétricos e acionamento dos disjuntores dos elementos (remoção ou inserção).</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Os cálculos de curtos-circuitos não são habilitados por padrão no cálculo contínuo e devem ser inseridos nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a>.</p></div></div><p>Os resultados do cálculo de curto-circuito são exibidos nos <a href="/PSP/docs/text">elementos de texto vinculado</a>, ao posicionar o mouse sobre os barramentos e em <a href="/PSP/docs/tabularReport">relatórios tabulares</a>.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="erros-comuns-na-execução-do-cálculo-de-curto-circuito"></a>Erros comuns na execução do cálculo de curto-circuito<a aria-hidden="true" tabindex="-1" class="hash-link" href="#erros-comuns-na-execução-do-cálculo-de-curto-circuito" title="Direct link to heading">#</a></h3><p>A seguir são apresentados os erros mais comuns relacionados ao calculo de curto-circuito.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="a-seguinte-mensagem-de-erro-é-exibida-falha-ao-inverter-a-matriz-admitância-de-sequência-zero"></a>A seguinte mensagem de erro é exibida: &quot;Falha ao inverter a matriz admitância de sequência zero&quot;<a aria-hidden="true" tabindex="-1" class="hash-link" href="#a-seguinte-mensagem-de-erro-é-exibida-falha-ao-inverter-a-matriz-admitância-de-sequência-zero" title="Direct link to heading">#</a></h4><ul><li><strong>Impossibilidade de circulação da corrente de sequência zero</strong>. Caso o gerador não seja aterrado, não circulará corrente de sequência zero por ele. Nesse caso, dependendo da conexão do transformador próximo ao gerador sem aterramento, a matriz admitância de sequência zero é singular. Para contornar esse problema escolha uma das duas soluções abaixo:<ul><li>Marque a opção &quot;Neutro aterrado&quot; e insira um alto valor de reatância de aterramento (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi><mn>9999</mn><mtext> </mtext><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">j9999~p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mspace nobreak"> </span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, por exemplo);</li><li>Ou, na barra do gerador, insira um reator de baixo valor de potência reativa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>0</mn><mtext> </mtext><mi>v</mi><mi>a</mi><mi>r</mi></mrow><annotation encoding="application/x-tex">1{,}0~var</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span><span class="mspace nobreak"> </span><span class="mord mathdefault" style="margin-right:0.03588em">v</span><span class="mord mathdefault">a</span><span class="mord mathdefault" style="margin-right:0.02778em">r</span></span></span></span></span>, por exemplo).</li></ul></li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="o-cálculo-de-curto-circuito"></a>O cálculo de curto-circuito<a aria-hidden="true" tabindex="-1" class="hash-link" href="#o-cálculo-de-curto-circuito" title="Direct link to heading">#</a></h2><p>Como já foi apresentado anteriormente, as faltas que ocorrem com maior frequência em sistemas de potência são assimétricas. Como qualquer falta assimétrica provoca fluxo de corrente desequilibrada é necessário empregar o método das componentes simétricas. Esse método permite o estudo de sistemas balanceados com cargas desbalanceadas.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="método-das-componentes-simétricas"></a>Método das componentes simétricas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#método-das-componentes-simétricas" title="Direct link to heading">#</a></h3><p>Esse método proposto por C. L. Fortescue, permite definir um sistema de n fasores desbalanceados em n – 1 sistemas de n fases balanceados e um sistema de fase zero. O sistema de fase zero é definido por todas as fases de mesmo módulo e ângulo.
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class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Curto-Circuito</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>O principal objetivo da análise de curto-circuito é o cálculo das correntes e tensões de falta para especificação de disjuntores, transformadores de corrente e a parametrização de relés de proteção. De 70 a 80% das faltas em linhas de transmissão são entre uma fase e terra, as quais ocorrem devido ao centelhamento de apenas uma fase da linha para a torre e então para a terra.O menor número de faltas, cerca de 5%, envolve todas as três fases, chamadas de faltas trifásicas. Os outros tipos de faltas envolvem duas fases e duas fases e a terra.</p><p>Todas essas falhas, exceto a trifásica, são assimétricas e causam desequilíbrio entre as fases.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="cálculo-de-curto-circuito-no-psp-ufu"></a>Cálculo de Curto-Circuito no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#cálculo-de-curto-circuito-no-psp-ufu" title="Direct link to heading">#</a></h2><p>O primeiro estágio do cálculo de curto-circuito é a determinação das tensões pré-falta, das potências de geração e cargas do sistema. Esses dados são obtidos por meio do estudo de <a href="/PSP/docs/powerFlow">fluxo de carga</a>.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Atualmente, o PSP-UFU fornece resultado para os seguintes tipos de falta:</p><ul><li>Falta Trifásica (3F-T);</li><li>Falta Fase-Terra (F-T);</li><li>Falta Fase-Fase (F-F);</li><li>Falta Fase-Fase-Terra (F-F-T).</li></ul></div></div><p>Os modelos dos elementos elétricos que constituem um sistema de potência para o estudo de curto-circuito são semelhantes aos do fluxo de carga, apresentando algumas divergências para as faltas desbalanceadas (F-T, F-F e F-F-T).</p><p>As faltas que ocorrem com maior frequência em sistemas de potência são assimétricas. Como qualquer falta assimétrica provoca fluxo de corrente desequilibrada é necessário empregar o método das componentes simétricas. Esse método permite o estudo de sistemas balanceados em conjunto cargas desbalanceadas.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="execução-do-cálculo-de-curto-circuito-no-psp-ufu"></a>Execução do cálculo de curto-circuito no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#execução-do-cálculo-de-curto-circuito-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Existem duas formas de se calcular o curto-circuito no PSP-UFU:</p><ul><li><strong>Falta</strong>: Calcula a falta inserida nas <a href="/PSP/docs/bus">barras</a>. Nesse tipo de cálculo é possível calcular faltas <em>shunt</em> nos <a href="/PSP/docs/bus">barramentos</a> balanceadas e desbalanceadas.</li><li><strong>Nível de curto-circuito</strong>: Calcula o nível de curto-circuito (falta trifásica) em todos <a href="/PSP/docs/bus">barramentos</a> do sistema.</li></ul><p>Após a construção do diagrama unifilar no <a href="/PSP/docs/powerEditor">editor de potência</a>, a execução do cálculo de curto-circuito é realizada no <a href="/PSP/docs/mainScreen#menu-ribbon">menu Simulação</a> clicando no botão <strong>Falta</strong>. Para calcular o nível de curto-circuito (falta trifásica) em todos <a href="/PSP/docs/bus">barramentos</a> do sistema, basta clicar no botão <strong>Nível de curto-circuito</strong>.</p><div><center><img src="/PSP/images/menuSimulationFaulta.svg" alt="Execução dos cálculos de curto-circuito" title="Execução dos cálculos de curto-circuito"></center></div><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>É possível calcular as faltas sem a execução do <a href="/PSP/docs/powerFlow">fluxo de carga</a>, porém <strong>não é recomendável</strong>, visto que os valores das correntes de falta são significativamente alteradas.</p></div></div><p><strong>Outra possibilidade</strong> é a execução por meio do cálculo contínuo, também presente no <a href="/PSP/docs/mainScreen#menu-ribbon">menu Simulação</a> e seu acionamento é realizado co clicar no botão <strong>Habilitar solução</strong>. Com essa opção, os cálculos estáticos selecionados nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a> são automaticamente realizados ao modificar quaisquer parâmetros da rede, como dados elétricos e acionamento dos disjuntores dos elementos (remoção ou inserção).</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Os cálculos de curtos-circuitos não são habilitados por padrão no cálculo contínuo e devem ser inseridos nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a>.</p></div></div><p>Os resultados do cálculo de curto-circuito são exibidos nos <a href="/PSP/docs/text">elementos de texto vinculado</a>, ao posicionar o mouse sobre os barramentos e em <a href="/PSP/docs/tabularReport">relatórios tabulares</a>.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="erros-comuns-na-execução-do-cálculo-de-curto-circuito"></a>Erros comuns na execução do cálculo de curto-circuito<a aria-hidden="true" tabindex="-1" class="hash-link" href="#erros-comuns-na-execução-do-cálculo-de-curto-circuito" title="Direct link to heading">#</a></h3><p>A seguir são apresentados os erros mais comuns relacionados ao calculo de curto-circuito.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="a-seguinte-mensagem-de-erro-é-exibida-falha-ao-inverter-a-matriz-admitância-de-sequência-zero"></a>A seguinte mensagem de erro é exibida: &quot;Falha ao inverter a matriz admitância de sequência zero&quot;<a aria-hidden="true" tabindex="-1" class="hash-link" href="#a-seguinte-mensagem-de-erro-é-exibida-falha-ao-inverter-a-matriz-admitância-de-sequência-zero" title="Direct link to heading">#</a></h4><ul><li><strong>Impossibilidade de circulação da corrente de sequência zero</strong>. Caso o gerador não seja aterrado, não circulará corrente de sequência zero por ele. Nesse caso, dependendo da conexão do transformador próximo ao gerador sem aterramento, a matriz admitância de sequência zero é singular. Para contornar esse problema escolha uma das duas soluções abaixo:<ul><li>Marque a opção &quot;Neutro aterrado&quot; e insira um alto valor de reatância de aterramento (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi><mn>9999</mn><mtext> </mtext><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">j9999~p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mspace nobreak"> </span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, por exemplo);</li><li>Ou, na barra do gerador, insira um reator de baixo valor de potência reativa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>0</mn><mtext> </mtext><mi>v</mi><mi>a</mi><mi>r</mi></mrow><annotation encoding="application/x-tex">1{,}0~var</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span><span class="mspace nobreak"> </span><span class="mord mathdefault" style="margin-right:0.03588em">v</span><span class="mord mathdefault">a</span><span class="mord mathdefault" style="margin-right:0.02778em">r</span></span></span></span></span>, por exemplo).</li></ul></li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="o-cálculo-de-curto-circuito"></a>O cálculo de curto-circuito<a aria-hidden="true" tabindex="-1" class="hash-link" href="#o-cálculo-de-curto-circuito" title="Direct link to heading">#</a></h2><p>Como já foi apresentado anteriormente, as faltas que ocorrem com maior frequência em sistemas de potência são assimétricas. Como qualquer falta assimétrica provoca fluxo de corrente desequilibrada é necessário empregar o método das componentes simétricas. Esse método permite o estudo de sistemas balanceados com cargas desbalanceadas.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="método-das-componentes-simétricas"></a>Método das componentes simétricas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#método-das-componentes-simétricas" title="Direct link to heading">#</a></h3><p>Esse método proposto por C. L. Fortescue, permite definir um sistema de n fasores desbalanceados em n – 1 sistemas de n fases balanceados e um sistema de fase zero. O sistema de fase zero é definido por todas as fases de mesmo módulo e ângulo.
 Para um sistema trifásico pode-se definir três componentes de sequência:</p><ol><li>Componentes de sequência positiva, constituindo em três fasores iguais em módulo, 120º defasados entre si, e tendo a mesma sequência de fase que os fasores originais;</li><li>Componentes de sequência negativa, constituindo em três fasores iguais em módulo, 120º defasados entre si, e tendo a sequência de fase oposta à dos fasores originais.</li><li>Componentes de sequência zero, constituindo em três fasores iguais em módulo e com defasagem nula entre si.</li></ol><p>Com isso pode-se decompor as tensões de fase em componentes simétricas pelas seguintes equações:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>a</mi></msub><mo>=</mo><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>1</mn></mrow></msub><mo>+</mo><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>2</mn></mrow></msub><mo>+</mo><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>b</mi></msub><mo>=</mo><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>b</mi><mn>1</mn></mrow></msub><mo>+</mo><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>b</mi><mn>2</mn></mrow></msub><mo>+</mo><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>b</mi><mn>0</mn></mrow></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>c</mi></msub><mo>=</mo><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>+</mo><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>+</mo><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>c</mi><mn>0</mn></mrow></msub></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} \dot{V}_a = \dot{V}_{a1} + \dot{V}_{a2} + \dot{V}_{a0}\\ \dot{V}_b = \dot{V}_{b1} + \dot{V}_{b2} + \dot{V}_{b0}\\ \dot{V}_c = \dot{V}_{c1} + \dot{V}_{c2} + \dot{V}_{c0} \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.32em;vertical-align:-1.9099999999999997em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" 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class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.97em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">b</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">b</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">b</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-1.5300000000000002em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.9099999999999997em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>A figura abaixo apresenta um exemplo de componentes simétricas e sua soma para obter os fasores desequilibrados.</p><div><center><img src="/PSP/images/fortescue.svg" alt="Exemplo de componentes simétricas e sua soma para obter os fasores desequilibrados" title="Exemplo de componentes simétricas e sua soma para obter os fasores desequilibrados"></center></div><p>Para simplificar os cálculos adota-se um operador “<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>a</mi><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">\overline{a}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.63056em;vertical-align:0em"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span></span></span>”, com o intuito de indicar a rotação de um fasor. Tal operador é um número complexo de módulo unitário e ângulo de 120º:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>a</mi><mo stretchy="true">‾</mo></mover><mo>=</mo><mn>1</mn><mi mathvariant="normal">∠</mi><mn>12</mn><msup><mn>0</mn><mo lspace="0em" rspace="0em">∘</mo></msup><mo>=</mo><mn>1</mn><msup><mi>e</mi><mrow><mi>j</mi><mn>2</mn><mi>π</mi><mi mathvariant="normal">/</mi><mn>3</mn></mrow></msup><mo>=</mo><mo>−</mo><mn>0</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>5</mn><mo>+</mo><mi>j</mi><mn>0</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>866</mn></mrow><annotation encoding="application/x-tex">\overline{a} = 1 \angle 120^{\circ} = 1 e^{j2\pi/3} = -0{,}5 + j0{,}866</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.63056em;vertical-align:0em"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.724115em;vertical-align:0em"></span><span class="mord">1</span><span class="mord">∠</span><span class="mord">1</span><span class="mord">2</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.724115em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∘</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.938em;vertical-align:0em"></span><span class="mord">1</span><span class="mord"><span class="mord mathdefault">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span><span class="mord mtight">2</span><span class="mord mathdefault mtight" style="margin-right:0.03588em">π</span><span class="mord mtight">/</span><span class="mord mtight">3</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em"></span><span class="mord">−</span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">8</span><span class="mord">6</span><span class="mord">6</span></span></span></span></span></div><p>Com isso pode-se utilizar as equações (de tensão apresentadas  em conjunto com o operador “<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>a</mi><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">\overline{a}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.63056em;vertical-align:0em"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span></span></span>” para construir a seguinte equação matricial:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>a</mi></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>b</mi></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>c</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mover><mover><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msup><mover accent="true"><mi>a</mi><mo stretchy="true">‾</mo></mover><mn>2</mn></msup></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mover accent="true"><mi>a</mi><mo stretchy="true">‾</mo></mover></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mover accent="true"><mi>a</mi><mo stretchy="true">‾</mo></mover></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msup><mover accent="true"><mi>a</mi><mo stretchy="true">‾</mo></mover><mn>2</mn></msup></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo stretchy="true">⏞</mo></mover><mrow><mo fence="true">[</mo><mi mathvariant="bold">A</mi><mo fence="true">]</mo></mrow></mover><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>1</mn></mrow></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>2</mn></mrow></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">\begin{bmatrix} \dot{V}_a\\ \dot{V}_b\\ \dot{V}_c \end{bmatrix} = \overbrace{ \begin{bmatrix} 1 &amp; 1 &amp; 1\\ 1 &amp; \overline{a}^2 &amp; \overline{a}\\ 1 &amp; \overline{a} &amp; \overline{a}^2 \end{bmatrix} }^{\left[ \bold{A} \right]} \begin{bmatrix} \dot{V}_{a0}\\ \dot{V}_{a1}\\ \dot{V}_{a2} \end{bmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.8405700000000005em;vertical-align:-1.6702850000000007em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0510099999999998em"><span style="top:-2.2500000000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-2.8099900000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.05101em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.170285em"><span style="top:-4.250095em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.9699049999999994em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-1.6897149999999994em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.6702850000000007em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0510099999999998em"><span style="top:-2.2500000000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-2.8099900000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.05101em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:5.2692950000000005em;vertical-align:-1.6702850000000007em"></span><span class="mord mover"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.59901em"><span style="top:-4.6990099999999995em"><span class="pstrut" style="height:4.6990099999999995em"></span><span class="mord mover"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.69901em"><span style="top:-4.05101em"><span class="pstrut" style="height:4.05101em"></span><span class="mord"><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0510099999999998em"><span style="top:-2.2500000000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-2.8099900000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.05101em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.05em"><span style="top:-4.21em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-3.0099999999999993em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-1.8099999999999994em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5500000000000007em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.05em"><span style="top:-4.21em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-3.0099999999999993em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-1.8099999999999994em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5500000000000007em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.05em"><span style="top:-4.21em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-3.0099999999999993em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span><span style="top:-1.8099999999999994em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5500000000000007em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0510099999999998em"><span style="top:-2.2500000000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-2.8099900000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.05101em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em"><span></span></span></span></span></span></span></span></span></span><span class="svg-align" style="top:-6.202019999999999em"><span class="pstrut" style="height:4.05101em"></span><span class="stretchy" style="height:0.548em;min-width:1.6em"><span class="brace-left" style="height:0.548em"><svg width="400em" height="0.548em" viewBox="0 0 400000 548" preserveAspectRatio="xMinYMin slice"><path d="M6 548l-6-6v-35l6-11c56-104 135.3-181.3 238-232 57.3-28.7 117
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@@ -29,15 +29,15 @@
 -6 6h-17c-12.7 0-19.3-.3-20-1-4-4-7.3-8.3-10-13-35.3-51.3-80.8-93.8-136.5-127.5
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 c124.7 8 235 61.7 331 161 31.3 33.3 59.7 72.7 85 118l7 13v35z"></path></svg></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em"><span></span></span></span></span></span></span><span style="top:-7.773019999999999em"><span class="pstrut" style="height:4.6990099999999995em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="minner mtight"><span class="mopen mtight delimcenter" style="top:0em"><span class="mtight">[</span></span><span class="mord mtight"><span class="mord mathbf mtight">A</span></span><span class="mclose mtight delimcenter" style="top:0em"><span class="mtight">]</span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0510099999999998em"><span style="top:-2.2500000000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-2.8099900000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.05101em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.170285em"><span style="top:-4.250095em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.9699049999999994em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-1.6897149999999994em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.6702850000000007em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0510099999999998em"><span style="top:-2.2500000000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-2.8099900000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.05101em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em"><span></span></span></span></span></span></span></span></span></span></span></span></div><p>Considerando a matriz quadrada da equação anterior sendo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">[</mo><mi mathvariant="bold">A</mi><mo fence="true">]</mo></mrow><annotation encoding="application/x-tex">\left[ \bold{A} \right]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">[</span><span class="mord"><span class="mord mathbf">A</span></span><span class="mclose delimcenter" style="top:0em">]</span></span></span></span></span></span>, pode-se encontrar as componentes simétricas pré-multiplicando ambos os lados dessa mesma equação por <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow><mo fence="true">[</mo><mi mathvariant="bold">A</mi><mo fence="true">]</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow><annotation encoding="application/x-tex">\left[ \bold{A} \right]^{-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.204008em;vertical-align:-0.25em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em">[</span><span class="mord"><span class="mord mathbf">A</span></span><span class="mclose delimcenter" style="top:0em">]</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.954008em"><span style="top:-3.2029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span></span></span></span>.</p><p>Da mesma forma que no estudo de fluxo de carga, a representação dos elementos do sistema para o estudo de curto-circuito é realizada por meio de circuitos equivalentes inseridos na matriz admitância de barras. Nas faltas assimétricas (F-T, F-F e F-F-T) é necessário formar três matrizes admitância de sequência: positiva, negativa e zero.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>As informações a respeito das particularidades dos modelos para o estudo de curto-circuito são apresentados individualmente nos <a href="/PSP/docs/powerEditor#editando-dados-el%C3%A9tricos">elementos de potência</a>.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="equações-do-curto-circuito"></a>Equações do curto-circuito<a aria-hidden="true" tabindex="-1" class="hash-link" href="#equações-do-curto-circuito" title="Direct link to heading">#</a></h3><p>Primeiramente será tratado o equacionamento para faltas balanceadas e então os estudos serão estendidos para as faltas desbalanceadas por meio da utilização do método das componentes simétricas.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="faltas-balanceadas"></a>Faltas balanceadas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#faltas-balanceadas" title="Direct link to heading">#</a></h4><p>Utiliza-se da matriz impedância de barras para o cálculo de curto-circuito, definida pela seguinte equação matricial:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mo stretchy="false">]</mo><mo>=</mo><mo stretchy="false">[</mo><msub><mi>Z</mi><mrow><mi>b</mi><mi>u</mi><mi>s</mi></mrow></msub><mo stretchy="false">]</mo><mo stretchy="false">[</mo><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[\dot{V}] = [Z_{bus}][\dot{I}]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.17019em;vertical-align:-0.25em"></span><span class="mopen">[</span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.17019em;vertical-align:-0.25em"></span><span class="mopen">[</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">Z</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">b</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">s</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose">]</span><span class="mopen">[</span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="mclose">]</span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><msub><mi>Z</mi><mrow><mi>b</mi><mi>u</mi><mi>s</mi></mrow></msub><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[Z_{bus}]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mopen">[</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">Z</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">b</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">s</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose">]</span></span></span></span></span> é a inversa da matriz admitância de barras, chamada de matriz impedância de barras.</li></ul><p>Por meio da expansão da equação anterior é possível calcular a corrente de falta trifásica na barra genérica <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em"></span><span class="mord mathdefault">i</span></span></span></span></span>:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mi>f</mi></msub><mo>=</mo><mfrac><msub><mover accent="true"><mi>E</mi><mo>˙</mo></mover><mi>i</mi></msub><mrow><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow></msub><mo>+</mo><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>f</mi></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">\dot{I}_f = \frac{\dot{E}_i}{\overline{z}_{ii}+\overline{z}_{f}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.206298em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.569298em;vertical-align:-0.972108em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5971899999999999em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.055550000000000016em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.972108em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mi>f</mi></msub></mrow><annotation encoding="application/x-tex">\dot{I}_f</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.206298em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span> é a corrente de falta trifásica na barra <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em"></span><span class="mord mathdefault">i</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>E</mi><mo>˙</mo></mover><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">\dot{E}_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.07019em;vertical-align:-0.15em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.055550000000000016em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> é a tensão pré-falta na barra <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em"></span><span class="mord mathdefault">i</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow></msub></mrow><annotation encoding="application/x-tex">\overline{z}_{ii}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.78056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> é a impedância equivalente de Thevenin vista pela barra <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em"></span><span class="mord mathdefault">i</span></span></span></span></span>, retirada da matriz impedância</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>f</mi></msub></mrow><annotation encoding="application/x-tex">\overline{z}_{f}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.916668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span> é a impedância de falta</li></ul><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="faltas-desbalanceadas"></a>Faltas desbalanceadas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#faltas-desbalanceadas" title="Direct link to heading">#</a></h4><p>O desenvolvimento das equações do cálculo de curto-circuito para faltas desbalanceadas é realizado seguindo o seguinte procedimento:</p><ol><li>Definir os diagramas no ponto da falta, mostrando as conexões de todas fases para a falta. Assume-se que apenas impedâncias balanceadas estão presentes em ambos os lados do ponto da falta e o equivalente Thevenin até esse ponto é conhecido;</li><li>Escrever as condições de contorno relacionando as tensões e corrente conhecidas para o tipo de falta estudada;</li><li>Transformar as correntes e tensões do item 2 de a-b-c para o sistema de coordenadas 0-1-2;</li><li>Encontrar a corrente do curto-circuito em estudo baseado no seguinte sistema de equações (para a fase A):<div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>1</mn></mrow></msub><mo>=</mo><msub><mover accent="true"><mi>E</mi><mo>˙</mo></mover><mi>a</mi></msub><mo>−</mo><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>1</mn></mrow></msub><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mn>1</mn></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>2</mn></mrow></msub><mo>=</mo><mo>−</mo><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>2</mn></mrow></msub><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mn>2</mn></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub><mo>=</mo><mo>−</mo><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mn>0</mn></msub></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} \dot{V}_{a1} = \dot{E}_a - \dot{I}_{a1} \overline{z}_1\\ \dot{V}_{a2} = - \dot{I}_{a2} \overline{z}_2\\ \dot{V}_{a0} = - \dot{I}_{a0} \overline{z}_0 \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.32em;vertical-align:-1.9099999999999997em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35002em"><span style="top:-2.19999em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.19499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.20499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.15001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.2950099999999996em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.30501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.60002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8500199999999998em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em"><span style="top:-4.41em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.055550000000000016em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.97em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord">−</span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-1.5300000000000002em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord">−</span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.9099999999999997em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div></li></ol><p>A tabela abaixo apresenta as equações para as faltas desbalanceadas após a execução do procedimento apresenteado:</p><table><thead><tr><th><strong>Falta</strong></th><th align="center"><strong>Seq. Positiva (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mi>f</mi><mn>1</mn></msubsup></mrow><annotation encoding="application/x-tex">\dot{I}_{f}^{1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.3394059999999999em;vertical-align:-0.4192159999999999em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-2.4168920000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4192159999999999em"><span></span></span></span></span></span></span></span></span></span></span>)</strong></th><th align="center"><strong>Seq. Negativa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mi>f</mi><mn>2</mn></msubsup></mrow><annotation encoding="application/x-tex">\dot{I}_{f}^{2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.3394059999999999em;vertical-align:-0.4192159999999999em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-2.4168920000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4192159999999999em"><span></span></span></span></span></span></span></span></span></span></span>)</strong></th><th align="center"><strong>Seq. Zero (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mi>f</mi><mn>0</mn></msubsup></mrow><annotation encoding="application/x-tex">\dot{I}_{f}^{0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.3394059999999999em;vertical-align:-0.4192159999999999em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-2.4168920000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4192159999999999em"><span></span></span></span></span></span></span></span></span></span></span>)</strong></th></tr></thead><tbody><tr><td><strong>F-T</strong></td><td align="center"><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><msub><mover accent="true"><mi>E</mi><mo>˙</mo></mover><mi>i</mi></msub><mrow><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>1</mn></msubsup><mo>+</mo><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>2</mn></msubsup><mo>+</mo><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>0</mn></msubsup><mo>+</mo><mn>3</mn><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>f</mi></msub></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">\dfrac{\dot{E}_i}{\overline{z}_{ii}^{1} + \overline{z}_{ii}^{2} + \overline{z}_{ii}^{0} + 3 \overline{z}_{f}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.6078659999999996em;vertical-align:-1.010676em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5971899999999999em"><span style="top:-2.275432em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-2.4530000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-2.4530000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-2.4530000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord">3</span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.055550000000000016em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.010676em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></td><td align="center"><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mi>f</mi><mn>1</mn></msubsup></mrow><annotation encoding="application/x-tex">\dot{I}_{f}^{1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.3394059999999999em;vertical-align:-0.4192159999999999em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-2.4168920000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4192159999999999em"><span></span></span></span></span></span></span></span></span></span></span></td><td align="center"><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mi>f</mi><mn>1</mn></msubsup></mrow><annotation encoding="application/x-tex">\dot{I}_{f}^{1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.3394059999999999em;vertical-align:-0.4192159999999999em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-2.4168920000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4192159999999999em"><span></span></span></span></span></span></span></span></span></span></span></td></tr><tr><td><strong>F-F</strong></td><td align="center"><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><msub><mover accent="true"><mi>E</mi><mo>˙</mo></mover><mi>i</mi></msub><mrow><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>1</mn></msubsup><mo>+</mo><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>2</mn></msubsup><mo>+</mo><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>f</mi></msub></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">\dfrac{\dot{E}_i}{\overline{z}_{ii}^{1} + \overline{z}_{ii}^{2} + \overline{z}_{f}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.6078659999999996em;vertical-align:-1.010676em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5971899999999999em"><span style="top:-2.275432em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-2.4530000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-2.4530000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.055550000000000016em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.010676em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></td><td align="center"><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><msubsup><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mi>f</mi><mn>1</mn></msubsup></mrow><annotation encoding="application/x-tex">- \dot{I}_{f}^{1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.3394059999999999em;vertical-align:-0.4192159999999999em"></span><span class="mord">−</span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-2.4168920000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4192159999999999em"><span></span></span></span></span></span></span></span></span></span></span></td><td align="center"><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">0{,}0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span></span></span></span></span></td></tr><tr><td><strong>F-F-T</strong></td><td align="center"><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><msub><mover accent="true"><mi>E</mi><mo>˙</mo></mover><mi>i</mi></msub><mrow><mo fence="true">(</mo><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>2</mn></msubsup><mo>+</mo><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>0</mn></msubsup><mo>+</mo><mn>3</mn><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>f</mi></msub><mo fence="true">)</mo></mrow></mrow><mrow><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>1</mn></msubsup><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>2</mn></msubsup><mo>+</mo><mn>3</mn><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>2</mn></msubsup><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>f</mi></msub><mo>+</mo><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>2</mn></msubsup><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>0</mn></msubsup><mo>+</mo><mn>3</mn><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>1</mn></msubsup><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>f</mi></msub><mo>+</mo><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>1</mn></msubsup><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>0</mn></msubsup></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">\dfrac{\dot{E}_i \left( \overline{z}_{ii}^{2} + \overline{z}_{ii}^{0} + 3 \overline{z}_{f} \right)}{\overline{z}_{ii}^{1} \overline{z}_{ii}^{2} + 3 \overline{z}_{ii}^{2} \overline{z}_{f} + \overline{z}_{ii}^{2} \overline{z}_{ii}^{0} + 3 \overline{z}_{ii}^{1} \overline{z}_{f} + \overline{z}_{ii}^{1} \overline{z}_{ii}^{0} }</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.670876em;vertical-align:-1.010676em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6602000000000001em"><span style="top:-2.275432em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-2.4530000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-2.4530000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord">3</span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-2.4530000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-2.4530000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-2.4530000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord">3</span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-2.4530000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-2.4530000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-2.4530000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.7400100000000003em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.055550000000000016em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-2.4530000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-2.4530000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord">3</span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.010676em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></td><td align="center"><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><msub><mover accent="true"><mi>E</mi><mo>˙</mo></mover><mi>i</mi></msub><mo>−</mo><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>1</mn></msubsup><msubsup><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mi>f</mi><mn>1</mn></msubsup></mrow><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>2</mn></msubsup></mfrac></mstyle></mrow><annotation encoding="application/x-tex">- \dfrac{\dot{E}_i - \overline{z}_{ii}^{1} \dot{I}_{f}^{1}}{\overline{z}_{ii}^{2}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.700974em;vertical-align:-0.971568em"></span><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.729406em"><span style="top:-2.275432em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" 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style="border-bottom-width:0.04em"></span></span><span style="top:-3.809216em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.055550000000000016em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-2.4530000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-2.4168920000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4192159999999999em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.971568em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></td><td align="center"><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><msub><mover accent="true"><mi>E</mi><mo>˙</mo></mover><mi>i</mi></msub><mo>−</mo><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>1</mn></msubsup><msubsup><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mi>f</mi><mn>1</mn></msubsup></mrow><mrow><msubsup><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow><mn>0</mn></msubsup><mo>+</mo><mn>3</mn><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>f</mi></msub></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">- \dfrac{\dot{E}_i - \overline{z}_{ii}^{1} \dot{I}_{f}^{1}}{\overline{z}_{ii}^{0} + 3 \overline{z}_{f}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.740082em;vertical-align:-1.010676em"></span><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.729406em"><span style="top:-2.275432em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-2.4530000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord">3</span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.809216em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.055550000000000016em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.834568em"><span style="top:-2.4530000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.08346em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-2.4168920000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4192159999999999em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.010676em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></td></tr></tbody></table><p>Para obter os valores em a-b-c é usada a equação matricial apresentada anteriormente, encerrando o cálculo de curto-circuito.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="referências"></a>Referências<a aria-hidden="true" tabindex="-1" class="hash-link" href="#referências" title="Direct link to heading">#</a></h2><ol><li>ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley &amp; Sons, New York, 2001. doi: <a href="https://doi.org/10.1002/9781118878286" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/9781118878286</a></li><li>STEVENSON JR.; WILLIAN, D. Elementos de Análise de Sistemas de Potência. 2ª ed. São Paulo: McGraw-Hill, 1986.</li><li>ANDERSON, P. M.; FOUAD, A. A. Power System Control and Stability. Wiley-IEEE Press, New York, 2002. doi: <a href="https://doi.org/10.1109/9780470545577" target="_blank" rel="noopener noreferrer">https://doi.org/10.1109/9780470545577</a></li><li>FORTESCUE, C. L. Method of Symmetrical Coordinates Applied to the Solution of Polyphase Networks. Trans. AIEE, v. 37, p.1027-1140, 1918. doi: <a href="https://doi.org/10.1109/T-AIEE.1918.4765570" target="_blank" rel="noopener noreferrer">https://doi.org/10.1109/T-AIEE.1918.4765570</a></li><li>ANDERSON, P. M. Analysis of faulted power systems. New York: IEEE Press, 1995.</li></ol></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/fault.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/powerFlow"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Fluxo de Potência</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/harmonics"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Harmônicos »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#cálculo-de-curto-circuito-no-psp-ufu" class="table-of-contents__link">Cálculo de Curto-Circuito no PSP-UFU</a></li><li><a href="#execução-do-cálculo-de-curto-circuito-no-psp-ufu" class="table-of-contents__link">Execução do cálculo de curto-circuito no PSP-UFU</a><ul><li><a href="#erros-comuns-na-execução-do-cálculo-de-curto-circuito" class="table-of-contents__link">Erros comuns na execução do cálculo de curto-circuito</a></li></ul></li><li><a href="#o-cálculo-de-curto-circuito" class="table-of-contents__link">O cálculo de curto-circuito</a><ul><li><a href="#método-das-componentes-simétricas" class="table-of-contents__link">Método das componentes simétricas</a></li><li><a href="#equações-do-curto-circuito" class="table-of-contents__link">Equações do curto-circuito</a></li></ul></li><li><a href="#referências" class="table-of-contents__link">Referências</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Ganho</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>O bloco de ganho multiplica o valor de entrada por uma constante definida pelo usuário, possuindo comportamento idêntico à combinação de uma <a href="/PSP/docs/const">constante</a> e um bloco <a href="/PSP/docs/multiplier">multiplicador</a>.</p><p>Esse valor de ganho permanece fixo durante todo o tempo de simulação e é identificado no elemento gráfico exibido no editor de elementos de controle.</p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/gain.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" 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docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Visualizador de Gráficos</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Para exibição dos resultados originados dos cálculos de <a href="/PSP/docs/stability">estabilidade</a> e <a href="/PSP/docs/harmonics">varredura de frequências</a>, desenvolveu-se um visualizador de gráficos, como mostra a figura abaixo:</p><div><center><img src="/PSP/images/graphViewer.png" alt="Visualizador de gráficos do PSP-UFU" title="Visualizador de gráficos do PSP-UFU"></center></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="criação-manipulação-e-navegação-de-curvas"></a>Criação, manipulação e navegação de curvas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#criação-manipulação-e-navegação-de-curvas" title="Direct link to heading">#</a></h2><p>Tal visualizador utiliza a biblioteca <a href="https://wxmathplot.sourceforge.io/" target="_blank" rel="noopener noreferrer">wxMathPlot</a>, e permite ao usuário imprimir todas as curvas no tempo originadas dos resultados de <a href="/PSP/docs/stability">estabilidade</a> e <a href="/PSP/docs/harmonics">varredura de frequências</a>, acessados em dados hierárquicos em forma de árvore, identificados pelo tipo e nome do elemento de potência, além do tipo de curva.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>As curvas podem ser plotadas com <strong>clique duplo</strong> sobre ela ou ao selecionar a caixa &quot;Plotar&quot; nas propriedades do traço.</p></div></div><p>Os gráficos impressos podem ser caracterizados pela edição de suas propriedades do traço, ou seja, pode-se alterar a cor, espessura e tipo de traço (seis tipos disponíveis). Por padrão o eixo vertical é o tempo (em estabilidade) ou frequência (varredura de frequências), porém o usuário pode alterar para qualquer curva disponível.</p><p>Várias propriedades gerais do gráfico podem ser editadas: título do gráfico, rótulos dos eixos x e y, margens e limites inferiores e superiores de ambos os eixos.</p><p>O menu <strong>Visualização</strong> permite a inserção de exibição de legenda, linhas de grade e coordenadas do ponteiro do mouse (utilizada para destacar pontos na curva), além da possibilidade de alternar o tema de impressão entre escuro e claro, facilitando a visualização ou exportação do gráfico.</p><p>No menu <strong>Arquivo</strong>, pode-se salvar o gráfico na forma de imagem (<em>.png</em>, <em>.jpg</em> ou <em>.bmp</em>) ou enviá-lo diretamente para a área de transferência. No mesmo menu também é permitido a exportação no formato <em><a href="https://en.wikipedia.org/wiki/Comma-separated_values" target="_blank" rel="noopener noreferrer">CSV (Comma-separated Values)</a></em>, o qual poderá ser utilizado em outros visualizadores de gráficos, como o Excel ou o <a href="http://www.gnuplot.info/" target="_blank" rel="noopener noreferrer">gnuplot</a>.</p><p>A área de plotagem permite a navegação utilizando ferramentas de zoom, por área de seleção e comandos de mouse, e arrasto das curvas impressas.</p><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Ao clicar com o botão direito sobre a área de plotagem as opções de manipulação são exibidas por meio de um menu de contexto.</p></div></div><p>Os seguintes <strong>comandos de mouse</strong> são utilizados para navegação das curvas:</p><table><thead><tr><th>Comando</th><th>Ação</th></tr></thead><tbody><tr><td>Botão esquerdo pressionado + Selecionar área</td><td>Seleciona a área de zoom</td></tr><tr><td>Botão direito pressionado + Mover mouse</td><td>Arrasta a curva</td></tr><tr><td>Roda do mouse</td><td>Arrasto vertical</td></tr><tr><td>Roda do mouse + Shift</td><td>Arrasto horizontal</td></tr><tr><td>Roda do mouse + Ctrl</td><td>Mais/menos zoom</td></tr></tbody></table></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/graphViewer.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/tabularReport"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Relatórios Tabulares</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/heatmap"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Mapa de Tensão »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#criação-manipulação-e-navegação-de-curvas" class="table-of-contents__link">Criação, manipulação e navegação de curvas</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Fonte de Corrente Harmônica</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>(<strong>Fonte de perturbação harmônica</strong>) Parte do sistema elétrico de potência ou das instalações a ele conectadas, que causa distorção harmônica da forma de onda da corrente e / ou tensão. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=614-01-16" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="fonte-de-corrente-harmônica-no-psp-ufu"></a>Fonte de corrente harmônica no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#fonte-de-corrente-harmônica-no-psp-ufu" title="Direct link to heading">#</a></h2><p>As fontes de corrente harmônica são responsáveis pela injeção de correntes harmônicas e são utilizadas pela ferramenta de cálculo de <a href="/PSP/docs/harmonics">distorções harmônicas</a>. Uma lista de correntes harmônicas pode ser inserida em um mesmo elemento, conforme é exibido na o formulário de edição de dados.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>A presença da fonte de corrente harmônica <strong>não é considerada</strong> nos estudos de <a href="/PSP/docs/powerFlow">fluxo de carga</a>, <a href="/PSP/docs/fault">curto-circuito</a> e <a href="/PSP/docs/stability">estabilidade</a>.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-das-fontes-de-corrente-harmônica"></a>Formulário de edição das fontes de corrente harmônica<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-das-fontes-de-corrente-harmônica" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados da fonte de corrente harmônica:</p><div><center><img src="/PSP/images/harmSourceForm.png" alt="Formulário dos indutores no PSP-UFU" title="Formulário dos indutores no PSP-UFU"></center></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="ordem"></a>Ordem<a aria-hidden="true" tabindex="-1" class="hash-link" href="#ordem" title="Direct link to heading">#</a></h4><p>Especifica a ordem harmônica a ser inserida na lista de correntes harmônicas do elemento. Caso a ordem harmônica já exista na lista, ela será substituída pelos novos parâmetros.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="corrente"></a>Corrente<a aria-hidden="true" tabindex="-1" class="hash-link" href="#corrente" title="Direct link to heading">#</a></h4><p>Módulo da corrente harmônica.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="unidade"></a>Unidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#unidade" title="Direct link to heading">#</a></h4><p>Unidade do módulo de corrente harmônica, em A ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="ângulo"></a>Ângulo<a aria-hidden="true" tabindex="-1" class="hash-link" href="#ângulo" title="Direct link to heading">#</a></h4><p>Ângulo da corrente harmônica, em graus.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="adicionar--remover"></a>Adicionar / Remover<a aria-hidden="true" tabindex="-1" class="hash-link" href="#adicionar--remover" title="Direct link to heading">#</a></h4><p>Insere ou modifica a nova ordem harmônica ao clicar em “Adicionar”. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Fonte de Corrente Harmônica</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>(<strong>Fonte de perturbação harmônica</strong>) Parte do sistema elétrico de potência ou das instalações a ele conectadas, que causa distorção harmônica da forma de onda da corrente e / ou tensão. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=614-01-16" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="fonte-de-corrente-harmônica-no-psp-ufu"></a>Fonte de corrente harmônica no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#fonte-de-corrente-harmônica-no-psp-ufu" title="Direct link to heading">#</a></h2><p>As fontes de corrente harmônica são responsáveis pela injeção de correntes harmônicas e são utilizadas pela ferramenta de cálculo de <a href="/PSP/docs/harmonics">distorções harmônicas</a>. Uma lista de correntes harmônicas pode ser inserida em um mesmo elemento, conforme é exibido na o formulário de edição de dados.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>A presença da fonte de corrente harmônica <strong>não é considerada</strong> nos estudos de <a href="/PSP/docs/powerFlow">fluxo de carga</a>, <a href="/PSP/docs/fault">curto-circuito</a> e <a href="/PSP/docs/stability">estabilidade</a>.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-das-fontes-de-corrente-harmônica"></a>Formulário de edição das fontes de corrente harmônica<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-das-fontes-de-corrente-harmônica" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados da fonte de corrente harmônica:</p><div><center><img src="/PSP/images/harmSourceForm.png" alt="Formulário dos indutores no PSP-UFU" title="Formulário dos indutores no PSP-UFU"></center></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="ordem"></a>Ordem<a aria-hidden="true" tabindex="-1" class="hash-link" href="#ordem" title="Direct link to heading">#</a></h4><p>Especifica a ordem harmônica a ser inserida na lista de correntes harmônicas do elemento. Caso a ordem harmônica já exista na lista, ela será substituída pelos novos parâmetros.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="corrente"></a>Corrente<a aria-hidden="true" tabindex="-1" class="hash-link" href="#corrente" title="Direct link to heading">#</a></h4><p>Módulo da corrente harmônica.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="unidade"></a>Unidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#unidade" title="Direct link to heading">#</a></h4><p>Unidade do módulo de corrente harmônica, em A ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="ângulo"></a>Ângulo<a aria-hidden="true" tabindex="-1" class="hash-link" href="#ângulo" title="Direct link to heading">#</a></h4><p>Ângulo da corrente harmônica, em graus.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="adicionar--remover"></a>Adicionar / Remover<a aria-hidden="true" tabindex="-1" class="hash-link" href="#adicionar--remover" title="Direct link to heading">#</a></h4><p>Insere ou modifica a nova ordem harmônica ao clicar em “Adicionar”. 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href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Harmônicos</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Duas ferramentas relacionadas a harmônicos foram desenvolvidas no PSP-UFU:</p><ul><li>Distorção Harmônica Total de Tensão (THD, do inglês <em>Total Harmonic Distortion</em>);</li><li>Resposta na Frequência.</li></ul><p>A ferramenta de <strong><a href="https://en.wikipedia.org/wiki/Total_harmonic_distortion" target="_blank" rel="noopener noreferrer">Distorção Harmônica Total</a></strong> calcula as tensões harmônicas causadas por <a href="/PSP/docs/harmSource">fontes de corrente harmônicas</a>, assim como o THD de todos os barramentos do sistema.</p><p>A ferramenta de <strong>Resposta na Frequência</strong> (ou análise de varredura de frequência) envolve a variação da impedância da rede em um espectro de frequências observado a partir de um certo barramento.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>A análise de varredura de frequência é amplamente usada no projeto de filtros harmônicos.</p></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Um arranjo série de uma <a href="/PSP/docs/line">linha</a> sem as susceptâncias <em>shunt</em>, um <a href="/PSP/docs/bus">barramento</a> e um <a href="/PSP/docs/capacitor">capacitor</a> pode ser utilizado para fabricar um filtro passivo nos <a href="/PSP/docs/harmonics">estudos harmônicos</a>. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.</p></div></div><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Na versão atual do programa não são consideradas as alterações das resistências do sistema causado pelo efeito pelicular. Versões futuras irão contemplar tal característica.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="execução-do-cálculo-de-harmônicos-no-psp-ufu"></a>Execução do cálculo de harmônicos no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#execução-do-cálculo-de-harmônicos-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Após a construção do diagrama unifilar no <a href="/PSP/docs/powerEditor">editor de potência</a>, a execução do cálculo das distorções harmônicas é realizada no <a href="/PSP/docs/mainScreen#menu-ribbon">menu Simulação</a> clicando no botão <strong>Distorções Harmônicas</strong>. Para acessar a ferramenta de de varredura de frequência, basta clicar no botão <strong>Resposta na Frequência</strong>.</p><div><center><img src="/PSP/images/menuSimulationHamonics.svg" alt="Acesso às ferramentas de estudo harmônico" title="Acesso às ferramentas de estudo harmônico"></center></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="distorções-harmônicas"></a>Distorções Harmônicas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#distorções-harmônicas" title="Direct link to heading">#</a></h3><p>Ao clicar sobre o botão &quot;Distorções Harmônicas&quot; as distorções causadas pelas <a href="/PSP/docs/harmSource">fontes de corrente harmônica</a> são calculadas em todos os barramentos do sistema.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Caso não forem inseridas <a href="/PSP/docs/harmSource">fontes de corrente harmônica</a> no sistema de potência, a distorção de tensão de todas as barras será <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>0</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">0{,}0~\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.94444em;vertical-align:-0.19444em"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span><span class="mspace nobreak"> </span><span class="mord">%</span></span></span></span></span>.</p></div></div><p><strong>Outra possibilidade</strong> é a execução por meio do cálculo contínuo, também presente no <a href="/PSP/docs/mainScreen#menu-ribbon">menu Simulação</a> e seu acionamento é realizado co clicar no botão <strong>Habilitar solução</strong>. Com essa opção, os cálculos estáticos selecionados nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a> são automaticamente realizados ao modificar quaisquer parâmetros da rede, como dados elétricos e acionamento dos disjuntores dos elementos (remoção ou inserção).</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Os cálculos dos níveis de THD <strong>não são habilitados por padrão</strong> no cálculo contínuo e devem ser inseridos nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a>.</p></div></div><p>Os resultados das distorções harmônicas são exibidos nos <a href="/PSP/docs/text">elementos de texto vinculados</a> e ao posicionar o mouse sobre um barramento.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="resposta-na-frequência"></a>Resposta na Frequência<a aria-hidden="true" tabindex="-1" class="hash-link" href="#resposta-na-frequência" title="Direct link to heading">#</a></h3><p>Ao clicar sobre o botão &quot;Resposta na Frequência&quot; será exibido um formulário para inserção dos parâmetros da ferramenta:</p><div><center><img src="/PSP/images/injHarmCurrent.png" alt="Acesso à ferramentas resposta na frequência" title="Acesso à ferramentas resposta na frequência"></center></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="frequência-inicial"></a>Frequência inicial<a aria-hidden="true" tabindex="-1" class="hash-link" href="#frequência-inicial" title="Direct link to heading">#</a></h4><p>Define a frequência inicial da varredura.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="frequência-final"></a>Frequência final<a aria-hidden="true" tabindex="-1" class="hash-link" href="#frequência-final" title="Direct link to heading">#</a></h4><p>Define a frequência final da varredura.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="passo-de-frequência"></a>Passo de frequência<a aria-hidden="true" tabindex="-1" class="hash-link" href="#passo-de-frequência" title="Direct link to heading">#</a></h4><p>Define o passo de incremento da frequência. Passos menores irão gerar gráficos mais precisos, porém podem aumentar muito o tempo de execução.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="corrente-injetada"></a>Corrente injetada<a aria-hidden="true" tabindex="-1" class="hash-link" href="#corrente-injetada" title="Direct link to heading">#</a></h4><p>Define o barramento o qual será injetada a corrente harmônica para análise.</p><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Esse campo pode ser entendido como: &quot;<em>A resposta das impedâncias harmônicas vistas pelos barramentos do sistema caso tenha uma fonte de corrente harmônica na barra selecionada</em>&quot;.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="botão-executar"></a>Botão Executar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#botão-executar" title="Direct link to heading">#</a></h4><p>Ao clicar no botão executar a varredura será executada e os resultados exibidos no <a href="/PSP/docs/graphViewer">vizualizador de gráficos</a>, como mostra a imagem abaixo.</p><div><center><img src="/PSP/images/freqScanPlot.png" alt="Exemplo de resposta na frequência" title="Exemplo de resposta na frequência"></center></div><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Para visualizar a varredura da impedância harmônica de um barramento, essa opção deve ser habilitada em seu <a href="/PSP/docs/bus#imprimir-imped%C3%A2ncia-harm%C3%B4nica-da-barra">formulário de edição de dados</a>.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="cálculos-das-ferramentas-harmônicas"></a>Cálculos das ferramentas harmônicas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#cálculos-das-ferramentas-harmônicas" title="Direct link to heading">#</a></h2><p>Ambos cálculos são realizados a partir da seguinte equação matricial:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mover accent="true"><mi>I</mi><mo>˙</mo></mover><msup><mo stretchy="false">]</mo><mi>h</mi></msup><mo>=</mo><mo stretchy="false">[</mo><msub><mi>Y</mi><mrow><mi>b</mi><mi>u</mi><mi>s</mi></mrow></msub><msup><mo stretchy="false">]</mo><mi>h</mi></msup><mo stretchy="false">[</mo><mover accent="true"><mi>V</mi><mo>˙</mo></mover><msup><mo stretchy="false">]</mo><mi>h</mi></msup></mrow><annotation encoding="application/x-tex">[\dot{I}]^h= [Y_{bus}]^h [\dot{V}]^h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.17019em;vertical-align:-0.25em"></span><span class="mopen">[</span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="mclose"><span class="mclose">]</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.17019em;vertical-align:-0.25em"></span><span class="mopen">[</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">b</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">s</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose"><span class="mclose">]</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span></span></span></span></span><span class="mopen">[</span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="mclose"><span class="mclose">]</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span></span></span></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mover accent="true"><mi>I</mi><mo>˙</mo></mover><msup><mo stretchy="false">]</mo><mi>h</mi></msup></mrow><annotation encoding="application/x-tex">[\dot{I}]^h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.17019em;vertical-align:-0.25em"></span><span class="mopen">[</span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="mclose"><span class="mclose">]</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span></span></span></span></span></span></span></span></span>	Vetor das correntes harmônicas injetadas nas barras</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><msub><mi>Y</mi><mrow><mi>b</mi><mi>u</mi><mi>s</mi></mrow></msub><msup><mo stretchy="false">]</mo><mi>h</mi></msup></mrow><annotation encoding="application/x-tex">[Y_{bus}]^h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.099108em;vertical-align:-0.25em"></span><span class="mopen">[</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">b</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">s</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose"><span class="mclose">]</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span></span></span></span></span></span></span></span></span>	Matriz admitância harmônica de barras</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mover accent="true"><mi>V</mi><mo>˙</mo></mover><msup><mo stretchy="false">]</mo><mi>h</mi></msup></mrow><annotation encoding="application/x-tex">[\dot{V}]^h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.17019em;vertical-align:-0.25em"></span><span class="mopen">[</span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="mclose"><span class="mclose">]</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span></span></span></span></span></span></span></span></span>	Vetor das tensões harmônicas nas barras</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em"></span><span class="mord mathdefault">h</span></span></span></span></span>	Ordem harmônica</li></ul><p>O vetor das correntes harmônicas injetadas é definido no programa utilizando um elemento de potência, chamado “fonte de corrente harmônica”, em que o usuário pode criar uma lista de correntes injetadas (em A e/ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>) em um barramento.</p><p>O programa define automaticamente as ordens harmônicas na simulação analisando todas as listas de fontes de corrente harmônicas previamente aos cálculos. Com isso são calculadas as admitâncias harmônicas necessárias de cada elemento pela multiplicação das reatâncias indutivas (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>x</mi><mi>l</mi><mn>1</mn></msubsup></mrow><annotation encoding="application/x-tex">x_{l}^1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.097216em;vertical-align:-0.2831079999999999em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span></span>) e susceptâncias capacitivas (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>b</mi><mi>c</mi><mn>1</mn></msubsup></mrow><annotation encoding="application/x-tex">b_{c}^1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.061108em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span></span></span></span></span>) fundamentais de cada elemento pelas ordens harmônicas:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>x</mi><mi>l</mi><mi>h</mi></msubsup><mo>=</mo><mi>h</mi><mo>×</mo><msubsup><mi>x</mi><mi>l</mi><mn>1</mn></msubsup><mspace linebreak="newline"></mspace><msubsup><mi>b</mi><mi>c</mi><mi>h</mi></msubsup><mo>=</mo><mi>h</mi><mo>×</mo><msubsup><mi>b</mi><mi>c</mi><mn>1</mn></msubsup></mrow><annotation encoding="application/x-tex">x_{l}^h=h×x_l^1\\ b_{c}^h=h×b_c^1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.146108em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999998em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em"></span><span class="mord mathdefault">h</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.1111079999999998em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.146108em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999998em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em"></span><span class="mord mathdefault">h</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.1111079999999998em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Uma vez calculadas as admitâncias harmônicas, são utilizados os mesmos modelos e algoritmos convencionais para construção da <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>Y</mi><mrow><mi>b</mi><mi>u</mi><mi>s</mi></mrow><mi>h</mi></msubsup></mrow><annotation encoding="application/x-tex">Y_{bus}^h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.132216em;vertical-align:-0.2831079999999999em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.4168920000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">b</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span></span>.</p><p>A equação matricial é resolvida usando o método de eliminação gaussiana para evitar a inversão de cada matriz de admitância harmônica. Este procedimento torna o cálculo das tensões harmônicas computacionalmente eficiente.</p><p>Uma vez calculadas as tensões harmônicas, a THD em uma barra genérica <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em"></span><span class="mord mathdefault">i</span></span></span></span></span> pode ser definida por:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mtext>THD</mtext><mi>i</mi></msub><mo>=</mo><mfrac><mrow><munderover><mo>∑</mo><mrow><mi>h</mi><mo>=</mo><mn>2</mn></mrow><mi>n</mi></munderover><msubsup><mi>V</mi><mi>i</mi><mi>h</mi></msubsup></mrow><msubsup><mi>V</mi><mi>i</mi><mn>1</mn></msubsup></mfrac></mrow><annotation encoding="application/x-tex">\text{THD}_i=\dfrac{\sum_{h=2}^{n} V_{i}^h}{V_i^1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord text"><span class="mord">THD</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.5016819999999997em;vertical-align:-0.9628639999999999em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.538818em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7959080000000001em"><span style="top:-2.4231360000000004em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.27686399999999994em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6897100000000003em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.804292em"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">h</span><span class="mrel mtight">=</span><span class="mord mtight">2</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.441336em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9628639999999999em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Na ferramenta de Resposta na Frequência uma corrente senoidal é injetada na barra em uma faixa de frequências e o conjunto de equações matriciais é usado para calcular a resposta da tensão. Este cálculo é repetido em etapas discretas cobrindo o espectro de frequência especificado.</p><p>O programa usa a matriz admitância de sequência positiva e uma corrente injetada de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>0</mn><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">1{,}0 p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> também de sequência positiva na equação matricial para calcular diretamente as impedâncias em p.u.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="referências"></a>Referências<a aria-hidden="true" tabindex="-1" class="hash-link" href="#referências" title="Direct link to heading">#</a></h2><ol><li>ARRILLAGA, J.; WATSON, N. R. Power System Harmonics. John Wiley &amp; Sons; Chichester, 2003. doi: <a href="https://doi.org/10.1002/0470871229" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/0470871229</a></li></ol></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/harmonics.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/fault"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Curto-Circuito</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/stability"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Estabilidade »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#execução-do-cálculo-de-harmônicos-no-psp-ufu" class="table-of-contents__link">Execução do cálculo de harmônicos no PSP-UFU</a><ul><li><a href="#distorções-harmônicas" class="table-of-contents__link">Distorções Harmônicas</a></li><li><a href="#resposta-na-frequência" class="table-of-contents__link">Resposta na Frequência</a></li></ul></li><li><a href="#cálculos-das-ferramentas-harmônicas" class="table-of-contents__link">Cálculos das ferramentas harmônicas</a></li><li><a href="#referências" class="table-of-contents__link">Referências</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Harmônicos</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Duas ferramentas relacionadas a harmônicos foram desenvolvidas no PSP-UFU:</p><ul><li>Distorção Harmônica Total de Tensão (THD, do inglês <em>Total Harmonic Distortion</em>);</li><li>Resposta na Frequência.</li></ul><p>A ferramenta de <strong><a href="https://en.wikipedia.org/wiki/Total_harmonic_distortion" target="_blank" rel="noopener noreferrer">Distorção Harmônica Total</a></strong> calcula as tensões harmônicas causadas por <a href="/PSP/docs/harmSource">fontes de corrente harmônicas</a>, assim como o THD de todos os barramentos do sistema.</p><p>A ferramenta de <strong>Resposta na Frequência</strong> (ou análise de varredura de frequência) envolve a variação da impedância da rede em um espectro de frequências observado a partir de um certo barramento.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>A análise de varredura de frequência é amplamente usada no projeto de filtros harmônicos.</p></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Um arranjo série de uma <a href="/PSP/docs/line">linha</a> sem as susceptâncias <em>shunt</em>, um <a href="/PSP/docs/bus">barramento</a> e um <a href="/PSP/docs/capacitor">capacitor</a> pode ser utilizado para fabricar um filtro passivo nos <a href="/PSP/docs/harmonics">estudos harmônicos</a>. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.</p></div></div><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Na versão atual do programa não são consideradas as alterações das resistências do sistema causado pelo efeito pelicular. Versões futuras irão contemplar tal característica.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="execução-do-cálculo-de-harmônicos-no-psp-ufu"></a>Execução do cálculo de harmônicos no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#execução-do-cálculo-de-harmônicos-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Após a construção do diagrama unifilar no <a href="/PSP/docs/powerEditor">editor de potência</a>, a execução do cálculo das distorções harmônicas é realizada no <a href="/PSP/docs/mainScreen#menu-ribbon">menu Simulação</a> clicando no botão <strong>Distorções Harmônicas</strong>. Para acessar a ferramenta de de varredura de frequência, basta clicar no botão <strong>Resposta na Frequência</strong>.</p><div><center><img src="/PSP/images/menuSimulationHamonics.svg" alt="Acesso às ferramentas de estudo harmônico" title="Acesso às ferramentas de estudo harmônico"></center></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="distorções-harmônicas"></a>Distorções Harmônicas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#distorções-harmônicas" title="Direct link to heading">#</a></h3><p>Ao clicar sobre o botão &quot;Distorções Harmônicas&quot; as distorções causadas pelas <a href="/PSP/docs/harmSource">fontes de corrente harmônica</a> são calculadas em todos os barramentos do sistema.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Caso não forem inseridas <a href="/PSP/docs/harmSource">fontes de corrente harmônica</a> no sistema de potência, a distorção de tensão de todas as barras será <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>0</mn><mtext> </mtext><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">0{,}0~\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.94444em;vertical-align:-0.19444em"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span><span class="mspace nobreak"> </span><span class="mord">%</span></span></span></span></span>.</p></div></div><p><strong>Outra possibilidade</strong> é a execução por meio do cálculo contínuo, também presente no <a href="/PSP/docs/mainScreen#menu-ribbon">menu Simulação</a> e seu acionamento é realizado co clicar no botão <strong>Habilitar solução</strong>. Com essa opção, os cálculos estáticos selecionados nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a> são automaticamente realizados ao modificar quaisquer parâmetros da rede, como dados elétricos e acionamento dos disjuntores dos elementos (remoção ou inserção).</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Os cálculos dos níveis de THD <strong>não são habilitados por padrão</strong> no cálculo contínuo e devem ser inseridos nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a>.</p></div></div><p>Os resultados das distorções harmônicas são exibidos nos <a href="/PSP/docs/text">elementos de texto vinculados</a> e ao posicionar o mouse sobre um barramento.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="resposta-na-frequência"></a>Resposta na Frequência<a aria-hidden="true" tabindex="-1" class="hash-link" href="#resposta-na-frequência" title="Direct link to heading">#</a></h3><p>Ao clicar sobre o botão &quot;Resposta na Frequência&quot; será exibido um formulário para inserção dos parâmetros da ferramenta:</p><div><center><img src="/PSP/images/injHarmCurrent.png" alt="Acesso à ferramentas resposta na frequência" title="Acesso à ferramentas resposta na frequência"></center></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="frequência-inicial"></a>Frequência inicial<a aria-hidden="true" tabindex="-1" class="hash-link" href="#frequência-inicial" title="Direct link to heading">#</a></h4><p>Define a frequência inicial da varredura.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="frequência-final"></a>Frequência final<a aria-hidden="true" tabindex="-1" class="hash-link" href="#frequência-final" title="Direct link to heading">#</a></h4><p>Define a frequência final da varredura.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="passo-de-frequência"></a>Passo de frequência<a aria-hidden="true" tabindex="-1" class="hash-link" href="#passo-de-frequência" title="Direct link to heading">#</a></h4><p>Define o passo de incremento da frequência. Passos menores irão gerar gráficos mais precisos, porém podem aumentar muito o tempo de execução.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="corrente-injetada"></a>Corrente injetada<a aria-hidden="true" tabindex="-1" class="hash-link" href="#corrente-injetada" title="Direct link to heading">#</a></h4><p>Define o barramento o qual será injetada a corrente harmônica para análise.</p><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Esse campo pode ser entendido como: &quot;<em>A resposta das impedâncias harmônicas vistas pelos barramentos do sistema caso tenha uma fonte de corrente harmônica na barra selecionada</em>&quot;.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="botão-executar"></a>Botão Executar<a aria-hidden="true" tabindex="-1" class="hash-link" href="#botão-executar" title="Direct link to heading">#</a></h4><p>Ao clicar no botão executar a varredura será executada e os resultados exibidos no <a href="/PSP/docs/graphViewer">vizualizador de gráficos</a>, como mostra a imagem abaixo.</p><div><center><img src="/PSP/images/freqScanPlot.png" alt="Exemplo de resposta na frequência" title="Exemplo de resposta na frequência"></center></div><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Para visualizar a varredura da impedância harmônica de um barramento, essa opção deve ser habilitada em seu <a href="/PSP/docs/bus#imprimir-imped%C3%A2ncia-harm%C3%B4nica-da-barra">formulário de edição de dados</a>.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="cálculos-das-ferramentas-harmônicas"></a>Cálculos das ferramentas harmônicas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#cálculos-das-ferramentas-harmônicas" title="Direct link to heading">#</a></h2><p>Ambos cálculos são realizados a partir da seguinte equação matricial:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mover accent="true"><mi>I</mi><mo>˙</mo></mover><msup><mo stretchy="false">]</mo><mi>h</mi></msup><mo>=</mo><mo stretchy="false">[</mo><msub><mi>Y</mi><mrow><mi>b</mi><mi>u</mi><mi>s</mi></mrow></msub><msup><mo stretchy="false">]</mo><mi>h</mi></msup><mo stretchy="false">[</mo><mover accent="true"><mi>V</mi><mo>˙</mo></mover><msup><mo stretchy="false">]</mo><mi>h</mi></msup></mrow><annotation encoding="application/x-tex">[\dot{I}]^h= [Y_{bus}]^h [\dot{V}]^h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.17019em;vertical-align:-0.25em"></span><span class="mopen">[</span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="mclose"><span class="mclose">]</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.17019em;vertical-align:-0.25em"></span><span class="mopen">[</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">b</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">s</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose"><span class="mclose">]</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span></span></span></span></span><span class="mopen">[</span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="mclose"><span class="mclose">]</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span></span></span></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mover accent="true"><mi>I</mi><mo>˙</mo></mover><msup><mo stretchy="false">]</mo><mi>h</mi></msup></mrow><annotation encoding="application/x-tex">[\dot{I}]^h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.17019em;vertical-align:-0.25em"></span><span class="mopen">[</span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="mclose"><span class="mclose">]</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span></span></span></span></span></span></span></span></span>	Vetor das correntes harmônicas injetadas nas barras</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><msub><mi>Y</mi><mrow><mi>b</mi><mi>u</mi><mi>s</mi></mrow></msub><msup><mo stretchy="false">]</mo><mi>h</mi></msup></mrow><annotation encoding="application/x-tex">[Y_{bus}]^h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.099108em;vertical-align:-0.25em"></span><span class="mopen">[</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">b</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">s</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose"><span class="mclose">]</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span></span></span></span></span></span></span></span></span>	Matriz admitância harmônica de barras</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mover accent="true"><mi>V</mi><mo>˙</mo></mover><msup><mo stretchy="false">]</mo><mi>h</mi></msup></mrow><annotation encoding="application/x-tex">[\dot{V}]^h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.17019em;vertical-align:-0.25em"></span><span class="mopen">[</span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="mclose"><span class="mclose">]</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span></span></span></span></span></span></span></span></span>	Vetor das tensões harmônicas nas barras</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em"></span><span class="mord mathdefault">h</span></span></span></span></span>	Ordem harmônica</li></ul><p>O vetor das correntes harmônicas injetadas é definido no programa utilizando um elemento de potência, chamado “fonte de corrente harmônica”, em que o usuário pode criar uma lista de correntes injetadas (em A e/ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>) em um barramento.</p><p>O programa define automaticamente as ordens harmônicas na simulação analisando todas as listas de fontes de corrente harmônicas previamente aos cálculos. Com isso são calculadas as admitâncias harmônicas necessárias de cada elemento pela multiplicação das reatâncias indutivas (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>x</mi><mi>l</mi><mn>1</mn></msubsup></mrow><annotation encoding="application/x-tex">x_{l}^1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.097216em;vertical-align:-0.2831079999999999em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span></span>) e susceptâncias capacitivas (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>b</mi><mi>c</mi><mn>1</mn></msubsup></mrow><annotation encoding="application/x-tex">b_{c}^1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.061108em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span></span></span></span></span>) fundamentais de cada elemento pelas ordens harmônicas:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>x</mi><mi>l</mi><mi>h</mi></msubsup><mo>=</mo><mi>h</mi><mo>×</mo><msubsup><mi>x</mi><mi>l</mi><mn>1</mn></msubsup><mspace linebreak="newline"></mspace><msubsup><mi>b</mi><mi>c</mi><mi>h</mi></msubsup><mo>=</mo><mi>h</mi><mo>×</mo><msubsup><mi>b</mi><mi>c</mi><mn>1</mn></msubsup></mrow><annotation encoding="application/x-tex">x_{l}^h=h×x_l^1\\ b_{c}^h=h×b_c^1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.146108em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999998em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em"></span><span class="mord mathdefault">h</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.1111079999999998em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.146108em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999998em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em"></span><span class="mord mathdefault">h</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.1111079999999998em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">c</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Uma vez calculadas as admitâncias harmônicas, são utilizados os mesmos modelos e algoritmos convencionais para construção da <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>Y</mi><mrow><mi>b</mi><mi>u</mi><mi>s</mi></mrow><mi>h</mi></msubsup></mrow><annotation encoding="application/x-tex">Y_{bus}^h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.132216em;vertical-align:-0.2831079999999999em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.4168920000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">b</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span></span>.</p><p>A equação matricial é resolvida usando o método de eliminação gaussiana para evitar a inversão de cada matriz de admitância harmônica. Este procedimento torna o cálculo das tensões harmônicas computacionalmente eficiente.</p><p>Uma vez calculadas as tensões harmônicas, a THD em uma barra genérica <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em"></span><span class="mord mathdefault">i</span></span></span></span></span> pode ser definida por:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mtext>THD</mtext><mi>i</mi></msub><mo>=</mo><mfrac><mrow><munderover><mo>∑</mo><mrow><mi>h</mi><mo>=</mo><mn>2</mn></mrow><mi>n</mi></munderover><msubsup><mi>V</mi><mi>i</mi><mi>h</mi></msubsup></mrow><msubsup><mi>V</mi><mi>i</mi><mn>1</mn></msubsup></mfrac></mrow><annotation encoding="application/x-tex">\text{THD}_i=\dfrac{\sum_{h=2}^{n} V_{i}^h}{V_i^1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord text"><span class="mord">THD</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.5016819999999997em;vertical-align:-0.9628639999999999em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.538818em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7959080000000001em"><span style="top:-2.4231360000000004em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.27686399999999994em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6897100000000003em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.804292em"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">h</span><span class="mrel mtight">=</span><span class="mord mtight">2</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.441336em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9628639999999999em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Na ferramenta de Resposta na Frequência uma corrente senoidal é injetada na barra em uma faixa de frequências e o conjunto de equações matriciais é usado para calcular a resposta da tensão. Este cálculo é repetido em etapas discretas cobrindo o espectro de frequência especificado.</p><p>O programa usa a matriz admitância de sequência positiva e uma corrente injetada de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>0</mn><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">1{,}0 p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> também de sequência positiva na equação matricial para calcular diretamente as impedâncias em p.u.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="referências"></a>Referências<a aria-hidden="true" tabindex="-1" class="hash-link" href="#referências" title="Direct link to heading">#</a></h2><ol><li>ARRILLAGA, J.; WATSON, N. R. Power System Harmonics. John Wiley &amp; Sons; Chichester, 2003. doi: <a href="https://doi.org/10.1002/0470871229" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/0470871229</a></li></ol></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/harmonics.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/fault"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Curto-Circuito</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/stability"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Estabilidade »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#execução-do-cálculo-de-harmônicos-no-psp-ufu" class="table-of-contents__link">Execução do cálculo de harmônicos no PSP-UFU</a><ul><li><a href="#distorções-harmônicas" class="table-of-contents__link">Distorções Harmônicas</a></li><li><a href="#resposta-na-frequência" class="table-of-contents__link">Resposta na Frequência</a></li></ul></li><li><a href="#cálculos-das-ferramentas-harmônicas" class="table-of-contents__link">Cálculos das ferramentas harmônicas</a></li><li><a href="#referências" class="table-of-contents__link">Referências</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item"><a class="menu__link menu__link--sublist menu__link--active" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a aria-current="page" class="menu__link menu__link--active active" tabindex="0" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Mapa de Tensão</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>A ferramenta Mapa de Tensão utiliza o concento de <a href="https://en.wikipedia.org/wiki/Heat_map" target="_blank" rel="noopener noreferrer">mapa de calor</a> para exibir os valores de tensão de todas as barras do sistema por meio de cores.</p><video autoplay="" loop="" muted="" playsinline="" controls=""><source src="/PSP/videos/heatmap.mp4" type="video/mp4"><source src="/PSP/videos/heatmap.webm" type="video/webm"></video><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Essa ferramenta é útil para identificação de barras com sub e sobretensões no sistema de potência, assim como o efeito da inserção / remoção de elementos do sistema.</p></div></div><p>A legenda que correlaciona os valores do módulo da tensão com as cores são exibidas à esquerda da área de trabalho.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="habilitando-a-ferramenta-mapa-de-tensão"></a>Habilitando a ferramenta Mapa de Tensão<a aria-hidden="true" tabindex="-1" class="hash-link" href="#habilitando-a-ferramenta-mapa-de-tensão" title="Direct link to heading">#</a></h2><p>A ferramenta pode ser habilitada ou desabilitada no <a href="/PSP/docs/mainScreen#menu-ribbon">submenu Ribbon <strong>Ferramentas</strong></a> clicando no botão <strong>Mapa de tensão</strong> ou pela tecla de atalho &quot;Ctrl + Shift + H&quot;.</p><p>As configurações da ferramenta podem ser também acessadas no <a href="/PSP/docs/mainScreen#menu-ribbon">submenu Ribbon <strong>Ferramentas</strong></a> clicando no botão <strong>Configurações do projeto</strong></p><div><center><img src="/PSP/images/heatmapForm.png" alt="Configurações da ferramenta Mapa de Tensão" title="Configurações da ferramenta Mapa de Tensão"></center></div><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Na versão atual do programa, somente as opções do mapa de tensão são exibidas nas configurações de projeto.</p></div></div><p>Os limites superiores e inferiores, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> são editados nesse formulário.</p><p>Alternativamente, o programa pode calcular automaticamente os limites. Nesse caso, o limite superior será a maior tensão do circuito e o limite inferior será a menor tensão do circuito.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>O cálculo automático dos limites pode prejudicar a identificação de barras com sub e sobretensões no sistema.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/heatmap.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/graphViewer"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Visualizador de Gráficos</div></a></div><div class="pagination-nav__item pagination-nav__item--next"></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#habilitando-a-ferramenta-mapa-de-tensão" class="table-of-contents__link">Habilitando a ferramenta Mapa de Tensão</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Motor de Indução</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Uma máquina assíncrona da qual apenas um enrolamento é energizado. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=411-31-10" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="motor-de-indução-trifásico-no-psp-ufu"></a>Motor de indução trifásico no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#motor-de-indução-trifásico-no-psp-ufu" title="Direct link to heading">#</a></h2><p>No PSP-UFU, os motores de indução são contemplados nos estudos de <a href="/PSP/docs/powerFLow">fluxo de carga</a> e no estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Os dados de estabilidade da máquina de indução são utilizados em conjunto com o fluxo de carga, <strong>calculando de forma correta a potência reativa das máquinas</strong> e consequentemente a tensão no barramento conectado.</p></div></div><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Ao marcar a opção &quot;Calcular a potência reativa no fluxo de carga&quot;, devem ser inseridos os dados corretos na aba &quot;Estabilidade&quot;, caso contrário, será atribuída uma potência reativa incorreta no motor.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="motor-de-indução-trifásico-no-cálculo-do-fluxo-de-carga"></a>Motor de indução trifásico no cálculo do fluxo de carga<a aria-hidden="true" tabindex="-1" class="hash-link" href="#motor-de-indução-trifásico-no-cálculo-do-fluxo-de-carga" title="Direct link to heading">#</a></h3><p>A figura abaixo apresenta o modelo do motor de indução trifásico (MIT) de gaiola simples.</p><div><center><img src="/PSP/images/indMotorModel.svg" alt="Circuito equivalente do motor de indução" title="Circuito equivalente do motor de indução"></center></div><p>As potências ativa e reativa podem ser calculadas em relação às variáveis e parâmetros do motor em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> como:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo>=</mo><mfrac><mrow><msup><mi>V</mi><mn>2</mn></msup><mrow><mo fence="true">{</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><msub><mi>r</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mo fence="true">]</mo></mrow><mo>+</mo><msub><mi>K</mi><mn>1</mn></msub><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">(</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mo fence="true">)</mo></mrow><mo>+</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo fence="true">]</mo></mrow><mo fence="true">}</mo></mrow></mrow><mrow><msup><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><msub><mi>r</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mo fence="true">]</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mo stretchy="false">(</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo fence="true">]</mo></mrow><mn>2</mn></msup></mrow></mfrac><mspace linebreak="newline"></mspace><mi>Q</mi><mo>=</mo><mfrac><mrow><mo>−</mo><msup><mi>V</mi><mn>2</mn></msup><mrow><mo fence="true">{</mo><msub><mi>K</mi><mn>1</mn></msub><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><msub><mi>r</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mo fence="true">]</mo></mrow><mo>−</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">(</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mo fence="true">)</mo></mrow><mo>+</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo fence="true">]</mo></mrow><mo fence="true">}</mo></mrow></mrow><mrow><msup><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><msub><mi>r</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mo fence="true">]</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mo stretchy="false">(</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo fence="true">]</mo></mrow><mn>2</mn></msup></mrow></mfrac><mspace linebreak="newline"></mspace><mtext> </mtext><mspace linebreak="newline"></mspace><msub><mi>K</mi><mn>1</mn></msub><mo>=</mo><msub><mi>x</mi><mn>2</mn></msub><mo>+</mo><msub><mi>x</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">P = \frac{V^2 \left\{ \left( \frac{r_2}{s} \right) \left[\left(\frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]+K_1 \left[\left(\frac{r_2}{s} \right) \left(x_m+x_1 \right) + r_1 K_1 \right] \right\} }{\left[\left( \frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]^2+\left[\left( \frac{r_2}{s} \right)(x_m+x_1 )+r_1 K_1 \right]^2}\\ Q = \frac{-V^2 \left\{ K_1 \left[\left(\frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]- \left( \frac{r_2}{s} \right) \left[\left(\frac{r_2}{s} \right) \left(x_m+x_1 \right) + r_1 K_1 \right] \right\} }{\left[\left( \frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]^2+\left[\left( \frac{r_2}{s} \right)(x_m+x_1 )+r_1 K_1 \right]^2}\\ ~\\ K_1=x_2+x_m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.884028em;vertical-align:-1.2940180000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.59001em"><span style="top:-2.11em"><span class="pstrut" style="height:3.054008em"></span><span class="mord"><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.054008em"><span style="top:-3.3029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.054008em"><span style="top:-3.3029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.284008em"><span class="pstrut" style="height:3.054008em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.7940180000000003em"><span class="pstrut" style="height:3.054008em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">{</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">}</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2940180000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">Q</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.884028em;vertical-align:-1.2940180000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.59001em"><span style="top:-2.11em"><span class="pstrut" style="height:3.054008em"></span><span class="mord"><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.054008em"><span style="top:-3.3029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.054008em"><span style="top:-3.3029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.284008em"><span class="pstrut" style="height:3.054008em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.7940180000000003em"><span class="pstrut" style="height:3.054008em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">{</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">}</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2940180000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0em;vertical-align:0em"></span><span class="mspace nobreak"> </span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Como pode ser observado nas equações acima, existem quatro variáveis e somente duas equações. Na prática, as variáveis podem ser reduzidas a três, uma vez que o módulo da tensão (V) é obtido nos resultados do <a href="/PSP/docs/powerFlow">fluxo de potência</a>. Para resolver as equações é necessário definir uma variável adicional. A variável escolhida como fixa no PSP-UFU é a potência ativa (P), por fornecer resultados numericamente corretos e adequados para motores em situações de estabilidade.</p><p>Portanto, nesse modelo estático, a potência ativa é mantida constante durante o cálculo do fluxo de carga e o escorregamento (s) é atualizado em cada iteração. A equação da potência ativa pode ser reescrita em relação ao escorregamento:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mn>2</mn></msup><mi>A</mi><mo>+</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mi>B</mi><mo>+</mo><mi>C</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\left(\frac{r_2}{s} \right)^2 A + \left(\frac{r_2}{s} \right) B + C = 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.040008em;vertical-align:-0.686em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">s</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.3540079999999999em"><span style="top:-3.6029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.8359999999999999em;vertical-align:-0.686em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">s</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span></div><p>Em que:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>=</mo><mi>P</mi><mrow><mo fence="true">(</mo><msubsup><mi>r</mi><mn>1</mn><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>K</mi><mn>3</mn><mn>2</mn></msubsup><mo fence="true">)</mo></mrow><mo>−</mo><msup><mi>V</mi><mn>2</mn></msup><msub><mi>r</mi><mn>1</mn></msub><mspace linebreak="newline"></mspace><mi>B</mi><mo>=</mo><mn>2</mn><mi>P</mi><mo stretchy="false">(</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>2</mn></msub><mo>+</mo><msub><mi>K</mi><mn>3</mn></msub><msub><mi>K</mi><mn>4</mn></msub><mo stretchy="false">)</mo><mo>−</mo><msup><mi>V</mi><mn>2</mn></msup><mrow><mo fence="true">(</mo><msub><mi>K</mi><mn>2</mn></msub><mo>+</mo><msub><mi>K</mi><mn>1</mn></msub><msub><mi>K</mi><mn>3</mn></msub><mo fence="true">)</mo></mrow><mspace linebreak="newline"></mspace><mi>C</mi><mo>=</mo><mi>P</mi><mrow><mo fence="true">(</mo><msubsup><mi>K</mi><mn>2</mn><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>K</mi><mn>4</mn><mn>2</mn></msubsup><mo fence="true">)</mo></mrow><mo>−</mo><msup><mi>V</mi><mn>2</mn></msup><msub><mi>K</mi><mn>1</mn></msub><msub><mi>K</mi><mn>4</mn></msub><mspace linebreak="newline"></mspace><msub><mi>K</mi><mn>2</mn></msub><mo>=</mo><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mspace linebreak="newline"></mspace><msub><mi>K</mi><mn>3</mn></msub><mo>=</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mspace linebreak="newline"></mspace><msub><mi>K</mi><mn>4</mn></msub><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">A = P \left( r_1^2 + K_3^2 \right) - V^2 r_1\\ B = 2P(r_1 K_2 + K_3 K_4) - V^2 \left(K_2 + K_1 K_3 \right)\\ C = P \left( K_2^2 + K_4^2 \right) - V^2 K_1 K_4\\ K_2 = -x_1 K_1 -x_2 x_m\\ K_3 = x_m + x_1\\ K_4 = r_1 K_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.2141179999999998em;vertical-align:-0.35001em"></span><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.0141079999999998em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.1141079999999999em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.2141179999999998em;vertical-align:-0.35001em"></span><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.0141079999999998em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord">−</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Esse modelo pode ser inserido na solução do <a href="/PSP/docs/powerFlow">fluxo de carga</a> seguindo os seguintes passos:</p><ol><li>As constantes <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>K</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">K_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> a <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>K</mi><mn>4</mn></msub></mrow><annotation encoding="application/x-tex">K_4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são inicialmente calculadas . Esses valores são mantidos constantes durante toda a solução;</li><li>Em cada iteração são calculados os coeficientes <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault">A</span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi></mrow><annotation encoding="application/x-tex">B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi></mrow><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span></span></span></span></span> utilizando o valor atualizado de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi></mrow><annotation encoding="application/x-tex">V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span></span></span>;</li><li>A equação quadrática é resolvida e dois valores de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(\frac{r_2}{s} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.20001em;vertical-align:-0.35001em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span></span></span></span></span> são obtidos, em que o maior deles é escolhido por estar na região estável da característica toque-escorregamento do motor;</li><li>Utilizando o novo valor de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(\frac{r_2}{s} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.20001em;vertical-align:-0.35001em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span></span></span></span></span>, a potência reativa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi></mrow><annotation encoding="application/x-tex">Q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">Q</span></span></span></span></span>) é obtida. O vetor de potências é então atualizado e os procedimentos convencionais de solução do fluxo de potência são realizados.</li></ol><p>Os passos de 2 a 4 são repetidos até que se obtenha a convergência.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>No PSP-UFU, os motores de indução não são considerados no cálculo de curto-circuito.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="motor-de-indução-trifásico-no-estudo-de-estabilidade"></a>Motor de indução trifásico no estudo de estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#motor-de-indução-trifásico-no-estudo-de-estabilidade" title="Direct link to heading">#</a></h3><p>Uma importante carga dinâmica são os motores de indução, uma vez que correspondem a uma parcela significativa das cargas presentes no sistema elétrico. O <a href="/PSP/docs/indMotor#motor-de-indu%C3%A7%C3%A3o-trif%C3%A1sico-no-c%C3%A1lculo-do-fluxo-de-carga">modelo da máquina de indução apresentado anteriormente</a>, a qual pode ser utilizada tanto como motor quanto como gerador, é bem estabelecida na literatura.</p><p>Como descrito na <a href="/PSP/docs/indMotor#motor-de-indu%C3%A7%C3%A3o-trif%C3%A1sico-no-c%C3%A1lculo-do-fluxo-de-carga">seção anterior</a>, a inicialização dessa máquina é realizada em conjunto com o fluxo de potência, visto que a potência reativa exigida pela máquina de indução é dependente dos parâmetros do motor, assim como a tensão do seu barramento. Essa abordagem é necessária, pois métodos convencionais conduzem a resultados errôneos em sistemas altamente carregados.</p><p>É necessário expressar a equação de movimento da máquina de indução em termos de torque e não potência, como é realizado com as máquinas síncronas. A simetria do rotor também faz com que a posição angular não seja importante e o escorregamento (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi></mrow><annotation encoding="application/x-tex">s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">s</span></span></span></span></span>) é utilizado no lugar da velocidade (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ω</mi></mrow><annotation encoding="application/x-tex">\omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span></span></span></span></span>), em que:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi><mo>=</mo><mi>f</mi><mi>r</mi><mi>a</mi><mi>c</mi><mrow><msub><mi mathvariant="normal">Ω</mi><mn>0</mn></msub><mo>−</mo><mi>ω</mi></mrow><msub><mi mathvariant="normal">Ω</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">s = frac{\Omega_0 - \omega}{\Omega_0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">s</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="mord mathdefault">a</span><span class="mord mathdefault">c</span><span class="mord"><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span></span><span class="mord"><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span></div><p>Desprezando as perdas por atrito e ventilação e a potência no eixo suave, as equações mecânicas do motor são expressas da seguinte forma:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mi>m</mi></msub><mo>=</mo><mi>A</mi><mo>−</mo><mi>B</mi><mi>s</mi><mo>+</mo><mi>C</mi><msup><mi>s</mi><mn>2</mn></msup><mspace linebreak="newline"></mspace><msub><mi>T</mi><mi>e</mi></msub><mo>=</mo><mfrac><mrow><mi>R</mi><mi>e</mi><mrow><mo fence="true">{</mo><mover accent="true"><mi>E</mi><mo>˙</mo></mover><msup><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mo>∗</mo></msup><mo fence="true">}</mo></mrow></mrow><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><mi>s</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mo fence="true">(</mo><msub><mi>T</mi><mi>m</mi></msub><mo>−</mo><msub><mi>T</mi><mi>e</mi></msub><mo fence="true">)</mo></mrow><mrow><mn>2</mn><mi>H</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">T_m = A -Bs + Cs^2\\ T_e = \frac{Re\left\{ \dot{E}\dot{I}^* \right\}}{\Omega_b}\\ \frac{ds}{dt} = \frac{\left( T_m - T_e \right)}{2H}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span><span class="mord mathdefault">s</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.8641079999999999em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:3.02602em;vertical-align:-0.8360000000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.19002em"><span style="top:-2.464em"><span class="pstrut" style="height:3.15em"></span><span class="mord"><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.38em"><span class="pstrut" style="height:3.15em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-4.1900200000000005em"><span class="pstrut" style="height:3.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="mord mathdefault">e</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">{</span></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.055550000000000016em"><span class="mord">˙</span></span></span></span></span></span></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.688696em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">}</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.05744em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.113em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.08125em">H</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">T_m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> é o torque mecânico;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mi>e</mi></msub></mrow><annotation encoding="application/x-tex">T_e</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> é o torque elétrico;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>H</mi></mrow><annotation encoding="application/x-tex">H</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.08125em">H</span></span></span></span></span> é a inércia do conjunto motor - carga mecânica</li></ul><p>Os termos <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault">A</span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi></mrow><annotation encoding="application/x-tex">B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi></mrow><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span></span></span></span></span> são termos que definem o comportamento do torque mecânico da carga de acordo com o escorregamento. O torque mecânico normalmente varia com a <strong>velocidade</strong>, podendo ser expressa proporcionalmente com a seguinte equação quadrática:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mi>m</mi></msub><mo>∝</mo><mi>a</mi><mo>+</mo><mi>b</mi><mi>ω</mi><mo>+</mo><mi>c</mi><msup><mi>ω</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">T_m \propto a + b\omega + c\omega^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em"></span><span class="mord mathdefault">a</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em"></span><span class="mord mathdefault">b</span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.8641079999999999em;vertical-align:0em"></span><span class="mord mathdefault">c</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></div><p>Em que:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>A</mi><mo>∝</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>B</mi><mo>∝</mo><mi>b</mi><mo>+</mo><mn>2</mn><mi>c</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>C</mi><mo>∝</mo><mi>c</mi></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} A \propto a + b + c \\ B \propto b + 2c \\ C \propto c \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.32em;vertical-align:-1.9099999999999997em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35002em"><span style="top:-2.19999em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.19499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.20499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.15001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.2950099999999996em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.30501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.60002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8500199999999998em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em"><span style="top:-4.41em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault">a</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault">b</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault">c</span></span></span><span style="top:-2.97em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em">B</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault">b</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord">2</span><span class="mord mathdefault">c</span></span></span><span style="top:-1.5300000000000002em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">C</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.9099999999999997em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>As equações elétricas do motor de indução de gaiola simples são baseadas no circuito equivalente da <a href="/PSP/docs/indMotor#motor-de-indu%C3%A7%C3%A3o-trif%C3%A1sico-no-c%C3%A1lculo-do-fluxo-de-carga">figura anterior</a>. De forma semelhante ao modelo transitório da máquina síncrona, o motor de indução pode ser modelado pelo circuito equivalente de Thevenin de tensão transitória <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>E</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">E&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span> atrás de uma resistência do estator <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">r_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e uma reatância transitória <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">x&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span>. A reatância transitória aparente de rotor bloqueado é dada por:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo>=</mo><msub><mi>x</mi><mn>1</mn></msub><mo>+</mo><mfrac><mrow><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub></mrow><mrow><msub><mi>x</mi><mn>2</mn></msub><mo>+</mo><msub><mi>x</mi><mi>m</mi></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">x&#x27; = x_1 + \frac{x_2 x_m}{x_2 + x_m}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.801892em;vertical-align:0em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.94356em;vertical-align:-0.8360000000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>A constante de tempo de circuito aberto do rotor (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>T</mi><mn>0</mn><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><annotation encoding="application/x-tex">T_0&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.24810799999999997em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4518920000000004em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24810799999999997em"><span></span></span></span></span></span></span></span></span></span></span>) é:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>T</mi><mn>0</mn><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>=</mo><mfrac><mrow><msub><mi>x</mi><mn>2</mn></msub><mo>+</mo><msub><mi>x</mi><mi>m</mi></msub></mrow><mrow><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><msub><mi>r</mi><mn>2</mn></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">T_0&#x27; = \frac{x_2 + x_m}{\Omega_b r_2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.09633em;vertical-align:-0.8360000000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2603300000000002em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>E a reatância de circuito aberto é:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>0</mn></msub><mo>=</mo><msub><mi>x</mi><mn>1</mn></msub><mo>+</mo><msub><mi>x</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">x_0 = x_1 + x_m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Uma vez que as reatâncias não são afetadas pela posição do rotor, as EADs do motor de indução podem ser expressar diretamente por componentes reais (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi></mrow><annotation encoding="application/x-tex">r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span></span></span></span></span>) e imaginárias (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi></mrow><annotation encoding="application/x-tex">m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">m</span></span></span></span></span>). Portanto, a descrição completa desse modelo é representada pelo seguinte sistema de equações algébrico-diferenciais:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>r</mi></msub><mo>−</mo><msubsup><mi>E</mi><mi>r</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>I</mi><mi>r</mi></msub><mo>−</mo><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><msub><mi>I</mi><mi>m</mi></msub><mspace linebreak="newline"></mspace><msub><mi>V</mi><mi>m</mi></msub><mo>−</mo><msubsup><mi>E</mi><mi>m</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>I</mi><mi>m</mi></msub><mo>−</mo><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><msub><mi>I</mi><mi>m</mi></msub><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>r</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><mi>s</mi><msubsup><mi>E</mi><mi>m</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><mfrac><mrow><msubsup><mi>E</mi><mi>r</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>+</mo><mrow><mo fence="true">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo>−</mo><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>m</mi></msub></mrow><msubsup><mi>T</mi><mn>0</mn><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>m</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><mi>s</mi><msubsup><mi>E</mi><mi>r</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><mfrac><mrow><msubsup><mi>E</mi><mi>m</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mi>i</mi><mrow><mo fence="true">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo>−</mo><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>r</mi></msub></mrow><msubsup><mi>T</mi><mn>0</mn><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mfrac></mrow><annotation encoding="application/x-tex">V_r - E_r&#x27; = r_1 I_r - x&#x27; I_m\\ V_m - E_m&#x27; = r_1 I_m - x&#x27; I_m\\ \frac{dE_r&#x27;}{dt} = \Omega_b s E_m&#x27; - \frac{E_r&#x27; + \left( x_0 - x&#x27; \right) I_m}{T_0&#x27;}\\ \frac{dE_m&#x27;}{dt} = \Omega_b s E_r&#x27; - \frac{E_m&#x27; i \left( x_0 - x&#x27; \right) I_r}{T_0&#x27;}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.9518920000000001em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.9518920000000001em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.114892em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.3811999999999998em;vertical-align:-0.9523079999999999em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.433692em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9523079999999999em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.114892em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.3811999999999998em;vertical-align:-0.9523079999999999em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.433692em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord mathdefault">i</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9523079999999999em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-dos-geradores-síncronos"></a>Formulário de edição dos geradores síncronos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-geradores-síncronos" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos motores de indução:</p><div><center><img src="/PSP/images/indMotorForm.png" alt="Formulário dos motores de indução no PSP-UFU" title="Formulário dos motores de indução no PSP-UFU"></center></div><p>No formulário pode ser observado o botão &quot;Chaveamento&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do motor durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/indMotorSw.png" alt="Formulário de chaveamento do motores de indução" title="Formulário de chaveamento do motores de indução"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_1w39 tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Estabilidade</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Botão Chaveamento</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal do gerador, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potências-ativa-e-reativa"></a>Potências ativa e reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potências-ativa-e-reativa" title="Direct link to heading">#</a></h4><p>Potências ativa (inserida em W, kW, MW ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>) e reativa (inserida em var, kvar, Mvar ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>) do motor.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Caso a opção “Calcular a potência reativa no fluxo de carga” esteja ativada, o campo de potência reativa é desativado para edição.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="calcular-a-potência-reativa-no-fluxo-de-carga"></a>Calcular a potência reativa no fluxo de carga<a aria-hidden="true" tabindex="-1" class="hash-link" href="#calcular-a-potência-reativa-no-fluxo-de-carga" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar os dados fornecidos no formulário de estabilidade para calcular a potência reativa do motor durante o processo iterativo do fluxo de carga.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Caso essa opção não seja utilizada o motor será considerado uma <a href="/PSP/docs/load">carga de potência constante</a> no estudo de <a href="/PSP/docs/powerFlow">fluxo de carga</a>.</p><p>A não utilização dessa opção poderá gerar erros de regime permamente no estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="utilizar-potência-nominal-como-base"></a>Utilizar potência nominal como base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-potência-nominal-como-base" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar a potência nominal do gerador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a potência base do sistema.</p></div></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="referências"></a>Referências<a aria-hidden="true" tabindex="-1" class="hash-link" href="#referências" title="Direct link to heading">#</a></h2><ol><li>SÁNCHEZ, J. C.; OLIVARES, T. I. A.; ORTIZ, G. R.; VEGA, D. R. Induction Motor Static Models for Power Flow and Voltage Stability Studies. In: IEEE Power and Energy Society General Meeting, 2012, San Diego. doi: <a href="https://doi.org/10.1109/PESGM.2012.6345618" target="_blank" rel="noopener noreferrer">https://doi.org/10.1109/PESGM.2012.6345618</a></li><li>IEEE Std 399-1997. IEEE Recommended Practice for Industrial and Commercial Power Systems Analysis (Brown Book). IEEE, New York, ago. 1998. doi: <a href="https://doi.org/10.1109/IEEESTD.1998.88568" target="_blank" rel="noopener noreferrer">https://doi.org/10.1109/IEEESTD.1998.88568</a></li><li>MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: <a href="https://doi.org/10.1007/978-3-642-13669-6" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/978-3-642-13669-6</a></li><li>ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley &amp; Sons, New York, 2001. doi: <a href="https://doi.org/10.1002/9781118878286" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/9781118878286</a></li></ol></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/indMotor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/syncMotor"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Compensador Síncrono</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/controlEditor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Editor de Controle »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#motor-de-indução-trifásico-no-psp-ufu" class="table-of-contents__link">Motor de indução trifásico no PSP-UFU</a><ul><li><a href="#motor-de-indução-trifásico-no-cálculo-do-fluxo-de-carga" class="table-of-contents__link">Motor de indução trifásico no cálculo do fluxo de carga</a></li><li><a href="#motor-de-indução-trifásico-no-estudo-de-estabilidade" class="table-of-contents__link">Motor de indução trifásico no estudo de estabilidade</a></li></ul></li><li><a href="#formulário-de-edição-dos-geradores-síncronos" class="table-of-contents__link">Formulário de edição dos geradores síncronos</a></li><li><a href="#referências" class="table-of-contents__link">Referências</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Motor de Indução</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Uma máquina assíncrona da qual apenas um enrolamento é energizado. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=411-31-10" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="motor-de-indução-trifásico-no-psp-ufu"></a>Motor de indução trifásico no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#motor-de-indução-trifásico-no-psp-ufu" title="Direct link to heading">#</a></h2><p>No PSP-UFU, os motores de indução são contemplados nos estudos de <a href="/PSP/docs/powerFLow">fluxo de carga</a> e no estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Os dados de estabilidade da máquina de indução são utilizados em conjunto com o fluxo de carga, <strong>calculando de forma correta a potência reativa das máquinas</strong> e consequentemente a tensão no barramento conectado.</p></div></div><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Ao marcar a opção &quot;Calcular a potência reativa no fluxo de carga&quot;, devem ser inseridos os dados corretos na aba &quot;Estabilidade&quot;, caso contrário, será atribuída uma potência reativa incorreta no motor.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="motor-de-indução-trifásico-no-cálculo-do-fluxo-de-carga"></a>Motor de indução trifásico no cálculo do fluxo de carga<a aria-hidden="true" tabindex="-1" class="hash-link" href="#motor-de-indução-trifásico-no-cálculo-do-fluxo-de-carga" title="Direct link to heading">#</a></h3><p>A figura abaixo apresenta o modelo do motor de indução trifásico (MIT) de gaiola simples.</p><div><center><img src="/PSP/images/indMotorModel.svg" alt="Circuito equivalente do motor de indução" title="Circuito equivalente do motor de indução"></center></div><p>As potências ativa e reativa podem ser calculadas em relação às variáveis e parâmetros do motor em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> como:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo>=</mo><mfrac><mrow><msup><mi>V</mi><mn>2</mn></msup><mrow><mo fence="true">{</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><msub><mi>r</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mo fence="true">]</mo></mrow><mo>+</mo><msub><mi>K</mi><mn>1</mn></msub><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">(</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mo fence="true">)</mo></mrow><mo>+</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo fence="true">]</mo></mrow><mo fence="true">}</mo></mrow></mrow><mrow><msup><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><msub><mi>r</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mo fence="true">]</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mo stretchy="false">(</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo fence="true">]</mo></mrow><mn>2</mn></msup></mrow></mfrac><mspace linebreak="newline"></mspace><mi>Q</mi><mo>=</mo><mfrac><mrow><mo>−</mo><msup><mi>V</mi><mn>2</mn></msup><mrow><mo fence="true">{</mo><msub><mi>K</mi><mn>1</mn></msub><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><msub><mi>r</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mo fence="true">]</mo></mrow><mo>−</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mrow><mo fence="true">(</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mo fence="true">)</mo></mrow><mo>+</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo fence="true">]</mo></mrow><mo fence="true">}</mo></mrow></mrow><mrow><msup><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><msub><mi>r</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mo fence="true">]</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mo fence="true">[</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mo stretchy="false">(</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo fence="true">]</mo></mrow><mn>2</mn></msup></mrow></mfrac><mspace linebreak="newline"></mspace><mtext> </mtext><mspace linebreak="newline"></mspace><msub><mi>K</mi><mn>1</mn></msub><mo>=</mo><msub><mi>x</mi><mn>2</mn></msub><mo>+</mo><msub><mi>x</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">P = \frac{V^2 \left\{ \left( \frac{r_2}{s} \right) \left[\left(\frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]+K_1 \left[\left(\frac{r_2}{s} \right) \left(x_m+x_1 \right) + r_1 K_1 \right] \right\} }{\left[\left( \frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]^2+\left[\left( \frac{r_2}{s} \right)(x_m+x_1 )+r_1 K_1 \right]^2}\\ Q = \frac{-V^2 \left\{ K_1 \left[\left(\frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]- \left( \frac{r_2}{s} \right) \left[\left(\frac{r_2}{s} \right) \left(x_m+x_1 \right) + r_1 K_1 \right] \right\} }{\left[\left( \frac{r_2}{s} \right) r_1-x_1 K_1-x_2 x_m \right]^2+\left[\left( \frac{r_2}{s} \right)(x_m+x_1 )+r_1 K_1 \right]^2}\\ ~\\ K_1=x_2+x_m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.884028em;vertical-align:-1.2940180000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.59001em"><span style="top:-2.11em"><span class="pstrut" style="height:3.054008em"></span><span class="mord"><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.054008em"><span style="top:-3.3029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.054008em"><span style="top:-3.3029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.284008em"><span class="pstrut" style="height:3.054008em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.7940180000000003em"><span class="pstrut" style="height:3.054008em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">{</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">}</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2940180000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">Q</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.884028em;vertical-align:-1.2940180000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.59001em"><span style="top:-2.11em"><span class="pstrut" style="height:3.054008em"></span><span class="mord"><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.054008em"><span style="top:-3.3029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.054008em"><span style="top:-3.3029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.284008em"><span class="pstrut" style="height:3.054008em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.7940180000000003em"><span class="pstrut" style="height:3.054008em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">{</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">}</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2940180000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0em;vertical-align:0em"></span><span class="mspace nobreak"> </span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Como pode ser observado nas equações acima, existem quatro variáveis e somente duas equações. Na prática, as variáveis podem ser reduzidas a três, uma vez que o módulo da tensão (V) é obtido nos resultados do <a href="/PSP/docs/powerFlow">fluxo de potência</a>. Para resolver as equações é necessário definir uma variável adicional. A variável escolhida como fixa no PSP-UFU é a potência ativa (P), por fornecer resultados numericamente corretos e adequados para motores em situações de estabilidade.</p><p>Portanto, nesse modelo estático, a potência ativa é mantida constante durante o cálculo do fluxo de carga e o escorregamento (s) é atualizado em cada iteração. A equação da potência ativa pode ser reescrita em relação ao escorregamento:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mn>2</mn></msup><mi>A</mi><mo>+</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><mi>B</mi><mo>+</mo><mi>C</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\left(\frac{r_2}{s} \right)^2 A + \left(\frac{r_2}{s} \right) B + C = 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.040008em;vertical-align:-0.686em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">s</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.3540079999999999em"><span style="top:-3.6029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.8359999999999999em;vertical-align:-0.686em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">s</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span></div><p>Em que:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>=</mo><mi>P</mi><mrow><mo fence="true">(</mo><msubsup><mi>r</mi><mn>1</mn><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>K</mi><mn>3</mn><mn>2</mn></msubsup><mo fence="true">)</mo></mrow><mo>−</mo><msup><mi>V</mi><mn>2</mn></msup><msub><mi>r</mi><mn>1</mn></msub><mspace linebreak="newline"></mspace><mi>B</mi><mo>=</mo><mn>2</mn><mi>P</mi><mo stretchy="false">(</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>2</mn></msub><mo>+</mo><msub><mi>K</mi><mn>3</mn></msub><msub><mi>K</mi><mn>4</mn></msub><mo stretchy="false">)</mo><mo>−</mo><msup><mi>V</mi><mn>2</mn></msup><mrow><mo fence="true">(</mo><msub><mi>K</mi><mn>2</mn></msub><mo>+</mo><msub><mi>K</mi><mn>1</mn></msub><msub><mi>K</mi><mn>3</mn></msub><mo fence="true">)</mo></mrow><mspace linebreak="newline"></mspace><mi>C</mi><mo>=</mo><mi>P</mi><mrow><mo fence="true">(</mo><msubsup><mi>K</mi><mn>2</mn><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>K</mi><mn>4</mn><mn>2</mn></msubsup><mo fence="true">)</mo></mrow><mo>−</mo><msup><mi>V</mi><mn>2</mn></msup><msub><mi>K</mi><mn>1</mn></msub><msub><mi>K</mi><mn>4</mn></msub><mspace linebreak="newline"></mspace><msub><mi>K</mi><mn>2</mn></msub><mo>=</mo><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub><mspace linebreak="newline"></mspace><msub><mi>K</mi><mn>3</mn></msub><mo>=</mo><msub><mi>x</mi><mi>m</mi></msub><mo>+</mo><msub><mi>x</mi><mn>1</mn></msub><mspace linebreak="newline"></mspace><msub><mi>K</mi><mn>4</mn></msub><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>K</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">A = P \left( r_1^2 + K_3^2 \right) - V^2 r_1\\ B = 2P(r_1 K_2 + K_3 K_4) - V^2 \left(K_2 + K_1 K_3 \right)\\ C = P \left( K_2^2 + K_4^2 \right) - V^2 K_1 K_4\\ K_2 = -x_1 K_1 -x_2 x_m\\ K_3 = x_m + x_1\\ K_4 = r_1 K_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.2141179999999998em;vertical-align:-0.35001em"></span><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.0141079999999998em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.1141079999999999em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.2141179999999998em;vertical-align:-0.35001em"></span><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.0141079999999998em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord">−</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Esse modelo pode ser inserido na solução do <a href="/PSP/docs/powerFlow">fluxo de carga</a> seguindo os seguintes passos:</p><ol><li>As constantes <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>K</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">K_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> a <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>K</mi><mn>4</mn></msub></mrow><annotation encoding="application/x-tex">K_4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são inicialmente calculadas . Esses valores são mantidos constantes durante toda a solução;</li><li>Em cada iteração são calculados os coeficientes <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault">A</span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi></mrow><annotation encoding="application/x-tex">B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi></mrow><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span></span></span></span></span> utilizando o valor atualizado de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi></mrow><annotation encoding="application/x-tex">V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span></span></span>;</li><li>A equação quadrática é resolvida e dois valores de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(\frac{r_2}{s} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.20001em;vertical-align:-0.35001em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span></span></span></span></span> são obtidos, em que o maior deles é escolhido por estar na região estável da característica toque-escorregamento do motor;</li><li>Utilizando o novo valor de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">(</mo><mfrac><msub><mi>r</mi><mn>2</mn></msub><mi>s</mi></mfrac><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(\frac{r_2}{s} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.20001em;vertical-align:-0.35001em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7114919999999999em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.4101em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em"><span style="top:-2.357em;margin-left:-0.02778em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span></span></span></span></span>, a potência reativa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi></mrow><annotation encoding="application/x-tex">Q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">Q</span></span></span></span></span>) é obtida. O vetor de potências é então atualizado e os procedimentos convencionais de solução do fluxo de potência são realizados.</li></ol><p>Os passos de 2 a 4 são repetidos até que se obtenha a convergência.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>No PSP-UFU, os motores de indução não são considerados no cálculo de curto-circuito.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="motor-de-indução-trifásico-no-estudo-de-estabilidade"></a>Motor de indução trifásico no estudo de estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#motor-de-indução-trifásico-no-estudo-de-estabilidade" title="Direct link to heading">#</a></h3><p>Uma importante carga dinâmica são os motores de indução, uma vez que correspondem a uma parcela significativa das cargas presentes no sistema elétrico. O <a href="/PSP/docs/indMotor#motor-de-indu%C3%A7%C3%A3o-trif%C3%A1sico-no-c%C3%A1lculo-do-fluxo-de-carga">modelo da máquina de indução apresentado anteriormente</a>, a qual pode ser utilizada tanto como motor quanto como gerador, é bem estabelecida na literatura.</p><p>Como descrito na <a href="/PSP/docs/indMotor#motor-de-indu%C3%A7%C3%A3o-trif%C3%A1sico-no-c%C3%A1lculo-do-fluxo-de-carga">seção anterior</a>, a inicialização dessa máquina é realizada em conjunto com o fluxo de potência, visto que a potência reativa exigida pela máquina de indução é dependente dos parâmetros do motor, assim como a tensão do seu barramento. Essa abordagem é necessária, pois métodos convencionais conduzem a resultados errôneos em sistemas altamente carregados.</p><p>É necessário expressar a equação de movimento da máquina de indução em termos de torque e não potência, como é realizado com as máquinas síncronas. A simetria do rotor também faz com que a posição angular não seja importante e o escorregamento (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi></mrow><annotation encoding="application/x-tex">s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">s</span></span></span></span></span>) é utilizado no lugar da velocidade (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ω</mi></mrow><annotation encoding="application/x-tex">\omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span></span></span></span></span>), em que:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi><mo>=</mo><mi>f</mi><mi>r</mi><mi>a</mi><mi>c</mi><mrow><msub><mi mathvariant="normal">Ω</mi><mn>0</mn></msub><mo>−</mo><mi>ω</mi></mrow><msub><mi mathvariant="normal">Ω</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">s = frac{\Omega_0 - \omega}{\Omega_0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">s</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="mord mathdefault">a</span><span class="mord mathdefault">c</span><span class="mord"><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span></span><span class="mord"><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span></div><p>Desprezando as perdas por atrito e ventilação e a potência no eixo suave, as equações mecânicas do motor são expressas da seguinte forma:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mi>m</mi></msub><mo>=</mo><mi>A</mi><mo>−</mo><mi>B</mi><mi>s</mi><mo>+</mo><mi>C</mi><msup><mi>s</mi><mn>2</mn></msup><mspace linebreak="newline"></mspace><msub><mi>T</mi><mi>e</mi></msub><mo>=</mo><mfrac><mrow><mi>R</mi><mi>e</mi><mrow><mo fence="true">{</mo><mover accent="true"><mi>E</mi><mo>˙</mo></mover><msup><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mo>∗</mo></msup><mo fence="true">}</mo></mrow></mrow><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><mi>s</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mo fence="true">(</mo><msub><mi>T</mi><mi>m</mi></msub><mo>−</mo><msub><mi>T</mi><mi>e</mi></msub><mo fence="true">)</mo></mrow><mrow><mn>2</mn><mi>H</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">T_m = A -Bs + Cs^2\\ T_e = \frac{Re\left\{ \dot{E}\dot{I}^* \right\}}{\Omega_b}\\ \frac{ds}{dt} = \frac{\left( T_m - T_e \right)}{2H}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span><span class="mord mathdefault">s</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.8641079999999999em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:3.02602em;vertical-align:-0.8360000000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.19002em"><span style="top:-2.464em"><span class="pstrut" style="height:3.15em"></span><span class="mord"><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.38em"><span class="pstrut" style="height:3.15em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-4.1900200000000005em"><span class="pstrut" style="height:3.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="mord mathdefault">e</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">{</span></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.055550000000000016em"><span class="mord">˙</span></span></span></span></span></span></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.688696em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">}</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.05744em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.113em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.08125em">H</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">T_m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> é o torque mecânico;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mi>e</mi></msub></mrow><annotation encoding="application/x-tex">T_e</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> é o torque elétrico;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>H</mi></mrow><annotation encoding="application/x-tex">H</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.08125em">H</span></span></span></span></span> é a inércia do conjunto motor - carga mecânica</li></ul><p>Os termos <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault">A</span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi></mrow><annotation encoding="application/x-tex">B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.05017em">B</span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi></mrow><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">C</span></span></span></span></span> são termos que definem o comportamento do torque mecânico da carga de acordo com o escorregamento. O torque mecânico normalmente varia com a <strong>velocidade</strong>, podendo ser expressa proporcionalmente com a seguinte equação quadrática:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mi>m</mi></msub><mo>∝</mo><mi>a</mi><mo>+</mo><mi>b</mi><mi>ω</mi><mo>+</mo><mi>c</mi><msup><mi>ω</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">T_m \propto a + b\omega + c\omega^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em"></span><span class="mord mathdefault">a</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em"></span><span class="mord mathdefault">b</span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.8641079999999999em;vertical-align:0em"></span><span class="mord mathdefault">c</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></div><p>Em que:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>A</mi><mo>∝</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>B</mi><mo>∝</mo><mi>b</mi><mo>+</mo><mn>2</mn><mi>c</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>C</mi><mo>∝</mo><mi>c</mi></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} A \propto a + b + c \\ B \propto b + 2c \\ C \propto c \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.32em;vertical-align:-1.9099999999999997em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35002em"><span style="top:-2.19999em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.19499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.20499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.15001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.2950099999999996em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.30501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.60002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8500199999999998em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em"><span style="top:-4.41em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathdefault">A</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault">a</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault">b</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault">c</span></span></span><span style="top:-2.97em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05017em">B</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault">b</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord">2</span><span class="mord mathdefault">c</span></span></span><span style="top:-1.5300000000000002em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">C</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.9099999999999997em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>As equações elétricas do motor de indução de gaiola simples são baseadas no circuito equivalente da <a href="/PSP/docs/indMotor#motor-de-indu%C3%A7%C3%A3o-trif%C3%A1sico-no-c%C3%A1lculo-do-fluxo-de-carga">figura anterior</a>. De forma semelhante ao modelo transitório da máquina síncrona, o motor de indução pode ser modelado pelo circuito equivalente de Thevenin de tensão transitória <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>E</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">E&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span> atrás de uma resistência do estator <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">r_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e uma reatância transitória <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">x&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span>. A reatância transitória aparente de rotor bloqueado é dada por:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo>=</mo><msub><mi>x</mi><mn>1</mn></msub><mo>+</mo><mfrac><mrow><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mi>m</mi></msub></mrow><mrow><msub><mi>x</mi><mn>2</mn></msub><mo>+</mo><msub><mi>x</mi><mi>m</mi></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">x&#x27; = x_1 + \frac{x_2 x_m}{x_2 + x_m}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.801892em;vertical-align:0em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.94356em;vertical-align:-0.8360000000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>A constante de tempo de circuito aberto do rotor (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>T</mi><mn>0</mn><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><annotation encoding="application/x-tex">T_0&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.24810799999999997em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4518920000000004em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24810799999999997em"><span></span></span></span></span></span></span></span></span></span></span>) é:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>T</mi><mn>0</mn><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>=</mo><mfrac><mrow><msub><mi>x</mi><mn>2</mn></msub><mo>+</mo><msub><mi>x</mi><mi>m</mi></msub></mrow><mrow><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><msub><mi>r</mi><mn>2</mn></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">T_0&#x27; = \frac{x_2 + x_m}{\Omega_b r_2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.09633em;vertical-align:-0.8360000000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2603300000000002em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>E a reatância de circuito aberto é:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>0</mn></msub><mo>=</mo><msub><mi>x</mi><mn>1</mn></msub><mo>+</mo><msub><mi>x</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">x_0 = x_1 + x_m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Uma vez que as reatâncias não são afetadas pela posição do rotor, as EADs do motor de indução podem ser expressar diretamente por componentes reais (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi></mrow><annotation encoding="application/x-tex">r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span></span></span></span></span>) e imaginárias (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi></mrow><annotation encoding="application/x-tex">m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">m</span></span></span></span></span>). Portanto, a descrição completa desse modelo é representada pelo seguinte sistema de equações algébrico-diferenciais:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>r</mi></msub><mo>−</mo><msubsup><mi>E</mi><mi>r</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>I</mi><mi>r</mi></msub><mo>−</mo><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><msub><mi>I</mi><mi>m</mi></msub><mspace linebreak="newline"></mspace><msub><mi>V</mi><mi>m</mi></msub><mo>−</mo><msubsup><mi>E</mi><mi>m</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>=</mo><msub><mi>r</mi><mn>1</mn></msub><msub><mi>I</mi><mi>m</mi></msub><mo>−</mo><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><msub><mi>I</mi><mi>m</mi></msub><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>r</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><mi>s</mi><msubsup><mi>E</mi><mi>m</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><mfrac><mrow><msubsup><mi>E</mi><mi>r</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>+</mo><mrow><mo fence="true">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo>−</mo><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>m</mi></msub></mrow><msubsup><mi>T</mi><mn>0</mn><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>m</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><mi>s</mi><msubsup><mi>E</mi><mi>r</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><mfrac><mrow><msubsup><mi>E</mi><mi>m</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mi>i</mi><mrow><mo fence="true">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo>−</mo><msup><mi>x</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>r</mi></msub></mrow><msubsup><mi>T</mi><mn>0</mn><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mfrac></mrow><annotation encoding="application/x-tex">V_r - E_r&#x27; = r_1 I_r - x&#x27; I_m\\ V_m - E_m&#x27; = r_1 I_m - x&#x27; I_m\\ \frac{dE_r&#x27;}{dt} = \Omega_b s E_m&#x27; - \frac{E_r&#x27; + \left( x_0 - x&#x27; \right) I_m}{T_0&#x27;}\\ \frac{dE_m&#x27;}{dt} = \Omega_b s E_r&#x27; - \frac{E_m&#x27; i \left( x_0 - x&#x27; \right) I_r}{T_0&#x27;}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.9518920000000001em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.9518920000000001em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.114892em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.3811999999999998em;vertical-align:-0.9523079999999999em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.433692em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9523079999999999em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.114892em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.3811999999999998em;vertical-align:-0.9523079999999999em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.433692em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord mathdefault">i</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9523079999999999em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-dos-geradores-síncronos"></a>Formulário de edição dos geradores síncronos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-geradores-síncronos" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos motores de indução:</p><div><center><img src="/PSP/images/indMotorForm.png" alt="Formulário dos motores de indução no PSP-UFU" title="Formulário dos motores de indução no PSP-UFU"></center></div><p>No formulário pode ser observado o botão &quot;Chaveamento&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do motor durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/indMotorSw.png" alt="Formulário de chaveamento do motores de indução" title="Formulário de chaveamento do motores de indução"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_1w39 tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Estabilidade</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Botão Chaveamento</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal do gerador, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potências-ativa-e-reativa"></a>Potências ativa e reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potências-ativa-e-reativa" title="Direct link to heading">#</a></h4><p>Potências ativa (inserida em W, kW, MW ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>) e reativa (inserida em var, kvar, Mvar ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>) do motor.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Caso a opção “Calcular a potência reativa no fluxo de carga” esteja ativada, o campo de potência reativa é desativado para edição.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="calcular-a-potência-reativa-no-fluxo-de-carga"></a>Calcular a potência reativa no fluxo de carga<a aria-hidden="true" tabindex="-1" class="hash-link" href="#calcular-a-potência-reativa-no-fluxo-de-carga" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar os dados fornecidos no formulário de estabilidade para calcular a potência reativa do motor durante o processo iterativo do fluxo de carga.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Caso essa opção não seja utilizada o motor será considerado uma <a href="/PSP/docs/load">carga de potência constante</a> no estudo de <a href="/PSP/docs/powerFlow">fluxo de carga</a>.</p><p>A não utilização dessa opção poderá gerar erros de regime permamente no estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="utilizar-potência-nominal-como-base"></a>Utilizar potência nominal como base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-potência-nominal-como-base" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar a potência nominal do gerador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a potência base do sistema.</p></div></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="referências"></a>Referências<a aria-hidden="true" tabindex="-1" class="hash-link" href="#referências" title="Direct link to heading">#</a></h2><ol><li>SÁNCHEZ, J. C.; OLIVARES, T. I. A.; ORTIZ, G. R.; VEGA, D. R. Induction Motor Static Models for Power Flow and Voltage Stability Studies. In: IEEE Power and Energy Society General Meeting, 2012, San Diego. doi: <a href="https://doi.org/10.1109/PESGM.2012.6345618" target="_blank" rel="noopener noreferrer">https://doi.org/10.1109/PESGM.2012.6345618</a></li><li>IEEE Std 399-1997. IEEE Recommended Practice for Industrial and Commercial Power Systems Analysis (Brown Book). IEEE, New York, ago. 1998. doi: <a href="https://doi.org/10.1109/IEEESTD.1998.88568" target="_blank" rel="noopener noreferrer">https://doi.org/10.1109/IEEESTD.1998.88568</a></li><li>MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: <a href="https://doi.org/10.1007/978-3-642-13669-6" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/978-3-642-13669-6</a></li><li>ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley &amp; Sons, New York, 2001. doi: <a href="https://doi.org/10.1002/9781118878286" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/9781118878286</a></li></ol></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/indMotor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/syncMotor"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Compensador Síncrono</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/controlEditor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Editor de Controle »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#motor-de-indução-trifásico-no-psp-ufu" class="table-of-contents__link">Motor de indução trifásico no PSP-UFU</a><ul><li><a href="#motor-de-indução-trifásico-no-cálculo-do-fluxo-de-carga" class="table-of-contents__link">Motor de indução trifásico no cálculo do fluxo de carga</a></li><li><a href="#motor-de-indução-trifásico-no-estudo-de-estabilidade" class="table-of-contents__link">Motor de indução trifásico no estudo de estabilidade</a></li></ul></li><li><a href="#formulário-de-edição-dos-geradores-síncronos" class="table-of-contents__link">Formulário de edição dos geradores síncronos</a></li><li><a href="#referências" class="table-of-contents__link">Referências</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">PSP-UFU</h1></header><div class="markdown"><div class="admonition admonition-important alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>important</h5></div><div class="admonition-content"><p>This user guide was written in Brazilian Portuguese. If you want to help me translate this guide, contact-me on <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> or <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="sobre-o-psp-ufu"></a>Sobre o PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#sobre-o-psp-ufu" title="Direct link to heading">#</a></h2><p>O PSP-UFU (Plataforma de Sistemas de Potência da Universidade Federal de Uberlândia) é um software <strong>multi-plataforma</strong>, <strong>multilíngue</strong>, <strong>livre e de código aberto (FOSS)</strong> com <strong>recursos avançados de GUI (<em>Graphical User Interface</em>)</strong> e <strong>ferramentas CAD (<em>Computer Aided Design</em>)</strong> para estudos de sistemas elétricos de potência.</p><p>O software permite a construção de qualquer rede de transmissão elétrica e sistemas de controle através da inserção de elementos visuais. Para a visualização dos resultados, o programa oferece <strong>elementos de texto vinculados</strong> na tela principal e também <strong>editores de tabelas e gráficos</strong>.</p><p>O PSP-UFU tem como objetivo fornecer ferramentas eficientes de simulação para fins de <strong>pesquisa</strong> e <strong>educação</strong>, além de <strong>aplicações industriais</strong> em sistemas elétricos de potência.</p><p>Resumidamente, o <em>software</em> pode executar os seguintes estudos:</p><ul><li>Fluxo de potência</li><li>Cálculo de curto-circuito</li><li>Harmônicos</li><li>Estabilidade transitória e dinâmica</li></ul><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="publicações"></a>Publicações<a aria-hidden="true" tabindex="-1" class="hash-link" href="#publicações" title="Direct link to heading">#</a></h3><p>Os artigos abaixo possuem maiores detalhes a respeito do PSP-UFU:</p><blockquote><p>Oliveira, T. L., Guimarães, G. C., &amp; Silva, L. R. C. (2019). PSP-UFU: An open-source, graphical, and multiplatform software for power system studies. <em>International Transactions on Electrical Energy Systems</em>, e12185. doi: <a href="https://doi.org/10.1002/2050-7038.12185" target="_blank" rel="noopener noreferrer">10.1002/2050-7038.12185</a></p></blockquote><blockquote><p>Oliveira, T. L., Guimarães, G. C., Silva, L. R., &amp; Rezende, J. O. (2019). Power system education and research applications using free and open-source, graphical and multiplatform PSP-UFU software. <em>The International Journal of Electrical Engineering &amp; Education</em>, 0020720919879058. doi: <a href="https://doi.org/10.1177/0020720919879058" target="_blank" rel="noopener noreferrer">10.1177/0020720919879058</a></p></blockquote><p>A Tese de Doutorado abaixo detalha em profundidade os cálculos envolvidos, arquitetura de software e ferramentas implementadas no PSP-UFU:</p><blockquote><p>Oliveira, T. L. (2019). Desenvolvimento de um programa computacional livre, gráfico, e multiplataforma para analisar sistemas elétricos de potência em regime permanente e dinâmico. doi: <a href="https://dx.doi.org/10.14393/ufu.te.2019.2444" target="_blank" rel="noopener noreferrer">10.14393/ufu.te.2019.2444</a></p></blockquote><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="contribuindo-com-o-projeto"></a>Contribuindo com o projeto<a aria-hidden="true" tabindex="-1" class="hash-link" href="#contribuindo-com-o-projeto" title="Direct link to heading">#</a></h3><p>Se você está interessado em contribuir com o PSP-UFU de alguma forma (desenvolvimento, críticas, sugestões, etc.), entre em contato pelo <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> ou <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="desenvolvedores"></a>Desenvolvedor<del>es</del><a aria-hidden="true" tabindex="-1" class="hash-link" href="#desenvolvedores" title="Direct link to heading">#</a></h3><p><a href="https://github.com/Thales1330" target="_blank" rel="noopener noreferrer">Thales Lima Oliveira</a></p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/aboutPSP.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/installation"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Instalação »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#sobre-o-psp-ufu" class="table-of-contents__link">Sobre o PSP-UFU</a><ul><li><a href="#publicações" class="table-of-contents__link">Publicações</a></li><li><a href="#contribuindo-com-o-projeto" class="table-of-contents__link">Contribuindo com o projeto</a></li><li><a href="#desenvolvedores" class="table-of-contents__link">Desenvolvedor<del>es</del></a></li></ul></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">PSP-UFU</h1></header><div class="markdown"><div class="admonition admonition-important alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>important</h5></div><div class="admonition-content"><p>This user guide was written in Brazilian Portuguese. If you want to help me translate this guide, contact-me on <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> or <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="sobre-o-psp-ufu"></a>Sobre o PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#sobre-o-psp-ufu" title="Direct link to heading">#</a></h2><p>O PSP-UFU (Plataforma de Sistemas de Potência da Universidade Federal de Uberlândia) é um software <strong>multi-plataforma</strong>, <strong>multilíngue</strong>, <strong>livre e de código aberto (FOSS)</strong> com <strong>recursos avançados de GUI (<em>Graphical User Interface</em>)</strong> e <strong>ferramentas CAD (<em>Computer Aided Design</em>)</strong> para estudos de sistemas elétricos de potência.</p><p>O software permite a construção de qualquer rede de transmissão elétrica e sistemas de controle através da inserção de elementos visuais. Para a visualização dos resultados, o programa oferece <strong>elementos de texto vinculados</strong> na tela principal e também <strong>editores de tabelas e gráficos</strong>.</p><p>O PSP-UFU tem como objetivo fornecer ferramentas eficientes de simulação para fins de <strong>pesquisa</strong> e <strong>educação</strong>, além de <strong>aplicações industriais</strong> em sistemas elétricos de potência.</p><p>Resumidamente, o <em>software</em> pode executar os seguintes estudos:</p><ul><li>Fluxo de potência</li><li>Cálculo de curto-circuito</li><li>Harmônicos</li><li>Estabilidade transitória e dinâmica</li></ul><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="publicações"></a>Publicações<a aria-hidden="true" tabindex="-1" class="hash-link" href="#publicações" title="Direct link to heading">#</a></h3><p>Os artigos abaixo possuem maiores detalhes a respeito do PSP-UFU:</p><blockquote><p>Oliveira, T. L., Guimarães, G. C., &amp; Silva, L. R. C. (2019). PSP-UFU: An open-source, graphical, and multiplatform software for power system studies. <em>International Transactions on Electrical Energy Systems</em>, e12185. doi: <a href="https://doi.org/10.1002/2050-7038.12185" target="_blank" rel="noopener noreferrer">10.1002/2050-7038.12185</a></p></blockquote><blockquote><p>Oliveira, T. L., Guimarães, G. C., Silva, L. R., &amp; Rezende, J. O. (2019). Power system education and research applications using free and open-source, graphical and multiplatform PSP-UFU software. <em>The International Journal of Electrical Engineering &amp; Education</em>, 0020720919879058. doi: <a href="https://doi.org/10.1177/0020720919879058" target="_blank" rel="noopener noreferrer">10.1177/0020720919879058</a></p></blockquote><p>A Tese de Doutorado abaixo detalha em profundidade os cálculos envolvidos, arquitetura de software e ferramentas implementadas no PSP-UFU:</p><blockquote><p>Oliveira, T. L. (2019). Desenvolvimento de um programa computacional livre, gráfico, e multiplataforma para analisar sistemas elétricos de potência em regime permanente e dinâmico. doi: <a href="https://dx.doi.org/10.14393/ufu.te.2019.2444" target="_blank" rel="noopener noreferrer">10.14393/ufu.te.2019.2444</a></p></blockquote><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="contribuindo-com-o-projeto"></a>Contribuindo com o projeto<a aria-hidden="true" tabindex="-1" class="hash-link" href="#contribuindo-com-o-projeto" title="Direct link to heading">#</a></h3><p>Se você está interessado em contribuir com o PSP-UFU de alguma forma (desenvolvimento, críticas, sugestões, etc.), entre em contato pelo <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> ou <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="desenvolvedores"></a>Desenvolvedor<del>es</del><a aria-hidden="true" tabindex="-1" class="hash-link" href="#desenvolvedores" title="Direct link to heading">#</a></h3><p><a href="https://github.com/Thales1330" target="_blank" rel="noopener noreferrer">Thales Lima Oliveira</a></p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/aboutPSP.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/installation"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Instalação »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#sobre-o-psp-ufu" class="table-of-contents__link">Sobre o PSP-UFU</a><ul><li><a href="#publicações" class="table-of-contents__link">Publicações</a></li><li><a href="#contribuindo-com-o-projeto" class="table-of-contents__link">Contribuindo com o projeto</a></li><li><a href="#desenvolvedores" class="table-of-contents__link">Desenvolvedor<del>es</del></a></li></ul></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Indutor</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Um reator destinado à conexão de derivação em uma rede para compensar a corrente capacitiva. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=421-01-03" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="indutor-no-psp-ufu"></a>Indutor no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#indutor-no-psp-ufu" title="Direct link to heading">#</a></h2><p>O elemento indutor (ou reator) representa, geralmente, reator <em>shunt</em> no circuito do PSP-UFU.</p><p>Os capacitores e reatores exigem somente sua potência reativa como parâmetro. Esses elementos passivos são somente inseridos na matriz admitância cuja impedância é calculada a partir de sua potência e tensão nominais.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-dos-indutores"></a>Formulário de edição dos indutores<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-indutores" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos indutores:</p><div><center><img src="/PSP/images/indForm.png" alt="Formulário dos indutores no PSP-UFU" title="Formulário dos indutores no PSP-UFU"></center></div><p>Além do único contexto geral, pode ser observado o botão &quot;Estabilidade&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do indutor durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/indSw.png" alt="Formulário de chaveamento do indutor" title="Formulário de chaveamento do indutor"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_1w39 tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Botão Estabilidade</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-reativa"></a>Potência reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-reativa" title="Direct link to heading">#</a></h4><p>Os capacitores e reatores exigem somente sua potência reativa como parâmetro, inserida em Mvar, kvar, var ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> (na base de potência do sistema). </p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/inductor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/capacitor"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Capacitor</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/harmSource"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Fonte de Corrente Harmônica »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#indutor-no-psp-ufu" class="table-of-contents__link">Indutor no PSP-UFU</a></li><li><a href="#formulário-de-edição-dos-indutores" class="table-of-contents__link">Formulário de edição dos indutores</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Indutor</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Um reator destinado à conexão de derivação em uma rede para compensar a corrente capacitiva. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=421-01-03" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="indutor-no-psp-ufu"></a>Indutor no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#indutor-no-psp-ufu" title="Direct link to heading">#</a></h2><p>O elemento indutor (ou reator) representa, geralmente, reator <em>shunt</em> no circuito do PSP-UFU.</p><p>Os capacitores e reatores exigem somente sua potência reativa como parâmetro. Esses elementos passivos são somente inseridos na matriz admitância cuja impedância é calculada a partir de sua potência e tensão nominais.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-dos-indutores"></a>Formulário de edição dos indutores<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-indutores" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos indutores:</p><div><center><img src="/PSP/images/indForm.png" alt="Formulário dos indutores no PSP-UFU" title="Formulário dos indutores no PSP-UFU"></center></div><p>Além do único contexto geral, pode ser observado o botão &quot;Estabilidade&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do indutor durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/indSw.png" alt="Formulário de chaveamento do indutor" title="Formulário de chaveamento do indutor"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_1w39 tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Botão Estabilidade</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-reativa"></a>Potência reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-reativa" title="Direct link to heading">#</a></h4><p>Os capacitores e reatores exigem somente sua potência reativa como parâmetro, inserida em Mvar, kvar, var ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> (na base de potência do sistema). </p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/inductor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/capacitor"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Capacitor</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/harmSource"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Fonte de Corrente Harmônica »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#indutor-no-psp-ufu" class="table-of-contents__link">Indutor no PSP-UFU</a></li><li><a href="#formulário-de-edição-dos-indutores" class="table-of-contents__link">Formulário de edição dos indutores</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Instalação</h1></header><div class="markdown"><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="download"></a>Download<a aria-hidden="true" tabindex="-1" class="hash-link" href="#download" title="Direct link to heading">#</a></h2><p>O download do PSP-UFU pode ser realizado pelo <a href="https://github.com/Thales1330/PSP/releases/latest" target="_blank" rel="noopener noreferrer">&quot;<em>last release</em>&quot; do repositório do PSP-UFU no GitHub</a>.</p><p>Ao acessar ao link, role a página até encontrar os <em>Assets</em>:</p><div><center><img src="/PSP/images/download.png" alt="Assets download" title="Informações da Figura"></center></div><p>Como o PSP-UFU é um <em>software</em> multiplataforma, você deve baixar o arquivo correto:</p><ul><li>Para o sistema operacional <a href="/PSP/docs/installation#windows">Windows</a> baixe os arquivos <em>.exe</em> (recomendado) ou <em>.zip</em>.</li><li>Para os sistemas <a href="/PSP/docs/installation#linux">Linux</a> baseados no Debian (por exemplo, Ubuntu, Mint) <em>64 bits</em> baixe o pacote de instalação <em>.deb</em>.</li></ul><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Se você está interessado em contribuir com o PSP-UFU construindo-o para outros sistemas operacionais (principalmente macOS!) entre em contato pelo <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> ou <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>.</p></div></div><p>Na sequência são apresentados o passo-a-passo para instalação dos SOs <a href="/PSP/docs/installation#windows">Windows</a> e <a href="/PSP/docs/installation#linux">Linux</a>. Também são apresentadas as soluções para os erros mais recorrentes.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="windows"></a>Windows<a aria-hidden="true" tabindex="-1" class="hash-link" href="#windows" title="Direct link to heading">#</a></h2><p>Após baixar o arquivo <em>.exe</em> avance em cada passo do instalador. O executável irá solicitar automaticamente a instalação do <strong>Microsoft Visual C++ Redistribuível</strong> e, caso não esteja instalado no seu computador, realize os procedimentos do programa.</p><p>Caso o executável falhe em abrir, baixe o arquivo <em>.zip</em> e descompacte em alguma pasta do seu sistema. Nesse caso é necessário baixar e instalar manualmente o <a href="https://aka.ms/vs/16/release/vc_redist.x86.exe" target="_blank" rel="noopener noreferrer"><strong>Microsoft Visual C++ Redistribuível 32 bits</strong></a>.</p><p>Após a conclusão da instalação abra o PSP-UFU para verificar a correta instalação. O executável está presente na pasta &quot;<em>&lt;local de instalação&gt;/PSP-UFU/bin/PSP-UFU.exe</em>&quot;.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="problemas-recorrentes-no-windows"></a>Problemas recorrentes no Windows<a aria-hidden="true" tabindex="-1" class="hash-link" href="#problemas-recorrentes-no-windows" title="Direct link to heading">#</a></h3><ul><li>Ao baixar o navegador pode <strong>falsamente</strong> sinalizar que é um arquivo perigoso, basta clicar em &quot;Manter arquivo&quot;;</li><li>Ao abrir o instalador, novamente o Windows sinaliza que o arquivo é perigoso, basta clicar em &quot;Executar assim mesmo&quot;;</li><li>Ao abrir o programa e alterar o seu idioma, uma mensagem de erro é exibida. Para resolver esse problema basta executar o PSP-UFU como administrador (clicar com botão direito no atalho do programa e posteriormente em executar como administrador). Altere novamente o idioma e reinicie o programa;</li><li>Ao criar um novo projeto a tela de trabalho não é exibida ou é exibida uma tela preta. Vá nas opções gerais e altere o renderizador para &quot;Device Context&quot;. Caso apareça uma mensagem de erro, execute o programa como administrador e repita o processo. Reinicie o programa.</li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="linux"></a>Linux<a aria-hidden="true" tabindex="-1" class="hash-link" href="#linux" title="Direct link to heading">#</a></h2><p>A instalação no sistema Linux é facilmente realizado pelo pacote de instalação automático <em>.deb</em>.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Note que essa versão para Linux está defasada e algumas funcionalidades do programa podem não estar presentes.</p><p>Caso queira contribuir com o projeto e construir a versão atual no sistema Linux baseado em Debian ou em outras distribuições entre em contato pelo <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> ou <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="problemas-recorrentes-no-linux"></a>Problemas recorrentes no Linux<a aria-hidden="true" tabindex="-1" class="hash-link" href="#problemas-recorrentes-no-linux" title="Direct link to heading">#</a></h3><p>Pode ser necessário adicionar o <a href="https://wiki.wxwidgets.org/Compiling_and_getting_started#Running_wxWidgets_projects" target="_blank" rel="noopener noreferrer">diretório das bibliotecas do wxWidgets</a> nas variáveis de ambiente.
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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Instalação</h1></header><div class="markdown"><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="download"></a>Download<a aria-hidden="true" tabindex="-1" class="hash-link" href="#download" title="Direct link to heading">#</a></h2><p>O download do PSP-UFU pode ser realizado pelo <a href="https://github.com/Thales1330/PSP/releases/latest" target="_blank" rel="noopener noreferrer">&quot;<em>last release</em>&quot; do repositório do PSP-UFU no GitHub</a>.</p><p>Ao acessar ao link, role a página até encontrar os <em>Assets</em>:</p><div><center><img src="/PSP/images/download.png" alt="Assets download" title="Informações da Figura"></center></div><p>Como o PSP-UFU é um <em>software</em> multiplataforma, você deve baixar o arquivo correto:</p><ul><li>Para o sistema operacional <a href="/PSP/docs/installation#windows">Windows</a> baixe os arquivos <em>.exe</em> (recomendado) ou <em>.zip</em>.</li><li>Para os sistemas <a href="/PSP/docs/installation#linux">Linux</a> baseados no Debian (por exemplo, Ubuntu, Mint) <em>64 bits</em> baixe o pacote de instalação <em>.deb</em>.</li></ul><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Se você está interessado em contribuir com o PSP-UFU construindo-o para outros sistemas operacionais (principalmente macOS!) entre em contato pelo <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> ou <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>.</p></div></div><p>Na sequência são apresentados o passo-a-passo para instalação dos SOs <a href="/PSP/docs/installation#windows">Windows</a> e <a href="/PSP/docs/installation#linux">Linux</a>. Também são apresentadas as soluções para os erros mais recorrentes.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="windows"></a>Windows<a aria-hidden="true" tabindex="-1" class="hash-link" href="#windows" title="Direct link to heading">#</a></h2><p>Após baixar o arquivo <em>.exe</em> avance em cada passo do instalador. O executável irá solicitar automaticamente a instalação do <strong>Microsoft Visual C++ Redistribuível</strong> e, caso não esteja instalado no seu computador, realize os procedimentos do programa.</p><p>Caso o executável falhe em abrir, baixe o arquivo <em>.zip</em> e descompacte em alguma pasta do seu sistema. Nesse caso é necessário baixar e instalar manualmente o <a href="https://aka.ms/vs/16/release/vc_redist.x86.exe" target="_blank" rel="noopener noreferrer"><strong>Microsoft Visual C++ Redistribuível 32 bits</strong></a>.</p><p>Após a conclusão da instalação abra o PSP-UFU para verificar a correta instalação. O executável está presente na pasta &quot;<em>&lt;local de instalação&gt;/PSP-UFU/bin/PSP-UFU.exe</em>&quot;.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="problemas-recorrentes-no-windows"></a>Problemas recorrentes no Windows<a aria-hidden="true" tabindex="-1" class="hash-link" href="#problemas-recorrentes-no-windows" title="Direct link to heading">#</a></h3><ul><li>Ao baixar o navegador pode <strong>falsamente</strong> sinalizar que é um arquivo perigoso, basta clicar em &quot;Manter arquivo&quot;;</li><li>Ao abrir o instalador, novamente o Windows sinaliza que o arquivo é perigoso, basta clicar em &quot;Executar assim mesmo&quot;;</li><li>Ao abrir o programa e alterar o seu idioma, uma mensagem de erro é exibida. Para resolver esse problema basta executar o PSP-UFU como administrador (clicar com botão direito no atalho do programa e posteriormente em executar como administrador). Altere novamente o idioma e reinicie o programa;</li><li>Ao criar um novo projeto a tela de trabalho não é exibida ou é exibida uma tela preta. Vá nas opções gerais e altere o renderizador para &quot;Device Context&quot;. Caso apareça uma mensagem de erro, execute o programa como administrador e repita o processo. Reinicie o programa.</li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="linux"></a>Linux<a aria-hidden="true" tabindex="-1" class="hash-link" href="#linux" title="Direct link to heading">#</a></h2><p>A instalação no sistema Linux é facilmente realizado pelo pacote de instalação automático <em>.deb</em>.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Note que essa versão para Linux está defasada e algumas funcionalidades do programa podem não estar presentes.</p><p>Caso queira contribuir com o projeto e construir a versão atual no sistema Linux baseado em Debian ou em outras distribuições entre em contato pelo <a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer">GitHub</a> ou <a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer">Twitter</a>.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="problemas-recorrentes-no-linux"></a>Problemas recorrentes no Linux<a aria-hidden="true" tabindex="-1" class="hash-link" href="#problemas-recorrentes-no-linux" title="Direct link to heading">#</a></h3><p>Pode ser necessário adicionar o <a href="https://wiki.wxwidgets.org/Compiling_and_getting_started#Running_wxWidgets_projects" target="_blank" rel="noopener noreferrer">diretório das bibliotecas do wxWidgets</a> nas variáveis de ambiente.
 Para isso, siga <strong>UM</strong> dos métodos apresentados abaixo:</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="método-i-recomendado"></a><em>Método I (recomendado)</em><a aria-hidden="true" tabindex="-1" class="hash-link" href="#método-i-recomendado" title="Direct link to heading">#</a></h4><p>Insira o seguinte comando no arquivo <strong>~/.bashrc</strong>:</p><div class="mdxCodeBlock_1XEh"><div class="codeBlockContent_1u-d"><button type="button" aria-label="Copy code to clipboard" class="copyButton_10dd">Copy</button><div tabindex="0" class="prism-code language-shell codeBlock_3iAC"><div class="codeBlockLines_b7E3" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token builtin class-name" style="color:rgb(255, 203, 107)">echo</span><span class="token plain"> </span><span class="token string" style="color:rgb(195, 232, 141)">&quot;export LD_LIBRARY_PATH=</span><span class="token string variable" style="color:rgb(191, 199, 213)">$LD_LIBRARY_PATH</span><span class="token string" style="color:rgb(195, 232, 141)">:/usr/local/lib&quot;</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">&gt;&gt;</span><span class="token plain"> ~/.bashrc</span></div></div></div></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="método-ii-não-recomendado"></a><em>Método II (não recomendado)</em><a aria-hidden="true" tabindex="-1" class="hash-link" href="#método-ii-não-recomendado" title="Direct link to heading">#</a></h4><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Utilizando esse método os passos abaixo devem ser executados <strong>todas as vezes</strong> que você quiser abrir o PSP-UFU.</p></div></div><ol><li>Abra o terminal e acesse o diretório onde está instalado o PSP-UFU:</li></ol><div class="mdxCodeBlock_1XEh"><div class="codeBlockContent_1u-d"><button type="button" aria-label="Copy code to clipboard" class="copyButton_10dd">Copy</button><div tabindex="0" class="prism-code language-shell codeBlock_3iAC"><div class="codeBlockLines_b7E3" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token builtin class-name" style="color:rgb(255, 203, 107)">cd</span><span class="token plain"> /usr/local/bin</span></div></div></div></div></div><ol start="2"><li>Insira as bibliotecas compartilhadas do wxWidgets nas variáveis de ambiente:</li></ol><div class="mdxCodeBlock_1XEh"><div class="codeBlockContent_1u-d"><button type="button" aria-label="Copy code to clipboard" class="copyButton_10dd">Copy</button><div tabindex="0" class="prism-code language-shell codeBlock_3iAC"><div class="codeBlockLines_b7E3" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token builtin class-name" style="color:rgb(255, 203, 107)">export</span><span class="token plain"> </span><span class="token assign-left variable" style="color:rgb(191, 199, 213)">LD_LIBRARY_PATH</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token variable" style="color:rgb(191, 199, 213)">$LD_LIBRARY_PATH</span><span class="token plain">:/usr/local/lib</span></div></div></div></div></div><ol start="3"><li>Então, execute o PSP-UFU na <strong>mesma seção</strong> do terminal:</li></ol><div class="mdxCodeBlock_1XEh"><div class="codeBlockContent_1u-d"><button type="button" aria-label="Copy code to clipboard" class="copyButton_10dd">Copy</button><div tabindex="0" class="prism-code language-shell codeBlock_3iAC"><div class="codeBlockLines_b7E3" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token plain">./PSP-UFU</span></div></div></div></div></div><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Verifique se o computador possui as unidades de vídeo instaladas corretamente, caso contrário, o programa não exibirá a área de trabalho para criar e editar diagramas de linha única ou diagramas de blocos de controle.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/installation.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav 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class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Entrada / Saída</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>As entradas e saída são variáveis relacionadas às máquinas síncronas. Cada tipo de entrada e saída está relacionada a um regulador da máquina: <strong>Regulador de Tensão (AVR, do inglês <em>Automatic Voltage Regulator</em>)</strong> e <strong>Regulador de Velocidade (RV)</strong>.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>O sistema de controle deve ter <strong>ao menos uma entrada e uma saída</strong>.</p></div></div><p>As entradas e saídas do sistema de controle são definidas por esses blocos, os quais são distintos para cada tipo de escopo. A figura abaixo apresenta um exemplo de um formulário de edição das entradas e saídas de um AVR:</p><div><center><img src="/PSP/images/ioForm.png" alt="Formulário de edição de entradas e saídas de sistemas de controle de um AVR" title="Formulário de edição de entradas e saídas de sistemas de controle de um AVR"></center></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="variáveis-de-entrada-e-saída"></a>Variáveis de entrada e saída<a aria-hidden="true" tabindex="-1" class="hash-link" href="#variáveis-de-entrada-e-saída" title="Direct link to heading">#</a></h2><p>O usuário deve sinalizar o tipo de bloco entre entrada e saída e, então, selecionar em uma lista a variável desejada. As seguintes variáveis de controle estão atualmente disponíveis no programa:</p><ul><li><p><strong>Tensão terminal</strong> (<em>entrada: AVR</em>): Módulo da tensão no barramento da máquina síncrona, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, variável no tempo. Essa variável é normalmente utilizada no cálculo do erro da tensão de referência do AVR;</p></li><li><p><strong>Velocidade</strong> (<em>entrada: AVR e RV</em>): Velocidade da máquina síncrona, em rad/s, variável no tempo. Normalmente utilizada no cálculo do erro de velocidade nos reguladores de velocidade, além de entrada do PSS em AVRs;</p></li><li><p><strong>Potência ativa e reativa</strong> (<em>entrada: AVR</em>): Potência ativa fornecida pela máquina síncrona, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, variável no tempo. Normalmente utilizada como entrada do PSS (potência ativa) e controle de sub e sobrecorrente de excitação nos AVRs;</p></li><li><p><strong>Tensão terminal inicial</strong> (<em>entrada: AVR</em>): Módulo da tensão no barramento da máquina síncrona prévia ao estudo dinâmico originado do fluxo de carga, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, fixo no tempo. Essa variável está normalmente associada à referência de tensão do AVR;</p></li><li><p><strong>Velocidade inicial</strong> (<em>entrada: AVR e RV</em>): Velocidade do sistema (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mi>π</mi><msub><mi>f</mi><mrow><mi>r</mi><mi>e</mi><mi>f</mi></mrow></msub></mrow><annotation encoding="application/x-tex">2 \pi f_{ref}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em"></span><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.03588em">π</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>), definida nas <a href="/PSP/docs/simulationConfig">opções de simulação</a>, em rad/s, fixa no tempo. Normalmente utiliza-se essa variável como referência de velocidade em RVs e normalização da velocidade;</p></li><li><p><strong>Potência mecânica inicial</strong> (<em>entrada: RV</em>): Potência mecânica inicial, calculada após a inicialização das máquinas síncronas com os dados originados do fluxo de carga, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, fixa no tempo. Normalmente é utilizada como referência de potência mecânica nos reguladores de velocidade;</p></li><li><p><strong>Variação de velocidade e potência ativa</strong> (<em>entrada: AVR</em>): Cálculo da variação dessas entradas entre os passos de integração normalizada pelo passo de integração, conforme a equação:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>x</mi><mo>=</mo><mfrac><mrow><msub><mi>x</mi><mi>n</mi></msub><mo>−</mo><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><mi>h</mi></mfrac></mrow><annotation encoding="application/x-tex">\Delta x = \frac{x_n-x_{n-1}}{h}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span><span class="mord mathdefault">x</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.9463300000000001em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.26033em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">h</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">\Delta x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span><span class="mord mathdefault">x</span></span></span></span></span>	é a variação da entrada (velocidade ou potência ativa);</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">x_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">x_{n-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.638891em;vertical-align:-0.208331em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span></span>	é a variável no passo atual e anterior, respectivamente;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em"></span><span class="mord mathdefault">h</span></span></span></span></span>	é o passo de integração.</li></ul><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>A normalização é necessária para a correta utilização da razão de passo de controle, definida nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a>.</p></div></div></li><li><p><strong>Tensão de campo</strong> (<em>saída: AVR</em>): Define a tensão aplicada ao campo na máquina síncrona, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> Utilizada como saída dos AVRs, controlando principalmente tensão no barramento conectado e/ou fator de potência da máquina;</p></li><li><p><strong>Potência mecânica</strong> (<em>saída: RV</em>): Define qual a potência mecânica aplicada no eixo da máquina síncrona. 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class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Entrada / Saída</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>As entradas e saída são variáveis relacionadas às máquinas síncronas. Cada tipo de entrada e saída está relacionada a um regulador da máquina: <strong>Regulador de Tensão (AVR, do inglês <em>Automatic Voltage Regulator</em>)</strong> e <strong>Regulador de Velocidade (RV)</strong>.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>O sistema de controle deve ter <strong>ao menos uma entrada e uma saída</strong>.</p></div></div><p>As entradas e saídas do sistema de controle são definidas por esses blocos, os quais são distintos para cada tipo de escopo. A figura abaixo apresenta um exemplo de um formulário de edição das entradas e saídas de um AVR:</p><div><center><img src="/PSP/images/ioForm.png" alt="Formulário de edição de entradas e saídas de sistemas de controle de um AVR" title="Formulário de edição de entradas e saídas de sistemas de controle de um AVR"></center></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="variáveis-de-entrada-e-saída"></a>Variáveis de entrada e saída<a aria-hidden="true" tabindex="-1" class="hash-link" href="#variáveis-de-entrada-e-saída" title="Direct link to heading">#</a></h2><p>O usuário deve sinalizar o tipo de bloco entre entrada e saída e, então, selecionar em uma lista a variável desejada. As seguintes variáveis de controle estão atualmente disponíveis no programa:</p><ul><li><p><strong>Tensão terminal</strong> (<em>entrada: AVR</em>): Módulo da tensão no barramento da máquina síncrona, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, variável no tempo. Essa variável é normalmente utilizada no cálculo do erro da tensão de referência do AVR;</p></li><li><p><strong>Velocidade</strong> (<em>entrada: AVR e RV</em>): Velocidade da máquina síncrona, em rad/s, variável no tempo. Normalmente utilizada no cálculo do erro de velocidade nos reguladores de velocidade, além de entrada do PSS em AVRs;</p></li><li><p><strong>Potência ativa e reativa</strong> (<em>entrada: AVR</em>): Potência ativa fornecida pela máquina síncrona, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, variável no tempo. Normalmente utilizada como entrada do PSS (potência ativa) e controle de sub e sobrecorrente de excitação nos AVRs;</p></li><li><p><strong>Tensão terminal inicial</strong> (<em>entrada: AVR</em>): Módulo da tensão no barramento da máquina síncrona prévia ao estudo dinâmico originado do fluxo de carga, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, fixo no tempo. Essa variável está normalmente associada à referência de tensão do AVR;</p></li><li><p><strong>Velocidade inicial</strong> (<em>entrada: AVR e RV</em>): Velocidade do sistema (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mi>π</mi><msub><mi>f</mi><mrow><mi>r</mi><mi>e</mi><mi>f</mi></mrow></msub></mrow><annotation encoding="application/x-tex">2 \pi f_{ref}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em"></span><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.03588em">π</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>), definida nas <a href="/PSP/docs/simulationConfig">opções de simulação</a>, em rad/s, fixa no tempo. Normalmente utiliza-se essa variável como referência de velocidade em RVs e normalização da velocidade;</p></li><li><p><strong>Potência mecânica inicial</strong> (<em>entrada: RV</em>): Potência mecânica inicial, calculada após a inicialização das máquinas síncronas com os dados originados do fluxo de carga, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, fixa no tempo. Normalmente é utilizada como referência de potência mecânica nos reguladores de velocidade;</p></li><li><p><strong>Variação de velocidade e potência ativa</strong> (<em>entrada: AVR</em>): Cálculo da variação dessas entradas entre os passos de integração normalizada pelo passo de integração, conforme a equação:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>x</mi><mo>=</mo><mfrac><mrow><msub><mi>x</mi><mi>n</mi></msub><mo>−</mo><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><mi>h</mi></mfrac></mrow><annotation encoding="application/x-tex">\Delta x = \frac{x_n-x_{n-1}}{h}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span><span class="mord mathdefault">x</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.9463300000000001em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.26033em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">h</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">\Delta x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span><span class="mord mathdefault">x</span></span></span></span></span>	é a variação da entrada (velocidade ou potência ativa);</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">x_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">x_{n-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.638891em;vertical-align:-0.208331em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span></span>	é a variável no passo atual e anterior, respectivamente;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em"></span><span class="mord mathdefault">h</span></span></span></span></span>	é o passo de integração.</li></ul><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>A normalização é necessária para a correta utilização da razão de passo de controle, definida nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a>.</p></div></div></li><li><p><strong>Tensão de campo</strong> (<em>saída: AVR</em>): Define a tensão aplicada ao campo na máquina síncrona, em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> Utilizada como saída dos AVRs, controlando principalmente tensão no barramento conectado e/ou fator de potência da máquina;</p></li><li><p><strong>Potência mecânica</strong> (<em>saída: RV</em>): Define qual a potência mecânica aplicada no eixo da máquina síncrona. Utilizada como saída dos reguladores de velocidade, controlando principalmente a potência ativa injetada pela máquina e sua frequência.</p></li></ul></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/io.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/controlEditor"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Editor de Controle</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/transferFunction"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Função Transferência »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#variáveis-de-entrada-e-saída" class="table-of-contents__link">Variáveis de entrada e saída</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Limitador absoluto</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Os blocos de limite absoluto cumprem a função de restringir os valores de entrada de acordo com os limites máximos e mínimos inseridos pelo usuário. Caso a entrada ultrapasse algum dos limites impostos, a saída será igual a esse valor limite até que a entrada retorne para a faixa permitida.</p><p>As restrições máximas e mínimas de valores dos sistemas de controle são modeladas utilizando um Limitador, cuja implementação é bastante simples e segue a seguinte expressão:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mi>n</mi></msub><mo>=</mo><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>L</mi><mrow><mi>s</mi><mi>u</mi><mi>p</mi></mrow></msub><mo separator="true" lspace="0em" rspace="0em">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>se </mtext><msub><mi>u</mi><mi>n</mi></msub><mo>&gt;</mo><msub><mi>L</mi><mrow><mi>s</mi><mi>u</mi><mi>p</mi></mrow></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>u</mi><mi>n</mi></msub><mo separator="true" lspace="0em" rspace="0em">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>se </mtext><msub><mi>L</mi><mrow><mi>i</mi><mi>n</mi><mi>f</mi></mrow></msub><mo>≤</mo><msub><mi>u</mi><mi>n</mi></msub><mo>≤</mo><msub><mi>L</mi><mrow><mi>s</mi><mi>u</mi><mi>p</mi></mrow></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>L</mi><mrow><mi>i</mi><mi>n</mi><mi>f</mi></mrow></msub><mo separator="true" lspace="0em" rspace="0em">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>se </mtext><msub><mi>u</mi><mi>n</mi></msub><mo>&lt;</mo><msub><mi>L</mi><mrow><mi>i</mi><mi>n</mi><mi>f</mi></mrow></msub></mrow></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">y_n = \begin{cases} L_{sup}{,} &amp; \text{se } u_n &gt; L_{sup} \\ u_n{,} &amp; \text{se } L_{inf} \le u_n \le L_{sup}\\ L_{inf}{,} &amp; \text{se } u_n &lt; L_{inf} \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:4.32em;vertical-align:-1.9099999999999997em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35002em"><span style="top:-2.19999em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.19499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.20499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.15001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.2950099999999996em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.30501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.60002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8500199999999998em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em"><span style="top:-4.41em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mord"><span class="mpunct">,</span></span></span></span><span style="top:-2.97em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mpunct">,</span></span></span></span><span style="top:-1.5300000000000002em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mord"><span class="mpunct">,</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.9099999999999997em"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em"><span style="top:-4.41em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">se </span></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-2.97em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">se </span></span><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-1.5300000000000002em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">se </span></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.9099999999999997em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">y_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	Éé o valor de saída atual do bloco</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mrow><mi>s</mi><mi>u</mi><mi>p</mi></mrow></msub></mrow><annotation encoding="application/x-tex">L_{sup}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mrow><mi>i</mi><mi>n</mi><mi>f</mi></mrow></msub></mrow><annotation encoding="application/x-tex">L_{inf}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>	são os limites superior e inferior, respectivamente</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">u_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	é o valor de entrada atual do bloco</li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-do-bloco-limitador"></a>Formulário de edição do bloco Limitador<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-do-bloco-limitador" title="Direct link to heading">#</a></h2><p>A figura abaixo apresenta o formulário de edição de dados do bloco limitador.</p><div><center><img src="/PSP/images/limiterForm.png" alt="Formulário de edição de dados do bloco limitador no PSP-UFU" title="Formulário de edição de dados do bloco limitador no PSP-UFU"></center></div><p>Esse bloco não linear é definido pelo <strong>limite superior e inferior</strong>, inseridos pelo usuário.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Tais blocos são bastante encontrados nos sistemas de controle para limitar a atuação do controlador, além de representar limites físicos de modelos implementados, como, por exemplo, valores máximos de corrente de excitação ou potência mecânica fornecida pelas turbinas.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/limiter.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/exponential"><div 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class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Limitador absoluto</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Os blocos de limite absoluto cumprem a função de restringir os valores de entrada de acordo com os limites máximos e mínimos inseridos pelo usuário. Caso a entrada ultrapasse algum dos limites impostos, a saída será igual a esse valor limite até que a entrada retorne para a faixa permitida.</p><p>As restrições máximas e mínimas de valores dos sistemas de controle são modeladas utilizando um Limitador, cuja implementação é bastante simples e segue a seguinte expressão:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mi>n</mi></msub><mo>=</mo><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>L</mi><mrow><mi>s</mi><mi>u</mi><mi>p</mi></mrow></msub><mo separator="true" lspace="0em" rspace="0em">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>se </mtext><msub><mi>u</mi><mi>n</mi></msub><mo>&gt;</mo><msub><mi>L</mi><mrow><mi>s</mi><mi>u</mi><mi>p</mi></mrow></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>u</mi><mi>n</mi></msub><mo separator="true" lspace="0em" rspace="0em">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>se </mtext><msub><mi>L</mi><mrow><mi>i</mi><mi>n</mi><mi>f</mi></mrow></msub><mo>≤</mo><msub><mi>u</mi><mi>n</mi></msub><mo>≤</mo><msub><mi>L</mi><mrow><mi>s</mi><mi>u</mi><mi>p</mi></mrow></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>L</mi><mrow><mi>i</mi><mi>n</mi><mi>f</mi></mrow></msub><mo separator="true" lspace="0em" rspace="0em">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>se </mtext><msub><mi>u</mi><mi>n</mi></msub><mo>&lt;</mo><msub><mi>L</mi><mrow><mi>i</mi><mi>n</mi><mi>f</mi></mrow></msub></mrow></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">y_n = \begin{cases} L_{sup}{,} &amp; \text{se } u_n &gt; L_{sup} \\ u_n{,} &amp; \text{se } L_{inf} \le u_n \le L_{sup}\\ L_{inf}{,} &amp; \text{se } u_n &lt; L_{inf} \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:4.32em;vertical-align:-1.9099999999999997em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35002em"><span style="top:-2.19999em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.19499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.20499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.15001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.2950099999999996em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.30501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.60002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8500199999999998em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em"><span style="top:-4.41em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mord"><span class="mpunct">,</span></span></span></span><span style="top:-2.97em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mpunct">,</span></span></span></span><span style="top:-1.5300000000000002em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mord"><span class="mpunct">,</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.9099999999999997em"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em"><span style="top:-4.41em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">se </span></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-2.97em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">se </span></span><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-1.5300000000000002em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">se </span></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.9099999999999997em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">y_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	Éé o valor de saída atual do bloco</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mrow><mi>s</mi><mi>u</mi><mi>p</mi></mrow></msub></mrow><annotation encoding="application/x-tex">L_{sup}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mrow><mi>i</mi><mi>n</mi><mi>f</mi></mrow></msub></mrow><annotation encoding="application/x-tex">L_{inf}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>	são os limites superior e inferior, respectivamente</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">u_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	é o valor de entrada atual do bloco</li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-do-bloco-limitador"></a>Formulário de edição do bloco Limitador<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-do-bloco-limitador" title="Direct link to heading">#</a></h2><p>A figura abaixo apresenta o formulário de edição de dados do bloco limitador.</p><div><center><img src="/PSP/images/limiterForm.png" alt="Formulário de edição de dados do bloco limitador no PSP-UFU" title="Formulário de edição de dados do bloco limitador no PSP-UFU"></center></div><p>Esse bloco não linear é definido pelo <strong>limite superior e inferior</strong>, inseridos pelo usuário.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Tais blocos são bastante encontrados nos sistemas de controle para limitar a atuação do controlador, além de representar limites físicos de modelos implementados, como, por exemplo, valores máximos de corrente de excitação ou potência mecânica fornecida pelas turbinas.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/limiter.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/exponential"><div 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href="/PSP/docs/controlEditor">Editor de Controle</a></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!" tabindex="-1">Elementos de Controle</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/io">Entrada / Saída</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/transferFunction">Função Transferência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/sum">Somador</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/multiplier">Multiplicador</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/divider">Divisor</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/exponential">Exponencial</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/limiter">Limitador absoluto</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/rateLimiter">Limitador de taxa</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/const">Constante</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/gain">Ganho</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Simulações</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerFlow">Fluxo de Potência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/fault">Curto-Circuito</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Linha</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Um meio de transmissão fabricado usado para transmitir energia eletromagnética entre dois pontos com um mínimo de radiação. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=704-02-02" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="linha-no-psp-ufu"></a>Linha no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#linha-no-psp-ufu" title="Direct link to heading">#</a></h2><p>As linhas no PSP-UFU são modelos <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> equilibradas. Podem ser utilizadas como linhas de transmissão e distribuição de sistemas elétricos de potência.</p><p>A figura abaixo mostra o modelo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> implementado no PSP-UFU:</p><div><center><img src="/PSP/images/lineModel.svg" alt="Modelo PI da linha" title="Modelo PI da linha"></center></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold">r</mi><mi mathvariant="bold">L</mi></msub></mrow><annotation encoding="application/x-tex">\bold{r_L}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.59444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord"><span class="mord mathbf">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33027699999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathbf mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a resistência da linha;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold">x</mi><mi mathvariant="bold">L</mi></msub></mrow><annotation encoding="application/x-tex">\bold{x_L}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.59444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33027699999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathbf mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a reatância indutiva da linha;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi mathvariant="bold">b</mi><mi mathvariant="bold">L</mi><mi mathvariant="bold">d</mi></msubsup></mrow><annotation encoding="application/x-tex">\bold{b_{L}^{d}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.126385em;vertical-align:-0.277277em"></span><span class="mord"><span class="mord"><span class="mord mathbf">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.4227230000000004em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathbf mtight">L</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathbf mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.277277em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a susceptância capacitiva <em>shunt</em> da linha.</li></ul><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>O modelo utilizado no PSP-UFU é <strong>equilibrado</strong> e <strong>não possui impedâncias mútuas</strong> entre as fases.</p></div></div><p>A linha pode ser inseridas com pontos de ancoragem, ou &quot;nós&quot;, para maior personalização gráfica do elemento, como apresentado nas <a href="/PSP/docs/cadTools#linha">Ferramentas CAD</a>.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>A linha deve ser inserida entre duas barras de <strong>mesma tensão nominal</strong>. Caso você tente inseri-la entre barras de tensão diferentes, uma mensagem de erro será exibida.</p></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Um arranjo série de uma <a href="/PSP/docs/line">linha</a> sem as susceptâncias <em>shunt</em>, um <a href="/PSP/docs/bus">barramento</a> e um <a href="/PSP/docs/capacitor">capacitor</a> pode ser utilizado para fabricar um filtro passivo nos <a href="/PSP/docs/harmonics">estudos harmônicos</a>. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-das-linhas"></a>Formulário de edição das linhas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-das-linhas" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados das linhas de transmissão:</p><div><center><img src="/PSP/images/lineForm.png" alt="Formulário das linhas no PSP-UFU" title="Formulário das linhas no PSP-UFU"></center></div><p>Esse formulário é subdividido em dois contextos distintos:</p><ul><li><strong>Geral</strong>: no qual são inseridas informações gerais da linha e informações do fluxo de carga;</li><li><strong>Falta</strong>: local onde as impedâncias de sequência zero são inseridas.</li></ul><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Os parâmetros necessários para construção da linha segundo seu modelo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> são inseridos na aba Geral, utilizados para construção da matriz admitância de sequência positiva e negativa.</p><p>Dados adicionais de impedâncias de sequência zero necessário para o cálculo de curtos-circuitos desbalanceados são editados na aba Falta, utilizados na construção da matriz admitância de sequência zero.</p></div></div><p>Além desses dois contextos, pode ser observado o botão &quot;Estabilidade&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção da linha durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/lineSw.png" alt="Formulário de chaveamento da linha" title="Formulário de chaveamento da linha"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_1w39 tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Falta</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Botão Estabilidade</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="tensão-nominal"></a>Tensão nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tensão-nominal" title="Direct link to heading">#</a></h4><p>Campo de informação <em>não editável</em> que apresenta a tensão nominal da linha. Para alterar esse campo é necessário editar o campo correspondente do <a href="/PSP/docs/bus#geral">barramento</a> conectado.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal da linha, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="parâmetros-do-modelo-pi"></a>Parâmetros do modelo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span><a aria-hidden="true" tabindex="-1" class="hash-link" href="#parâmetros-do-modelo-pi" title="Direct link to heading">#</a></h4><p>Resistência (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><mi>L</mi></msub></mrow><annotation encoding="application/x-tex">r_L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>), Reatância indutiva (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>L</mi></msub></mrow><annotation encoding="application/x-tex">x_L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) série e Susceptância capacitiva shunt <strong>total</strong> (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><msubsup><mi>b</mi><mi>L</mi><mi>d</mi></msubsup></mrow><annotation encoding="application/x-tex">2b_{L}^{d}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.124439em;vertical-align:-0.275331em"></span><span class="mord">2</span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.424669em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.275331em"><span></span></span></span></span></span></span></span></span></span></span>) presentes no modelo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> da linha.</p><p>Esses parâmetros são inseridos em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Ω</span></span></span></span></span> ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi><mi mathvariant="normal">/</mi><mi>k</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">\Omega/km</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">Ω</span><span class="mord">/</span><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="mord mathdefault">m</span></span></span></span></span> (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi></mrow><annotation encoding="application/x-tex">S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.05764em">S</span></span></span></span></span> ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mi mathvariant="normal">/</mi><mi>k</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">S/km</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathdefault" style="margin-right:0.05764em">S</span><span class="mord">/</span><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="mord mathdefault">m</span></span></span></span></span> para <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>b</mi><mi>L</mi><mi>d</mi></msubsup></mrow><annotation encoding="application/x-tex">b_{L}^{d}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.124439em;vertical-align:-0.275331em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.424669em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.275331em"><span></span></span></span></span></span></span></span></span></span></span>).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="comprimento-da-linha"></a>Comprimento da linha<a aria-hidden="true" tabindex="-1" class="hash-link" href="#comprimento-da-linha" title="Direct link to heading">#</a></h4><p>Utilizado para calcular o valor dos parâmetros da linha inseridos em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi><mi mathvariant="normal">/</mi><mi>k</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">\Omega/km</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">Ω</span><span class="mord">/</span><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="mord mathdefault">m</span></span></span></span></span> (ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mi mathvariant="normal">/</mi><mi>k</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">S/km</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathdefault" style="margin-right:0.05764em">S</span><span class="mord">/</span><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="mord mathdefault">m</span></span></span></span></span>).</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>O comprimento da linha é ignorado caso não sejam utilizadas as unidades por quilometro.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="utilizar-potência-nominal-como-base"></a>Utilizar potência nominal como base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-potência-nominal-como-base" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar a potência nominal da linha como base para a conversão das unidades, caso contrário será usada a <a href="/PSP/docs/simulationConfig">potência base do sistema</a>.</p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/line.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Linha</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Um meio de transmissão fabricado usado para transmitir energia eletromagnética entre dois pontos com um mínimo de radiação. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=704-02-02" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="linha-no-psp-ufu"></a>Linha no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#linha-no-psp-ufu" title="Direct link to heading">#</a></h2><p>As linhas no PSP-UFU são modelos <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> equilibradas. Podem ser utilizadas como linhas de transmissão e distribuição de sistemas elétricos de potência.</p><p>A figura abaixo mostra o modelo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> implementado no PSP-UFU:</p><div><center><img src="/PSP/images/lineModel.svg" alt="Modelo PI da linha" title="Modelo PI da linha"></center></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold">r</mi><mi mathvariant="bold">L</mi></msub></mrow><annotation encoding="application/x-tex">\bold{r_L}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.59444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord"><span class="mord mathbf">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33027699999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathbf mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a resistência da linha;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold">x</mi><mi mathvariant="bold">L</mi></msub></mrow><annotation encoding="application/x-tex">\bold{x_L}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.59444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33027699999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathbf mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a reatância indutiva da linha;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi mathvariant="bold">b</mi><mi mathvariant="bold">L</mi><mi mathvariant="bold">d</mi></msubsup></mrow><annotation encoding="application/x-tex">\bold{b_{L}^{d}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.126385em;vertical-align:-0.277277em"></span><span class="mord"><span class="mord"><span class="mord mathbf">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.4227230000000004em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathbf mtight">L</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathbf mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.277277em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a susceptância capacitiva <em>shunt</em> da linha.</li></ul><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>O modelo utilizado no PSP-UFU é <strong>equilibrado</strong> e <strong>não possui impedâncias mútuas</strong> entre as fases.</p></div></div><p>A linha pode ser inseridas com pontos de ancoragem, ou &quot;nós&quot;, para maior personalização gráfica do elemento, como apresentado nas <a href="/PSP/docs/cadTools#linha">Ferramentas CAD</a>.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>A linha deve ser inserida entre duas barras de <strong>mesma tensão nominal</strong>. Caso você tente inseri-la entre barras de tensão diferentes, uma mensagem de erro será exibida.</p></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Um arranjo série de uma <a href="/PSP/docs/line">linha</a> sem as susceptâncias <em>shunt</em>, um <a href="/PSP/docs/bus">barramento</a> e um <a href="/PSP/docs/capacitor">capacitor</a> pode ser utilizado para fabricar um filtro passivo nos <a href="/PSP/docs/harmonics">estudos harmônicos</a>. Em versões futuras, um elemento de filtro passivo será implementado no PSP-UFU.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-das-linhas"></a>Formulário de edição das linhas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-das-linhas" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados das linhas de transmissão:</p><div><center><img src="/PSP/images/lineForm.png" alt="Formulário das linhas no PSP-UFU" title="Formulário das linhas no PSP-UFU"></center></div><p>Esse formulário é subdividido em dois contextos distintos:</p><ul><li><strong>Geral</strong>: no qual são inseridas informações gerais da linha e informações do fluxo de carga;</li><li><strong>Falta</strong>: local onde as impedâncias de sequência zero são inseridas.</li></ul><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Os parâmetros necessários para construção da linha segundo seu modelo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> são inseridos na aba Geral, utilizados para construção da matriz admitância de sequência positiva e negativa.</p><p>Dados adicionais de impedâncias de sequência zero necessário para o cálculo de curtos-circuitos desbalanceados são editados na aba Falta, utilizados na construção da matriz admitância de sequência zero.</p></div></div><p>Além desses dois contextos, pode ser observado o botão &quot;Estabilidade&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção da linha durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/lineSw.png" alt="Formulário de chaveamento da linha" title="Formulário de chaveamento da linha"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_1w39 tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Falta</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Botão Estabilidade</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="tensão-nominal"></a>Tensão nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tensão-nominal" title="Direct link to heading">#</a></h4><p>Campo de informação <em>não editável</em> que apresenta a tensão nominal da linha. Para alterar esse campo é necessário editar o campo correspondente do <a href="/PSP/docs/bus#geral">barramento</a> conectado.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal da linha, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="parâmetros-do-modelo-pi"></a>Parâmetros do modelo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span><a aria-hidden="true" tabindex="-1" class="hash-link" href="#parâmetros-do-modelo-pi" title="Direct link to heading">#</a></h4><p>Resistência (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>r</mi><mi>L</mi></msub></mrow><annotation encoding="application/x-tex">r_L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>), Reatância indutiva (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>L</mi></msub></mrow><annotation encoding="application/x-tex">x_L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) série e Susceptância capacitiva shunt <strong>total</strong> (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><msubsup><mi>b</mi><mi>L</mi><mi>d</mi></msubsup></mrow><annotation encoding="application/x-tex">2b_{L}^{d}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.124439em;vertical-align:-0.275331em"></span><span class="mord">2</span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.424669em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.275331em"><span></span></span></span></span></span></span></span></span></span></span>) presentes no modelo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> da linha.</p><p>Esses parâmetros são inseridos em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Ω</span></span></span></span></span> ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi><mi mathvariant="normal">/</mi><mi>k</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">\Omega/km</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">Ω</span><span class="mord">/</span><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="mord mathdefault">m</span></span></span></span></span> (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi></mrow><annotation encoding="application/x-tex">S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.05764em">S</span></span></span></span></span> ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mi mathvariant="normal">/</mi><mi>k</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">S/km</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathdefault" style="margin-right:0.05764em">S</span><span class="mord">/</span><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="mord mathdefault">m</span></span></span></span></span> para <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>b</mi><mi>L</mi><mi>d</mi></msubsup></mrow><annotation encoding="application/x-tex">b_{L}^{d}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.124439em;vertical-align:-0.275331em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.424669em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.275331em"><span></span></span></span></span></span></span></span></span></span></span>).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="comprimento-da-linha"></a>Comprimento da linha<a aria-hidden="true" tabindex="-1" class="hash-link" href="#comprimento-da-linha" title="Direct link to heading">#</a></h4><p>Utilizado para calcular o valor dos parâmetros da linha inseridos em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi><mi mathvariant="normal">/</mi><mi>k</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">\Omega/km</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">Ω</span><span class="mord">/</span><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="mord mathdefault">m</span></span></span></span></span> (ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mi mathvariant="normal">/</mi><mi>k</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">S/km</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathdefault" style="margin-right:0.05764em">S</span><span class="mord">/</span><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="mord mathdefault">m</span></span></span></span></span>).</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>O comprimento da linha é ignorado caso não sejam utilizadas as unidades por quilometro.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="utilizar-potência-nominal-como-base"></a>Utilizar potência nominal como base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-potência-nominal-como-base" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar a potência nominal da linha como base para a conversão das unidades, caso contrário será usada a <a href="/PSP/docs/simulationConfig">potência base do sistema</a>.</p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/line.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Carga</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><ol><li>a potência ativa, reativa ou aparente gerada, transmitida ou distribuída dentro de um sistema;</li><li>a potência demandada por um grupo de consumidores classificados de acordo com suas particularidades e características, por exemplo, carga de aquecimento, carga reativa diurna, etc. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=601-01-15" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</li></ol></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="carga-no-psp-ufu"></a>Carga no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#carga-no-psp-ufu" title="Direct link to heading">#</a></h2><p>As cargas são os elementos de potência consumidores de potência genéricos. Nos estudos de fluxo de carga é possível modelar a carga como <strong>potência ou impedância constante</strong> e em estabilidade pode-se compor a carga na proporção desejada em três tipos (<strong>carga ZIP</strong>): potência constante, impedância constante e corrente constante.</p><p>As cargas de potência constante nos estudos de fluxo de carga são inseridos no vetor de potências e permanecem fixos durante toda a simulação.</p><p>Os elementos shunt, como reatores, banco de capacitores e cargas de impedância constante, são representados simplesmente por suas admitâncias em derivação. Como os parâmetros de entrada geralmente se constituem de suas potências ativa (P) e reativa (Q) nominais (no caso de reatores e capacitores, P=0), deve-se, portanto, encontrar sua admitância com a equação abaixo para inseri-la na matriz admitância:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mo>=</mo><mfrac><mrow><mi>P</mi><mo>−</mo><mi>j</mi><mi>Q</mi></mrow><msup><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mn>2</mn></msup></mfrac></mrow><annotation encoding="application/x-tex">\overline{y} = \frac{P-jQ}{\dot{V}^2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.825em;vertical-align:-0.19444em"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.17052em;vertical-align:-0.8101900000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3603299999999998em"><span style="top:-2.18981em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span><span class="mord mathdefault">Q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8101900000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Para os estudos de <strong>curto-circuito</strong> e <strong>harmônicos</strong> as cargas são modeladas como impedância constante, independentemente da sinalização indicada em seu formulário de edição de dados.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="carga-no-estudo-de-estabilidade"></a>Carga no estudo de estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#carga-no-estudo-de-estabilidade" title="Direct link to heading">#</a></h3><p>A modelagem das cargas do sistema de forma exata se torna impraticável em um problemas de estabilidade, visto à grande quantidade e variedade dos componentes envolvidos, além de apresentar modificações em suas composições causado por vários fatores, como tempo, condições climáticas e economia. Portanto várias aproximações devem ser utilizadas na formulação de um modelo de carga nos estudos aqui postos.</p><p>Uma forma interessante de se representar cargas dependentes da tensão são as cargas ZIP, as quais são funções quadráticas, possuindo três parcelas: impedância constante (Z), corrente constante (I) e potência constante (P). As potências ativa e reativa são obtidas pelas seguintes equações:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mi>L</mi></msub><mo>=</mo><msub><mi>P</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub><msup><mrow><mo fence="true">(</mo><mfrac><msub><mi>V</mi><mi>i</mi></msub><msub><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub></mfrac><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msub><mi>P</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub><mrow><mo fence="true">(</mo><mfrac><msub><mi>V</mi><mi>i</mi></msub><mrow><msub><mi>V</mi><mi>i</mi></msub><mn>0</mn></mrow></mfrac><mo fence="true">)</mo></mrow><mo>+</mo><msub><mi>P</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_L=P_{Z0} \left(\frac{V_i}{V_{i0}} \right)^2+P_{I0} \left(\frac{V_i}{V_i0} \right)+P_{P0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.604038em;vertical-align:-0.95003em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.6540080000000001em"><span style="top:-3.9029000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mi>L</mi></msub><mo>=</mo><msub><mi>Q</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub><msup><mrow><mo fence="true">(</mo><mfrac><msub><mi>V</mi><mi>i</mi></msub><msub><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub></mfrac><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msub><mi>Q</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub><mrow><mo fence="true">(</mo><mfrac><msub><mi>V</mi><mi>i</mi></msub><mrow><msub><mi>V</mi><mi>i</mi></msub><mn>0</mn></mrow></mfrac><mo fence="true">)</mo></mrow><mo>+</mo><msub><mi>Q</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_L=Q_{Z0} \left(\frac{V_i}{V_{i0}} \right)^2+Q_{I0} \left(\frac{V_i}{V_i0} \right)+Q_{P0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.604038em;vertical-align:-0.95003em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.6540080000000001em"><span style="top:-3.9029000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Em que:</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mi>L</mi></msub></mrow><annotation encoding="application/x-tex">P_L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mi>L</mi></msub></mrow><annotation encoding="application/x-tex">Q_L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	são as potências ativa e reativa da carga ZIP, respectivamente, conectadas em uma barra genérica i;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">V_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> é a tensão atual de uma barra genérica i;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">V_{i0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> é a tensão inicial de uma barra genérica i, obtida do estudo de fluxo de carga;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_{Z0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_{Z0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são as parcelas de impedância constante para potências ativa e reativa, respectivamente;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_{I0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_{I0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são as parcelas de corrente constante para potências ativa e reativa, respectivamente;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_{P0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_{P0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são as parcelas de potência constante para potências ativa e reativa, respectivamente.</p><p>Os valores das parcelas de potência da carga ZIP são obtidos utilizando as potências da carga após a convergência do cálculo do fluxo de carga (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_{L0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>, para a potência ativa e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_{L0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>, para a potência reativa), utilizando as seguintes expressões:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>P</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub><mo>=</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mi>k</mi><mrow><mi>P</mi><mi>Z</mi></mrow></msub><mn>100</mn></mfrac><mfrac><msub><mi>P</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub><msubsup><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow><mn>2</mn></msubsup></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>P</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub><mo>=</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mi>k</mi><mrow><mi>P</mi><mi>I</mi></mrow></msub><mn>100</mn></mfrac><mfrac><msub><mi>P</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub><msub><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>P</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub><mo>=</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mi>k</mi><mrow><mi>P</mi><mi>P</mi></mrow></msub><mn>100</mn></mfrac><msub><mi>P</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub></mstyle></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} P_{Z0}=\displaystyle \frac{k_{PZ}}{100} \frac{P_{L0}}{V_{i0}^2}\\ P_{I0}=\displaystyle \frac{k_{PI}}{100} \frac{P_{L0}}{V_{i0}}\\ P_{P0}=\displaystyle \frac{k_{PP}}{100} P_{L0} \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:6.60004em;vertical-align:-3.05002em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5500200000000004em"><span style="top:-0.9999899999999999em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-0.99499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-1.2899900000000002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-1.5849900000000003em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-1.8799900000000005em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.1749900000000006em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.2049900000000004em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.1500100000000004em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.29501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.59001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.885010000000001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-5.180010000000001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-5.475010000000001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-5.50501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-5.80002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.05002em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5495919999999996em"><span style="top:-5.549592em"><span class="pstrut" style="height:3.3714399999999998em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span><span class="mord">0</span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7959080000000001em"><span style="top:-2.4231360000000004em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.27686399999999994em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9628639999999999em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-3.215288em"><span class="pstrut" style="height:3.3714399999999998em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span><span class="mord">0</span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-1.007848em"><span class="pstrut" style="height:3.3714399999999998em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span><span class="mord">0</span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.0495919999999996em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Os valores de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>P</mi><mi>Z</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{PZ}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>P</mi><mi>I</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{PI}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>P</mi><mi>P</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{PP}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> representam a composição em impedância, corrente e potência constantes, respectivamente, da parcela ativa da carga, os quais são inseridos pelo usuário na forma de porcentagem, sendo a soma desses três valores necessariamente igual a 100%. Os parâmetros <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>Q</mi><mi>Z</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{QZ}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">Q</span><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>Q</mi><mi>I</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{QI}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">Q</span><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>Q</mi><mi>P</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{QP}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">Q</span><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span> podem ser interpretados de forma análoga, porém compõe a parcela reativa da carga.</p><p>O comportamento das potências, retiradas de simulações no PSP-UFU, de cada parcela que compõe a carga ZIP são evidenciadas na figura abaixo.</p><div><center><img src="/PSP/images/loadModel.svg" alt="Comportamento da carga ZIP implementada no software: (a) curva de Tensão x Potência; (b) Curva de Tensão x Corrente" title="Comportamento da carga ZIP implementada no software: (a) curva de Tensão x Potência; (b) Curva de Tensão x Corrente"></center></div><p>Cargas de corrente e potência constantes possuem problemas em tensões muito baixas. À medida que a tensão diminui as correntes dessas cargas não reduz, como pode ser observado na figura acima, resultando em perda de precisão e problemas na convergência de processos iterativos. Para contornar esse problema utiliza-se uma tensão pré-definida pelo usuário (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mrow><mi>l</mi><mi>o</mi><mi>w</mi></mrow></msub></mrow><annotation encoding="application/x-tex">V_{low}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight" style="margin-right:0.02691em">w</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>), a qual as cargas (ou parcelas) de corrente e potência constantes são modeladas como impedância constante, resultando no comportamento de potência e corrente apresentados na figura acima.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-das-cargas"></a>Formulário de edição das cargas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-das-cargas" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados das cargas:</p><div><center><img src="/PSP/images/loadForm.png" alt="Formulário das cargas no PSP-UFU" title="Formulário das cargas no PSP-UFU"></center></div><p>Esse formulário é subdividido em dois contextos distintos:</p><ul><li><strong>Geral</strong>: no qual são inseridas informações gerais das cargas, informações e o tipo de carga no fluxo de carga;</li><li><strong>Estabilidade</strong>: contendo opções de visualização de dados da carga em gráficos no tempo e opções de parametrização da carga ZIP.</li></ul><p>Além desses dois contextos, pode ser observado o botão &quot;Chaveamento&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção da carga durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/loadSw.png" alt="Formulário de chaveamento da carga" title="Formulário de chaveamento da carga"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_1w39 tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Estabilidade</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Botão Chaveamento</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-ativa"></a>Potência ativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-ativa" title="Direct link to heading">#</a></h4><p>Parcela de potência ativa da carga. Pode ser inserido em MW, kW W ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> (na base do sistema).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-reativa"></a>Potência reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-reativa" title="Direct link to heading">#</a></h4><p>Parcela de potência reativa da carga. Pode ser inserido em Mvar, kvar var ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> (na base do sistema).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="tipo-de-carga-fluxo-de-carga"></a>Tipo de carga (fluxo de carga)<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tipo-de-carga-fluxo-de-carga" title="Direct link to heading">#</a></h4><p>Tipo da carga para o estudo de fluxo de carga, podendo ser selecionado dois tipos: Potência constante e Impedância constante. As cargas de potência constantes são inseridas nos vetores de potência e permanecem invariantes no cálculo, enquanto que para as cargas de impedância constante determina-se o valor da impedância utilizando a potência e tensão nominal, a qual é inserida na matriz admitância.</p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/load.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/transformer"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Transformador</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/capacitor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Capacitor »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#carga-no-psp-ufu" class="table-of-contents__link">Carga no PSP-UFU</a><ul><li><a href="#carga-no-estudo-de-estabilidade" class="table-of-contents__link">Carga no estudo de estabilidade</a></li></ul></li><li><a href="#formulário-de-edição-das-cargas" class="table-of-contents__link">Formulário de edição das cargas</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Carga</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><ol><li>a potência ativa, reativa ou aparente gerada, transmitida ou distribuída dentro de um sistema;</li><li>a potência demandada por um grupo de consumidores classificados de acordo com suas particularidades e características, por exemplo, carga de aquecimento, carga reativa diurna, etc. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=601-01-15" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</li></ol></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="carga-no-psp-ufu"></a>Carga no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#carga-no-psp-ufu" title="Direct link to heading">#</a></h2><p>As cargas são os elementos de potência consumidores de potência genéricos. Nos estudos de fluxo de carga é possível modelar a carga como <strong>potência ou impedância constante</strong> e em estabilidade pode-se compor a carga na proporção desejada em três tipos (<strong>carga ZIP</strong>): potência constante, impedância constante e corrente constante.</p><p>As cargas de potência constante nos estudos de fluxo de carga são inseridos no vetor de potências e permanecem fixos durante toda a simulação.</p><p>Os elementos shunt, como reatores, banco de capacitores e cargas de impedância constante, são representados simplesmente por suas admitâncias em derivação. Como os parâmetros de entrada geralmente se constituem de suas potências ativa (P) e reativa (Q) nominais (no caso de reatores e capacitores, P=0), deve-se, portanto, encontrar sua admitância com a equação abaixo para inseri-la na matriz admitância:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mo>=</mo><mfrac><mrow><mi>P</mi><mo>−</mo><mi>j</mi><mi>Q</mi></mrow><msup><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mn>2</mn></msup></mfrac></mrow><annotation encoding="application/x-tex">\overline{y} = \frac{P-jQ}{\dot{V}^2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.825em;vertical-align:-0.19444em"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.17052em;vertical-align:-0.8101900000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3603299999999998em"><span style="top:-2.18981em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span><span class="mord mathdefault">Q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8101900000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Para os estudos de <strong>curto-circuito</strong> e <strong>harmônicos</strong> as cargas são modeladas como impedância constante, independentemente da sinalização indicada em seu formulário de edição de dados.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="carga-no-estudo-de-estabilidade"></a>Carga no estudo de estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#carga-no-estudo-de-estabilidade" title="Direct link to heading">#</a></h3><p>A modelagem das cargas do sistema de forma exata se torna impraticável em um problemas de estabilidade, visto à grande quantidade e variedade dos componentes envolvidos, além de apresentar modificações em suas composições causado por vários fatores, como tempo, condições climáticas e economia. Portanto várias aproximações devem ser utilizadas na formulação de um modelo de carga nos estudos aqui postos.</p><p>Uma forma interessante de se representar cargas dependentes da tensão são as cargas ZIP, as quais são funções quadráticas, possuindo três parcelas: impedância constante (Z), corrente constante (I) e potência constante (P). As potências ativa e reativa são obtidas pelas seguintes equações:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mi>L</mi></msub><mo>=</mo><msub><mi>P</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub><msup><mrow><mo fence="true">(</mo><mfrac><msub><mi>V</mi><mi>i</mi></msub><msub><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub></mfrac><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msub><mi>P</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub><mrow><mo fence="true">(</mo><mfrac><msub><mi>V</mi><mi>i</mi></msub><mrow><msub><mi>V</mi><mi>i</mi></msub><mn>0</mn></mrow></mfrac><mo fence="true">)</mo></mrow><mo>+</mo><msub><mi>P</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_L=P_{Z0} \left(\frac{V_i}{V_{i0}} \right)^2+P_{I0} \left(\frac{V_i}{V_i0} \right)+P_{P0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.604038em;vertical-align:-0.95003em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.6540080000000001em"><span style="top:-3.9029000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mi>L</mi></msub><mo>=</mo><msub><mi>Q</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub><msup><mrow><mo fence="true">(</mo><mfrac><msub><mi>V</mi><mi>i</mi></msub><msub><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub></mfrac><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msub><mi>Q</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub><mrow><mo fence="true">(</mo><mfrac><msub><mi>V</mi><mi>i</mi></msub><mrow><msub><mi>V</mi><mi>i</mi></msub><mn>0</mn></mrow></mfrac><mo fence="true">)</mo></mrow><mo>+</mo><msub><mi>Q</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_L=Q_{Z0} \left(\frac{V_i}{V_{i0}} \right)^2+Q_{I0} \left(\frac{V_i}{V_i0} \right)+Q_{P0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.604038em;vertical-align:-0.95003em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.6540080000000001em"><span style="top:-3.9029000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Em que:</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mi>L</mi></msub></mrow><annotation encoding="application/x-tex">P_L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mi>L</mi></msub></mrow><annotation encoding="application/x-tex">Q_L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">L</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	são as potências ativa e reativa da carga ZIP, respectivamente, conectadas em uma barra genérica i;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">V_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> é a tensão atual de uma barra genérica i;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">V_{i0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> é a tensão inicial de uma barra genérica i, obtida do estudo de fluxo de carga;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_{Z0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_{Z0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são as parcelas de impedância constante para potências ativa e reativa, respectivamente;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_{I0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_{I0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são as parcelas de corrente constante para potências ativa e reativa, respectivamente;</p><p><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_{P0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_{P0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são as parcelas de potência constante para potências ativa e reativa, respectivamente.</p><p>Os valores das parcelas de potência da carga ZIP são obtidos utilizando as potências da carga após a convergência do cálculo do fluxo de carga (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P_{L0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>, para a potência ativa e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">Q_{L0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>, para a potência reativa), utilizando as seguintes expressões:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>P</mi><mrow><mi>Z</mi><mn>0</mn></mrow></msub><mo>=</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mi>k</mi><mrow><mi>P</mi><mi>Z</mi></mrow></msub><mn>100</mn></mfrac><mfrac><msub><mi>P</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub><msubsup><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow><mn>2</mn></msubsup></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>P</mi><mrow><mi>I</mi><mn>0</mn></mrow></msub><mo>=</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mi>k</mi><mrow><mi>P</mi><mi>I</mi></mrow></msub><mn>100</mn></mfrac><mfrac><msub><mi>P</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub><msub><mi>V</mi><mrow><mi>i</mi><mn>0</mn></mrow></msub></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>P</mi><mrow><mi>P</mi><mn>0</mn></mrow></msub><mo>=</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mi>k</mi><mrow><mi>P</mi><mi>P</mi></mrow></msub><mn>100</mn></mfrac><msub><mi>P</mi><mrow><mi>L</mi><mn>0</mn></mrow></msub></mstyle></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} P_{Z0}=\displaystyle \frac{k_{PZ}}{100} \frac{P_{L0}}{V_{i0}^2}\\ P_{I0}=\displaystyle \frac{k_{PI}}{100} \frac{P_{L0}}{V_{i0}}\\ P_{P0}=\displaystyle \frac{k_{PP}}{100} P_{L0} \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:6.60004em;vertical-align:-3.05002em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5500200000000004em"><span style="top:-0.9999899999999999em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-0.99499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-1.2899900000000002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-1.5849900000000003em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-1.8799900000000005em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.1749900000000006em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.2049900000000004em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.1500100000000004em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.29501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.59001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.885010000000001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-5.180010000000001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-5.475010000000001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-5.50501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-5.80002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.05002em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5495919999999996em"><span style="top:-5.549592em"><span class="pstrut" style="height:3.3714399999999998em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span><span class="mord">0</span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7959080000000001em"><span style="top:-2.4231360000000004em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.27686399999999994em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9628639999999999em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-3.215288em"><span class="pstrut" style="height:3.3714399999999998em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span><span class="mord">0</span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.36033em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-1.007848em"><span class="pstrut" style="height:3.3714399999999998em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span><span class="mord">0</span><span class="mord">0</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">L</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.0495919999999996em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Os valores de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>P</mi><mi>Z</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{PZ}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>P</mi><mi>I</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{PI}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>P</mi><mi>P</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{PP}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> representam a composição em impedância, corrente e potência constantes, respectivamente, da parcela ativa da carga, os quais são inseridos pelo usuário na forma de porcentagem, sendo a soma desses três valores necessariamente igual a 100%. Os parâmetros <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>Q</mi><mi>Z</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{QZ}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">Q</span><span class="mord mathdefault mtight" style="margin-right:0.07153em">Z</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>Q</mi><mi>I</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{QI}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">Q</span><span class="mord mathdefault mtight" style="margin-right:0.07847em">I</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>k</mi><mrow><mi>Q</mi><mi>P</mi></mrow></msub></mrow><annotation encoding="application/x-tex">k_{QP}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03148em">k</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.328331em"><span style="top:-2.5500000000000003em;margin-left:-0.03148em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">Q</span><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span> podem ser interpretados de forma análoga, porém compõe a parcela reativa da carga.</p><p>O comportamento das potências, retiradas de simulações no PSP-UFU, de cada parcela que compõe a carga ZIP são evidenciadas na figura abaixo.</p><div><center><img src="/PSP/images/loadModel.svg" alt="Comportamento da carga ZIP implementada no software: (a) curva de Tensão x Potência; (b) Curva de Tensão x Corrente" title="Comportamento da carga ZIP implementada no software: (a) curva de Tensão x Potência; (b) Curva de Tensão x Corrente"></center></div><p>Cargas de corrente e potência constantes possuem problemas em tensões muito baixas. À medida que a tensão diminui as correntes dessas cargas não reduz, como pode ser observado na figura acima, resultando em perda de precisão e problemas na convergência de processos iterativos. Para contornar esse problema utiliza-se uma tensão pré-definida pelo usuário (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mrow><mi>l</mi><mi>o</mi><mi>w</mi></mrow></msub></mrow><annotation encoding="application/x-tex">V_{low}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight" style="margin-right:0.02691em">w</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>), a qual as cargas (ou parcelas) de corrente e potência constantes são modeladas como impedância constante, resultando no comportamento de potência e corrente apresentados na figura acima.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-das-cargas"></a>Formulário de edição das cargas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-das-cargas" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados das cargas:</p><div><center><img src="/PSP/images/loadForm.png" alt="Formulário das cargas no PSP-UFU" title="Formulário das cargas no PSP-UFU"></center></div><p>Esse formulário é subdividido em dois contextos distintos:</p><ul><li><strong>Geral</strong>: no qual são inseridas informações gerais das cargas, informações e o tipo de carga no fluxo de carga;</li><li><strong>Estabilidade</strong>: contendo opções de visualização de dados da carga em gráficos no tempo e opções de parametrização da carga ZIP.</li></ul><p>Além desses dois contextos, pode ser observado o botão &quot;Chaveamento&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção da carga durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/loadSw.png" alt="Formulário de chaveamento da carga" title="Formulário de chaveamento da carga"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_1w39 tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Estabilidade</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Botão Chaveamento</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-ativa"></a>Potência ativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-ativa" title="Direct link to heading">#</a></h4><p>Parcela de potência ativa da carga. Pode ser inserido em MW, kW W ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> (na base do sistema).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-reativa"></a>Potência reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-reativa" title="Direct link to heading">#</a></h4><p>Parcela de potência reativa da carga. Pode ser inserido em Mvar, kvar var ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> (na base do sistema).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="tipo-de-carga-fluxo-de-carga"></a>Tipo de carga (fluxo de carga)<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tipo-de-carga-fluxo-de-carga" title="Direct link to heading">#</a></h4><p>Tipo da carga para o estudo de fluxo de carga, podendo ser selecionado dois tipos: Potência constante e Impedância constante. As cargas de potência constantes são inseridas nos vetores de potência e permanecem invariantes no cálculo, enquanto que para as cargas de impedância constante determina-se o valor da impedância utilizando a potência e tensão nominal, a qual é inserida na matriz admitância.</p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/load.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/transformer"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Transformador</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/capacitor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Capacitor »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#carga-no-psp-ufu" class="table-of-contents__link">Carga no PSP-UFU</a><ul><li><a href="#carga-no-estudo-de-estabilidade" class="table-of-contents__link">Carga no estudo de estabilidade</a></li></ul></li><li><a href="#formulário-de-edição-das-cargas" class="table-of-contents__link">Formulário de edição das cargas</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Tela Principal</h1></header><div class="markdown"><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="organização-da-tela-principal"></a>Organização da tela principal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#organização-da-tela-principal" title="Direct link to heading">#</a></h2><p>A tela principal do PSP-UFU é dividida em três seções: <em><a href="/PSP/docs/mainScreen#menu-ribbon">Menu &quot;Ribbon&quot;</a></em>, <em><a href="/PSP/docs/mainScreen#%C3%A1rea-de-trabalho">Área de Trabalho</a></em> e <em><a href="/PSP/docs/mainScreen#barra-de-status">Barra de Status</a></em>.</p><div><center><img src="/PSP/images/mainScreen.svg" alt="Tela principal" title="Tela principal do PSP-UFU no Windows"></center></div><p>Resumidamente, no <strong>Menu Ribbon</strong> são acessadas as ferramentas do PSP-UFU; na <strong>Área de Trabalho</strong> são criados os diagramas unifilares de potência; e na <strong>Barra de Status</strong> são exibidas importantes informações acerca do estado da Área de Trabalho.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="menu-ribbon"></a>Menu Ribbon<a aria-hidden="true" tabindex="-1" class="hash-link" href="#menu-ribbon" title="Direct link to heading">#</a></h3><blockquote><p>Em informática o ribbon (faixa, em inglês) é um formato de apresentação de interface baseada na GUI onde a barra de ferramentas é mostrada através de uma barra mais larga com icones maiores possibilitando o uso dos aplicativos por dispositivos <em>touch screen</em>.
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href="/PSP/docs/controlEditor">Editor de Controle</a></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!" tabindex="-1">Elementos de Controle</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/io">Entrada / Saída</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/transferFunction">Função Transferência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/sum">Somador</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/multiplier">Multiplicador</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/divider">Divisor</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/exponential">Exponencial</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/limiter">Limitador absoluto</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/rateLimiter">Limitador de taxa</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/const">Constante</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/gain">Ganho</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Simulações</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerFlow">Fluxo de Potência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/fault">Curto-Circuito</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Tela Principal</h1></header><div class="markdown"><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="organização-da-tela-principal"></a>Organização da tela principal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#organização-da-tela-principal" title="Direct link to heading">#</a></h2><p>A tela principal do PSP-UFU é dividida em três seções: <em><a href="/PSP/docs/mainScreen#menu-ribbon">Menu &quot;Ribbon&quot;</a></em>, <em><a href="/PSP/docs/mainScreen#%C3%A1rea-de-trabalho">Área de Trabalho</a></em> e <em><a href="/PSP/docs/mainScreen#barra-de-status">Barra de Status</a></em>.</p><div><center><img src="/PSP/images/mainScreen.svg" alt="Tela principal" title="Tela principal do PSP-UFU no Windows"></center></div><p>Resumidamente, no <strong>Menu Ribbon</strong> são acessadas as ferramentas do PSP-UFU; na <strong>Área de Trabalho</strong> são criados os diagramas unifilares de potência; e na <strong>Barra de Status</strong> são exibidas importantes informações acerca do estado da Área de Trabalho.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="menu-ribbon"></a>Menu Ribbon<a aria-hidden="true" tabindex="-1" class="hash-link" href="#menu-ribbon" title="Direct link to heading">#</a></h3><blockquote><p>Em informática o ribbon (faixa, em inglês) é um formato de apresentação de interface baseada na GUI onde a barra de ferramentas é mostrada através de uma barra mais larga com icones maiores possibilitando o uso dos aplicativos por dispositivos <em>touch screen</em>.
 <a href="https://pt.wikipedia.org/wiki/Ribbon_(inform%C3%A1tica)" target="_blank" rel="noopener noreferrer">Wikipedia</a></p></blockquote><p>O menu Ribbon é composto de três submenus: “Arquivo”, “Ferramentas” e “Simulação”.</p><div><center><img src="/PSP/images/menuFile.png" alt="Menu Arquivo" title="Menu Arquivo"></center></div><p>Em <strong>Arquivo</strong> estão as ferramentas gerais do programa, as quais permitem ao usuário criar e salvar novos projetos, além daquelas que possibilitam carregar os projetos já existentes e importar arquivos de outros programas. Esse submenu também possui opções gerais do programa e acesso a informações sobre o programa.</p><div><center><img src="/PSP/images/menuTools.png" alt="Menu Ferramentas" title="Menu Ferramentas"></center></div><p>Em <strong>Ferramentas</strong> estão presentes os itens específicos, os quais estão relacionados à criação e manipulação da rede elétrica de potência, relatórios tabulares de saída de dados e acesso ao formulário de criação de gráficos no tempo. Algumas configurações específicas do projeto ativo são acessadas por esse menu.</p><div><center><img src="/PSP/images/menuSimulation.png" alt="Menu Simulação" title="Menu Simulação"></center></div><p>Finalmente, o submenu <strong>Simulação</strong> proporciona o acesso do usuário aos cálculos realizados pelo <em>software</em> e suas configurações, além da ferramenta de “solução contínua”, a qual resolve os cálculos estáticos (fluxo de potência, curto-circuito e harmônicos) após quaisquer mudanças na rede de potência, como remoção de componente ou alteração de seus dados. Todas as configurações de simulação do projeto ativo são acessadas por esse menu.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="área-de-trabalho"></a>Área de Trabalho<a aria-hidden="true" tabindex="-1" class="hash-link" href="#área-de-trabalho" title="Direct link to heading">#</a></h3><p>Na área de trabalho estão presentes os projetos em execução, os quais são divididos por abas identificadas pelo nome do projeto (caso já esteja gravado no disco). É nessa área que são inseridos e excluídos os elementos elétricos, cujas ferramentas são acessadas por meio do <a href="/PSP/docs/mainScreen#menu-ribbon">Menu Ribbon</a>.</p><p>As edições gráficas dos elementos, como posição, conexão e tamanho dos barramentos, são realizadas por meio da ação <em>drag-and-drop</em> (arrastar e soltar) com a utilização do mouse. A edição dos dados elétricos é feita por meio de formulários de dados acessados clicando duas vezes sobre os elementos.</p><div><center><img src="/PSP/images/workspace.png" alt="Área de Trabalho" title="Área de Trabalho"></center></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="barra-de-status"></a>Barra de Status<a aria-hidden="true" tabindex="-1" class="hash-link" href="#barra-de-status" title="Direct link to heading">#</a></h3><p>A barra de status é responsável por informações interessantes sobre as circunstâncias atuais do programa: modo de operação do mouse (editar, mover, arrastar), zoom aplicado e posição do mouse na área de trabalho, além de dados sobre as ações dos usuários, como: inserção de elementos, informação sobre copiar e colar, etc.</p><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p><strong>Sempre fique atendo à barra de status</strong>, pois são fornecidas informações importantes acerca da operação do programa. Caso tenha alguma dúvida siga as instruções apresentadas nesse componente.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="configurações-gerais"></a>Configurações gerais<a aria-hidden="true" tabindex="-1" class="hash-link" href="#configurações-gerais" title="Direct link to heading">#</a></h2><p>As configurações gerais do programa são acessadas no submenu Ribbon <strong>Arquivo</strong>. Essas configurações são aplicadas para todos os projetos e permanecem gravadas no disco.</p><div><center><img src="/PSP/images/generalSettings.png" alt="Configurações gerais" title="Configurações gerais"></center></div><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado</h5></div><div class="admonition-content"><p>Algumas configurações de segurança do seu computador (principalmente em sistemas Windows) podem gerar uma mensagem de erro ao confirmar as alterações das configurações gerais.</p><p>Para resolver esse problema basta <strong>executar o PSP-UFU como administrador</strong> (clicar com botão direito no atalho do programa e posteriormente em executar como administrador). Altere novamente as configurações e reinicie o programa.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="idioma"></a>Idioma<a aria-hidden="true" tabindex="-1" class="hash-link" href="#idioma" title="Direct link to heading">#</a></h3><p>Atualmente os seguintes idiomas estão disponíveis no PSP-UFU:</p><ul><li>Inglês</li><li>Português</li></ul><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>O programa deve ser reiniciado para surtir efeito da alteração do idioma.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="renderização"></a>Renderização<a aria-hidden="true" tabindex="-1" class="hash-link" href="#renderização" title="Direct link to heading">#</a></h3><p>Define como os elementos gráficos do <a href="/PSP/docs/powerEditor">editor de potência</a> e do <a href="/PSP/docs/controlEditor">editor de controle</a> são desenhados na tela. Atualmente duas opções estão disponíveis:</p><ul><li><a href="https://www.opengl.org/about/" target="_blank" rel="noopener noreferrer">OpenGL</a></li><li><a href="https://docs.wxwidgets.org/3.0/classwx_graphics_context.html" target="_blank" rel="noopener noreferrer">Device Context</a></li></ul><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>o OpenGL pode não ser suportado pelo seu computador. Nesse caso, ao criar um novo projeto a tela de trabalho não é exibida ou é exibida uma tela preta. A solução é alterar o renderizador para &quot;Device Context&quot;. </p><p>Caso apareça uma mensagem de erro, execute o programa como administrador e repita o processo.</p></div></div><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>O programa deve ser reiniciado para surtir efeito de alteração do renderizador.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="arquivos-de-projeto-do-psp-ufu"></a>Arquivos de projeto do PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#arquivos-de-projeto-do-psp-ufu" title="Direct link to heading">#</a></h2><p>As opções de criação, gravação e abertura de projetos no disco, assim como importação de arquivos de outros programas estão presentes no submenu Ribbon <strong>Arquivo</strong>.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="novo-projeto"></a>Novo projeto<a aria-hidden="true" tabindex="-1" class="hash-link" href="#novo-projeto" title="Direct link to heading">#</a></h3><p>A criação de um novo projeto é realizada clicando no botão <strong>Novo projeto</strong> no <a href="/PSP/docs/mainScreen#menu-ribbon">submenu <strong>Arquivo</strong></a>. Essa ação cria um sistema em branco na área de trabalho, local onde é possível inserir os elementos elétricos por meio do <a href="/PSP/docs/mainScreen#menu-ribbon">submenu <strong>Ferramentas</strong></a> ou pelas <a href="/PSP/docs/powerEditor#teclas-de-atalho">teclas de atalho</a>.</p><p>Esse sistema em branco pode ser ciado utilizando o <a href="/PSP/docs/powerEditor">Editor de Potência</a>.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="salvar-e-salvar-como"></a>Salvar e Salvar como...<a aria-hidden="true" tabindex="-1" class="hash-link" href="#salvar-e-salvar-como" title="Direct link to heading">#</a></h3><p>A opção &quot;Salvar&quot; sobrepõe as alterações realizadas no projeto aberto e grava no disco. A opção &quot;Salvar como...&quot; cria um novo arquivo e grava o projeto no disco com o auxílio de uma janela de seleção de pasta (e definição do nome do arquivo).</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Para projetos que estão sendo gravados pela primeira vez a opção &quot;Salvar&quot; se comporta de forma idêntica à opção &quot;Salvar como...&quot;.</p></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>O PSP-UFU grava os arquivos com a extensão <em>.psp</em>. Esses arquivos nada mais são que arquivos de texto utilizando a <a href="https://en.wikipedia.org/wiki/Markup_language" target="_blank" rel="noopener noreferrer">linguagem de marcação</a> XML (<a href="https://en.wikipedia.org/wiki/XML" target="_blank" rel="noopener noreferrer">eXtensible Markup Language</a>), que define uma série de regras de formatação dos dados de forma que eles são tanto legíveis por humanos quanto por máquinas.</p><p>Portanto, os dados elétricos contidos neles podem ser facilmente identificados e alterados, caso necessário.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="abrir-projeto"></a>Abrir projeto<a aria-hidden="true" tabindex="-1" class="hash-link" href="#abrir-projeto" title="Direct link to heading">#</a></h3><p>Essa opção abre os projetos gravados no disco por meio com o auxílio de uma janela de seleção de arquivos. </p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="importar-projeto"></a>Importar projeto<a aria-hidden="true" tabindex="-1" class="hash-link" href="#importar-projeto" title="Direct link to heading">#</a></h3><p>O PSP-UFU permite a importação de arquivos dos seguintes programas:</p><ul><li><a href="http://www.cepel.br/pt_br/produtos/programas-computacionais-por-categoria/menu/anarede-analise-de-redes-eletricas.htm" target="_blank" rel="noopener noreferrer">ANAREDE</a></li><li><a href="https://matpower.org/" target="_blank" rel="noopener noreferrer">Matpower</a></li></ul><p>Para importação dos arquivos do <strong>ANAREDE</strong> são utilizados tanto o arquivo de dados elétricos (<em>.pwf</em>) quanto de dados gráficos dos elementos (<em>.lst</em>).</p><p>Uma vez que o arquivo do <strong>Matpower</strong> (<em>.m</em>) não possui dados gráficos dos elementos elétricos, o diagrama unifilar é automaticamente gerado pelo PSP-UFU ao importá-lo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="geração-automática-do-layout-de-diagramas-unifilares"></a>Geração automática do <em>layout</em> de diagramas unifilares<a aria-hidden="true" tabindex="-1" class="hash-link" href="#geração-automática-do-layout-de-diagramas-unifilares" title="Direct link to heading">#</a></h4><p>Para criar o <em>layout</em> automático, utilizou-se a teoria dos grafos baseada no posicionamento direcionado à força e aplicação de grafos com arestas ponderadas. De acordo com a teoria dos grafos, o sistema é modelado como vértices e arestas. Nesse contexto, os barramentos são os vértices e os ramos do sistema (linhas e transformadores) são as arestas. As localizações de elementos de derivação, assim como os nós dos elementos, são automaticamente controladas pelo PSP-UFU.</p><p>A ferramenta de <em>layout</em> automático é composta por um processo iterativo e os resultados são mais refinados com um número maior de iterações. Os melhores resultados são obtidos utilizando o número de iterações igual ou superior a cinco vezes o número de barramentos do sistema.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>O <em>layout</em> automático ainda está em desenvolvimento e algumas melhorias podem ser feitas para evitar cruzamentos e sobreposições, porém, em seu estado atual, é totalmente funcional e satisfatório.</p></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Uma vez que o Matpower pode converter os formatos CDF (<em>Common Data Format</em>) e PSS/E RAW para arquivos <em>.m</em>, estes podem ser importados de forma indireta para o PSP-UFU.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/mainScreen.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/installation"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Instalação</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/cadTools"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Ferramentas CAD »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#organização-da-tela-principal" class="table-of-contents__link">Organização da tela principal</a><ul><li><a href="#menu-ribbon" class="table-of-contents__link">Menu Ribbon</a></li><li><a href="#área-de-trabalho" class="table-of-contents__link">Área de Trabalho</a></li><li><a href="#barra-de-status" class="table-of-contents__link">Barra de Status</a></li></ul></li><li><a href="#configurações-gerais" class="table-of-contents__link">Configurações gerais</a><ul><li><a href="#idioma" class="table-of-contents__link">Idioma</a></li><li><a href="#renderização" class="table-of-contents__link">Renderização</a></li></ul></li><li><a href="#arquivos-de-projeto-do-psp-ufu" class="table-of-contents__link">Arquivos de projeto do PSP-UFU</a><ul><li><a href="#novo-projeto" class="table-of-contents__link">Novo projeto</a></li><li><a href="#salvar-e-salvar-como" class="table-of-contents__link">Salvar e Salvar como...</a></li><li><a href="#abrir-projeto" class="table-of-contents__link">Abrir projeto</a></li><li><a href="#importar-projeto" class="table-of-contents__link">Importar projeto</a></li></ul></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a 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docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Expressão Matemática</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>O bloco de expressão matemática utiliza a biblioteca externa <a href="http://warp.povusers.org/FunctionParser/" target="_blank" rel="noopener noreferrer">fparser</a> e permite ao usuário inserir expressões matemáticas genéricas de qualquer complexidade combinadas a estruturas condicionais em um diagrama de controle, aumentando significativamente a capacidade de generalização do programa.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="sintaxe-das-expressões-matemáticas"></a>Sintaxe das expressões matemáticas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#sintaxe-das-expressões-matemáticas" title="Direct link to heading">#</a></h2><p>As sintaxes das operações (para expressões <code>A</code> e <code>B</code>) são apresentadas na tabela abaixo:</p><table><thead><tr><th>Operador</th><th>Expressão</th></tr></thead><tbody><tr><td><code>( )</code></td><td>Expressão em parênteses primeiro</td></tr><tr><td><code>A unit</code></td><td>Um multiplicador de unidade (se um estiver sido adicionado)</td></tr><tr><td><code>A^B</code></td><td>Exponenciação (<code>A</code> elevado à potência <code>B</code>)</td></tr><tr><td><code>-A</code></td><td>Operação unária de oposto</td></tr><tr><td><code>!A</code></td><td>Operação lógica unária de negação (resulta em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span></span></span></span></span> se <code>int(A)</code> é <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span>, senão <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span>)</td></tr><tr><td><code>A*B</code> <code>A/B</code> <code>A%B</code></td><td>Multiplicação, divisão e módulo</td></tr><tr><td><code>A+B</code> <code>A-B</code></td><td>Adição e subtração</td></tr><tr><td><code>A=B</code> <code>A&lt;B</code> <code>A&lt;=B</code> <code>A!=B</code> <code>A&gt;B</code> <code>A&gt;=B</code></td><td>Comparação entre <code>A</code> e <code>B</code> (resulta em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span></span></span></span></span> ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span>)</td></tr><tr><td><code>A&amp;B</code></td><td>Resulta em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span></span></span></span></span> se <code>int(A)</code> e <code>int(B)</code> forem diferentes de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span>, senão <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span></td></tr><tr><td><code>A</code>|<code>B</code></td><td>Resulta em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span></span></span></span></span> se <code>int(A)</code> ou <code>int(B)</code> forem diferentes de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span>, senão <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span></td></tr></tbody></table><p>As <strong>funções matemáticas</strong> suportadas pela biblioteca, as quais podem ser utilizadas na construção de diagrama de blocos, são descritas na tabela abaixo:</p><table><thead><tr><th>Expressão</th><th>Descrição</th></tr></thead><tbody><tr><td><code>abs(A)</code></td><td>Valor absoluto de <code>A</code>. Para números reais, se <code>A</code> é negativo, retorna <code>–A</code>, senão retorna <code>A</code>. Para números complexos a expressão é equivalente a <code>hypot(real(x),imag(x))</code>.</td></tr><tr><td><code>acos(A)</code></td><td>Arco cosseno de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>acosh(A)</code></td><td>O mesmo que <code>acos()</code> mas para cosseno hiperbólico</td></tr><tr><td><code>arg(A)</code></td><td>Ângulo de fase de um número complexo <code>A</code>.</td></tr><tr><td><code>asin(A)</code></td><td>Arco seno de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>asinh(A)</code></td><td>Mesmo que <code>asin()</code>, mas para seno hiperbólico</td></tr><tr><td><code>atan(A)</code></td><td>Arco tangente de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>atan2(A,B)</code></td><td>Arco tangente de <code>A/B</code>, a qual os sinais dos dois argumentos para determinar o quadrante do resultado. Retorna a solução de do seguinte sistema: <code>hypot(A,B)*sin(x)=A, hypot(A,B)*cos(x)=B</code>. O valor retornado varia de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mi>π</mi></mrow><annotation encoding="application/x-tex">-\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em"></span><span class="mord">−</span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> a <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span>.</td></tr><tr><td><code>atanh(A)</code></td><td>Mesmo que <code>atan()</code>, mas para tangente hiperbólica.</td></tr><tr><td><code>cbrt(A)</code></td><td>Raiz cúbica de <code>A</code>.</td></tr><tr><td><code>conj(A)</code></td><td>Conjugado complexo de <code>A</code>.</td></tr><tr><td><code>ceil(A)</code></td><td>Teto de <code>A</code>. Arredonda para o próximo maior inteiro.</td></tr><tr><td><code>cos(A)</code></td><td>Cosseno de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>cosh(A)</code></td><td>Mesmo que <code>cos()</code>, mas para cosseno hiperbólico</td></tr><tr><td><code>cot(A)</code></td><td>Cotangente de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>csc(A)</code></td><td>Cossecante de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>exp(A)</code></td><td>Exponencial de <code>A</code>. Retorna o valor de e elevado a potência A.</td></tr><tr><td><code>exp2(A)</code></td><td>Exponencial de <code>A</code> na base <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn></mrow><annotation encoding="application/x-tex">2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">2</span></span></span></span></span>.</td></tr><tr><td><code>floor(A)</code></td><td>Piso de <code>A</code>. Arredonda para o próximo menor inteiro.</td></tr><tr><td><code>hypot(A,B)</code></td><td>Função de distância Euclidiana.</td></tr><tr><td><code>if(A,B,C)</code></td><td>Se <code>int(A)</code> é diferente de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span>, retorna o valor de <code>B</code>, senão retorna <code>C</code>.</td></tr><tr><td><code>imag(A)</code></td><td>Retorna a parte imaginária do número complexo <code>A</code>.</td></tr><tr><td><code>int(A)</code></td><td>Arredonda <code>A</code> para o inteiro mais próximo.</td></tr><tr><td><code>log(A)</code></td><td>Logaritmo natural (base <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>e</mi></mrow><annotation encoding="application/x-tex">e</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">e</span></span></span></span></span>) de <code>A</code>.</td></tr><tr><td><code>log2(A)</code></td><td>Logaritmo na base <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn></mrow><annotation encoding="application/x-tex">2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">2</span></span></span></span></span> de <code>A</code>.</td></tr><tr><td><code>log10(A)</code></td><td>Logaritmo na base <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>10</mn></mrow><annotation encoding="application/x-tex">10</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span><span class="mord">0</span></span></span></span></span> de A.</td></tr><tr><td><code>max(A,B)</code></td><td>Se <code>A&gt;B</code>, o resultado é <code>A</code>, senão é <code>B</code>.</td></tr><tr><td><code>min(A,B)</code></td><td>Se <code>A&lt;B</code>, o resultado é <code>A</code>, senão é <code>B</code>.</td></tr><tr><td><code>polar(A,B)</code></td><td>Retorna o número complexo de magnitude <code>A</code> e ângulo de fase <code>B</code> (em radianos).</td></tr><tr><td><code>pow(A,B)</code></td><td>Exponenciação (<code>A</code> elevado à potência <code>B</code>)</td></tr><tr><td><code>real(A,B)</code></td><td>Retorna a parte real do número complexo <code>A</code>.</td></tr><tr><td><code>sec(A)</code></td><td>Secante de <code>A</code>.</td></tr><tr><td><code>sin(A)</code></td><td>Seno de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>sinh(A)</code></td><td>Mesmo que <code>sin()</code>, mas para seno hiperbólico.</td></tr><tr><td><code>sqrt(A)</code></td><td>Raiz quadrada de <code>A</code>.</td></tr><tr><td><code>tan(A)</code></td><td>Tangente de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>tanh(A)</code></td><td>Mesmo que <code>tan()</code>, mas para tangente hiperbólica.</td></tr><tr><td><code>trunc(A)</code></td><td>Valor truncado de <code>A</code>. Retorna o número inteiro de <code>A</code> sem a parcela fracionada.</td></tr></tbody></table><p>É possível atribuir novas variáveis utilizando a seguinte sintaxe: </p><div class="mdxCodeBlock_1XEh"><div class="codeBlockContent_1u-d"><button type="button" aria-label="Copy code to clipboard" class="copyButton_10dd">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_3iAC"><div class="codeBlockLines_b7E3" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token operator" style="color:rgb(137, 221, 255)">&lt;</span><span class="token plain">nome da variável</span><span class="token operator" style="color:rgb(137, 221, 255)">&gt;</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">&lt;</span><span class="token plain">expressão</span><span class="token operator" style="color:rgb(137, 221, 255)">&gt;</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">&lt;</span><span class="token plain">função</span><span class="token operator" style="color:rgb(137, 221, 255)">&gt;</span></div></div></div></div></div><p>Por exemplo:</p><div class="mdxCodeBlock_1XEh"><div class="codeBlockContent_1u-d"><button type="button" aria-label="Copy code to clipboard" class="copyButton_10dd">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_3iAC"><div class="codeBlockLines_b7E3" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token plain">comprimento </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token function" style="color:rgb(130, 170, 255)">sqrt</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">x</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain">x</span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain">y</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain">y</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"> </span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain">comprimento</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token function" style="color:rgb(130, 170, 255)">sin</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">comprimento</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span></div></div></div></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>O caractere de espaço e de nova linha são ignorados na interpretação da expressão, portanto para maior organização, o código anterior pode ser escrito da seguinte forma:</p><div class="mdxCodeBlock_1XEh"><div class="codeBlockContent_1u-d"><button type="button" aria-label="Copy code to clipboard" class="copyButton_10dd">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_3iAC"><div class="codeBlockLines_b7E3" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token plain">comprimento </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token function" style="color:rgb(130, 170, 255)">sqrt</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">x</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain">x</span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain">y</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain">y</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain"></span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain">comprimento</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token function" style="color:rgb(130, 170, 255)">sin</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">comprimento</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span></div></div></div></div></div></div></div><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Note que a expressão que determina o valor de saída do bloco <strong>não possui</strong> o caractere <code>;</code> em seu final.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-de-dados-do-bloco-de-expressão-matemática"></a>Formulário de edição de dados do bloco de Expressão Matemática<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-de-dados-do-bloco-de-expressão-matemática" title="Direct link to heading">#</a></h2><p>O formulário de inserção e edição das entradas do bloco e da expressão matemática genérica, assim como ferramentas de auxílio de sua construção é apresentado na figura abaixo.</p><div><center><img src="/PSP/images/mathExpressionForm.png" alt="Formulário de edição de dados do bloco de expressão matemática no PSP-UFU" title="Formulário de edição de dados do bloco de expressão matemática no PSP-UFU"></center></div><p>No campo de “Variáveis de entrada” é inserida uma lista com os nomes das entradas separados por espaços. Um número qualquer de entrada pode ser definido nessa lista esses nomes são apresentados no ícone gráfico presente no editor de controle, além de serem destacados na expressão inserida pelo usuário. O número de entradas e saídas se comporta de forma semelhante aos <a href="/PSP/docs/sum">blocos somadores</a>.</p><p>Abaixo do campo das variáveis de entrada está presente o local para inserção da expressão matemática. A sintaxe da expressão inserida pelo usuário possui realce (por meio de diferentes formas e cores da fonte) para números, operadores, variáveis de entrada, funções e constantes, facilitando a criação, manipulação e identificação de erros de digitação e lógica.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Como ferramenta de auxílio ao usuário foi desenvolvida uma verificação da expressão inserida.</p></div></div><p>Tal ferramenta irá encontrar erros e indicará ao usuário qual o tipo do erro, além da sua localização, destacando-o. A figura anterior exemplifica a identificação automática do erro pelo PSP-UFU, assim como sua posição na expressão inserida.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="exemplo-de-expressão-matemática"></a>Exemplo de Expressão Matemática<a aria-hidden="true" tabindex="-1" class="hash-link" href="#exemplo-de-expressão-matemática" title="Direct link to heading">#</a></h2><p>A corrente de campo em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> pode ser estimada de forma aproximada utilizando as potências ativa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi></mrow><annotation encoding="application/x-tex">P</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.13889em">P</span></span></span></span></span>) e reativa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi></mrow><annotation encoding="application/x-tex">Q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">Q</span></span></span></span></span>), assim como as reatâncias transitórias de eixo direto (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>d</mi></msub></mrow><annotation encoding="application/x-tex">x_d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) e em quadratura (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>q</mi></msub></mrow><annotation encoding="application/x-tex">x_q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>) e o módulo da tensão terminal (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi></mrow><annotation encoding="application/x-tex">V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span></span></span>) da máquina:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>i</mi><mi>f</mi></msub><mo>≈</mo><msqrt><mrow><msup><mrow><mo fence="true">(</mo><mi>V</mi><mo>+</mo><msup><mi>Q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mi>P</mi><mn>2</mn></msup></mrow></msqrt><mo>+</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>x</mi><mi>d</mi></msub><msub><mi>x</mi><mi>q</mi></msub></mfrac><mo>+</mo><mn>1</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>0</mn><mo fence="true">)</mo></mrow><mo>×</mo><mfrac><mrow><msup><mi>Q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mrow><mo fence="true">(</mo><mi>V</mi><mo>+</mo><msup><mi>Q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo fence="true">)</mo></mrow><mo>+</mo><msup><msup><mi>P</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mn>2</mn></msup></mrow><msqrt><mrow><msup><mrow><mo fence="true">(</mo><mi>V</mi><mo>+</mo><msup><mi>Q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mi>P</mi><mn>2</mn></msup></mrow></msqrt></mfrac></mrow><annotation encoding="application/x-tex">i_f \approx \sqrt{ \left( V + Q&#x27; \right)^2 + P^2} + \left(\frac{x_d}{x_q} +1{,}0 \right) \times \frac{Q&#x27; \left( V + Q&#x27; \right) + {P&#x27;}^2}{\sqrt{\left( V + Q&#x27;\right)^2 + P^2}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9456279999999999em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">i</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.84em;vertical-align:-0.454121em"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.385879em"><span class="svg-align" style="top:-3.8em"><span class="pstrut" style="height:3.8em"></span><span class="mord" style="padding-left:1em"><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6778919999999999em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.954008em"><span style="top:-3.2029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.345879em"><span class="pstrut" style="height:3.8em"></span><span class="hide-tail" style="min-width:1.02em;height:1.8800000000000001em"><svg width="400em" height="1.8800000000000001em" viewBox="0 0 400000 1944" preserveAspectRatio="xMinYMin slice"><path d="M983 90
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docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Expressão Matemática</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>O bloco de expressão matemática utiliza a biblioteca externa <a href="http://warp.povusers.org/FunctionParser/" target="_blank" rel="noopener noreferrer">fparser</a> e permite ao usuário inserir expressões matemáticas genéricas de qualquer complexidade combinadas a estruturas condicionais em um diagrama de controle, aumentando significativamente a capacidade de generalização do programa.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="sintaxe-das-expressões-matemáticas"></a>Sintaxe das expressões matemáticas<a aria-hidden="true" tabindex="-1" class="hash-link" href="#sintaxe-das-expressões-matemáticas" title="Direct link to heading">#</a></h2><p>As sintaxes das operações (para expressões <code>A</code> e <code>B</code>) são apresentadas na tabela abaixo:</p><table><thead><tr><th>Operador</th><th>Expressão</th></tr></thead><tbody><tr><td><code>( )</code></td><td>Expressão em parênteses primeiro</td></tr><tr><td><code>A unit</code></td><td>Um multiplicador de unidade (se um estiver sido adicionado)</td></tr><tr><td><code>A^B</code></td><td>Exponenciação (<code>A</code> elevado à potência <code>B</code>)</td></tr><tr><td><code>-A</code></td><td>Operação unária de oposto</td></tr><tr><td><code>!A</code></td><td>Operação lógica unária de negação (resulta em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span></span></span></span></span> se <code>int(A)</code> é <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span>, senão <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span>)</td></tr><tr><td><code>A*B</code> <code>A/B</code> <code>A%B</code></td><td>Multiplicação, divisão e módulo</td></tr><tr><td><code>A+B</code> <code>A-B</code></td><td>Adição e subtração</td></tr><tr><td><code>A=B</code> <code>A&lt;B</code> <code>A&lt;=B</code> <code>A!=B</code> <code>A&gt;B</code> <code>A&gt;=B</code></td><td>Comparação entre <code>A</code> e <code>B</code> (resulta em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span></span></span></span></span> ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span>)</td></tr><tr><td><code>A&amp;B</code></td><td>Resulta em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span></span></span></span></span> se <code>int(A)</code> e <code>int(B)</code> forem diferentes de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span>, senão <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span></td></tr><tr><td><code>A</code>|<code>B</code></td><td>Resulta em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span></span></span></span></span> se <code>int(A)</code> ou <code>int(B)</code> forem diferentes de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span>, senão <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span></td></tr></tbody></table><p>As <strong>funções matemáticas</strong> suportadas pela biblioteca, as quais podem ser utilizadas na construção de diagrama de blocos, são descritas na tabela abaixo:</p><table><thead><tr><th>Expressão</th><th>Descrição</th></tr></thead><tbody><tr><td><code>abs(A)</code></td><td>Valor absoluto de <code>A</code>. Para números reais, se <code>A</code> é negativo, retorna <code>–A</code>, senão retorna <code>A</code>. Para números complexos a expressão é equivalente a <code>hypot(real(x),imag(x))</code>.</td></tr><tr><td><code>acos(A)</code></td><td>Arco cosseno de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>acosh(A)</code></td><td>O mesmo que <code>acos()</code> mas para cosseno hiperbólico</td></tr><tr><td><code>arg(A)</code></td><td>Ângulo de fase de um número complexo <code>A</code>.</td></tr><tr><td><code>asin(A)</code></td><td>Arco seno de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>asinh(A)</code></td><td>Mesmo que <code>asin()</code>, mas para seno hiperbólico</td></tr><tr><td><code>atan(A)</code></td><td>Arco tangente de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>atan2(A,B)</code></td><td>Arco tangente de <code>A/B</code>, a qual os sinais dos dois argumentos para determinar o quadrante do resultado. Retorna a solução de do seguinte sistema: <code>hypot(A,B)*sin(x)=A, hypot(A,B)*cos(x)=B</code>. O valor retornado varia de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mi>π</mi></mrow><annotation encoding="application/x-tex">-\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em"></span><span class="mord">−</span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span> a <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.03588em">π</span></span></span></span></span>.</td></tr><tr><td><code>atanh(A)</code></td><td>Mesmo que <code>atan()</code>, mas para tangente hiperbólica.</td></tr><tr><td><code>cbrt(A)</code></td><td>Raiz cúbica de <code>A</code>.</td></tr><tr><td><code>conj(A)</code></td><td>Conjugado complexo de <code>A</code>.</td></tr><tr><td><code>ceil(A)</code></td><td>Teto de <code>A</code>. Arredonda para o próximo maior inteiro.</td></tr><tr><td><code>cos(A)</code></td><td>Cosseno de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>cosh(A)</code></td><td>Mesmo que <code>cos()</code>, mas para cosseno hiperbólico</td></tr><tr><td><code>cot(A)</code></td><td>Cotangente de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>csc(A)</code></td><td>Cossecante de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>exp(A)</code></td><td>Exponencial de <code>A</code>. Retorna o valor de e elevado a potência A.</td></tr><tr><td><code>exp2(A)</code></td><td>Exponencial de <code>A</code> na base <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn></mrow><annotation encoding="application/x-tex">2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">2</span></span></span></span></span>.</td></tr><tr><td><code>floor(A)</code></td><td>Piso de <code>A</code>. Arredonda para o próximo menor inteiro.</td></tr><tr><td><code>hypot(A,B)</code></td><td>Função de distância Euclidiana.</td></tr><tr><td><code>if(A,B,C)</code></td><td>Se <code>int(A)</code> é diferente de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">0</span></span></span></span></span>, retorna o valor de <code>B</code>, senão retorna <code>C</code>.</td></tr><tr><td><code>imag(A)</code></td><td>Retorna a parte imaginária do número complexo <code>A</code>.</td></tr><tr><td><code>int(A)</code></td><td>Arredonda <code>A</code> para o inteiro mais próximo.</td></tr><tr><td><code>log(A)</code></td><td>Logaritmo natural (base <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>e</mi></mrow><annotation encoding="application/x-tex">e</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">e</span></span></span></span></span>) de <code>A</code>.</td></tr><tr><td><code>log2(A)</code></td><td>Logaritmo na base <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn></mrow><annotation encoding="application/x-tex">2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">2</span></span></span></span></span> de <code>A</code>.</td></tr><tr><td><code>log10(A)</code></td><td>Logaritmo na base <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>10</mn></mrow><annotation encoding="application/x-tex">10</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span><span class="mord">0</span></span></span></span></span> de A.</td></tr><tr><td><code>max(A,B)</code></td><td>Se <code>A&gt;B</code>, o resultado é <code>A</code>, senão é <code>B</code>.</td></tr><tr><td><code>min(A,B)</code></td><td>Se <code>A&lt;B</code>, o resultado é <code>A</code>, senão é <code>B</code>.</td></tr><tr><td><code>polar(A,B)</code></td><td>Retorna o número complexo de magnitude <code>A</code> e ângulo de fase <code>B</code> (em radianos).</td></tr><tr><td><code>pow(A,B)</code></td><td>Exponenciação (<code>A</code> elevado à potência <code>B</code>)</td></tr><tr><td><code>real(A,B)</code></td><td>Retorna a parte real do número complexo <code>A</code>.</td></tr><tr><td><code>sec(A)</code></td><td>Secante de <code>A</code>.</td></tr><tr><td><code>sin(A)</code></td><td>Seno de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>sinh(A)</code></td><td>Mesmo que <code>sin()</code>, mas para seno hiperbólico.</td></tr><tr><td><code>sqrt(A)</code></td><td>Raiz quadrada de <code>A</code>.</td></tr><tr><td><code>tan(A)</code></td><td>Tangente de <code>A</code>. Retorna o ângulo em radianos.</td></tr><tr><td><code>tanh(A)</code></td><td>Mesmo que <code>tan()</code>, mas para tangente hiperbólica.</td></tr><tr><td><code>trunc(A)</code></td><td>Valor truncado de <code>A</code>. Retorna o número inteiro de <code>A</code> sem a parcela fracionada.</td></tr></tbody></table><p>É possível atribuir novas variáveis utilizando a seguinte sintaxe: </p><div class="mdxCodeBlock_1XEh"><div class="codeBlockContent_1u-d"><button type="button" aria-label="Copy code to clipboard" class="copyButton_10dd">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_3iAC"><div class="codeBlockLines_b7E3" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token operator" style="color:rgb(137, 221, 255)">&lt;</span><span class="token plain">nome da variável</span><span class="token operator" style="color:rgb(137, 221, 255)">&gt;</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">&lt;</span><span class="token plain">expressão</span><span class="token operator" style="color:rgb(137, 221, 255)">&gt;</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">&lt;</span><span class="token plain">função</span><span class="token operator" style="color:rgb(137, 221, 255)">&gt;</span></div></div></div></div></div><p>Por exemplo:</p><div class="mdxCodeBlock_1XEh"><div class="codeBlockContent_1u-d"><button type="button" aria-label="Copy code to clipboard" class="copyButton_10dd">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_3iAC"><div class="codeBlockLines_b7E3" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token plain">comprimento </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token function" style="color:rgb(130, 170, 255)">sqrt</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">x</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain">x</span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain">y</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain">y</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"> </span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain">comprimento</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token function" style="color:rgb(130, 170, 255)">sin</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">comprimento</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span></div></div></div></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>O caractere de espaço e de nova linha são ignorados na interpretação da expressão, portanto para maior organização, o código anterior pode ser escrito da seguinte forma:</p><div class="mdxCodeBlock_1XEh"><div class="codeBlockContent_1u-d"><button type="button" aria-label="Copy code to clipboard" class="copyButton_10dd">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_3iAC"><div class="codeBlockLines_b7E3" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token plain">comprimento </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token function" style="color:rgb(130, 170, 255)">sqrt</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">x</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain">x</span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain">y</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain">y</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain"></span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain">comprimento</span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token function" style="color:rgb(130, 170, 255)">sin</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">comprimento</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span></div></div></div></div></div></div></div><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Note que a expressão que determina o valor de saída do bloco <strong>não possui</strong> o caractere <code>;</code> em seu final.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-de-dados-do-bloco-de-expressão-matemática"></a>Formulário de edição de dados do bloco de Expressão Matemática<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-de-dados-do-bloco-de-expressão-matemática" title="Direct link to heading">#</a></h2><p>O formulário de inserção e edição das entradas do bloco e da expressão matemática genérica, assim como ferramentas de auxílio de sua construção é apresentado na figura abaixo.</p><div><center><img src="/PSP/images/mathExpressionForm.png" alt="Formulário de edição de dados do bloco de expressão matemática no PSP-UFU" title="Formulário de edição de dados do bloco de expressão matemática no PSP-UFU"></center></div><p>No campo de “Variáveis de entrada” é inserida uma lista com os nomes das entradas separados por espaços. Um número qualquer de entrada pode ser definido nessa lista esses nomes são apresentados no ícone gráfico presente no editor de controle, além de serem destacados na expressão inserida pelo usuário. O número de entradas e saídas se comporta de forma semelhante aos <a href="/PSP/docs/sum">blocos somadores</a>.</p><p>Abaixo do campo das variáveis de entrada está presente o local para inserção da expressão matemática. A sintaxe da expressão inserida pelo usuário possui realce (por meio de diferentes formas e cores da fonte) para números, operadores, variáveis de entrada, funções e constantes, facilitando a criação, manipulação e identificação de erros de digitação e lógica.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Como ferramenta de auxílio ao usuário foi desenvolvida uma verificação da expressão inserida.</p></div></div><p>Tal ferramenta irá encontrar erros e indicará ao usuário qual o tipo do erro, além da sua localização, destacando-o. A figura anterior exemplifica a identificação automática do erro pelo PSP-UFU, assim como sua posição na expressão inserida.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="exemplo-de-expressão-matemática"></a>Exemplo de Expressão Matemática<a aria-hidden="true" tabindex="-1" class="hash-link" href="#exemplo-de-expressão-matemática" title="Direct link to heading">#</a></h2><p>A corrente de campo em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> pode ser estimada de forma aproximada utilizando as potências ativa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi></mrow><annotation encoding="application/x-tex">P</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.13889em">P</span></span></span></span></span>) e reativa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi></mrow><annotation encoding="application/x-tex">Q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">Q</span></span></span></span></span>), assim como as reatâncias transitórias de eixo direto (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>d</mi></msub></mrow><annotation encoding="application/x-tex">x_d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) e em quadratura (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>q</mi></msub></mrow><annotation encoding="application/x-tex">x_q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>) e o módulo da tensão terminal (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi></mrow><annotation encoding="application/x-tex">V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span></span></span>) da máquina:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>i</mi><mi>f</mi></msub><mo>≈</mo><msqrt><mrow><msup><mrow><mo fence="true">(</mo><mi>V</mi><mo>+</mo><msup><mi>Q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mi>P</mi><mn>2</mn></msup></mrow></msqrt><mo>+</mo><mrow><mo fence="true">(</mo><mfrac><msub><mi>x</mi><mi>d</mi></msub><msub><mi>x</mi><mi>q</mi></msub></mfrac><mo>+</mo><mn>1</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>0</mn><mo fence="true">)</mo></mrow><mo>×</mo><mfrac><mrow><msup><mi>Q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mrow><mo fence="true">(</mo><mi>V</mi><mo>+</mo><msup><mi>Q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo fence="true">)</mo></mrow><mo>+</mo><msup><msup><mi>P</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mn>2</mn></msup></mrow><msqrt><mrow><msup><mrow><mo fence="true">(</mo><mi>V</mi><mo>+</mo><msup><mi>Q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo fence="true">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mi>P</mi><mn>2</mn></msup></mrow></msqrt></mfrac></mrow><annotation encoding="application/x-tex">i_f \approx \sqrt{ \left( V + Q&#x27; \right)^2 + P^2} + \left(\frac{x_d}{x_q} +1{,}0 \right) \times \frac{Q&#x27; \left( V + Q&#x27; \right) + {P&#x27;}^2}{\sqrt{\left( V + Q&#x27;\right)^2 + P^2}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9456279999999999em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">i</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.84em;vertical-align:-0.454121em"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.385879em"><span class="svg-align" style="top:-3.8em"><span class="pstrut" style="height:3.8em"></span><span class="mord" style="padding-left:1em"><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6778919999999999em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.954008em"><span style="top:-3.2029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.345879em"><span class="pstrut" style="height:3.8em"></span><span class="hide-tail" style="min-width:1.02em;height:1.8800000000000001em"><svg width="400em" height="1.8800000000000001em" viewBox="0 0 400000 1944" preserveAspectRatio="xMinYMin slice"><path d="M983 90
 l0 -0
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 H1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7
@@ -37,15 +37,15 @@
 c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5
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 M1001 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.502996em"><span></span></span></span></span></span></span></span><span style="top:-3.5670040000000003em"><span class="pstrut" style="height:3.3370040000000003em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-4.014004em"><span class="pstrut" style="height:3.3370040000000003em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9559em"><span style="top:-3.2047920000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.73em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>P</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo>=</mo><msub><mi>x</mi><mi>q</mi></msub><mo>×</mo><mfrac><mi>P</mi><mi>V</mi></mfrac></mrow><annotation encoding="application/x-tex">P&#x27; = x_q \times \frac{P}{V}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.8694379999999999em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.217331em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.872331em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.22222em">V</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>Q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo>=</mo><msub><mi>x</mi><mi>q</mi></msub><mo>×</mo><mfrac><mi>Q</mi><mi>V</mi></mfrac></mrow><annotation encoding="application/x-tex">Q&#x27; = x_q \times \frac{Q}{V}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.946332em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.8694379999999999em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.269439em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.924439em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.22222em">V</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.446108em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">Q</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></li></ul><p>Primeiramente, deve-se inserir no campo &quot;variáveis de entrada&quot; as grandezas fornecidas pelo PSP-UFU. Nesse caso, como pode ser observado no bloco de <a href="/PSP/docs/io">entrada / saída</a>, todas as variáveis necessárias são fornecidas: <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi></mrow><annotation encoding="application/x-tex">P</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.13889em">P</span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi></mrow><annotation encoding="application/x-tex">Q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">Q</span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi></mrow><annotation encoding="application/x-tex">V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span></span></span>. Essas variáveis devem ser inseridas separadas por espaço: <code>p q v</code>.</p><p>Utilizando três blocos de <a href="/PSP/docs/io">entrada / saída</a> pode-se fornecer tais dados ao conectá-los ao bloco de expressão matemática.</p><p>As reatâncias transitórias de eixo direto (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>d</mi></msub></mrow><annotation encoding="application/x-tex">x_d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) e em quadratura (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>q</mi></msub></mrow><annotation encoding="application/x-tex">x_q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>) podem ser definidas diretamente na expressão matemática:</p><div class="mdxCodeBlock_1XEh"><div class="codeBlockContent_1u-d"><button type="button" aria-label="Copy code to clipboard" class="copyButton_10dd">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_3iAC"><div class="codeBlockLines_b7E3" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token plain">xd </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token number" style="color:rgb(247, 140, 108)">0.146</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain">xq </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token number" style="color:rgb(247, 140, 108)">0.0969</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span></div></div></div></div></div><p>Os valores de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>P</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">P&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>Q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">Q&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.946332em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span> podem ser também calculados:</p><div class="mdxCodeBlock_1XEh"><div class="codeBlockContent_1u-d"><button type="button" aria-label="Copy code to clipboard" class="copyButton_10dd">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_3iAC"><div class="codeBlockLines_b7E3" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token plain">yp </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> xq </span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain"> p </span><span class="token operator" style="color:rgb(137, 221, 255)">/</span><span class="token plain"> v</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain">yq </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> xq </span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain"> q </span><span class="token operator" style="color:rgb(137, 221, 255)">/</span><span class="token plain"> v</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span></div></div></div></div></div><p>Com todos os dados necessários pode-se calcular a corrente de campo:</p><div class="mdxCodeBlock_1XEh"><div class="codeBlockContent_1u-d"><button type="button" aria-label="Copy code to clipboard" class="copyButton_10dd">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_3iAC"><div class="codeBlockLines_b7E3" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token plain">i_f </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token function" style="color:rgb(130, 170, 255)">sqrt</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">v </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> yq</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> p</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">xd </span><span class="token operator" style="color:rgb(137, 221, 255)">/</span><span class="token plain"> xq </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> </span><span class="token number" style="color:rgb(247, 140, 108)">1.0</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain">       </span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">yq </span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">v </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> yq</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> yp</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">/</span><span class="token plain"> </span><span class="token function" style="color:rgb(130, 170, 255)">sqrt</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">v </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> yq</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> p</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span></div></div></div></div></div><p>Finalmente, pode-se definir a saída do bloco (não inserindo <code>;</code>):</p><div class="mdxCodeBlock_1XEh"><div class="codeBlockContent_1u-d"><button type="button" aria-label="Copy code to clipboard" class="copyButton_10dd">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_3iAC"><div class="codeBlockLines_b7E3" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token plain">i_f</span></div></div></div></div></div><p>Portanto, para as entradas definidas como <code>p q v</code>, a expressão matemática total para cálculo da corrente de campo será:</p><div class="mdxCodeBlock_1XEh"><div class="codeBlockContent_1u-d"><button type="button" aria-label="Copy code to clipboard" class="copyButton_10dd">Copy</button><div tabindex="0" class="prism-code language-cpp codeBlock_3iAC"><div class="codeBlockLines_b7E3" style="color:#bfc7d5;background-color:#292d3e"><div class="token-line" style="color:#bfc7d5"><span class="token plain">xd </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token number" style="color:rgb(247, 140, 108)">0.146</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain">xq </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token number" style="color:rgb(247, 140, 108)">0.0969</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain">yp </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> xq </span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain"> p </span><span class="token operator" style="color:rgb(137, 221, 255)">/</span><span class="token plain"> v</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain">yq </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> xq </span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain"> q </span><span class="token operator" style="color:rgb(137, 221, 255)">/</span><span class="token plain"> v</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain">i_f </span><span class="token operator" style="color:rgb(137, 221, 255)">:</span><span class="token operator" style="color:rgb(137, 221, 255)">=</span><span class="token plain"> </span><span class="token function" style="color:rgb(130, 170, 255)">sqrt</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">v </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> yq</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> p</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">xd </span><span class="token operator" style="color:rgb(137, 221, 255)">/</span><span class="token plain"> xq </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> </span><span class="token number" style="color:rgb(247, 140, 108)">1.0</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain">       </span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">yq </span><span class="token operator" style="color:rgb(137, 221, 255)">*</span><span class="token plain"> </span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">v </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> yq</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> yp</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">/</span><span class="token plain"> </span><span class="token function" style="color:rgb(130, 170, 255)">sqrt</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token punctuation" style="color:rgb(199, 146, 234)">(</span><span class="token plain">v </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> yq</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token plain"> </span><span class="token operator" style="color:rgb(137, 221, 255)">+</span><span class="token plain"> p</span><span class="token operator" style="color:rgb(137, 221, 255)">^</span><span class="token number" style="color:rgb(247, 140, 108)">2</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token punctuation" style="color:rgb(199, 146, 234)">)</span><span class="token punctuation" style="color:rgb(199, 146, 234)">;</span><span class="token plain"></span></div><div class="token-line" style="color:#bfc7d5"><span class="token plain">i_f</span></div></div></div></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="referências"></a>Referências<a aria-hidden="true" tabindex="-1" class="hash-link" href="#referências" title="Direct link to heading">#</a></h2><ul><li>NIEMINEN, J.; YLILUOMA, J. Function Parser for C++ v4.5.2. Disponível em: <a href="http://warp.povusers.org/FunctionParser/" target="_blank" rel="noopener noreferrer">http://warp.povusers.org/FunctionParser/</a>. </li></ul></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/mathExpression.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/gain"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Ganho</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/powerFlow"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Fluxo de Potência »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#sintaxe-das-expressões-matemáticas" class="table-of-contents__link">Sintaxe das expressões matemáticas</a></li><li><a href="#formulário-de-edição-de-dados-do-bloco-de-expressão-matemática" class="table-of-contents__link">Formulário de edição de dados do bloco de Expressão Matemática</a></li><li><a href="#exemplo-de-expressão-matemática" class="table-of-contents__link">Exemplo de Expressão Matemática</a></li><li><a href="#referências" class="table-of-contents__link">Referências</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Editor de Potência</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>O Editor de Elementos de Potência no PSP-UFU permite a inserção, manipulação e edição de elementos elétricos de potência por meio de um diagrama unifilar.</p><blockquote><p>(<strong>Diagrama unifilar</strong>) Um diagrama do sistema no qual as linhas polifásicas são representados por sua única linha equivalente. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=601-02-04" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Todos os elementos inseridos pode ser manipulados e editados utilizando as <a href="/PSP/docs/cadTools">Ferramentas CAD</a>.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="novo-projeto"></a>Novo projeto<a aria-hidden="true" tabindex="-1" class="hash-link" href="#novo-projeto" title="Direct link to heading">#</a></h2><p>A criação de um novo projeto é realizada clicando no item <strong>Novo projeto</strong> no <a href="/PSP/docs/mainScreen#menu-ribbon">submenu <strong>Arquivo</strong></a>. Essa ação cria um sistema em branco na área de trabalho, local onde é possível inserir os elementos elétricos por meio do <a href="/PSP/docs/mainScreen#menu-ribbon">submenu <strong>Ferramentas</strong></a> ou pelas <a href="/PSP/docs/powerEditor#teclas-de-atalho">teclas de atalho</a>.</p><p>Abaixo são apresentados os elementos elétricos de potência que podem ser inseridos no PSP-UFU:</p><ul><li><a href="/PSP/docs/bus">Barramento</a></li><li>Elementos de ramo<ul><li><a href="/PSP/docs/line">Linha</a></li><li><a href="/PSP/docs/transformer">Transformador</a></li></ul></li><li>Elementos Shunt<ul><li><a href="/PSP/docs/load">Carga</a></li><li><a href="/PSP/docs/capacitor">Capacitor</a></li><li><a href="/PSP/docs/inductor">Indutor</a></li><li><a href="/PSP/docs/harmSource">Fonte de Corrente Harmônica</a></li></ul></li><li>Máquinas<ul><li><a href="/PSP/docs/syncGenerator">Gerador Síncrono</a></li><li><a href="/PSP/docs/syncMotor">Compensador Síncrono</a></li><li><a href="/PSP/docs/indMotor">Motor de Indução</a></li></ul></li></ul><div><center><img src="/PSP/images/powerElements.svg" alt="Elementos de potência" title="Elementos de potência"></center></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="inserindo-elementos"></a>Inserindo elementos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#inserindo-elementos" title="Direct link to heading">#</a></h2><p>Por meio do submenu <strong>Ferramentas</strong> pode-se inserir os elementos de potência, como é apresentado na imagem abaixo.</p><div><center><img src="/PSP/images/addPowerElements.png" alt="Adicionar elementos de potência" title="Adicionar elementos de potência"></center></div><p>No caso de inserção de um barramento, o usuário deve apenas clicar na posição desejada, já para os outros componentes será solicitado que o usuário selecione em uma ou duas barras, o qual o novo componente será conectado.</p><p>Sempre que são inseridos novos elementos, um formulário de dados é exibido e pode-se editar os dados elétricos e acessar formulários adicionais, como dados de estabilidade.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>O primeiro elemento que a ser inserido no projeto <strong>deve</strong> ser um barramento. Os demais elementos elétricos devem ser conectados em uma ou mais barras.</p></div></div><p>Além dos elementos de potência pode-se inserir os elementos de <em>texto vinculado</em>, os quais estão associados a uma grandeza que se deseja vizualizar diretamente na <a href="/PSP/docs/mainScreen#%C3%A1rea-de-trabalho">Área de Trabalho</a>.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Ao inserir um barramento, a mesma irá acompanhar o ponteiro do mouse até que você clique na posição desejada. Para os demais elementos <strong>deve-se clicar em uma mais barras</strong> para exibir o elemento inserido.</p><p><strong>Sempre fique atento às instruções da <a href="/PSP/docs/mainScreen#barra-de-status">Barra de Status</a>.</strong></p></div></div><video autoplay="" loop="" muted="" controls=""><source src="/PSP/videos/timelapseBuild.mp4" type="video/mp4"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="teclas-de-atalho"></a>Teclas de atalho<a aria-hidden="true" tabindex="-1" class="hash-link" href="#teclas-de-atalho" title="Direct link to heading">#</a></h3><p>É possível inserir todos os elementos de potência por meio de teclas de atalho, facilitando e agilizando a criação dos diagramas unifilares no PSP-UFU. A tabela abaixo apresenta tais atalhos:</p><table><thead><tr><th>Elemento</th><th align="center">Atalho</th><th>Elemento</th><th align="center">Atalho</th></tr></thead><tbody><tr><td>Barramento</td><td align="center">B</td><td>Carga</td><td align="center">Shift + L</td></tr><tr><td>Linha</td><td align="center">L</td><td>Capacitor</td><td align="center">Shift + C</td></tr><tr><td>Transformador</td><td align="center">T</td><td>Indutor</td><td align="center">Shift + I</td></tr><tr><td>Gerador</td><td align="center">G</td><td>Corrente harmônica</td><td align="center">Shift + H</td></tr><tr><td>Motor de indução</td><td align="center">I</td><td>Texto</td><td align="center">A</td></tr><tr><td>Compensador síncrono</td><td align="center">K</td><td></td><td align="center"></td></tr></tbody></table><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="editando-dados-elétricos"></a>Editando dados elétricos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#editando-dados-elétricos" title="Direct link to heading">#</a></h2><p>Ao inserir um elemento, seu respectivo formulário de edição é exibido para inserção dos dados elétricos d elemento. Todos os dados podem ser <strong>alterados</strong> ao <strong>clicar duas vezes sobre o elemento</strong> ou por opção do <strong>menu de contexto</strong> exibido ao clicar com o botão direito sobre o elemento.</p><p>Cada formulário de edição de dados elétricos dos elementos possuem suas particularidades e são descritos em documentação específica: <a href="/PSP/docs/bus">Barramento</a>, <a href="/PSP/docs/line">Linha</a>, <a href="/PSP/docs/transformer">Transformador</a>, <a href="/PSP/docs/load">Carga</a>, <a href="/PSP/docs/capacitor">Capacitor</a>, <a href="/PSP/docs/inductor">Indutor</a>, <a href="/PSP/docs/harmSource">Fonte de Corrente Harmônica</a>, <a href="/PSP/docs/syncGenerator">Gerador Síncrono</a>, <a href="/PSP/docs/syncMotor">Compensador Síncrono</a>, <a href="/PSP/docs/indMotor">Motor de Indução</a>.</p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/powerEditor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/cadTools"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Ferramentas CAD</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/bus"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Barramento »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#novo-projeto" class="table-of-contents__link">Novo projeto</a></li><li><a href="#inserindo-elementos" class="table-of-contents__link">Inserindo elementos</a><ul><li><a href="#teclas-de-atalho" class="table-of-contents__link">Teclas de atalho</a></li></ul></li><li><a href="#editando-dados-elétricos" class="table-of-contents__link">Editando dados elétricos</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Editor de Potência</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>O Editor de Elementos de Potência no PSP-UFU permite a inserção, manipulação e edição de elementos elétricos de potência por meio de um diagrama unifilar.</p><blockquote><p>(<strong>Diagrama unifilar</strong>) Um diagrama do sistema no qual as linhas polifásicas são representados por sua única linha equivalente. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=601-02-04" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Todos os elementos inseridos pode ser manipulados e editados utilizando as <a href="/PSP/docs/cadTools">Ferramentas CAD</a>.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="novo-projeto"></a>Novo projeto<a aria-hidden="true" tabindex="-1" class="hash-link" href="#novo-projeto" title="Direct link to heading">#</a></h2><p>A criação de um novo projeto é realizada clicando no item <strong>Novo projeto</strong> no <a href="/PSP/docs/mainScreen#menu-ribbon">submenu <strong>Arquivo</strong></a>. Essa ação cria um sistema em branco na área de trabalho, local onde é possível inserir os elementos elétricos por meio do <a href="/PSP/docs/mainScreen#menu-ribbon">submenu <strong>Ferramentas</strong></a> ou pelas <a href="/PSP/docs/powerEditor#teclas-de-atalho">teclas de atalho</a>.</p><p>Abaixo são apresentados os elementos elétricos de potência que podem ser inseridos no PSP-UFU:</p><ul><li><a href="/PSP/docs/bus">Barramento</a></li><li>Elementos de ramo<ul><li><a href="/PSP/docs/line">Linha</a></li><li><a href="/PSP/docs/transformer">Transformador</a></li></ul></li><li>Elementos Shunt<ul><li><a href="/PSP/docs/load">Carga</a></li><li><a href="/PSP/docs/capacitor">Capacitor</a></li><li><a href="/PSP/docs/inductor">Indutor</a></li><li><a href="/PSP/docs/harmSource">Fonte de Corrente Harmônica</a></li></ul></li><li>Máquinas<ul><li><a href="/PSP/docs/syncGenerator">Gerador Síncrono</a></li><li><a href="/PSP/docs/syncMotor">Compensador Síncrono</a></li><li><a href="/PSP/docs/indMotor">Motor de Indução</a></li></ul></li></ul><div><center><img src="/PSP/images/powerElements.svg" alt="Elementos de potência" title="Elementos de potência"></center></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="inserindo-elementos"></a>Inserindo elementos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#inserindo-elementos" title="Direct link to heading">#</a></h2><p>Por meio do submenu <strong>Ferramentas</strong> pode-se inserir os elementos de potência, como é apresentado na imagem abaixo.</p><div><center><img src="/PSP/images/addPowerElements.png" alt="Adicionar elementos de potência" title="Adicionar elementos de potência"></center></div><p>No caso de inserção de um barramento, o usuário deve apenas clicar na posição desejada, já para os outros componentes será solicitado que o usuário selecione em uma ou duas barras, o qual o novo componente será conectado.</p><p>Sempre que são inseridos novos elementos, um formulário de dados é exibido e pode-se editar os dados elétricos e acessar formulários adicionais, como dados de estabilidade.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>O primeiro elemento que a ser inserido no projeto <strong>deve</strong> ser um barramento. Os demais elementos elétricos devem ser conectados em uma ou mais barras.</p></div></div><p>Além dos elementos de potência pode-se inserir os elementos de <em><a href="/PSP/docs/text">texto vinculado</a></em>, os quais estão associados a uma grandeza que se deseja vizualizar diretamente na <a href="/PSP/docs/mainScreen#%C3%A1rea-de-trabalho">Área de Trabalho</a>.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Ao inserir um barramento, a mesma irá acompanhar o ponteiro do mouse até que você clique na posição desejada. Para os demais elementos <strong>deve-se clicar em uma mais barras</strong> para exibir o elemento inserido.</p><p><strong>Sempre fique atento às instruções da <a href="/PSP/docs/mainScreen#barra-de-status">Barra de Status</a>.</strong></p></div></div><video autoplay="" loop="" muted="" playsinline="" controls=""><source src="/PSP/videos/timelapseBuild.mp4" type="video/mp4"></video><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="teclas-de-atalho"></a>Teclas de atalho<a aria-hidden="true" tabindex="-1" class="hash-link" href="#teclas-de-atalho" title="Direct link to heading">#</a></h3><p>É possível inserir todos os elementos de potência por meio de teclas de atalho, facilitando e agilizando a criação dos diagramas unifilares no PSP-UFU. A tabela abaixo apresenta tais atalhos:</p><table><thead><tr><th>Elemento</th><th align="center">Atalho</th><th>Elemento</th><th align="center">Atalho</th></tr></thead><tbody><tr><td>Barramento</td><td align="center">B</td><td>Carga</td><td align="center">Shift + L</td></tr><tr><td>Linha</td><td align="center">L</td><td>Capacitor</td><td align="center">Shift + C</td></tr><tr><td>Transformador</td><td align="center">T</td><td>Indutor</td><td align="center">Shift + I</td></tr><tr><td>Gerador</td><td align="center">G</td><td>Corrente harmônica</td><td align="center">Shift + H</td></tr><tr><td>Motor de indução</td><td align="center">I</td><td>Texto</td><td align="center">A</td></tr><tr><td>Compensador síncrono</td><td align="center">K</td><td></td><td align="center"></td></tr></tbody></table><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="editando-dados-elétricos"></a>Editando dados elétricos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#editando-dados-elétricos" title="Direct link to heading">#</a></h2><p>Ao inserir um elemento, seu respectivo formulário de edição é exibido para inserção dos dados elétricos d elemento. Todos os dados podem ser <strong>alterados</strong> ao <strong>clicar duas vezes sobre o elemento</strong> ou por opção do <strong>menu de contexto</strong> exibido ao clicar com o botão direito sobre o elemento.</p><p>Cada formulário de edição de dados elétricos dos elementos possuem suas particularidades e são descritos em documentação específica: <a href="/PSP/docs/bus">Barramento</a>, <a href="/PSP/docs/line">Linha</a>, <a href="/PSP/docs/transformer">Transformador</a>, <a href="/PSP/docs/load">Carga</a>, <a href="/PSP/docs/capacitor">Capacitor</a>, <a href="/PSP/docs/inductor">Indutor</a>, <a href="/PSP/docs/harmSource">Fonte de Corrente Harmônica</a>, <a href="/PSP/docs/syncGenerator">Gerador Síncrono</a>, <a href="/PSP/docs/syncMotor">Compensador Síncrono</a>, <a href="/PSP/docs/indMotor">Motor de Indução</a>.</p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/powerEditor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/cadTools"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Ferramentas CAD</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/bus"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Barramento »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#novo-projeto" class="table-of-contents__link">Novo projeto</a></li><li><a href="#inserindo-elementos" class="table-of-contents__link">Inserindo elementos</a><ul><li><a href="#teclas-de-atalho" class="table-of-contents__link">Teclas de atalho</a></li></ul></li><li><a href="#editando-dados-elétricos" class="table-of-contents__link">Editando dados elétricos</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Fluxo de Potência</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Um estudo fundamental no planejamento da expansão e operação de um sistema elétrico é o <strong>fluxo de potência (ou fluxo de carga)</strong> uma vez que a operação satisfatória desse sistema depende do conhecimento dos efeitos da interligação, de novas cargas, de novas centrais geradoras e de novas linhas antes que elas sejam instaladas. Esse estudo tem como objetivo encontrar o fluxo de potência nos ramos e as tensões nodais do Sistema Elétrico de Potência (SEP) impostas pela geração e a carga.</p><p>As equações formuladas a partir dos modelos dos elementos presentes no estudo de fluxo de carga são não lineares e não possuem solução analítica explícita. Portanto é necessária a utilização de métodos numéricos iterativos para solução do problema de fluxo de carga.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulação-do-problema-de-fluxo-de-carga"></a>Formulação do problema de fluxo de carga<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulação-do-problema-de-fluxo-de-carga" title="Direct link to heading">#</a></h2><p>O problema de fluxo de carga pode ser representado por um sistema de equações e inequações algébricas não-lineares que correspondem às leis de Kirchhoff e a um conjunto de restrições de operação impostos pelos componentes de uma rede elétrica.
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class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Fluxo de Potência</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Um estudo fundamental no planejamento da expansão e operação de um sistema elétrico é o <strong>fluxo de potência (ou fluxo de carga)</strong> uma vez que a operação satisfatória desse sistema depende do conhecimento dos efeitos da interligação, de novas cargas, de novas centrais geradoras e de novas linhas antes que elas sejam instaladas. Esse estudo tem como objetivo encontrar o fluxo de potência nos ramos e as tensões nodais do Sistema Elétrico de Potência (SEP) impostas pela geração e a carga.</p><p>As equações formuladas a partir dos modelos dos elementos presentes no estudo de fluxo de carga são não lineares e não possuem solução analítica explícita. Portanto é necessária a utilização de métodos numéricos iterativos para solução do problema de fluxo de carga.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulação-do-problema-de-fluxo-de-carga"></a>Formulação do problema de fluxo de carga<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulação-do-problema-de-fluxo-de-carga" title="Direct link to heading">#</a></h2><p>O problema de fluxo de carga pode ser representado por um sistema de equações e inequações algébricas não-lineares que correspondem às leis de Kirchhoff e a um conjunto de restrições de operação impostos pelos componentes de uma rede elétrica.
 Na formulação do problema a cada barra da rede são associadas quatro variáveis, sendo que duas delas surgem como dados e duas como incógnitas (em uma barra de índice <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em"></span><span class="mord mathdefault">i</span></span></span></span></span>):</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">V_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	é a magnitude da tensão na barra <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em"></span><span class="mord mathdefault">i</span></span></span></span></span>;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>θ</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">θ_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	é o ângulo da tensão na barra <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em"></span><span class="mord mathdefault">i</span></span></span></span></span>;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">P_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	é a injeção líquida de potência ativa na barra <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em"></span><span class="mord mathdefault">i</span></span></span></span></span>;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">Q_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	é a injeção líquida de potência reativa na barra <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em"></span><span class="mord mathdefault">i</span></span></span></span></span>.</li></ul><p>Relativo às variáveis que são incógnitas e os dados do sistema, podem ser definidos <strong>três tipos de barras</strong>:</p><ul><li><strong>Barra PQ</strong>:	<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">P_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">Q_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são dados, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">V_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>θ</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">θ_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são calculados;</li><li><strong>Barra PV</strong>:	<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">P_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">V_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são dados, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">Q_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>θ</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">θ_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são calculados;</li><li><strong>Barra de Referência</strong>	<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>V</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">V_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>θ</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">θ_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são dados, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">P_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">Q_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> são calculados.</li></ul><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>As <strong>barras PQ</strong> geralmente são representadas pelos barramentos de carga, os quais não há geração e controle de tensão.</p><p>As <strong>barras PV</strong> se caracterizam pelo controle de tensão mediante a injeção ou absorção de potência reativa por meio do controle da excitação de uma máquina síncrona.</p><p>A <strong>barra de Referência</strong> (ou de folga, de oscilação) tem como função, assim como o próprio nome diz, servir de referência de tensão e ângulo do sistema. Essa barra é necessariamente geradora, uma vez que ela é responsável pelo equilíbrio do balanço de potência do sistema.</p></div></div><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>O tipo de barra deve ser definido no <a href="/PSP/docs/bus">elemento barramento</a>.</p><p>Note que <strong>o sistema deve possuir somente uma barra de referência</strong>.</p></div></div><p>Como mencionado anteriormente, as equações são não-lineares e a solução analítica não é prática. As soluções dessas equações seguem <strong><a href="https://en.wikipedia.org/wiki/Iterative_method" target="_blank" rel="noopener noreferrer">processos iterativos</a></strong>, em que são atribuídos valores estimados (ou iniciais) para as barras com tensões desconhecidas e, baseado na potência ativa e reativa e módulo da tensão especificados, calcula-se por meio das equações previamente apresentadas as novas tensões complexas em cada nó do sistema.</p><p>Na sequência, esse conjunto de valores para as tensões em cada barra é utilizado para novamente calcular outro grupo de tensões. Cada cálculo de um novo conjunto de tensões é chamado iteração. O processo iterativo é repetido até que as mudanças em todas as barras sejam menores do que um valor pré-estipulado, obtendo assim a convergência.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="execução-do-fluxo-de-carga-no-psp-ufu"></a>Execução do fluxo de carga no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#execução-do-fluxo-de-carga-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Após a construção do diagrama unifilar no <a href="/PSP/docs/powerEditor">editor de potência</a>, a execução do fluxo de carga é realizada no <a href="/PSP/docs/mainScreen#menu-ribbon">menu Simulação</a> clicando no botão <strong>Fluxo de carga</strong>.</p><div><center><img src="/PSP/images/menuSimulationPF.svg" alt="Menu Simulação" title="Menu Simulação"></center></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Caso o fluxo de carga tenha sido executado com sucesso, as setas de potência serão exibidas, a barra de status indicará sucesso na operação e os <a href="/PSP/docs/text">elementos de texto</a> serão atualizados.</p></div></div><p><strong>Outra possibilidade</strong> é a execução por meio do cálculo contínuo, também presente no <a href="/PSP/docs/mainScreen#menu-ribbon">menu Simulação</a> e seu acionamento é realizado co clicar no botão <strong>Habilitar solução</strong>. Com essa opção, os cálculos estáticos selecionados nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a> são automaticamente realizados ao modificar quaisquer parâmetros da rede, como dados elétricos e acionamento dos disjuntores dos elementos (remoção ou inserção).</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Evite construir o circuito com o cálculo contínuo habilitado, uma vez que configurações temporárias podem levar a erros de execução da simulação.</p><p>Para desabilitar o cálculo contínuo clique no botão <strong>Desabilitar solução</strong>.</p></div></div><p>Os resultados do fluxo de carga são exibidos nos <a href="/PSP/docs/text">elementos de texto vinculado</a>, ao posicionar o mouse sobre os elementos e em <a href="/PSP/docs/tabularReport">relatórios tabulares</a>.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="erros-comuns-na-execução-do-fluxo-de-carga"></a>Erros comuns na execução do fluxo de carga<a aria-hidden="true" tabindex="-1" class="hash-link" href="#erros-comuns-na-execução-do-fluxo-de-carga" title="Direct link to heading">#</a></h3><p>A seguir são apresentados os erros mais comuns relacionados ao fluxo de carga.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="a-seguinte-mensagem-de-erro-é-exibida-o-número-máximo-de-iterações-foi-alcançado"></a>A seguinte mensagem de erro é exibida: &quot;O número máximo de iterações foi alcançado&quot;<a aria-hidden="true" tabindex="-1" class="hash-link" href="#a-seguinte-mensagem-de-erro-é-exibida-o-número-máximo-de-iterações-foi-alcançado" title="Direct link to heading">#</a></h4><p>Essa mensagem de erro é exibida quando o método de solução numérica selecionado nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a> atinge o número máximo de iterações inserido. As seguintes situações podem ocasionar esse erro:</p><ul><li><strong>Os parâmetros do circuito estão incorretos</strong>. caso parâmetros muito fora dos valores padrão dos elementos elétricos sejam inseridos, o cálculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente.</li><li><strong>Algum elemento possui parâmetros discrepantes dos demais</strong>. Caso um dos elementos inseridos possua um valor de impedância muito distinto dos demais, como por exemplo uma linha com impedância muito elevada ou uma carga muito pequena, pode levar à divergência do método numérico. Nesse caso, reconsidere a necessidade de representação desses elementos no circuito e alterne entre os métodos numéricos de solução disponíveis.</li><li><strong>O número máximo de iterações está muito baixo</strong>. Alguns circuitos exigem um número maior de iterações, portanto altere o valor do máximo de iterações nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a>. Também tente alternar entre os métodos numéricos de solução disponíveis.</li><li><strong>Os parâmetros de simulação estão inadequados</strong>. Caso um parâmetro do método de solução esteja inadequado, como fator de aceleração ou tolerância, o cálculo pode não alcançar a convergência. Altere esses parâmetros nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a>.</li></ul><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="os-dados-de-saída-são-exibidos-como-nan-ou-nan"></a>Os dados de saída são exibidos como &quot;NaN&quot; ou &quot;nan&quot;<a aria-hidden="true" tabindex="-1" class="hash-link" href="#os-dados-de-saída-são-exibidos-como-nan-ou-nan" title="Direct link to heading">#</a></h4><p>Isso ocorre devido a erros de operações matemáticas nos cálculos de fluxo de carga. &quot;NaN&quot; significa <em>Not a Number</em>.</p><ul><li><strong>Algum barramento está isolado</strong>. Esse erro é bastante comum e pode ocorrer ao inserir um barramento sem conectá-lo ao sistema ou ao remover os elementos de ramo que conectam uma barra ao sistema. A solução é eliminar essa barra do diagrama.</li><li><strong>Os parâmetros do circuito estão incorretos</strong>. caso parâmetros muito fora dos valores padrão dos elementos elétricos sejam inseridos, o cálculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente.</li><li><strong>Algum elemento possui parâmetros discrepantes dos demais</strong>. Caso um dos elementos inseridos possua um valor de impedância muito distinto dos demais, como por exemplo uma linha com impedância muito elevada ou uma carga muito pequena, pode levar à divergência do método numérico. Nesse caso, reconsidere a necessidade de representação desses elementos no circuito e alterne entre os métodos numéricos de solução disponíveis.</li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="métodos-de-solução-numérica-do-fluxo-de-carga-no-psp-ufu"></a>Métodos de solução numérica do fluxo de carga no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#métodos-de-solução-numérica-do-fluxo-de-carga-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Os métodos implementados no programa para solução do problema de fluxo de carga no PSP-UFU são <strong>Gauss-Seidel (GS)</strong> e <strong>Newton-Raphson (NR)</strong>. Além desses métodos clássicos, um método híbrido pode ser utilizado (definido nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a>), em que é utilizado inicialmente o GS e na sequência o NR, aumentando a chance de convergência do NR.</p><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="gauss-seidel"></a>Gauss-Seidel<a aria-hidden="true" tabindex="-1" class="hash-link" href="#gauss-seidel" title="Direct link to heading">#</a></h3><p>O método de Gauss-Seidel tem sido bastante utilizado nas últimas décadas para solução do problema de fluxo de carga, uma vez que não há a necessidade de fatorar a matrizes, reduzindo o esforço computacional. Atualmente, restrições computacionais são menos problemáticas e outros métodos são normalmente escolhidos, porém o Gauss-Seidel ainda possui valor didático e, visto que o PSP-UFU também possui fins educacionais, optou-se pela implementação desse método.</p><p>Para iniciar as iterações do método são necessários valores iniciais para as tensões (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>i</mi><mn>0</mn></msubsup></mrow><annotation encoding="application/x-tex">\dot{V}_i^0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.178854em;vertical-align:-0.258664em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-2.441336em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em"><span></span></span></span></span></span></span></span></span></span></span>) que devem ser calculadas. Normalmente para barras do tipo PQ tem-se <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>i</mi><mn>0</mn></msubsup><mo>=</mo><mn>1</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>0</mn><mo>+</mo><mi>j</mi><mn>0</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>0</mn><mtext> </mtext><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">\dot{V}_i^0=1{,}0+j0{,}0~p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.178854em;vertical-align:-0.258664em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-2.441336em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em"></span><span class="mord">1</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span><span class="mspace nobreak"> </span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> e para barras do tipo PV <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>i</mi><mn>0</mn></msubsup><mo>=</mo><msubsup><mi>V</mi><mi>i</mi><mrow><mi>e</mi><mi>s</mi><mi>p</mi></mrow></msubsup><mo>+</mo><mi>j</mi><mn>0</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\dot{V}_i^0=V_i^{esp}+j0{,}0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.178854em;vertical-align:-0.258664em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-2.441336em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.059164em;vertical-align:-0.276864em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7823em"><span style="top:-2.4231360000000004em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.1809080000000005em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">0</span></span></span></span></span> [p.u.], em que <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>V</mi><mi>i</mi><mrow><mi>e</mi><mi>s</mi><mi>p</mi></mrow></msubsup></mrow><annotation encoding="application/x-tex">V_i^{esp}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.059164em;vertical-align:-0.276864em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7823em"><span style="top:-2.4231360000000004em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.1809080000000005em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em"><span></span></span></span></span></span></span></span></span></span></span> é o módulo da tensão especificada para a barra PV. A barra de referência tem o módulo e ângulo de tensão fixos e não participam no processo iterativo.</p><p>O método de Gauss-Seidel mostra um <strong>número excessivo de iterações</strong> e, com o intuito reduzi-los, multiplicam-se as correções de tensões por uma constante. Essa operação amplia o valor da correção, trazendo a tensão para mais perto do valor do valor final. Os multiplicadores que realizam essa convergência melhorada são chamados de fatores de aceleração. Para qualquer sistema existem valores ótimos para os fatores de aceleração e uma escolha inadequada pode resultar em uma convergência mais lenta ou torná-la impossível. Normalmente é utilizado um fator de aceleração igual a 1,6, valor definido como padrão no programa. A utilização do fator de aceleração é realizada por meio da equação:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mover accent="true"><mi>V</mi><mo>˙</mo></mover><msub><mi>i</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mrow><mo stretchy="false">(</mo><mi>v</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></msubsup><mo>=</mo><mi>α</mi><mrow><mo fence="true">(</mo><msubsup><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>i</mi><mrow><mo stretchy="false">(</mo><mi>v</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></msubsup><mo>−</mo><msubsup><mover accent="true"><mi>V</mi><mo>˙</mo></mover><msub><mi>i</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mrow><mo stretchy="false">(</mo><mi>v</mi><mo stretchy="false">)</mo></mrow></msubsup><mo fence="true">)</mo></mrow><mo>+</mo><msubsup><mover accent="true"><mi>V</mi><mo>˙</mo></mover><msub><mi>i</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mrow><mo stretchy="false">(</mo><mi>v</mi><mo stretchy="false">)</mo></mrow></msubsup></mrow><annotation encoding="application/x-tex">\dot{V}_{i_{AC}}^{(v + 1)} = \alpha \left( \dot{V}_{i}^{(v + 1)}- \dot{V}_{i_{AC}}^{(v)} \right) + \dot{V}_{i_{AC}}^{(v)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.4219689999999998em;vertical-align:-0.377169em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.4231360000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em"><span style="top:-2.3567071428571427em;margin-left:0em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">A</span><span class="mord mathdefault mtight" style="margin-right:0.07153em">C</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.14329285714285717em"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight" style="margin-right:0.03588em">v</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.377169em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.80002em;vertical-align:-0.65002em"></span><span class="mord mathdefault" style="margin-right:0.0037em">α</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">(</span></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.4231360000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight" style="margin-right:0.03588em">v</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.4231360000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em"><span style="top:-2.3567071428571427em;margin-left:0em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">A</span><span class="mord mathdefault mtight" style="margin-right:0.07153em">C</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.14329285714285717em"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight" style="margin-right:0.03588em">v</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.377169em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">)</span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.4219689999999998em;vertical-align:-0.377169em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.4231360000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em"><span style="top:-2.3567071428571427em;margin-left:0em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">A</span><span class="mord mathdefault mtight" style="margin-right:0.07153em">C</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.14329285714285717em"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight" style="margin-right:0.03588em">v</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.377169em"><span></span></span></span></span></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mover accent="true"><mi>V</mi><mo>˙</mo></mover><msub><mi>i</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mrow><mo stretchy="false">(</mo><mi>v</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></msubsup></mrow><annotation encoding="application/x-tex">\dot{V}_{i_{AC}}^{(v + 1)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.4219689999999998em;vertical-align:-0.377169em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.4231360000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em"><span style="top:-2.3567071428571427em;margin-left:0em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">A</span><span class="mord mathdefault mtight" style="margin-right:0.07153em">C</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.14329285714285717em"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight" style="margin-right:0.03588em">v</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.377169em"><span></span></span></span></span></span></span></span></span></span></span> é a tensão complexa da iteração atual com fator de aceleração aplicado</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>i</mi><mrow><mo stretchy="false">(</mo><mi>v</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></msubsup></mrow><annotation encoding="application/x-tex">\dot{V}_{i}^{(v + 1)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.321664em;vertical-align:-0.27686399999999994em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.4231360000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight" style="margin-right:0.03588em">v</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.27686399999999994em"><span></span></span></span></span></span></span></span></span></span></span> é a tensão complexa da iteração atual</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mover accent="true"><mi>V</mi><mo>˙</mo></mover><msub><mi>i</mi><mrow><mi>A</mi><mi>C</mi></mrow></msub><mrow><mo stretchy="false">(</mo><mi>v</mi><mo stretchy="false">)</mo></mrow></msubsup></mrow><annotation encoding="application/x-tex">\dot{V}_{i_{AC}}^{(v)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.4219689999999998em;vertical-align:-0.377169em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.4231360000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em"><span style="top:-2.3567071428571427em;margin-left:0em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">A</span><span class="mord mathdefault mtight" style="margin-right:0.07153em">C</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.14329285714285717em"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight" style="margin-right:0.03588em">v</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.377169em"><span></span></span></span></span></span></span></span></span></span></span> é a tensão complexa da iteração anterior com fator de aceleração aplicado</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>α</mi></mrow><annotation encoding="application/x-tex">\alpha</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.0037em">α</span></span></span></span></span> é o fator de aceleração</li></ul><p>O fluxograma abaixo demonstra como o método de Gauss-Seidel foi implementado no PSP-UFU:</p><div><center><img src="/PSP/images/gaussSeidel.svg" alt="Método numérico de Gauss-Seidel para fluxo de carga" title="Método numérico de Gauss-Seidel para fluxo de carga"></center></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="newton-raphson"></a>Newton-Raphson<a aria-hidden="true" tabindex="-1" class="hash-link" href="#newton-raphson" title="Direct link to heading">#</a></h3><p>O método de Newton-Raphson (também conhecido como método de Newton ou Newton-Fourier) para solução do fluxo de carga é descrito em vários livros e artigos. Atualmente é o algoritmo mais utilizado para solução do fluxo de carga. Para casos bem condicionados, esse método geralmente converge em 4 a 5 iterações, porém existe a possibilidade da técnica contornar o ponto da solução sem nunca atingi-la, o que também justifica implementação do método de Gauss-Seidel no <em>software</em>.</p><p>A expansão da <a href="https://en.wikipedia.org/wiki/Taylor_series" target="_blank" rel="noopener noreferrer">série de Taylor</a> para uma função de duas ou mais variáveis é a base do método de Newton-Raphson para resolver o problema do fluxo de carga. Fazendo a expansão em série de Taylor, para duas equações e duas incógnitas (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mn>1</mn></msub><mrow><mo fence="true">(</mo><msub><mi>x</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>x</mi><mn>2</mn></msub><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">f_1\left( x_{1}, x_{2} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mn>2</mn></msub><mrow><mo fence="true">(</mo><msub><mi>x</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>x</mi><mn>2</mn></msub><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">f_2\left( x_{1}, x_{2} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span></span>), sem listar as derivadas parciais maiores que 1 na forma matricial, obtêm-se:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>K</mi><mn>1</mn></msub><mo>−</mo><msub><mi>f</mi><mn>1</mn></msub><mrow><mo fence="true">(</mo><msubsup><mi>x</mi><mn>1</mn><mrow><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msubsup><mo separator="true">,</mo><msubsup><mi>x</mi><mn>2</mn><mrow><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msubsup><mo fence="true">)</mo></mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>K</mi><mn>2</mn></msub><mo>−</mo><msub><mi>f</mi><mn>2</mn></msub><mrow><mo fence="true">(</mo><msubsup><mi>x</mi><mn>1</mn><mrow><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msubsup><mo separator="true">,</mo><msubsup><mi>x</mi><mn>2</mn><mrow><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msubsup><mo fence="true">)</mo></mrow></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>f</mi><mn>1</mn></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>x</mi><mn>1</mn></msub></mrow></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>f</mi><mn>1</mn></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>x</mi><mn>2</mn></msub></mrow></mfrac></mstyle></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>f</mi><mn>2</mn></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>x</mi><mn>1</mn></msub></mrow></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>f</mi><mn>2</mn></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>x</mi><mn>2</mn></msub></mrow></mfrac></mstyle></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="normal">Δ</mi><msubsup><mi>x</mi><mn>1</mn><mrow><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msubsup></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="normal">Δ</mi><msubsup><mi>x</mi><mn>2</mn><mrow><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msubsup></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">\begin{bmatrix} K_1 - f_1\left( x_{1}^{(0)}, x_{2}^{(0)} \right)\\ K_2 - f_2\left( x_{1}^{(0)}, x_{2}^{(0)} \right) \end{bmatrix} = \begin{bmatrix} \displaystyle\frac{\partial f_1}{\partial x_1} &amp; \displaystyle\frac{\partial f_1}{\partial x_2}\\ \displaystyle\frac{\partial f_2}{\partial x_1} &amp; \displaystyle\frac{\partial f_2}{\partial x_2} \end{bmatrix} \begin{bmatrix} \Delta x_{1}^{(0)}\\ \Delta x_{2}^{(0)} \end{bmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.6010299999999997em;vertical-align:-1.55002em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0510099999999998em"><span style="top:-2.2500000000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-2.8099900000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.05101em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.05002em"><span style="top:-4.05002em"><span class="pstrut" style="height:3.15em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">(</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.433692em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">0</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.433692em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">0</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">)</span></span></span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.15em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">(</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.433692em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">0</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.433692em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">0</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">)</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0510099999999998em"><span style="top:-2.2500000000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-2.8099900000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.05101em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:4.41488em;vertical-align:-1.95744em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.352005em"><span style="top:-1.9499950000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-3.0999950000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.1109850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.352005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.850025em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.45744em"><span style="top:-4.45744em"><span class="pstrut" style="height:3.3714399999999998em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714399999999998em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.3714399999999998em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714399999999998em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.95744em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.45744em"><span style="top:-4.45744em"><span class="pstrut" style="height:3.3714399999999998em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714399999999998em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.3714399999999998em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714399999999998em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.95744em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.352005em"><span style="top:-1.9499950000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-3.0999950000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.1109850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.352005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.850025em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6548em"><span style="top:-3.6548em"><span class="pstrut" style="height:3.0448em"></span><span class="mord"><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.433692em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">0</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span></span></span><span style="top:-2.2499999999999996em"><span class="pstrut" style="height:3.0448em"></span><span class="mord"><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.433692em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">0</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.1548000000000005em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size4">]</span></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>K</mi></mrow><annotation encoding="application/x-tex">K</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">K</span></span></span></span></span> é o resultado da equação <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mrow><mo fence="true">(</mo><msub><mi>x</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>x</mi><mn>2</mn></msub><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">f\left( x_{1}, x_{2} \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mrow><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msup></mrow><annotation encoding="application/x-tex">x^{(0)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8879999999999999em;vertical-align:0em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8879999999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">0</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span></span></span></span></span> é a estimativa iniciais de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">x</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">\Delta x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span><span class="mord mathdefault">x</span></span></span></span></span> é o valor acrescido de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mrow><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msup></mrow><annotation encoding="application/x-tex">x^{(0)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8879999999999999em;vertical-align:0em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8879999999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">0</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span></span></span></span></span> que resulta em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">x</span></span></span></span></span>, ou seja: <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mrow><mo fence="true">(</mo><msub><mi>x</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>x</mi><mn>2</mn></msub><mo fence="true">)</mo></mrow><mo>=</mo><msub><mi>f</mi><mn>1</mn></msub><mrow><mo fence="true">(</mo><msubsup><mi>x</mi><mn>1</mn><mrow><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msubsup><mo>+</mo><mi mathvariant="normal">Δ</mi><msub><mi>x</mi><mn>1</mn></msub><mo separator="true">,</mo><msubsup><mi>x</mi><mn>2</mn><mrow><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msubsup><mo>+</mo><mi mathvariant="normal">Δ</mi><msub><mi>x</mi><mn>2</mn></msub><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">f\left( x_{1}, x_{2} \right) = f_1\left( x_{1}^{(0)} + \Delta x_1, x_{2}^{(0)} + \Delta x_2 \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.80002em;vertical-align:-0.65002em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">(</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.433692em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">0</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.433692em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">0</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">)</span></span></span></span></span></span></span></li></ul><p>Essa expressão pode ser resumida em:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="normal">Δ</mi><msubsup><mi>K</mi><mn>1</mn><mrow><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msubsup></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="normal">Δ</mi><msubsup><mi>K</mi><mn>2</mn><mrow><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msubsup></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><msup><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>J</mi></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mrow><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msup><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="normal">Δ</mi><msubsup><mi>x</mi><mn>1</mn><mrow><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msubsup></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="normal">Δ</mi><msubsup><mi>x</mi><mn>2</mn><mrow><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msubsup></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">\begin{bmatrix} \Delta K_1^{(0)}\\ \Delta K_2^{(0)} \end{bmatrix} = \begin{bmatrix} J \end{bmatrix}^{(0)} \begin{bmatrix} \Delta x_{1}^{(0)}\\ \Delta x_{2}^{(0)} \end{bmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6548em"><span style="top:-3.6548em"><span class="pstrut" style="height:3.0448em"></span><span class="mord"><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.433692em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">0</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span></span></span><span style="top:-2.2499999999999996em"><span class="pstrut" style="height:3.0448em"></span><span class="mord"><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.433692em;margin-left:-0.07153em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">0</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.1548000000000005em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size4">]</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em"></span><span class="minner"><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.09618em">J</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.1279000000000001em"><span style="top:-3.3029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">0</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6548em"><span style="top:-3.6548em"><span class="pstrut" style="height:3.0448em"></span><span class="mord"><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.433692em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">0</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span></span></span><span style="top:-2.2499999999999996em"><span class="pstrut" style="height:3.0448em"></span><span class="mord"><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.433692em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">0</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.1548000000000005em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size4">]</span></span></span></span></span></span></span></div><p>Em que <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mi>J</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[J]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mopen">[</span><span class="mord mathdefault" style="margin-right:0.09618em">J</span><span class="mclose">]</span></span></span></span></span> é a <strong>Matriz Jacobiana</strong></p><p>Com a equação acima é possível calcular os valores de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msubsup><mi>x</mi><mn>1</mn><mrow><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msubsup></mrow><annotation encoding="application/x-tex">\Delta x_{1}^{(0)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.311108em;vertical-align:-0.26630799999999993em"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.433692em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">0</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msubsup><mi>x</mi><mn>2</mn><mrow><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msubsup></mrow><annotation encoding="application/x-tex">\Delta x_{2}^{(0)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.311108em;vertical-align:-0.26630799999999993em"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.433692em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">0</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span></span></span></span></span>. Entretanto, esses valores somados às estimativas iniciais não determinam a solução correta, sendo necessário repetir o processo de determinação das constantes, formação da matriz jacobiana e solução da equação acima, o qual será refeito determinando novas estimativas <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msubsup><mi>x</mi><mn>1</mn><mrow><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></msubsup></mrow><annotation encoding="application/x-tex">\Delta x_{1}^{(1)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.311108em;vertical-align:-0.26630799999999993em"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.433692em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">1</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msubsup><mi>x</mi><mn>2</mn><mrow><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></msubsup></mrow><annotation encoding="application/x-tex">\Delta x_{2}^{(1)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.311108em;vertical-align:-0.26630799999999993em"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.433692em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">1</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.26630799999999993em"><span></span></span></span></span></span></span></span></span></span></span>.</p><p>Esse processo é repetido até que as correções se tornem tão pequenas que satisfaçam uma precisão escolhida.</p><p>Para aplicar o método de Newton-Raphson à solução das equações do fluxo de carga, utiliza-se as equações que representam as potências ativa e reativa injetadas em uma barra.</p><p>Assim como no método de Gauss-Seidel, a barra de referência é omitida da solução iterativa para determinar as tensões, pois a tensão complexa dessa barra é especificada. Como é conhecido o valor da potência ativa injetada (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>P</mi><mi>i</mi><mrow><mi>e</mi><mi>s</mi><mi>p</mi></mrow></msubsup></mrow><annotation encoding="application/x-tex">P_i^{esp}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.059164em;vertical-align:-0.276864em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7823em"><span style="top:-2.4231360000000004em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.1809080000000005em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em"><span></span></span></span></span></span></span></span></span></span></span>) nas barras do tipo PQ e PV, além da potência reativa injetada (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>Q</mi><mi>i</mi><mrow><mi>e</mi><mi>s</mi><mi>p</mi></mrow></msubsup></mrow><annotation encoding="application/x-tex">Q_i^{esp}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.059164em;vertical-align:-0.276864em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7823em"><span style="top:-2.4231360000000004em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.1809080000000005em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em"><span></span></span></span></span></span></span></span></span></span></span>) nas barras PQ pode-se definir <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>P</mi><mi>i</mi><mrow><mi>e</mi><mi>s</mi><mi>p</mi></mrow></msubsup></mrow><annotation encoding="application/x-tex">P_i^{esp}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.059164em;vertical-align:-0.276864em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7823em"><span style="top:-2.4231360000000004em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.1809080000000005em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>Q</mi><mi>i</mi><mrow><mi>e</mi><mi>s</mi><mi>p</mi></mrow></msubsup></mrow><annotation encoding="application/x-tex">Q_i^{esp}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.059164em;vertical-align:-0.276864em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7823em"><span style="top:-2.4231360000000004em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.1809080000000005em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em"><span></span></span></span></span></span></span></span></span></span></span> como os valores de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>K</mi></mrow><annotation encoding="application/x-tex">K</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.07153em">K</span></span></span></span></span>. Os valores estimados do módulo e ângulo da tensão correspondem aos valores estimados para <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">x_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">x_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>.</p><p>O jacobiano consiste nas derivadas parciais de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">P_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Q</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">Q_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> em relação a cada uma das variáveis das equações injeção de potência líquida na barra <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em"></span><span class="mord mathdefault">i</span></span></span></span></span>. A matriz coluna formada por <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msub><mi>x</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">\Delta x_{1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msub><mi>x</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">\Delta x_{2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> corresponde às correções de ângulo (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msub><mi>θ</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">\Delta \theta_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) e módulo (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msub><mi>V</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">\Delta V_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) das tensões de barra.</p><p>Com isso pode-se escrever a equação matricial de um sistema de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">n</span></span></span></span></span> barras, em que a barra número 1 corresponde à barra de referência e as barras de número 2 a n são barras do tipo PQ:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtable rowspacing="0.15999999999999992em" columnalign="right" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>NPQ</mtext><mo>+</mo><mtext>NPV</mtext><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mtext> </mtext></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mtext> </mtext></mstyle></mtd></mtr></mtable></mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mtext> </mtext></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>NPQ</mtext><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mtext> </mtext></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mtext> </mtext></mstyle></mtd></mtr></mtable></mrow></mrow></mstyle></mtd></mtr></mtable><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="normal">Δ</mi><msub><mi>P</mi><mn>2</mn></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="normal">Δ</mi><msub><mi>P</mi><mi>n</mi></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="normal">Δ</mi><msub><mi>Q</mi><mn>2</mn></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="normal">Δ</mi><msub><mi>Q</mi><mi>n</mi></msub></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>P</mi><mn>2</mn></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>θ</mi><mn>2</mn></msub></mrow></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">…</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>P</mi><mn>2</mn></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>θ</mi><mi>n</mi></msub></mrow></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>P</mi><mn>2</mn></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>V</mi><mn>2</mn></msub></mrow></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">…</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>P</mi><mn>2</mn></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>V</mi><mi>n</mi></msub></mrow></mfrac></mstyle></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋱</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋱</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>P</mi><mi>n</mi></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>θ</mi><mn>2</mn></msub></mrow></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">…</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>P</mi><mi>n</mi></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>θ</mi><mi>n</mi></msub></mrow></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>P</mi><mi>n</mi></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>V</mi><mn>2</mn></msub></mrow></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">…</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>P</mi><mi>n</mi></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>V</mi><mi>n</mi></msub></mrow></mfrac></mstyle></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>Q</mi><mn>2</mn></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>θ</mi><mn>2</mn></msub></mrow></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">…</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>Q</mi><mn>2</mn></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>θ</mi><mi>n</mi></msub></mrow></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>Q</mi><mn>2</mn></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>V</mi><mn>2</mn></msub></mrow></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">…</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>Q</mi><mn>2</mn></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>V</mi><mi>n</mi></msub></mrow></mfrac></mstyle></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋱</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋱</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>Q</mi><mi>n</mi></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>θ</mi><mn>2</mn></msub></mrow></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">…</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>Q</mi><mi>n</mi></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>θ</mi><mi>n</mi></msub></mrow></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>Q</mi><mi>n</mi></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>V</mi><mn>2</mn></msub></mrow></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">…</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi mathvariant="normal">∂</mi><msub><mi>Q</mi><mi>n</mi></msub></mrow><mrow><mi mathvariant="normal">∂</mi><msub><mi>V</mi><mi>n</mi></msub></mrow></mfrac></mstyle></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="normal">Δ</mi><msub><mi>θ</mi><mn>2</mn></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="normal">Δ</mi><msub><mi>θ</mi><mn>2</mn></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="normal">Δ</mi><msub><mi>V</mi><mn>2</mn></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="normal">Δ</mi><msub><mi>V</mi><mi>n</mi></msub></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">\begin{array}{r} \text{NPQ} + \text{NPV} \begin{cases} ~\\ ~ \end{cases}\\ ~\\ \text{NPQ} \begin{cases} ~\\ ~ \end{cases} \end{array} \begin{bmatrix} \Delta P_2\\ \vdots\\ \Delta P_n\\ \Delta Q_2\\ \vdots\\ \Delta Q_n\\ \end{bmatrix} = \begin{bmatrix} \displaystyle\frac{\partial P_2}{\partial \theta_2} &amp; \dots &amp; \displaystyle\frac{\partial P_2}{\partial \theta_n} &amp; \displaystyle\frac{\partial P_2}{\partial V_2} &amp; \dots &amp; \displaystyle\frac{\partial P_2}{\partial V_n}\\ \vdots &amp; \ddots &amp; \vdots &amp; \vdots &amp; \ddots &amp; \vdots\\ \displaystyle\frac{\partial P_n}{\partial \theta_2} &amp; \dots &amp; \displaystyle\frac{\partial P_n}{\partial \theta_n} &amp; \displaystyle\frac{\partial P_n}{\partial V_2} &amp; \dots &amp; \displaystyle\frac{\partial P_n}{\partial V_n}\\ \displaystyle\frac{\partial Q_2}{\partial \theta_2} &amp; \dots &amp; \displaystyle\frac{\partial Q_2}{\partial \theta_n} &amp; \displaystyle\frac{\partial Q_2}{\partial V_2} &amp; \dots &amp; \displaystyle\frac{\partial Q_2}{\partial V_n}\\ \vdots &amp; \ddots &amp; \vdots &amp; \vdots &amp; \ddots &amp; \vdots\\ \displaystyle\frac{\partial Q_n}{\partial \theta_2} &amp; \dots &amp; \displaystyle\frac{\partial Q_n}{\partial \theta_n} &amp; \displaystyle\frac{\partial Q_n}{\partial V_2} &amp; \dots &amp; \displaystyle\frac{\partial Q_n}{\partial V_n} \end{bmatrix} \begin{bmatrix} \Delta \theta_2\\ \vdots\\ \Delta \theta_2\\ \Delta V_2\\ \vdots\\ \Delta V_n\\ \end{bmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:8.520000000000003em;vertical-align:-4.010000000000001em"></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.8500299999999994em"><span style="top:-5.850029999999999em"><span class="pstrut" style="height:3.75em"></span><span class="mord"><span class="mord text"><span class="mord">NPQ</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord text"><span class="mord">NPV</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em"><span style="top:-3.69em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mspace nobreak"> </span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mspace nobreak"> </span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-3.7599999999999993em"><span class="pstrut" style="height:3.75em"></span><span class="mord"><span class="mspace nobreak"> </span></span></span><span style="top:-1.6499999999999997em"><span class="pstrut" style="height:3.75em"></span><span class="mord"><span class="mord text"><span class="mord">NPQ</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em"><span style="top:-3.69em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mspace nobreak"> </span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mspace nobreak"> </span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.3500300000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:4.458970000000001em"><span style="top:0.1500399999999994em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-0.9999600000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-1.5959600000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.191960000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.787960000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.3839600000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.9799600000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.57596em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.17196em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.217950000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-6.458970000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.9500599999999997em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:4.510000000000002em"><span style="top:-7.357500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-5.497500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-4.297500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.0975000000000006em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-1.2375000000000005em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-0.03749999999999937em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:4.010000000000001em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:4.458970000000001em"><span style="top:0.1500399999999994em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-0.9999600000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-1.5959600000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.191960000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.787960000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.3839600000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.9799600000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.57596em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.17196em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.217950000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-6.458970000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.9500599999999997em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:12.61603em;vertical-align:-6.050095em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:6.5659350000000005em"><span style="top:2.2500749999999994em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:1.1000749999999995em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:0.5040749999999994em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-0.0919250000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-0.6879250000000008em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-1.2839250000000009em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-1.879925000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.475925000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.071925000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6679250000000008em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.263925em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.8599250000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.455925000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-6.051925000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-6.647925000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-7.243925000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-7.324915000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-8.565935000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:6.050095em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:6.52488em"><span style="top:-8.84094em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-6.5049399999999995em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-4.773499999999999em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.5660599999999993em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714399999999998em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-0.23005999999999965em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:1.5013799999999995em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714399999999998em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:6.02488em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:6.52488em"><span style="top:-8.65344em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">…</span></span></span><span style="top:-6.3174399999999995em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋱</span></span></span><span style="top:-4.585999999999999em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">…</span></span></span><span style="top:-2.3785599999999993em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">…</span></span></span><span style="top:-0.042559999999999654em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋱</span></span></span><span style="top:1.6888799999999995em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">…</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:6.02488em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:6.52488em"><span style="top:-8.84094em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-6.5049399999999995em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-4.773499999999999em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.5660599999999993em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714399999999998em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-0.23005999999999965em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:1.5013799999999995em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714399999999998em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:6.02488em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:6.52488em"><span style="top:-8.84094em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-6.5049399999999995em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-4.773499999999999em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.5660599999999993em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714399999999998em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-0.23005999999999965em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:1.5013799999999995em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714399999999998em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:6.02488em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:6.52488em"><span style="top:-8.65344em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">…</span></span></span><span style="top:-6.3174399999999995em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋱</span></span></span><span style="top:-4.585999999999999em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">…</span></span></span><span style="top:-2.3785599999999993em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">…</span></span></span><span style="top:-0.042559999999999654em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋱</span></span></span><span style="top:1.6888799999999995em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">…</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:6.02488em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:6.52488em"><span style="top:-8.84094em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-6.5049399999999995em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-4.773499999999999em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.5660599999999993em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714399999999998em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-0.23005999999999965em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:1.5013799999999995em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714399999999998em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord" style="margin-right:0.05556em">∂</span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8360000000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:6.02488em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:6.5659350000000005em"><span style="top:2.2500749999999994em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:1.1000749999999995em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:0.5040749999999994em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-0.0919250000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-0.6879250000000008em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-1.2839250000000009em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-1.879925000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.475925000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.071925000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6679250000000008em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.263925em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.8599250000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.455925000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-6.051925000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-6.647925000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-7.243925000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-7.324915000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-8.565935000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:6.050095em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:4.458970000000001em"><span style="top:0.1500399999999994em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-0.9999600000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-1.5959600000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.191960000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.787960000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.3839600000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.9799600000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.57596em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.17196em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.217950000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-6.458970000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.9500599999999997em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:4.510000000000002em"><span style="top:-7.357500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-5.497500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-4.297500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.0975000000000006em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-1.2375000000000005em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-0.03749999999999937em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:4.010000000000001em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:4.458970000000001em"><span style="top:0.1500399999999994em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-0.9999600000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-1.5959600000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.191960000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.787960000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.3839600000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.9799600000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.57596em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.17196em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.217950000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-6.458970000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.9500599999999997em"><span></span></span></span></span></span></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>NPQ</mtext></mrow><annotation encoding="application/x-tex">\text{NPQ}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord text"><span class="mord">NPQ</span></span></span></span></span></span> é o número de barras PQ</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>NPV</mtext></mrow><annotation encoding="application/x-tex">\text{NPV}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord text"><span class="mord">NPV</span></span></span></span></span></span> é o número de barras PV</li></ul><p>O processo iterativo se inicia calculando as potências ativas (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>P</mi><mi>i</mi><mrow><mi>c</mi><mi>a</mi><mi>l</mi><mi>c</mi></mrow></msubsup></mrow><annotation encoding="application/x-tex">P_i^{calc}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.107772em;vertical-align:-0.258664em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.441336em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span><span class="mord mathdefault mtight">c</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em"><span></span></span></span></span></span></span></span></span></span></span>) para as barras PQ e PV e as potências reativas (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>Q</mi><mi>i</mi><mrow><mi>c</mi><mi>a</mi><mi>l</mi><mi>c</mi></mrow></msubsup></mrow><annotation encoding="application/x-tex">Q_i^{calc}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.107772em;vertical-align:-0.258664em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.441336em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span><span class="mord mathdefault mtight">c</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em"><span></span></span></span></span></span></span></span></span></span></span>) para as barras PQ, ambas as equações utilizando as estimativas iniciais das tensões complexas. Calcula-se, então, as correções de potência (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">\Delta P</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span><span class="mord mathdefault" style="margin-right:0.13889em">P</span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>Q</mi></mrow><annotation encoding="application/x-tex">\Delta Q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord">Δ</span><span class="mord mathdefault">Q</span></span></span></span></span>):</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>P</mi><mo>=</mo><msubsup><mi>P</mi><mi>i</mi><mrow><mi>e</mi><mi>s</mi><mi>p</mi></mrow></msubsup><mo>−</mo><msubsup><mi>P</mi><mi>i</mi><mrow><mi>c</mi><mi>a</mi><mi>l</mi><mi>c</mi></mrow></msubsup><mspace linebreak="newline"></mspace><mi mathvariant="normal">Δ</mi><mi>Q</mi><mo>=</mo><msubsup><mi>Q</mi><mi>i</mi><mrow><mi>e</mi><mi>s</mi><mi>p</mi></mrow></msubsup><mo>−</mo><msubsup><mi>Q</mi><mi>i</mi><mrow><mi>c</mi><mi>a</mi><mi>l</mi><mi>c</mi></mrow></msubsup></mrow><annotation encoding="application/x-tex">\Delta P = P_i^{esp} - P_i^{calc}\\ \Delta Q = Q_i^{esp} - Q_i^{calc}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.059164em;vertical-align:-0.276864em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7822999999999999em"><span style="top:-2.4231360000000004em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.180908em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.146108em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999998em"><span style="top:-2.4530000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span><span class="mord mathdefault mtight">c</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em"></span><span class="mord">Δ</span><span class="mord mathdefault">Q</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.059164em;vertical-align:-0.276864em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7822999999999999em"><span style="top:-2.4231360000000004em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.180908em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">s</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.146108em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999998em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span><span class="mord mathdefault mtight">c</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span></span></span></span></span></div><p>O passo seguinte é a formação da matriz jacobiana. Com isso é possível calcular as correções de módulo e ângulo das tensões de todas as barras (com exceção da barra de referência). Para tanto, no PSP-UFU utiliza-se o método de <a href="https://en.wikipedia.org/wiki/Gaussian_elimination" target="_blank" rel="noopener noreferrer">Eliminação Gaussiana</a> e em sequência a substituição regressiva. Esse procedimento diminui o esforço computacional, uma vez que a inversão da matriz jacobiana em todas as iterações é evitada.</p><p>Com as correções de módulo e ângulo das tensões das barras calculados, aplicam-se as seguintes equações:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>θ</mi><mi>i</mi><mrow><mo stretchy="false">(</mo><mi>v</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></msubsup><mo>=</mo><msubsup><mi>θ</mi><mi>i</mi><mrow><mo stretchy="false">(</mo><mi>v</mi><mo stretchy="false">)</mo></mrow></msubsup><mo>+</mo><mi mathvariant="normal">Δ</mi><msubsup><mi>θ</mi><mi>i</mi><mrow><mo stretchy="false">(</mo><mi>v</mi><mo stretchy="false">)</mo></mrow></msubsup><mspace linebreak="newline"></mspace><msubsup><mi>V</mi><mi>i</mi><mrow><mo stretchy="false">(</mo><mi>v</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></msubsup><mo>=</mo><msubsup><mi>V</mi><mi>i</mi><mrow><mo stretchy="false">(</mo><mi>v</mi><mo stretchy="false">)</mo></mrow></msubsup><mo>+</mo><mi mathvariant="normal">Δ</mi><msubsup><mi>V</mi><mi>i</mi><mrow><mo stretchy="false">(</mo><mi>v</mi><mo stretchy="false">)</mo></mrow></msubsup></mrow><annotation encoding="application/x-tex">\theta_i^{(v+1)}=\theta_i^{(v)}+\Delta \theta_i^{(v)}\\ V_i^{(v+1)}=V_i^{(v)}+\Delta V_i^{(v)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.321664em;vertical-align:-0.276864em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.4231360000000004em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight" style="margin-right:0.03588em">v</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.321664em;vertical-align:-0.276864em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.4231360000000004em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight" style="margin-right:0.03588em">v</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.321664em;vertical-align:-0.276864em"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">θ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.4231360000000004em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight" style="margin-right:0.03588em">v</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.321664em;vertical-align:-0.276864em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.4231360000000004em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight" style="margin-right:0.03588em">v</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.321664em;vertical-align:-0.276864em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.4231360000000004em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight" style="margin-right:0.03588em">v</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.321664em;vertical-align:-0.276864em"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em"><span style="top:-2.4231360000000004em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.2198em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight" style="margin-right:0.03588em">v</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em"><span></span></span></span></span></span></span></span></span></span></span></div><p>O processo é então reiniciado e será repetido até que se obtenha a convergência, quando as correções se tornam tão pequenas que satisfaçam uma tolerância pré-estipulada.</p><p>O fluxograma abaixo mostra o método de Newton-Raphson para solução do fluxo de carga implementado.</p><div><center><img src="/PSP/images/newtonRaphson.svg" alt="Método numérico de Newton-Raphson para fluxo de carga" title="Método numérico de Newton-Raphson para fluxo de carga"></center></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="controles-e-limites-em-um-problema-de-fluxo-de-carga"></a>Controles e limites em um problema de fluxo de carga<a aria-hidden="true" tabindex="-1" class="hash-link" href="#controles-e-limites-em-um-problema-de-fluxo-de-carga" title="Direct link to heading">#</a></h2><p>Nas barras de <a href="/PSP/docs/syncGenerator">geração</a> e também naquelas em que se encontra um <a href="/PSP/docs/syncMotor">compensador síncrono</a> conectado, o controle da magnitude da tensão no barramento é realizado por meio do ajuste da corrente de campo das máquinas síncronas, as quais podem operar sobrexcitadas (injetando reativos) ou subexcitadas (absorvendo reativos). Os valores limites de potência reativa que podem ser injetadas ou absorvidas dependem da máquina síncrona em estudo. Esses limites são incluídos no fluxo de carga com a criação de dois novos parâmetros, a potência reativa máxima (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>Q</mi><mi>i</mi><mrow><mi>m</mi><mover accent="true"><mi>a</mi><mo>ˊ</mo></mover><mi>x</mi></mrow></msubsup></mrow><annotation encoding="application/x-tex">Q_i^{máx}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.107772em;vertical-align:-0.258664em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.441336em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">m</span><span class="mord accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.69444em"><span style="top:-2.7em"><span class="pstrut" style="height:2.7em"></span><span class="mord mathdefault mtight">a</span></span><span style="top:-2.7em"><span class="pstrut" style="height:2.7em"></span><span class="accent-body" style="left:-0.25em"><span class="mord mtight">ˊ</span></span></span></span></span></span></span><span class="mord mathdefault mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em"><span></span></span></span></span></span></span></span></span></span></span>) e potência reativa mínima (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>Q</mi><mi>i</mi><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msubsup></mrow><annotation encoding="application/x-tex">Q_i^{min}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0833279999999998em;vertical-align:-0.258664em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.824664em"><span style="top:-2.441336em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">m</span><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em"><span></span></span></span></span></span></span></span></span></span></span>), sendo esses valores a soma dos limites individuais das máquinas em uma mesma barra genérica <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em"></span><span class="mord mathdefault">i</span></span></span></span></span>.</p><p>A manutenção da potência reativa dentro dos limites é realizada pela troca do tipo de barra, ou seja, as barras violadoras que controlam a tensão (PV), passam a ser barras de carga (PQ), cuja potência é fixada como o limite que seria ultrapassado (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>Q</mi><mi>i</mi><mrow><mi>m</mi><mover accent="true"><mi>a</mi><mo>ˊ</mo></mover><mi>x</mi></mrow></msubsup></mrow><annotation encoding="application/x-tex">Q_i^{máx}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.107772em;vertical-align:-0.258664em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-2.441336em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">m</span><span class="mord accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.69444em"><span style="top:-2.7em"><span class="pstrut" style="height:2.7em"></span><span class="mord mathdefault mtight">a</span></span><span style="top:-2.7em"><span class="pstrut" style="height:2.7em"></span><span class="accent-body" style="left:-0.25em"><span class="mord mtight">ˊ</span></span></span></span></span></span></span><span class="mord mathdefault mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em"><span></span></span></span></span></span></span></span></span></span></span> ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>Q</mi><mi>i</mi><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msubsup></mrow><annotation encoding="application/x-tex">Q_i^{min}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0833279999999998em;vertical-align:-0.258664em"></span><span class="mord"><span class="mord mathdefault">Q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.824664em"><span style="top:-2.441336em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">m</span><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em"><span></span></span></span></span></span></span></span></span></span></span>) e a tensão deixa de ser controlada partir de então.</p><p>A verificação de violação e troca de tipo de barra pode ser realizada a cada iteração ou ao final da convergência do cálculo. No PSP-UFU foi implementada a última estratégia, uma vez que separa os conceitos de cálculo e de verificação de limites, tornando mais fácil o desenvolvimento de novos métodos numéricos e limites. Nessa abordagem, ao ajustar o sistema para a nova situação não violadora o cálculo iterativo deve ser retomado até que obtenha novamente a convergência.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="referências"></a>Referências<a aria-hidden="true" tabindex="-1" class="hash-link" href="#referências" title="Direct link to heading">#</a></h2><ol><li>MONTICELLI, A. J. Fluxo de Carga em Redes de Energia Elétrica. São Paulo: Edgar Blücher, 1983.</li><li>STEVENSON JR.; WILLIAN, D. Elementos de Análise de Sistemas de Potência. 2ª ed. São Paulo: McGraw-Hill, 1986.</li><li>MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: <a href="https://doi.org/10.1007/978-3-642-13669-6" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/978-3-642-13669-6</a></li><li>ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley &amp; Sons, New York, 2001. doi: <a href="https://doi.org/10.1002/9781118878286" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/9781118878286</a></li><li>TINNEY, W. F.; HART, C. E. Power Flow Solution by Newton’s Method. IEEE Transaction on Power Apparatus and Systems, v. PAS-86, n. 11, nov. 1967. doi: <a href="https://doi.org/10.1109/TPAS.1967.291823" target="_blank" rel="noopener noreferrer">https://doi.org/10.1109/TPAS.1967.291823</a></li></ol></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/powerFlow.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/mathExpression"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Expressão Matemática</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/fault"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Curto-Circuito »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#formulação-do-problema-de-fluxo-de-carga" class="table-of-contents__link">Formulação do problema de fluxo de carga</a></li><li><a href="#execução-do-fluxo-de-carga-no-psp-ufu" class="table-of-contents__link">Execução do fluxo de carga no PSP-UFU</a><ul><li><a href="#erros-comuns-na-execução-do-fluxo-de-carga" class="table-of-contents__link">Erros comuns na execução do fluxo de carga</a></li></ul></li><li><a href="#métodos-de-solução-numérica-do-fluxo-de-carga-no-psp-ufu" class="table-of-contents__link">Métodos de solução numérica do fluxo de carga no PSP-UFU</a><ul><li><a href="#gauss-seidel" class="table-of-contents__link">Gauss-Seidel</a></li><li><a href="#newton-raphson" class="table-of-contents__link">Newton-Raphson</a></li></ul></li><li><a href="#controles-e-limites-em-um-problema-de-fluxo-de-carga" class="table-of-contents__link">Controles e limites em um problema de fluxo de carga</a></li><li><a href="#referências" class="table-of-contents__link">Referências</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Limitador de taxa</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Os blocos de limite de taxa têm como objetivo conter a taxa de crescimento ou decrescimento da sua entrada a valores inseridos pelo usuário. A taxa de variação é calculada a partir dos valores de entrada atual e passado e, caso seja violada, será definida uma saída que respeite essas taxas (de crescimento ou decrescimento).</p><p>A taxa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi></mrow><annotation encoding="application/x-tex">r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span></span></span></span></span>) é calculada de acordo com a equação:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi><mo>=</mo><mfrac><mrow><msub><mi>u</mi><mi>n</mi></msub><mo>−</mo><msub><mi>y</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><mi>h</mi></mfrac></mrow><annotation encoding="application/x-tex">r = \frac{u_n - y_{n-1}}{h}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.9463300000000001em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.26033em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">h</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">u_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	é a entrada atual do bloco</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">y_{n-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.638891em;vertical-align:-0.208331em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span></span>	é o valor de saída anterior do bloco</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em"></span><span class="mord mathdefault">h</span></span></span></span></span>	é o passo de integração</li></ul><p>Obtida a taxa, o bloco irá resultar em um valor calculado pelas seguintes condições:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>h</mi><mo>×</mo><msub><mi>R</mi><mrow><mi>c</mi><mi>r</mi><mi>e</mi></mrow></msub><mo separator="true" lspace="0em" rspace="0em">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>se </mtext><mi>r</mi><mo>&gt;</mo><msub><mi>R</mi><mrow><mi>c</mi><mi>r</mi><mi>e</mi></mrow></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>u</mi><mi>n</mi></msub><mo separator="true" lspace="0em" rspace="0em">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>se </mtext><msub><mi>R</mi><mrow><mi>d</mi><mi>e</mi><mi>c</mi></mrow></msub><mo>≤</mo><mi>r</mi><mo>≤</mo><msub><mi>R</mi><mrow><mi>c</mi><mi>r</mi><mi>e</mi></mrow></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>h</mi><mo>×</mo><msub><mi>R</mi><mrow><mi>d</mi><mi>e</mi><mi>c</mi></mrow></msub><mo separator="true" lspace="0em" rspace="0em">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>se </mtext><mi>r</mi><mo>&lt;</mo><msub><mi>R</mi><mrow><mi>d</mi><mi>e</mi><mi>c</mi></mrow></msub></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} h \times R_{cre}{,} &amp; \text{se } r &gt; R_{cre} \\ u_n{,} &amp; \text{se } R_{dec} \le r \le R_{cre}\\ h \times R_{dec}{,} &amp; \text{se } r &lt; R_{dec} \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.32em;vertical-align:-1.9099999999999997em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35002em"><span style="top:-2.19999em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.19499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.20499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.15001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.2950099999999996em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.30501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.60002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8500199999999998em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em"><span style="top:-4.41em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathdefault">h</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">e</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mpunct">,</span></span></span></span><span style="top:-2.97em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mpunct">,</span></span></span></span><span style="top:-1.5300000000000002em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathdefault">h</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">c</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mpunct">,</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.9099999999999997em"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em"><span style="top:-4.41em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">se </span></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">e</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.97em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">se </span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">c</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">e</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-1.5300000000000002em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">se </span></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">c</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.9099999999999997em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mrow><mi>c</mi><mi>r</mi><mi>e</mi></mrow></msub></mrow><annotation encoding="application/x-tex">R_{cre}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">e</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mrow><mi>d</mi><mi>e</mi><mi>c</mi></mrow></msub></mrow><annotation encoding="application/x-tex">R_{dec}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">c</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	são as taxas de crescimento e decaimento, respectivamente</li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-de-dados-do-limitador-de-taxa"></a>Formulário de edição de dados do Limitador de taxa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-de-dados-do-limitador-de-taxa" title="Direct link to heading">#</a></h2><p>A figura abaixo apresenta o formulário de edição de dados do bloco limitador de taxa.</p><div><center><img src="/PSP/images/rateLimitForm.png" alt="Formulário de edição de dados do bloco limitador de taxa no PSP-UFU" title="Formulário de edição de dados do bloco limitador de taxa no PSP-UFU"></center></div><p>Esse bloco é definido pelo <strong>limite superior (taxa de crescimento máxima) e inferior (taxa de decrescimento máxima)</strong>, inseridos pelo usuário.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Esses blocos são úteis para limitar variações bruscas na entrada que possam comprometer o controle ou limites físicos de modelos de turbina, por exemplo.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div 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docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Limitador de taxa</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Os blocos de limite de taxa têm como objetivo conter a taxa de crescimento ou decrescimento da sua entrada a valores inseridos pelo usuário. A taxa de variação é calculada a partir dos valores de entrada atual e passado e, caso seja violada, será definida uma saída que respeite essas taxas (de crescimento ou decrescimento).</p><p>A taxa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi></mrow><annotation encoding="application/x-tex">r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span></span></span></span></span>) é calculada de acordo com a equação:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi><mo>=</mo><mfrac><mrow><msub><mi>u</mi><mi>n</mi></msub><mo>−</mo><msub><mi>y</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><mi>h</mi></mfrac></mrow><annotation encoding="application/x-tex">r = \frac{u_n - y_{n-1}}{h}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.9463300000000001em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.26033em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">h</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>u</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">u_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	é a entrada atual do bloco</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">y_{n-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.638891em;vertical-align:-0.208331em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span></span>	é o valor de saída anterior do bloco</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em"></span><span class="mord mathdefault">h</span></span></span></span></span>	é o passo de integração</li></ul><p>Obtida a taxa, o bloco irá resultar em um valor calculado pelas seguintes condições:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.3599999999999999em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>h</mi><mo>×</mo><msub><mi>R</mi><mrow><mi>c</mi><mi>r</mi><mi>e</mi></mrow></msub><mo separator="true" lspace="0em" rspace="0em">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>se </mtext><mi>r</mi><mo>&gt;</mo><msub><mi>R</mi><mrow><mi>c</mi><mi>r</mi><mi>e</mi></mrow></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msub><mi>u</mi><mi>n</mi></msub><mo separator="true" lspace="0em" rspace="0em">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>se </mtext><msub><mi>R</mi><mrow><mi>d</mi><mi>e</mi><mi>c</mi></mrow></msub><mo>≤</mo><mi>r</mi><mo>≤</mo><msub><mi>R</mi><mrow><mi>c</mi><mi>r</mi><mi>e</mi></mrow></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>h</mi><mo>×</mo><msub><mi>R</mi><mrow><mi>d</mi><mi>e</mi><mi>c</mi></mrow></msub><mo separator="true" lspace="0em" rspace="0em">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>se </mtext><mi>r</mi><mo>&lt;</mo><msub><mi>R</mi><mrow><mi>d</mi><mi>e</mi><mi>c</mi></mrow></msub></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} h \times R_{cre}{,} &amp; \text{se } r &gt; R_{cre} \\ u_n{,} &amp; \text{se } R_{dec} \le r \le R_{cre}\\ h \times R_{dec}{,} &amp; \text{se } r &lt; R_{dec} \end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.32em;vertical-align:-1.9099999999999997em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35002em"><span style="top:-2.19999em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.19499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-2.20499em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.15001em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.2950099999999996em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.30501em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.60002em"><span class="pstrut" style="height:3.15em"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8500199999999998em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em"><span style="top:-4.41em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathdefault">h</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">e</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mpunct">,</span></span></span></span><span style="top:-2.97em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mpunct">,</span></span></span></span><span style="top:-1.5300000000000002em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathdefault">h</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">c</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mpunct">,</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.9099999999999997em"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em"><span style="top:-4.41em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">se </span></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">e</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.97em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">se </span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">c</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">e</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-1.5300000000000002em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord">se </span></span><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">c</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.9099999999999997em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mrow><mi>c</mi><mi>r</mi><mi>e</mi></mrow></msub></mrow><annotation encoding="application/x-tex">R_{cre}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">e</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mrow><mi>d</mi><mi>e</mi><mi>c</mi></mrow></msub></mrow><annotation encoding="application/x-tex">R_{dec}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight">c</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	são as taxas de crescimento e decaimento, respectivamente</li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-de-dados-do-limitador-de-taxa"></a>Formulário de edição de dados do Limitador de taxa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-de-dados-do-limitador-de-taxa" title="Direct link to heading">#</a></h2><p>A figura abaixo apresenta o formulário de edição de dados do bloco limitador de taxa.</p><div><center><img src="/PSP/images/rateLimitForm.png" alt="Formulário de edição de dados do bloco limitador de taxa no PSP-UFU" title="Formulário de edição de dados do bloco limitador de taxa no PSP-UFU"></center></div><p>Esse bloco é definido pelo <strong>limite superior (taxa de crescimento máxima) e inferior (taxa de decrescimento máxima)</strong>, inseridos pelo usuário.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Esses blocos são úteis para limitar variações bruscas na entrada que possam comprometer o controle ou limites físicos de modelos de turbina, por exemplo.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div 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class="pagination-nav__label">Constante »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#formulário-de-edição-de-dados-do-limitador-de-taxa" class="table-of-contents__link">Formulário de edição de dados do Limitador de taxa</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a 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padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Configurações da Simulação</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>As parametrizações e configurações das simulações são acessadas no <a href="/PSP/docs/mainScreen#menu-ribbon">menu Simulação</a> clicando no ícone do botão <strong>Configurações de simulação</strong>.</p><div><center><img src="/PSP/images/menuSimulationSettings.svg" alt="Menu Simulação" title="Menu Simulação"></center></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-das-configurações-de-simulação"></a>Formulário de edição das configurações de simulação<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-das-configurações-de-simulação" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de edição das configurações de simulação:</p><div><center><img src="/PSP/images/simulationConfigForm.png" alt="Configurações de simulação" title="Configurações de simulação"></center></div><p>Esse formulário é subdividido em quatro contextos distintos:</p><ul><li><strong>Geral</strong>: no qual são inseridas informações gerais e comuns a várias simulações;</li><li><strong>Fluxo de carga</strong>: local onde é selecionado o <a href="/PSP/docs/powerFlow#m%C3%A9todos-de-solu%C3%A7%C3%A3o-num%C3%A9rica-do-fluxo-de-carga-no-psp-ufu">método de solução numérica</a>, assim como seus parâmetros;</li><li><strong>Estabilidade</strong>: contendo opções de simulação no tempo e parâmetros do <a href="/PSP/docs/stability#integra%C3%A7%C3%A3o-num%C3%A9rica">método de integração</a>;</li><li><strong>Carga ZIP</strong>: contém as opções gerais das <a href="/PSP/docs/load#carga-no-estudo-de-estabilidade">cargas do tipo ZIP</a> no estudo de <a href="/PSP/docs/stability">estabilidade</a>.</li></ul><hr><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_1w39 tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Fluxo de carga</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Estabilidade</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Carga ZIP</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-base"></a>Potência base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-base" title="Direct link to heading">#</a></h4><p>Potência base do sistema utilizada para conversão dos dados reais em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> e vice-versa. Pode ser inserido em VA, kVA ou MVA.</p><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>A potência base de cada elemento pode ser distinta da potência base do sistema. Para isso, basta marcar a opção &quot;Utilizar potência nominal [<em>do elemento</em>] como base&quot;, presente em seus respectivos <a href="/PSP/docs/powerEditor">formulários de edição da dados</a>.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="frequência-do-sistema"></a>Frequência do sistema<a aria-hidden="true" tabindex="-1" class="hash-link" href="#frequência-do-sistema" title="Direct link to heading">#</a></h4><p>Define a frequência nominal do sistema.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Ao alterar a frequência nominal atente-se ao campo &quot;<a href="/PSP/docs/syncGenerator#frequ%C3%AAncia-de-circuito-aberto">Frequência de circuito aberto</a>&quot; das máquinas síncronas.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="cálculo-contínuo"></a>Cálculo contínuo<a aria-hidden="true" tabindex="-1" class="hash-link" href="#cálculo-contínuo" title="Direct link to heading">#</a></h4><p>Habilita ou desabilita o cálculo contínuo para os cálculos de <a href="/PSP/docs/fault">curto-circuito</a>, <a href="/PSP/docs/fault">nível de curto-circuito</a> e <a href="/PSP/docs/harmonics">distorções harmônicas</a>. O cálculo contínuo para o <a href="/PSP/docs/powerFlow">fluxo de carga</a> é sempre habilitado.</p><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Para habilitar o cálculo contínuo aperte o botão <strong>Habilitar solução</strong> presente no <a href="/PSP/docs/mainScreen#menu-ribbon">menu Simulação</a>.</p><p>Com essa opção, os cálculos estáticos selecionados são automaticamente realizados ao modificar quaisquer parâmetros da rede, como dados elétricos e acionamento dos disjuntores dos elementos (remoção ou inserção).</p></div></div></div></div></div><hr></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/simulationConfig.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/stability"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Estabilidade</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/text"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Texto Vinculado »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#formulário-de-edição-das-configurações-de-simulação" class="table-of-contents__link">Formulário de edição das configurações de simulação</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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absoluto</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/rateLimiter">Limitador de taxa</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/const">Constante</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/gain">Ganho</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/mathExpression">Expressão Matemática</a></li></ul></li></ul></li><li class="menu__list-item"><a class="menu__link menu__link--sublist menu__link--active" href="#!">Simulações</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/powerFlow">Fluxo de Potência</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/fault">Curto-Circuito</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a aria-current="page" class="menu__link menu__link--active active" tabindex="0" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Configurações da Simulação</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>As parametrizações e configurações das simulações são acessadas no <a href="/PSP/docs/mainScreen#menu-ribbon">menu Simulação</a> clicando no ícone do botão <strong>Configurações de simulação</strong>.</p><div><center><img src="/PSP/images/menuSimulationSettings.svg" alt="Menu Simulação" title="Menu Simulação"></center></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-das-configurações-de-simulação"></a>Formulário de edição das configurações de simulação<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-das-configurações-de-simulação" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de edição das configurações de simulação:</p><div><center><img src="/PSP/images/simulationConfigForm.png" alt="Configurações de simulação" title="Configurações de simulação"></center></div><p>Esse formulário é subdividido em quatro contextos distintos:</p><ul><li><strong>Geral</strong>: no qual são inseridas informações gerais e comuns a várias simulações;</li><li><strong>Fluxo de carga</strong>: local onde é selecionado o <a href="/PSP/docs/powerFlow#m%C3%A9todos-de-solu%C3%A7%C3%A3o-num%C3%A9rica-do-fluxo-de-carga-no-psp-ufu">método de solução numérica</a>, assim como seus parâmetros;</li><li><strong>Estabilidade</strong>: contendo opções de simulação no tempo e parâmetros do <a href="/PSP/docs/stability#integra%C3%A7%C3%A3o-num%C3%A9rica">método de integração</a>;</li><li><strong>Carga ZIP</strong>: contém as opções gerais das <a href="/PSP/docs/load#carga-no-estudo-de-estabilidade">cargas do tipo ZIP</a> no estudo de <a href="/PSP/docs/stability">estabilidade</a>.</li></ul><hr><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_1w39 tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Fluxo de carga</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Estabilidade</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Carga ZIP</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-base"></a>Potência base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-base" title="Direct link to heading">#</a></h4><p>Potência base do sistema utilizada para conversão dos dados reais em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> e vice-versa. Pode ser inserido em VA, kVA ou MVA.</p><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>A potência base de cada elemento pode ser distinta da potência base do sistema. Para isso, basta marcar a opção &quot;Utilizar potência nominal [<em>do elemento</em>] como base&quot;, presente em seus respectivos <a href="/PSP/docs/powerEditor">formulários de edição da dados</a>.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="frequência-do-sistema"></a>Frequência do sistema<a aria-hidden="true" tabindex="-1" class="hash-link" href="#frequência-do-sistema" title="Direct link to heading">#</a></h4><p>Define a frequência nominal do sistema.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>Ao alterar a frequência nominal atente-se ao campo &quot;<a href="/PSP/docs/syncGenerator#frequ%C3%AAncia-de-circuito-aberto">Frequência de circuito aberto</a>&quot; das máquinas síncronas.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="cálculo-contínuo"></a>Cálculo contínuo<a aria-hidden="true" tabindex="-1" class="hash-link" href="#cálculo-contínuo" title="Direct link to heading">#</a></h4><p>Habilita ou desabilita o cálculo contínuo para os cálculos de <a href="/PSP/docs/fault">curto-circuito</a>, <a href="/PSP/docs/fault">nível de curto-circuito</a> e <a href="/PSP/docs/harmonics">distorções harmônicas</a>. O cálculo contínuo para o <a href="/PSP/docs/powerFlow">fluxo de carga</a> é sempre habilitado.</p><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Para habilitar o cálculo contínuo aperte o botão <strong>Habilitar solução</strong> presente no <a href="/PSP/docs/mainScreen#menu-ribbon">menu Simulação</a>.</p><p>Com essa opção, os cálculos estáticos selecionados são automaticamente realizados ao modificar quaisquer parâmetros da rede, como dados elétricos e acionamento dos disjuntores dos elementos (remoção ou inserção).</p></div></div></div></div></div><hr></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/simulationConfig.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/stability"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Estabilidade</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/text"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Texto Vinculado »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#formulário-de-edição-das-configurações-de-simulação" class="table-of-contents__link">Formulário de edição das configurações de simulação</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Estabilidade</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Estabilidade de sistemas de potência é a habilidade de um Sistema Elétrico de Potência (SEP), para uma certa condição de operação, de reestabelecer um estado de operação de equilíbrio após ser submetido a um distúrbio físico. A estabilidade é reconhecida como um importante problema para a segurança da operação desde a década de 1920. Muitos <em>blackouts</em> de grande porte causados pela instabilidade do SEP têm ilustrado a importância desse fenômeno.</p><div><center><img src="/PSP/images/stability.svg" alt="Estabilidade" title="Estabilidade"></center></div><p>Normalmente são realizados dois tipos de estudos de estabilidade (uma classificação mais aprofundada pode ser observada <a href="https://doi.org/10.1109/TPWRS.2004.825981" target="_blank" rel="noopener noreferrer">nesse artigo</a>). A recuperação de uma rápida e brusca perturbação é chamada de <strong>estabilidade transitória</strong>, e sua solução é geralmente obtida no domínio do tempo. Outro estudo é denominado <strong>estabilidade dinâmica</strong>, utilizado para descrever a resposta do sistema frente a pequenas perturbações ao longo de muito tempo, o qual pode ser resolvido tanto no domínio da frequência quanto no domínio do tempo.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>No PSP-UFU, a estabilidade dinâmica é tratada como uma extensão da estabilidade transitória, em que os efeitos de pequenas constantes de tempo devem ser ignorados.</p></div></div><p>O modelo para representação do SEP em um estudo de estabilidade transitória é feito por meio do sistema de equações algébrico-diferenciais (EADs), em que o estado inicial é considerado estável e originado de um estudo de <a href="/PSP/docs/powerFlow">fluxo de carga</a>. A solução das equações se dá por meio de um <a href="https://en.wikipedia.org/wiki/Numerical_integration" target="_blank" rel="noopener noreferrer">método de integração numérica</a> e, então, é observada a resposta do sistema de potência.</p><p>Caso a solução no domínio do tempo, após alguma perturbação, leve um ou mais parâmetros do sistema a valores fisicamente impossíveis ou, até mesmo, a solução das equações diferenciais não obtenha convergência em processos iterativos, o sistema é dito <strong>instável</strong>. Em contrapartida, caso as variáveis de estado dos elementos do sistema oscilem após uma perturbação e se estabeleçam em um novo ponto de operação, mesmo que distinto dos valores iniciais, o sistema é considerado <strong>estável</strong>.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="execução-do-estudo-de-estabilidade-no-psp-ufu"></a>Execução do estudo de estabilidade no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#execução-do-estudo-de-estabilidade-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Após a construção do diagrama unifilar no <a href="/PSP/docs/powerEditor">editor de potência</a>, assim como os <a href="/PSP/docs/controlEditor">controles</a> das <a href="/PSP/docs/syncGenerator">máquinas síncronas</a>, a execução da estabilidade é realizada no <a href="/PSP/docs/mainScreen#menu-ribbon">menu Simulação</a> clicando no ícone do botão <strong>Executar Estabilidade</strong>. Ao clicar na parte inferior do botão &quot;Executar Estabilidade&quot; será exibido um menu suspenso com a opção <strong>Lista de eventos de estabilidade</strong>.</p><div><center><img src="/PSP/images/menuSimulationStability.svg" alt="Menu Simulação" title="Menu Simulação"></center></div><p>Ao executar o cálculo de estabilidade, uma caixa com o status do processo de simulação será exibida, indicando primeiramente a inicialização do estudo e posteriormente o tempo de simulação calculado.</p><p>Ao clicar na lista de eventos de estabilidade, será exibida uma janela com a descrição dos eventos de estabilidade inseridos.</p><div><center><img src="/PSP/images/stabList.png" alt="Lista de eventos de estabilidade" title="Lista de eventos de estabilidade"></center></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="inserindo-um-evento-de-estabilidade"></a>Inserindo um evento de estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#inserindo-um-evento-de-estabilidade" title="Direct link to heading">#</a></h3><p>Os distúrbios mais comuns aplicados em estudos de estabilidade transitória são faltas e chaveamentos. Tais operações são facilmente realizadas no PSP-UFU:</p><ul><li><p><strong>Faltas</strong>: Curtos-circuitos trifásicos podem ser inseridos nos <a href="/PSP/docs/bus">barramentos</a> do sistema por meio da inclusão da impedância de falta na matriz admitância de barras da mesma maneira realizada em um elemento <em>shunt</em>. Tal valor é definido pelo usuário e caso seja um curto-circuito franco, um valor não nulo, mas suficientemente próximo de zero, é aplicado, de forma que a tensão no barramento é levada a zero durante o distúrbio.</p></li><li><p><strong>Chaveamento de ramo</strong>: Da mesma forma que as faltas, o chaveamento de ramos é realizado por meio da alteração na matriz admitância, removendo ou inserindo os parâmetros do elemento a ser chaveado.
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padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Estabilidade</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Estabilidade de sistemas de potência é a habilidade de um Sistema Elétrico de Potência (SEP), para uma certa condição de operação, de reestabelecer um estado de operação de equilíbrio após ser submetido a um distúrbio físico. A estabilidade é reconhecida como um importante problema para a segurança da operação desde a década de 1920. Muitos <em>blackouts</em> de grande porte causados pela instabilidade do SEP têm ilustrado a importância desse fenômeno.</p><div><center><img src="/PSP/images/stability.svg" alt="Estabilidade" title="Estabilidade"></center></div><p>Normalmente são realizados dois tipos de estudos de estabilidade (uma classificação mais aprofundada pode ser observada <a href="https://doi.org/10.1109/TPWRS.2004.825981" target="_blank" rel="noopener noreferrer">nesse artigo</a>). A recuperação de uma rápida e brusca perturbação é chamada de <strong>estabilidade transitória</strong>, e sua solução é geralmente obtida no domínio do tempo. Outro estudo é denominado <strong>estabilidade dinâmica</strong>, utilizado para descrever a resposta do sistema frente a pequenas perturbações ao longo de muito tempo, o qual pode ser resolvido tanto no domínio da frequência quanto no domínio do tempo.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>No PSP-UFU, a estabilidade dinâmica é tratada como uma extensão da estabilidade transitória, em que os efeitos de pequenas constantes de tempo devem ser ignorados.</p></div></div><p>O modelo para representação do SEP em um estudo de estabilidade transitória é feito por meio do sistema de equações algébrico-diferenciais (EADs), em que o estado inicial é considerado estável e originado de um estudo de <a href="/PSP/docs/powerFlow">fluxo de carga</a>. A solução das equações se dá por meio de um <a href="https://en.wikipedia.org/wiki/Numerical_integration" target="_blank" rel="noopener noreferrer">método de integração numérica</a> e, então, é observada a resposta do sistema de potência.</p><p>Caso a solução no domínio do tempo, após alguma perturbação, leve um ou mais parâmetros do sistema a valores fisicamente impossíveis ou, até mesmo, a solução das equações diferenciais não obtenha convergência em processos iterativos, o sistema é dito <strong>instável</strong>. Em contrapartida, caso as variáveis de estado dos elementos do sistema oscilem após uma perturbação e se estabeleçam em um novo ponto de operação, mesmo que distinto dos valores iniciais, o sistema é considerado <strong>estável</strong>.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="execução-do-estudo-de-estabilidade-no-psp-ufu"></a>Execução do estudo de estabilidade no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#execução-do-estudo-de-estabilidade-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Após a construção do diagrama unifilar no <a href="/PSP/docs/powerEditor">editor de potência</a>, assim como os <a href="/PSP/docs/controlEditor">controles</a> das <a href="/PSP/docs/syncGenerator">máquinas síncronas</a>, a execução da estabilidade é realizada no <a href="/PSP/docs/mainScreen#menu-ribbon">menu Simulação</a> clicando no ícone do botão <strong>Executar Estabilidade</strong>. Ao clicar na parte inferior do botão &quot;Executar Estabilidade&quot; será exibido um menu suspenso com a opção <strong>Lista de eventos de estabilidade</strong>.</p><div><center><img src="/PSP/images/menuSimulationStability.svg" alt="Menu Simulação" title="Menu Simulação"></center></div><p>Ao executar o cálculo de estabilidade, uma caixa com o status do processo de simulação será exibida, indicando primeiramente a inicialização do estudo e posteriormente o tempo de simulação calculado.</p><p>Ao clicar na lista de eventos de estabilidade, será exibida uma janela com a descrição dos eventos de estabilidade inseridos.</p><div><center><img src="/PSP/images/stabList.png" alt="Lista de eventos de estabilidade" title="Lista de eventos de estabilidade"></center></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="inserindo-um-evento-de-estabilidade"></a>Inserindo um evento de estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#inserindo-um-evento-de-estabilidade" title="Direct link to heading">#</a></h3><p>Os distúrbios mais comuns aplicados em estudos de estabilidade transitória são faltas e chaveamentos. Tais operações são facilmente realizadas no PSP-UFU:</p><ul><li><p><strong>Faltas</strong>: Curtos-circuitos trifásicos podem ser inseridos nos <a href="/PSP/docs/bus">barramentos</a> do sistema por meio da inclusão da impedância de falta na matriz admitância de barras da mesma maneira realizada em um elemento <em>shunt</em>. Tal valor é definido pelo usuário e caso seja um curto-circuito franco, um valor não nulo, mas suficientemente próximo de zero, é aplicado, de forma que a tensão no barramento é levada a zero durante o distúrbio.</p></li><li><p><strong>Chaveamento de ramo</strong>: Da mesma forma que as faltas, o chaveamento de ramos é realizado por meio da alteração na matriz admitância, removendo ou inserindo os parâmetros do elemento a ser chaveado.
 Cada <a href="/PSP/docs/powerEditor">elemento de potência</a> possui um botão de &quot;Chaveamento&quot; ou &quot;Estabilidade&quot;, em que pode ser inserido os tempos de remoção e/ou inserção do componente.</p></li><li><p><strong>Chaveamento de máquinas</strong>: A remoção de uma máquina síncrona é efetivada com a retirada de sua participação no vetor de correntes, além da remoção de sua admitância fictícia.
 Assim como os <a href="/PSP/docs/powerEditor">elementos de potência</a>, as <a href="/PSP/docs/syncGenerator">máquinas síncronas</a> possui um botão &quot;Chaveamento&quot;, em que pode ser inserido os tempos de remoção e/ou inserção do componente.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Mesmo que removida da barra, os parâmetros das <a href="/PSP/docs/syncGenerator">máquinas síncronas</a> continuam a ser calculados com a corrente do estator nula, podendo fornecer resultados em uma eventual reconexão.</p></div></div></li></ul><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Eventos nos <strong>sistemas de controle</strong> podem ser facilmente introduzidos com o bloco de <a href="/PSP/docs/mathExpression">expressão matemática</a>. Nesse caso, tais eventos <strong>não</strong> serão exibidos na lista de eventos de estabilidade.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="erros-comuns-na-execução-do-estudo-de-estabilidade"></a>Erros comuns na execução do estudo de estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#erros-comuns-na-execução-do-estudo-de-estabilidade" title="Direct link to heading">#</a></h3><p>A seguir são apresentados os erros mais comuns relacionados ao estudo de estabilidade.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="a-seguinte-mensagem-de-erro-é-exibida-não-foi-possível-construir-a-matriz-admitância"></a>A seguinte mensagem de erro é exibida: &quot;Não foi possível construir a matriz admitância&quot;<a aria-hidden="true" tabindex="-1" class="hash-link" href="#a-seguinte-mensagem-de-erro-é-exibida-não-foi-possível-construir-a-matriz-admitância" title="Direct link to heading">#</a></h4><p>Essa mensagem de erro é exibida quando não é possível construir a matriz admitância de barras. As seguintes situações podem ocasionar esse erro:</p><ul><li><strong>Os parâmetros do circuito estão incorretos</strong>. Caso parâmetros muito fora dos valores padrão dos elementos elétricos sejam inseridos, o cálculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente.</li><li><strong>Algum barramento está isolado</strong>. Esse erro é bastante comum e pode ocorrer ao inserir um barramento sem conectá-lo ao sistema ou ao remover os elementos de ramo que conectam uma barra ao sistema. A solução é eliminar essa barra do diagrama.</li><li><strong>Algum elemento possui parâmetros discrepantes dos demais</strong>. Caso um dos elementos inseridos possua um valor de impedância muito distinto dos demais, como por exemplo uma linha com impedância muito elevada ou uma carga muito pequena, pode levar à divergência do método numérico. Nesse caso, reconsidere a necessidade de representação desses elementos no circuito e alterne entre os métodos numéricos de solução disponíveis.</li></ul><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="a-seguinte-mensagem-de-erro-é-exibida-erro-ao-inicializar-os-valores-de-saturação-do"></a>A seguinte mensagem de erro é exibida: &quot;Erro ao inicializar os valores de saturação do...&quot;<a aria-hidden="true" tabindex="-1" class="hash-link" href="#a-seguinte-mensagem-de-erro-é-exibida-erro-ao-inicializar-os-valores-de-saturação-do" title="Direct link to heading">#</a></h4><p>Essa mensagem de erro é exibida quando não é possível calcular os fatores de saturação da <a href="/PSP/docs/syncGenerator">máquina síncrona</a>. As seguintes situações podem ocasionar esse erro:</p><ul><li><strong>O fator de saturação é menor que 1,2</strong>. Esse valor deve ser maior que 1,2, ou irá gerar erros na simulação. Caso não seja informado, a saturação da máquina não é considerada nos cálculos.</li><li><strong>Os parâmetros da máquina síncrona estão incorretos</strong>. Caso parâmetros muito fora dos valores padrão das máquinas síncronas sejam inseridos, o cálculo dos fatores de saturação pode divergir. Verifique se os dados foram inseridos corretamente.</li></ul><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="a-seguinte-mensagem-de-erro-é-exibida-erro-ao-inicializar-o-avr--regulador-de-velocidade"></a>A seguinte mensagem de erro é exibida: &quot;Erro ao inicializar o AVR / regulador de velocidade...&quot;<a aria-hidden="true" tabindex="-1" class="hash-link" href="#a-seguinte-mensagem-de-erro-é-exibida-erro-ao-inicializar-o-avr--regulador-de-velocidade" title="Direct link to heading">#</a></h4><p>Essa mensagem de erro é exibida quando não é possível <a href="/PSP/docs/controlEditor#inicializa%C3%A7%C3%A3o-do-sistema-de-controle">inicializar o sistema de controle</a> de uma <a href="/PSP/docs/syncGenerator">máquina síncrona</a>. As seguintes situações podem ocasionar esse erro:</p><ul><li><strong>O sistema de controle está vazio</strong>. Caso esteja habilitado o AVR e/ou o regulador de velocidade e o controle não foi inserido, esse erro pode ser acionado. Insira o controle da máquina ou desmarque a opção de utilização do AVR e/ou regulador de velocidade.</li><li><strong>O sistema de controle não possui ao menos uma entrada e uma saída</strong>. O sistema de controle deve ter ao menos uma <a href="/PSP/docs/io">entrada e uma saída</a>, caso contrário apresentará erro de execução.</li><li><strong>O passo de integração está muito pequeno</strong>. Caso o passo de integração esteja muito pequeno, os cálculos gerarão erros e irão divergir. Reduza o passo de integração nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a>.</li></ul><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="a-seguinte-mensagem-de-erro-é-exibida-impossível-resolver-as-máquinas-do-sistema"></a>A seguinte mensagem de erro é exibida: &quot;Impossível resolver as máquinas do sistema&quot;<a aria-hidden="true" tabindex="-1" class="hash-link" href="#a-seguinte-mensagem-de-erro-é-exibida-impossível-resolver-as-máquinas-do-sistema" title="Direct link to heading">#</a></h4><p>Essa mensagem de erro é exibida quando não é possível resolver as EADs das máquinas síncronas inseridas no sistemas. As seguintes situações podem ocasionar esse erro:</p><ul><li><strong>Os parâmetros da máquina síncrona estão incorretos</strong>. Caso parâmetros muito fora dos valores padrão das máquinas síncronas sejam inseridos, o cálculo das EADs pode se tornar impossível. Verifique se os dados foram inseridos corretamente.</li><li><strong>O passo de integração está muito pequeno</strong>. Caso o passo de integração esteja muito pequeno, os cálculos gerarão erros e irão divergir. Reduza o passo de integração nas <a href="/PSP/docs/simulationConfig">configurações de simulação</a>.</li><li><strong>Os parâmetros do circuito estão incorretos</strong>. Caso parâmetros muito fora dos valores padrão dos elementos elétricos sejam inseridos, o cálculo de fluxo de carga pode divergir. Verifique se os dados foram inseridos corretamente.</li><li><strong>Algum barramento está isolado</strong>. Esse erro é bastante comum e pode ocorrer ao inserir um barramento sem conectá-lo ao sistema ou ao remover os elementos de ramo que conectam uma barra ao sistema. A solução é eliminar essa barra do diagrama.</li><li><strong>Algum elemento possui parâmetros discrepantes dos demais</strong>. Caso um dos elementos inseridos possua um valor de impedância muito distinto dos demais, como por exemplo uma linha com impedância muito elevada ou uma carga muito pequena, pode levar à divergência do método numérico. Nesse caso, reconsidere a necessidade de representação desses elementos no circuito e alterne entre os métodos numéricos de solução disponíveis.</li></ul><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="a-seguinte-mensagem-de-erro-é-exibida-erro-ao-inicializar-o-escorregamento-do-motor"></a>A seguinte mensagem de erro é exibida: &quot;Erro ao inicializar o escorregamento do motor...&quot;<a aria-hidden="true" tabindex="-1" class="hash-link" href="#a-seguinte-mensagem-de-erro-é-exibida-erro-ao-inicializar-o-escorregamento-do-motor" title="Direct link to heading">#</a></h4><p>Essa mensagem de erro é exibida quando não é possível calcular o valor de escorregamento inicial do motor de indução. As seguintes situações podem ocasionar esse erro:</p><ul><li><strong>Os parâmetros de estabilidade do motor estão incorretos</strong>. Caso parâmetros muito fora dos valores padrão dos motores de indução sejam inseridos, o cálculo do escorregamento pode se tornar impossível. Verifique se os dados foram inseridos corretamente.</li></ul><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="estrutura-da-ferramenta-de-estabilidade"></a>Estrutura da ferramenta de estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#estrutura-da-ferramenta-de-estabilidade" title="Direct link to heading">#</a></h2><p>A estabilidade de um SEP é um problema dinâmico e necessita de modelos mais elaborados de elementos de potência comparados àqueles apresentados nos outros estudos. Esses modelos são descritos individualmente, com destaque às <a href="/PSP/docs/syncGenerator#gerador-s%C3%ADncrono-no-estudo-de-estabilidade">máquinas síncronas</a>, <a href="/PSP/docs/load#carga-no-estudo-de-estabilidade">cargas ZIP</a> e <a href="/PSP/docs/indMotor#motor-de-indu%C3%A7%C3%A3o-trif%C3%A1sico-no-estudo-de-estabilidade">motores de indução</a>.</p><p>A representação dos demais componentes do sistema elétrico: <a href="/PSP/docs/line">linhas de transmissão</a>, <a href="/PSP/docs/transformer">transformadores</a> e elementos <em>shunt</em> (com exceção de cargas ZIP), que formam a rede de transmissão ou distribuição balanceada, é realizada utilizando os mesmos modelos do <a href="/PSP/docs/powerFlow">fluxo de carga</a>.</p><p>Os modelos dinâmicos para a análise no domínio do tempo são na forma de um sistema de equações algébrico-diferenciais (EADs), descritas a seguir:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><mi>x</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo separator="true">,</mo><mi>u</mi><mo stretchy="false">)</mo><mspace linebreak="newline"></mspace><mi>g</mi><mo>=</mo><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\dfrac{dx}{dt}= f(x,y,u)\\ g = f(x,y)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.05744em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">x</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord mathdefault">u</span><span class="mclose">)</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.03588em">g</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord mathdefault" style="margin-right:0.10764em">f</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="mclose">)</span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">x</span></span></span></span></span>	são as variáveis de estado</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span></span></span>	são as variáveis de algébricas</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>u</mi></mrow><annotation encoding="application/x-tex">u</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">u</span></span></span></span></span>	são as variáveis de entrada</li></ul><p>As variáveis de entrada são inseridas pelo usuário e permanecem constantes durante todo o processo de cálculo. Para o problema de estabilidade, as variáveis algébricas iniciais correspondem às tensões e ângulos das barras calculadas no <a href="/PSP/docs/powerFlow">fluxo de carga</a>. As variáveis de estado iniciais são estimadas após a convergência do fluxo de potência (inicialização dos elementos dinâmicos).</p><p>Na sequência é apresentado, na forma de fluxogramas, a estrutura do módulo de estabilidade implementado no PSP-UFU. O fluxograma abaixo mostra a estrutura geral da ferramenta de estabilidade.</p><div><center><img src="/PSP/images/stabGeneral.svg" alt="Estrutura geral da ferramenta de estabilidade" title="Estrutura geral da ferramenta de estabilidade"></center></div><p>A inicialização da rede elétrica e dos elementos dinâmicos, assim como o precesso iterativo para solução das EADs são apresentados nos dois fluxogramas conseguintes.</p><div><center><img src="/PSP/images/stabInit.svg" alt="Inicialização da ferramenta de estabilidade" title="Inicialização da ferramenta de estabilidade"></center></div><div><center><img src="/PSP/images/stabIterative.svg" alt="Processo iterativo para cálculo dos elementos dinâmicos" title="Estrutura geral da ferramenta de estabilidade"></center></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="integração-numérica"></a>Integração numérica<a aria-hidden="true" tabindex="-1" class="hash-link" href="#integração-numérica" title="Direct link to heading">#</a></h3><p>Para resolver as equações diferenciais da máquina é necessário um método de integração numérica. Tais métodos são classificados em dois grupos: métodos explícitos e métodos implícitos. Os métodos explícitos, devido à sua formulação, calculam diretamente o estado do sistema em um instante de tempo posterior, enquanto métodos implícitos envolvem estados atuais e posteriores em suas equações, exigindo, portanto, um processo iterativo.</p><p>As constantes de tempo presentes no estudo de estabilidade têm uma grande variação em seu valor (podem variar de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><msup><mn>0</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mtext> </mtext><mi>s</mi></mrow><annotation encoding="application/x-tex">10^{-3}~s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141079999999999em;vertical-align:0em"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">3</span></span></span></span></span></span></span></span></span><span class="mspace nobreak"> </span><span class="mord mathdefault">s</span></span></span></span></span> a <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>10</mn><mtext> </mtext><mi>s</mi></mrow><annotation encoding="application/x-tex">10~s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span><span class="mord">0</span><span class="mspace nobreak"> </span><span class="mord mathdefault">s</span></span></span></span></span>). Isso torna o sistema de equações diferenciais da máquina síncrona como um sistema rígido (<em><a href="https://en.wikipedia.org/wiki/Stiff_equation" target="_blank" rel="noopener noreferrer">stiff equation</a></em>). Caso a análise da estabilidade numérica tanto das equações diferenciais rígidas quanto do método de integração obtenham o mesmo comportamento, o método é chamado de absolutamente estável, ou A-estável.</p><p>Métodos de integração numérica explícitos, como por exemplo o <a href="https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods" target="_blank" rel="noopener noreferrer">Runge-Kutta</a> de quarta ordem, não podem ser A-estáveis e, portanto, normalmente possuem comportamento ruim em problemas com equações diferenciais rígidas. Por outro lado, métodos implícitos podem ser A-estáveis. Um método implícito adequado para solução do comportamento dinâmico de sistemas elétricos é o <strong>Trapezoidal Implícito</strong>, por possuir as seguintes vantagens:</p><ul><li>É numericamente estável (A-estável);</li><li>É bastante rápida;</li><li>Possui boa precisão (dependendo somente do passo de integração utilizado).</li></ul><p>Tal método foi implementado no PSP-UFU tanto para solução das equações diferenciais da máquina síncrona quanto nas <a href="/PSP/docs/transferFunction">funções transferência</a> do <a href="/PSP/docs/controlEditor">sistema de controle</a>. Sua formulação é dada pela seguinte expressão:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><msub><mi>y</mi><mi>n</mi></msub><mo>+</mo><mn>0</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>5</mn><mi>h</mi><mrow><mo fence="true">(</mo><msubsup><mi>y</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>+</mo><msubsup><mi>y</mi><mi>n</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">y_{n+1}=y_n + 0{,}5 h \left(y_{n+1}&#x27; + y_{n}&#x27; \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.638891em;vertical-align:-0.208331em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.7777700000000001em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.20001em;vertical-align:-0.35001em"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mord mathdefault">h</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.305331em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span></span></span></span></span></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em"></span><span class="mord mathdefault">h</span></span></span></span></span>	é o passo de integração</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">y_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>	é o valor do estado no passo anterior (instante <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>t</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">t_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76508em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>)</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">y_{n+1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.638891em;vertical-align:-0.208331em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span></span>	é o valor do estado no passo atual (instante <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>t</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">t_{n+1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8234109999999999em;vertical-align:-0.208331em"></span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span></span>)</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>y</mi><mi>n</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><annotation encoding="application/x-tex">y_{n}&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.998892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span></span></span></span></span>	é a equação diferencial no passo anterior</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>y</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><annotation encoding="application/x-tex">y_{n+1}&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.058331em;vertical-align:-0.30643899999999996em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.451892em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.30643899999999996em"><span></span></span></span></span></span></span></span></span></span></span>	é a equação diferencial no passo atual</li></ul><p>Nota-se nessa equação que o método é implícito devido ao termo <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">n+1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em"></span><span class="mord mathdefault">n</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span></span></span></span></span> aparecer em ambos os lados da equação, por isso é necessário um processo iterativo para sua solução.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="referências"></a>Referências<a aria-hidden="true" tabindex="-1" class="hash-link" href="#referências" title="Direct link to heading">#</a></h2><ol><li>MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: <a href="https://doi.org/10.1007/978-3-642-13669-6" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/978-3-642-13669-6</a></li><li>KUNDUR, P.; et al. Definition and classification of power system stability. IEEE Transactions Power Systems, v. 19, n. 2, mai 2004, p. 1387-1401. doi: <a href="https://doi.org/10.1109/TPWRS.2004.825981" target="_blank" rel="noopener noreferrer">https://doi.org/10.1109/TPWRS.2004.825981</a></li><li>ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley &amp; Sons, New York, 2001. doi: <a href="https://doi.org/10.1002/9781118878286" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/9781118878286</a></li><li>PARK, R. H. Two-reactions Theory of Synchronous Machine. Generalized Method of Analysis – Part I. AIEE Transactions, v. 48, n. 3, jul 1929. doi: <a href="https://doi.org/10.1109/T-AIEE.1929.5055275" target="_blank" rel="noopener noreferrer">https://doi.org/10.1109/T-AIEE.1929.5055275</a></li><li>ANDERSON, P. M.; FOUAD, A. A. Power System Control and Stability. Wiley-IEEE Press, New York, 2002. doi: <a href="https://doi.org/10.1109/9780470545577" target="_blank" rel="noopener noreferrer">https://doi.org/10.1109/9780470545577</a></li><li>SAUER, P. W.; PAI, M. A. Power System Dynamics and Stability. Pretience Hall, Upper Saddle River, 1998.</li><li>KUNDUR, P. Power System Stability and Control. McGraw-Hill, New York, 1994.</li><li>DOMMEL, H. W.; SATO, N. Fast Transient Stability Solutions. IEEE Transactions on Power Aparatus and Systems, v. PAS-91, n. 4, jul 1972, p. 1643-1650. doi: <a href="https://doi.org/10.1109/TPAS.1972.293341" target="_blank" rel="noopener noreferrer">https://doi.org/10.1109/TPAS.1972.293341</a></li></ol></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/stability.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/harmonics"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Harmônicos</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/simulationConfig"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Configurações da Simulação »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#execução-do-estudo-de-estabilidade-no-psp-ufu" class="table-of-contents__link">Execução do estudo de estabilidade no PSP-UFU</a><ul><li><a href="#inserindo-um-evento-de-estabilidade" class="table-of-contents__link">Inserindo um evento de estabilidade</a></li><li><a href="#erros-comuns-na-execução-do-estudo-de-estabilidade" class="table-of-contents__link">Erros comuns na execução do estudo de estabilidade</a></li></ul></li><li><a href="#estrutura-da-ferramenta-de-estabilidade" class="table-of-contents__link">Estrutura da ferramenta de estabilidade</a><ul><li><a href="#integração-numérica" class="table-of-contents__link">Integração numérica</a></li></ul></li><li><a href="#referências" class="table-of-contents__link">Referências</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Somador</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Como o próprio nome sugere, os somadores são elementos de controle capazes de somar qualquer quantidade de valores reais.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-de-dados-do-somador"></a>Formulário de edição de dados do somador<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-de-dados-do-somador" title="Direct link to heading">#</a></h2><p>A quantidade de entradas, assim como seus sinais são definidas pelo usuário, como mostra a figura abaixo.</p><div><center><img src="/PSP/images/sumForm.png" alt="Formulário de edição de dados do somador no PSP-UFU" title="Formulário de edição de dados do somador no PSP-UFU"></center></div><p>No seu único campo “<strong>Sinais</strong>” é inserida uma lista de sinais <strong>separados por espaços</strong> contendo os símbolos “+” para uma entrada positiva e “-” para negativa.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>O usuário pode inserir duas ou mais entradas de sinais no bloco.</p></div></div><p>Uma vez inseridas novas entradas, nós correspondentes serão incluídos no elemento gráfico do somador, o qual poderá ser conectado por meio das linhas de conexão.</p><p>De forma 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href="/PSP/docs/harmonics">Harmônicos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Somador</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Como o próprio nome sugere, os somadores são elementos de controle capazes de somar qualquer quantidade de valores reais.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-de-dados-do-somador"></a>Formulário de edição de dados do somador<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-de-dados-do-somador" title="Direct link to heading">#</a></h2><p>A quantidade de entradas, assim como seus sinais são definidas pelo usuário, como mostra a figura abaixo.</p><div><center><img src="/PSP/images/sumForm.png" alt="Formulário de edição de dados do somador no PSP-UFU" title="Formulário de edição de dados do somador no PSP-UFU"></center></div><p>No seu único campo “<strong>Sinais</strong>” é inserida uma lista de sinais <strong>separados por espaços</strong> contendo os símbolos “+” para uma entrada positiva e “-” para negativa.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>O usuário pode inserir duas ou mais entradas de sinais no bloco.</p></div></div><p>Uma vez inseridas novas entradas, nós correspondentes serão incluídos no elemento gráfico do somador, o qual poderá ser conectado por meio das linhas de conexão.</p><p>De forma semelhante, o usuário poderá excluir entradas de sinais pré-existentes, as quais serão removidas no ícone gráfico pela remoção do nó e da linha (caso exista alguma conectada).</p></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/sum.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/transferFunction"><div class="pagination-nav__sublabel">Previous</div><div 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Gerador Síncrono</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Uma máquina de corrente alternada na qual a frequência das tensões geradas e a velocidade da máquina estão em uma proporção constante. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=411-31-08" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="gerador-síncrono-no-psp-ufu"></a>Gerador Síncrono no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#gerador-síncrono-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Os geradores síncronos são a fonte de potência para o cálculo do fluxo de carga e estabilidade, além de serem um dos principais contribuintes para as correntes de falta.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Somente barramentos que possuem esse elemento conectado podem ser considerados <a href="/PSP/docs/powerFlow">barras de referência</a>. <a href="/PSP/docs/powerFlow">Barras do tipo PV</a> devem conter um gerador síncrono ou um <a href="/PSP/docs/syncMotor">motor síncrono (compensador síncrono)</a>.</p></div></div><p>O formulário de dados é dividido em dois, sendo o primeiro responsável pelos dados gerais, de <a href="/PSP/docs/powerFlow">fluxo de carga</a> e de <a href="/PSP/docs/fault">falta</a> e um segundo pelos dados de <a href="/PSP/docs/stability">estabilidade</a> . Esse último também permite o acesso aos controles das máquinas síncronas manipulados pelo editor de controle.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Os dados referentes às <strong>impedâncias de sequência positiva do gerador síncrono</strong> inseridas no <a href="/PSP/docs/syncGenerator#falta">contexto (aba) &quot;Falta&quot;</a> são utilizados <strong>tanto para os estudos de <a href="/PSP/docs/fault">curto-circuito</a> quanto para os estudos de <a href="/PSP/docs/harmonics">harmônicos</a></strong>.</p><p>Esses dados são ignorados nos estudos de <a href="/PSP/docs/powerFlow">fluxo de carga</a> (<em>não são utilizado nesse estudo</em>) e <a href="/PSP/docs/stability">estabilidade</a> (<em>são utilizados dados inseridos em formulário específico</em>).</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="gerador-síncrono-no-fluxo-de-carga"></a>Gerador Síncrono no fluxo de carga<a aria-hidden="true" tabindex="-1" class="hash-link" href="#gerador-síncrono-no-fluxo-de-carga" title="Direct link to heading">#</a></h3><p>O gerador síncrono é a fonte de potência do PSP-UFU no estudo de fluxo de carga. Seu comportamento difere de acordo com o tipo de barra conectada:</p><ul><li><a href="/PSP/docs/powerFlow">Barra de referência</a>: Os dados de potência ativa e reativa inseridos são desprezados, uma vez que esse elemento será utilizado para completar o balanço de potência do estudo de fluxo d carga;</li><li><a href="/PSP/docs/powerFlow">Barra PV</a>: O dado de potência ativa é considerado, porém o dados de potência reativa são desprezados. O valor da potência reativa é utilizado para manter o módulo da tensão constante no barramento conectado;</li><li><a href="/PSP/docs/powerFlow">Barra PQ</a>: Para os geradores conectados a essa barra tanto a potência ativa quanto reativa inseridas são consideradas.</li></ul><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>Caso o limite de potência reativa seja excedido, o programa automaticamente transforma a <a href="/PSP/docs/powerFlow">Barra PV</a> conectada em uma <a href="/PSP/docs/powerFlow">Barra PQ</a>, utilizando o valor limite de potência reativa que seria ultrapassado.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="gerador-síncrono-no-estudo-de-curto-circuito"></a>Gerador Síncrono no estudo de curto-circuito<a aria-hidden="true" tabindex="-1" class="hash-link" href="#gerador-síncrono-no-estudo-de-curto-circuito" title="Direct link to heading">#</a></h3><p>Enquanto os geradores no estudo de fluxo de carga são modelados somente por correntes injetadas nas barras, para o curto-circuito utiliza-se uma tensão atrás de uma impedância. A figura abaixo mostra o caminho da corrente e o circuito equivalente de cada sequência nos geradores.</p><div><center><img src="/PSP/images/sycGeneratorSeq.svg" alt="Caminho das correntes e circuito equivalente: (a) sequência positiva; (b) sequência negativa; (c) sequência zero" title="Caminho das correntes e circuito equivalente: (a) sequência positiva; (b) sequência negativa; (c) sequência zero"></center></div><p>As tensões geradas são somente de sequência positiva, uma vez que o gerador fornece sempre tensões trifásicas equilibradas. Portanto a rede de sequência positiva é composta de uma tensão pré-falta atrás de uma impedância de sequência positiva. As redes de sequência negativa e zero não contêm forças eletromotrizes, porém incluem as impedâncias do gerador de sequência negativa e zero.</p><p>A corrente que circula na impedância <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\overline{z}_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.78056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> entre o neutro e a terra é <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">3\dot{I}_{a0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.07019em;vertical-align:-0.15em"></span><span class="mord">3</span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>. Pela figura acima (c), observa-se que a queda de tensão de sequência zero do ponto a para terra (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">\dot{V}_{a0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.07019em;vertical-align:-0.15em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) é:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub><mo>=</mo><mo>−</mo><mn>3</mn><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub><mo>−</mo><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>g</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">\dot{V}_{a0} = -3\dot{I}_{a0}\overline{z}_n - \dot{I}_{a0}\overline{z}_{g0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.07019em;vertical-align:-0.15em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.07019em;vertical-align:-0.15em"></span><span class="mord">−</span><span class="mord">3</span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.206298em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">g</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span></div><p>A rede de sequência zero, que é um circuito monofásico pelo qual se supõe que circule apenas corrente de sequência zero e deve, portanto, ter uma impedância definida pela seguinte equação:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mn>0</mn></msub><mo>=</mo><mn>3</mn><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub><mo>+</mo><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>g</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">\overline{z}_{0} = 3\overline{z}_n + \overline{z}_{g0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.78056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.79444em;vertical-align:-0.15em"></span><span class="mord">3</span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.916668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">g</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Caso o gerador não seja aterrado, não circulará corrente de sequência zero por ele. Nesse caso, dependendo da conexão do transformador próximo ao gerador sem aterramento, a seguinte mensagem de erro pode ser exibida:</p><p><center>&quot;<i>Falha ao inverter a matriz admitância de sequência zero</i>&quot;</center></p><p>Isso ocorre porque a matriz admitância de sequência zero é singular. Para contornar esse problema escolha <strong>uma</strong> das duas soluções abaixo:</p><ol><li>Marque a opção &quot;Neutro aterrado&quot; e insira um alto valor de reatância de aterramento (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi><mn>9999</mn><mtext> </mtext><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">j9999~p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mspace nobreak"> </span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, por exemplo);</li><li><strong>Ou</strong>, na barra do gerador, insira um <a href="/PSP/docs/inductor">reator</a> de baixo valor de potência reativa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo separator="true">,</mo><mn>0</mn><mtext> </mtext><mi>v</mi><mi>a</mi><mi>r</mi></mrow><annotation encoding="application/x-tex">1,0~var</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span><span class="mspace nobreak"> </span><span class="mord mathdefault" style="margin-right:0.03588em">v</span><span class="mord mathdefault">a</span><span class="mord mathdefault" style="margin-right:0.02778em">r</span></span></span></span></span>, por exemplo).</li></ol></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="gerador-síncrono-no-estudo-de-estabilidade"></a>Gerador Síncrono no estudo de estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#gerador-síncrono-no-estudo-de-estabilidade" title="Direct link to heading">#</a></h3><p>A relação de valores observados em testes adequados (definidos na <a href="https://doi.org/10.1109/IEEESTD.2020.9050934" target="_blank" rel="noopener noreferrer">IEEE Std. 115-2019</a>), denominados parâmetros padrões, são utilizados para modelar a máquina síncrona no estudo de estabilidade do PSP-UFU.</p><p>Os parâmetros da máquina síncrona que influenciam rapidamente no decaimento de valores são chamados <strong>subtransitórios</strong> (indicados por <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msup></mrow><annotation encoding="application/x-tex">&#x27;&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span>), aqueles que influenciam mais lentamente são chamados <strong>transitórios</strong> (indicados por <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span>) e, finalmente, aqueles que influenciam continuamente são chamados de parâmetros <strong>síncronos</strong> (sem indicação de sobrescrito).</p><p>Um conjunto de equações algébrico-diferenciais determinam o comportamento da máquina síncrona no estudo de estabilidade:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><msub><mi>V</mi><mi>q</mi></msub><mo>=</mo><msub><mi>r</mi><mi>a</mi></msub><msub><mi>I</mi><mi>q</mi></msub><mo>−</mo><msubsup><mi>x</mi><mrow><mi>d</mi><mi>s</mi></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mi>I</mi><mi>d</mi><mspace linebreak="newline"></mspace><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><msub><mi>V</mi><mi>d</mi></msub><mo>=</mo><msub><mi>r</mi><mi>a</mi></msub><msub><mi>I</mi><mi>d</mi></msub><mo>−</mo><msubsup><mi>x</mi><mrow><mi>q</mi><mi>s</mi></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mi>I</mi><mi>q</mi><mspace linebreak="newline"></mspace><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mo>−</mo><msub><mi>V</mi><mi>q</mi></msub><mo>=</mo><msub><mi>r</mi><mi>a</mi></msub><msub><mi>I</mi><mi>q</mi></msub><mo>−</mo><msubsup><mi>x</mi><mrow><mi>d</mi><mi>s</mi></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mi>I</mi><mi>d</mi><mspace linebreak="newline"></mspace><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mo>−</mo><msub><mi>V</mi><mi>d</mi></msub><mo>=</mo><msub><mi>r</mi><mi>a</mi></msub><msub><mi>I</mi><mi>d</mi></msub><mo>−</mo><msubsup><mi>x</mi><mrow><mi>q</mi><mi>s</mi></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mi>I</mi><mi>q</mi><mspace linebreak="newline"></mspace><mtext> </mtext><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>V</mi><mrow><mi>f</mi><mi>d</mi></mrow></msub><mo>+</mo><mrow><mo fence="true">(</mo><msub><mi>x</mi><mi>d</mi></msub><mo>−</mo><msubsup><mi>x</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>d</mi></msub><mo>−</mo><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><msubsup><mi>T</mi><mrow><mi>d</mi><mn>0</mn></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>−</mo><mrow><mo fence="true">(</mo><msub><mi>x</mi><mi>q</mi></msub><mo>−</mo><msubsup><mi>x</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>q</mi></msub><mo>−</mo><msub><mi>s</mi><mi>q</mi></msub><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><msubsup><mi>T</mi><mrow><mi>q</mi><mn>0</mn></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>+</mo><mrow><mo fence="true">(</mo><msubsup><mi>x</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><msubsup><mi>x</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>d</mi></msub><mo>−</mo><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><msubsup><mi>T</mi><mrow><mi>d</mi><mn>0</mn></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>+</mo><mrow><mo fence="true">(</mo><msubsup><mi>x</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><msubsup><mi>x</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>q</mi></msub><mo>−</mo><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><msubsup><mi>T</mi><mrow><mi>q</mi><mn>0</mn></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mfrac><mspace linebreak="newline"></mspace><mtext> </mtext><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><mi>ω</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><msub><mi>ω</mi><mi>r</mi></msub><mrow><mn>2</mn><mi>H</mi></mrow></mfrac><mrow><mo fence="true">[</mo><msub><mi>P</mi><mi>m</mi></msub><mo>−</mo><msub><mi>P</mi><mi>e</mi></msub><mo>−</mo><msub><mi>D</mi><mi>a</mi></msub><mrow><mo fence="true">(</mo><mi>ω</mi><mo>−</mo><msub><mi>ω</mi><mi>r</mi></msub><mo fence="true">)</mo></mrow><mo fence="true">]</mo></mrow><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><mi>δ</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><mrow><mo fence="true">(</mo><mi>ω</mi><mo>−</mo><msub><mi>ω</mi><mi>r</mi></msub><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">E_{q}&#x27; - V_q = r_aI_q - x_{ds}&#x27;Id\\ E_{d}&#x27; - V_d = r_aI_d - x_{qs}&#x27;Iq\\ E_{q}&#x27;&#x27; - V_q = r_aI_q - x_{ds}&#x27;&#x27;Id\\ E_{d}&#x27;&#x27; - V_d = r_aI_d - x_{qs}&#x27;&#x27;Iq\\ ~\\ \frac{dE_{q}&#x27;}{dt} = \frac{V_{fd} + \left( x_d - x_{d}&#x27; \right)I_d - s_d E_{q}&#x27;}{T_{d0}&#x27;}\\ \frac{dE_{d}&#x27;}{dt} = \frac{- \left( x_q - x_{q}&#x27; \right)I_q - s_q E_{d}&#x27;}{T_{q0}&#x27;}\\ \frac{dE_{q}&#x27;&#x27;}{dt} = \frac{s_dE_{q}&#x27; + \left( x_{d}&#x27; - x_{d}&#x27;&#x27; \right)I_d - s_d E_{q}&#x27;&#x27;}{T_{d0}&#x27;&#x27;}\\ \frac{dE_{d}&#x27;&#x27;}{dt} = \frac{s_dE_{d}&#x27; + \left( x_{q}&#x27; - x_{q}&#x27;&#x27; \right)I_q - s_d E_{d}&#x27;&#x27;}{T_{q0}&#x27;&#x27;}\\ ~\\ \frac{d\omega}{dt} = \frac{\omega_r}{2H} \left[ P_m - P_e - D_a \left( \omega - \omega_r \right) \right]\\ \frac{d\delta}{dt} = \Omega_b\left( \omega - \omega_r \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.185em;vertical-align:-0.383108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="mord mathdefault">d</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.185em;vertical-align:-0.383108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="mord mathdefault" style="margin-right:0.03588em">q</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.185em;vertical-align:-0.383108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="mord mathdefault">d</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.185em;vertical-align:-0.383108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="mord mathdefault" style="margin-right:0.03588em">q</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0em;vertical-align:0em"></span><span class="mspace nobreak"> </span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.211em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.525em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.512308em;vertical-align:-0.9873080000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.525em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.398692em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.30130799999999996em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9873080000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.114892em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.7115240000000003em;vertical-align:-1.088416em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6231080000000002em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.4336920000000006em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4024159999999999em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">−</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.088416em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.211em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.525em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.512308em;vertical-align:-0.9873080000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.525em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.398692em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.30130799999999996em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9873080000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.114892em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.7115240000000003em;vertical-align:-1.088416em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6231080000000002em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.4336920000000006em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4024159999999999em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.088416em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0em;vertical-align:0em"></span><span class="mspace nobreak"> </span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.05744em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.7935599999999998em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.08125em">H</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">[</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mclose delimcenter" style="top:0em">]</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.05744em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault" style="margin-right:0.03785em">δ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span></span></div><p>As duas últimas equações diferenciais são as equações mecânicas da máquina; e as demais são equações elétricas (consulte essa <a href="https://dx.doi.org/10.14393/ufu.te.2019.2444" target="_blank" rel="noopener noreferrer">tese</a> para maiores detalhes acerca dos parâmetros dessas equações).</p><p>Utilizando as equações transitórias e subtransitórias podem-se definir cinco modelos de distintas complexidades.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>O modelo da máquina síncrona é <strong>selecionado automaticamente</strong> de acordo com os dados fornecidos ao programa.</p></div></div><p>Na sequência são apresentados tais modelos, incluídos os efeitos da saturação magnética, em conjunto com seus diagramas de blocos:</p><ul><li><strong>Modelo 1</strong>: Corresponde a uma tensão constante atrás de uma reatância transitória de eixo direto (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>x</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><annotation encoding="application/x-tex">x_{d}&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.035em;vertical-align:-0.2831079999999999em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span></span>), não exigindo equações diferenciais;</li><li><strong>Modelo 2</strong>: São representados os efeitos transitórios de eixo direto, sendo necessária a solução de uma equação diferencial (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>), cujo diagrama de blocos é apresentado na figura abaixo:</li></ul><div><center><img src="/PSP/images/model2SyncGenerator.svg" alt="Diagrama de blocos do Modelo 2 das máquinas síncronas" title="Diagrama de blocos do Modelo 2 das máquinas síncronas"></center></div><ul><li><strong>Modelo 3</strong>: São representados os efeitos transitórios de eixo direto e em quadratura, exigindo duas equações diferenciais (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{d}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.43468em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.08968em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.5102em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>), cujo diagrama de blocos é apresentado na figura abaixo:</li></ul><div><center><img src="/PSP/images/model3SyncGenerator.svg" alt="Diagrama de blocos do Modelo 3 das máquinas síncronas" title="Diagrama de blocos do Modelo 3 das máquinas síncronas"></center></div><ul><li><strong>Modelo 4</strong>: São representados os efeitos subtransitórios de eixo direto e em quadratura, sendo necessária a solução de três equações diferenciais (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{d}&#x27;&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.43468em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.08968em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.5102em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>), cujo diagrama de blocos é apresentado na figura abaixo:</li></ul><div><center><img src="/PSP/images/model4SyncGenerator.svg" alt="Diagrama de blocos do Modelo 4 das máquinas síncronas" title="Diagrama de blocos do Modelo 4 das máquinas síncronas"></center></div><ul><li><strong>Modelo 5</strong>: São representados os efeitos subtransitórios de eixo direto e em quadratura, sendo necessária a solução de quatro equações diferenciais (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{d}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.43468em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.08968em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.5102em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{d}&#x27;&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.43468em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.08968em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.5102em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>), cujo diagrama de blocos é apresentado na figura abaixo:</li></ul><div><center><img src="/PSP/images/model5SyncGenerator.svg" alt="Diagrama de blocos do Modelo 4 das máquinas síncronas" title="Diagrama de blocos do Modelo 4 das máquinas síncronas"></center></div><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Em todos os modelos as equações diferenciais mecânicas são solucionadas.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="saturação"></a>Saturação<a aria-hidden="true" tabindex="-1" class="hash-link" href="#saturação" title="Direct link to heading">#</a></h4><p>Para representar matematicamente o efeito da saturação nas equações das máquinas síncronas são introduzidos “fatores de saturação” que modificam as impedâncias do circuito equivalente, os quais dependem de uma reatância de dispersão efetiva, chamada de reatância de Potier (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">x_p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>).</p><p>Tal reatância pode ser obtida por meio de ensaios (utilizando curvas de saturação de circuito aberto e carga de fator de potência zero) ou estimadas de forma aproximada por outros parâmetros da máquina. A reatância de dispersão (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>l</mi></msub></mrow><annotation encoding="application/x-tex">x_l</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>), aqui substituída de forma aproximada por <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">x_p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>, representa a parcela da reatância da máquina originados do fluxo magnético que percorrem o ar na maioria de seu caminho e, portanto, é independente da saturação.</p><p>O método implementado no programa permite reproduzir a saturação em ambos os eixos (direto e em quadratura), diferindo entre si devido à divergência no tamanho do entreferro. É assumido que a soma vetorial das duas componentes do fluxo magnético saturado está em fase com a f.m.m. e proporcional à Tensão de Potier (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>E</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">E_p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>, a qual é a tensão atrás da reatância de Potier).</p><p>Para isso, são utilizados internamente dois fatores de saturação, sendo um no eixo direto (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>s</mi><mi>d</mi></msub></mrow><annotation encoding="application/x-tex">s_d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) e outro no eixo em quadratura (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>s</mi><mi>q</mi></msub></mrow><annotation encoding="application/x-tex">s_q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>). Esses fatores de saturação são <strong>automaticamente calculados</strong> a cada passo de integração e dependem da curva de saturação da máquina definida pelo <a href="/PSP/docs/syncGenerator#fator-de-satura%C3%A7%C3%A3o">fator de saturação inserido no formulário de edição de dados</a>.</p><p>Portanto as reatâncias saturadas, que devem ser inseridas nas equações algébricas da máquina, são definidas pelas seguintes equações:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mrow><mi>d</mi><mi>s</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>x</mi><mi>d</mi></msub><mo>−</mo><msub><mi>x</mi><mi>p</mi></msub></mrow><mrow><msub><mi>s</mi><mi>d</mi></msub><mo>+</mo><msub><mi>x</mi><mi>p</mi></msub></mrow></mfrac><mspace linebreak="newline"></mspace><msub><mi>x</mi><mrow><mi>q</mi><mi>s</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>x</mi><mi>q</mi></msub><mo>−</mo><msub><mi>x</mi><mi>p</mi></msub></mrow><mrow><msub><mi>s</mi><mi>q</mi></msub><mo>+</mo><msub><mi>x</mi><mi>p</mi></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">x_{ds}=\frac{x_d-x_p}{s_d +x_p}\\ x_{qs}=\frac{x_q-x_p}{s_q +x_p}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">s</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.232438em;vertical-align:-0.972108em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.26033em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.972108em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mathdefault mtight">s</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.232438em;vertical-align:-0.972108em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.26033em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.972108em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Essas equações também são utilizadas para as reatâncias transitórias e subtransitórias, visto que o valor da reatância de Potier (ou de dispersão) não é alterada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="barramento-infinito"></a>Barramento infinito<a aria-hidden="true" tabindex="-1" class="hash-link" href="#barramento-infinito" title="Direct link to heading">#</a></h4><p>Algumas referências incluem um modelo sem equações diferenciais, em que a máquina é somente representada por uma tensão constante atrás de uma reatância transitória de eixo direto. Tal é utilizado na representação de um <strong>barramento infinito</strong>, o qual é normalmente constituído de um subsistema muito maior àquele simulado.</p><p>No PSP-UFU a <strong>representação de um barramento infinito</strong> pode ser obtido por meio da utilização de uma máquina representada pelo Modelo 1 cujo valor da constante de inércia (H) é infinito ou muito grande (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>9999</mn><mtext> </mtext><mi>s</mi></mrow><annotation encoding="application/x-tex">9999~s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mspace nobreak"> </span><span class="mord mathdefault">s</span></span></span></span></span>, por exemplo) em relação às demais máquinas do sistema, e o valor de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>x</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><annotation encoding="application/x-tex">x_{d}&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.035em;vertical-align:-0.2831079999999999em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span></span> deve ser um valor muito pequeno (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><msup><mn>0</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mtext> </mtext><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">10^{-3}~p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.008548em;vertical-align:-0.19444em"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">3</span></span></span></span></span></span></span></span></span><span class="mspace nobreak"> </span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, por exemplo).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="centro-de-inércia"></a>Centro de inércia<a aria-hidden="true" tabindex="-1" class="hash-link" href="#centro-de-inércia" title="Direct link to heading">#</a></h4><p>Normalmente utiliza-se a velocidade de referência como sendo a síncrona e portanto, nesse caso, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ω</mi><mi>r</mi></msub><mo>=</mo><msub><mi>ω</mi><mi>b</mi></msub><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>0</mn><mtext> </mtext><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">\omega_r = \omega_b = 1,0~p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span><span class="mspace nobreak"> </span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> Essa abordagem, adotada por vários livros de estabilidade, considera como referência uma máquina fictícia girando sempre na velocidade síncrona independente das perturbações aplicadas no sistema. No PSP-UFU foi implementado o conceito de centro de inércia (COI, do inglês, <em>Center of Inertia</em>), que constitui uma soma ponderada das velocidades das máquinas presentes no sistema:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ω</mi><mi>r</mi></msub><mo>=</mo><mfrac><mrow><mo fence="true">(</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>H</mi><mi>i</mi></msub><msub><mi>ω</mi><mi>i</mi></msub><mo fence="true">)</mo></mrow><mrow><mo fence="true">(</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>H</mi><mi>i</mi></msub><mo fence="true">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">\omega_r=\frac{\left( \sum_{i=1}^{n} H_i \omega_i \right)}{\left( \sum_{i=1}^{n} H_i \right)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.488004em;vertical-align:-0.994002em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.494002em"><span style="top:-2.305708em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.804292em"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6897100000000003em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.804292em"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.994002em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:
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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Gerador Síncrono</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Uma máquina de corrente alternada na qual a frequência das tensões geradas e a velocidade da máquina estão em uma proporção constante. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=411-31-08" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="gerador-síncrono-no-psp-ufu"></a>Gerador Síncrono no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#gerador-síncrono-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Os geradores síncronos são a fonte de potência para o cálculo do fluxo de carga e estabilidade, além de serem um dos principais contribuintes para as correntes de falta.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Somente barramentos que possuem esse elemento conectado podem ser considerados <a href="/PSP/docs/powerFlow">barras de referência</a>. <a href="/PSP/docs/powerFlow">Barras do tipo PV</a> devem conter um gerador síncrono ou um <a href="/PSP/docs/syncMotor">motor síncrono (compensador síncrono)</a>.</p></div></div><p>O formulário de dados é dividido em dois, sendo o primeiro responsável pelos dados gerais, de <a href="/PSP/docs/powerFlow">fluxo de carga</a> e de <a href="/PSP/docs/fault">falta</a> e um segundo pelos dados de <a href="/PSP/docs/stability">estabilidade</a> . Esse último também permite o acesso aos controles das máquinas síncronas manipulados pelo editor de controle.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Os dados referentes às <strong>impedâncias de sequência positiva do gerador síncrono</strong> inseridas no <a href="/PSP/docs/syncGenerator#falta">contexto (aba) &quot;Falta&quot;</a> são utilizados <strong>tanto para os estudos de <a href="/PSP/docs/fault">curto-circuito</a> quanto para os estudos de <a href="/PSP/docs/harmonics">harmônicos</a></strong>.</p><p>Esses dados são ignorados nos estudos de <a href="/PSP/docs/powerFlow">fluxo de carga</a> (<em>não são utilizado nesse estudo</em>) e <a href="/PSP/docs/stability">estabilidade</a> (<em>são utilizados dados inseridos em formulário específico</em>).</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="gerador-síncrono-no-fluxo-de-carga"></a>Gerador Síncrono no fluxo de carga<a aria-hidden="true" tabindex="-1" class="hash-link" href="#gerador-síncrono-no-fluxo-de-carga" title="Direct link to heading">#</a></h3><p>O gerador síncrono é a fonte de potência do PSP-UFU no estudo de fluxo de carga. Seu comportamento difere de acordo com o tipo de barra conectada:</p><ul><li><a href="/PSP/docs/powerFlow">Barra de referência</a>: Os dados de potência ativa e reativa inseridos são desprezados, uma vez que esse elemento será utilizado para completar o balanço de potência do estudo de fluxo d carga;</li><li><a href="/PSP/docs/powerFlow">Barra PV</a>: O dado de potência ativa é considerado, porém o dados de potência reativa são desprezados. O valor da potência reativa é utilizado para manter o módulo da tensão constante no barramento conectado;</li><li><a href="/PSP/docs/powerFlow">Barra PQ</a>: Para os geradores conectados a essa barra tanto a potência ativa quanto reativa inseridas são consideradas.</li></ul><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>Caso o limite de potência reativa seja excedido, o programa automaticamente transforma a <a href="/PSP/docs/powerFlow">Barra PV</a> conectada em uma <a href="/PSP/docs/powerFlow">Barra PQ</a>, utilizando o valor limite de potência reativa que seria ultrapassado.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="gerador-síncrono-no-estudo-de-curto-circuito"></a>Gerador Síncrono no estudo de curto-circuito<a aria-hidden="true" tabindex="-1" class="hash-link" href="#gerador-síncrono-no-estudo-de-curto-circuito" title="Direct link to heading">#</a></h3><p>Enquanto os geradores no estudo de fluxo de carga são modelados somente por correntes injetadas nas barras, para o curto-circuito utiliza-se uma tensão atrás de uma impedância. A figura abaixo mostra o caminho da corrente e o circuito equivalente de cada sequência nos geradores.</p><div><center><img src="/PSP/images/sycGeneratorSeq.svg" alt="Caminho das correntes e circuito equivalente: (a) sequência positiva; (b) sequência negativa; (c) sequência zero" title="Caminho das correntes e circuito equivalente: (a) sequência positiva; (b) sequência negativa; (c) sequência zero"></center></div><p>As tensões geradas são somente de sequência positiva, uma vez que o gerador fornece sempre tensões trifásicas equilibradas. Portanto a rede de sequência positiva é composta de uma tensão pré-falta atrás de uma impedância de sequência positiva. As redes de sequência negativa e zero não contêm forças eletromotrizes, porém incluem as impedâncias do gerador de sequência negativa e zero.</p><p>A corrente que circula na impedância <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\overline{z}_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.78056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> entre o neutro e a terra é <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">3\dot{I}_{a0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.07019em;vertical-align:-0.15em"></span><span class="mord">3</span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>. Pela figura acima (c), observa-se que a queda de tensão de sequência zero do ponto a para terra (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">\dot{V}_{a0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.07019em;vertical-align:-0.15em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) é:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub><mo>=</mo><mo>−</mo><mn>3</mn><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub><mo>−</mo><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>a</mi><mn>0</mn></mrow></msub><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>g</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">\dot{V}_{a0} = -3\dot{I}_{a0}\overline{z}_n - \dot{I}_{a0}\overline{z}_{g0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.07019em;vertical-align:-0.15em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.07019em;vertical-align:-0.15em"></span><span class="mord">−</span><span class="mord">3</span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.206298em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">g</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span></div><p>A rede de sequência zero, que é um circuito monofásico pelo qual se supõe que circule apenas corrente de sequência zero e deve, portanto, ter uma impedância definida pela seguinte equação:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mn>0</mn></msub><mo>=</mo><mn>3</mn><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub><mo>+</mo><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mrow><mi>g</mi><mn>0</mn></mrow></msub></mrow><annotation encoding="application/x-tex">\overline{z}_{0} = 3\overline{z}_n + \overline{z}_{g0}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.78056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.79444em;vertical-align:-0.15em"></span><span class="mord">3</span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.916668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">g</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Caso o gerador não seja aterrado, não circulará corrente de sequência zero por ele. Nesse caso, dependendo da conexão do transformador próximo ao gerador sem aterramento, a seguinte mensagem de erro pode ser exibida:</p><p><center>&quot;<i>Falha ao inverter a matriz admitância de sequência zero</i>&quot;</center></p><p>Isso ocorre porque a matriz admitância de sequência zero é singular. Para contornar esse problema escolha <strong>uma</strong> das duas soluções abaixo:</p><ol><li>Marque a opção &quot;Neutro aterrado&quot; e insira um alto valor de reatância de aterramento (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi><mn>9999</mn><mtext> </mtext><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">j9999~p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mspace nobreak"> </span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, por exemplo);</li><li><strong>Ou</strong>, na barra do gerador, insira um <a href="/PSP/docs/inductor">reator</a> de baixo valor de potência reativa (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo separator="true">,</mo><mn>0</mn><mtext> </mtext><mi>v</mi><mi>a</mi><mi>r</mi></mrow><annotation encoding="application/x-tex">1,0~var</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span><span class="mspace nobreak"> </span><span class="mord mathdefault" style="margin-right:0.03588em">v</span><span class="mord mathdefault">a</span><span class="mord mathdefault" style="margin-right:0.02778em">r</span></span></span></span></span>, por exemplo).</li></ol></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="gerador-síncrono-no-estudo-de-estabilidade"></a>Gerador Síncrono no estudo de estabilidade<a aria-hidden="true" tabindex="-1" class="hash-link" href="#gerador-síncrono-no-estudo-de-estabilidade" title="Direct link to heading">#</a></h3><p>A relação de valores observados em testes adequados (definidos na <a href="https://doi.org/10.1109/IEEESTD.2020.9050934" target="_blank" rel="noopener noreferrer">IEEE Std. 115-2019</a>), denominados parâmetros padrões, são utilizados para modelar a máquina síncrona no estudo de estabilidade do PSP-UFU.</p><p>Os parâmetros da máquina síncrona que influenciam rapidamente no decaimento de valores são chamados <strong>subtransitórios</strong> (indicados por <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msup></mrow><annotation encoding="application/x-tex">&#x27;&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span>), aqueles que influenciam mais lentamente são chamados <strong>transitórios</strong> (indicados por <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.751892em;vertical-align:0em"></span><span class="mord"><span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span>) e, finalmente, aqueles que influenciam continuamente são chamados de parâmetros <strong>síncronos</strong> (sem indicação de sobrescrito).</p><p>Um conjunto de equações algébrico-diferenciais determinam o comportamento da máquina síncrona no estudo de estabilidade:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><msub><mi>V</mi><mi>q</mi></msub><mo>=</mo><msub><mi>r</mi><mi>a</mi></msub><msub><mi>I</mi><mi>q</mi></msub><mo>−</mo><msubsup><mi>x</mi><mrow><mi>d</mi><mi>s</mi></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mi>I</mi><mi>d</mi><mspace linebreak="newline"></mspace><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><msub><mi>V</mi><mi>d</mi></msub><mo>=</mo><msub><mi>r</mi><mi>a</mi></msub><msub><mi>I</mi><mi>d</mi></msub><mo>−</mo><msubsup><mi>x</mi><mrow><mi>q</mi><mi>s</mi></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mi>I</mi><mi>q</mi><mspace linebreak="newline"></mspace><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mo>−</mo><msub><mi>V</mi><mi>q</mi></msub><mo>=</mo><msub><mi>r</mi><mi>a</mi></msub><msub><mi>I</mi><mi>q</mi></msub><mo>−</mo><msubsup><mi>x</mi><mrow><mi>d</mi><mi>s</mi></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mi>I</mi><mi>d</mi><mspace linebreak="newline"></mspace><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mo>−</mo><msub><mi>V</mi><mi>d</mi></msub><mo>=</mo><msub><mi>r</mi><mi>a</mi></msub><msub><mi>I</mi><mi>d</mi></msub><mo>−</mo><msubsup><mi>x</mi><mrow><mi>q</mi><mi>s</mi></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mi>I</mi><mi>q</mi><mspace linebreak="newline"></mspace><mtext> </mtext><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>V</mi><mrow><mi>f</mi><mi>d</mi></mrow></msub><mo>+</mo><mrow><mo fence="true">(</mo><msub><mi>x</mi><mi>d</mi></msub><mo>−</mo><msubsup><mi>x</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>d</mi></msub><mo>−</mo><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><msubsup><mi>T</mi><mrow><mi>d</mi><mn>0</mn></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>−</mo><mrow><mo fence="true">(</mo><msub><mi>x</mi><mi>q</mi></msub><mo>−</mo><msubsup><mi>x</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>q</mi></msub><mo>−</mo><msub><mi>s</mi><mi>q</mi></msub><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><msubsup><mi>T</mi><mrow><mi>q</mi><mn>0</mn></mrow><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>+</mo><mrow><mo fence="true">(</mo><msubsup><mi>x</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><msubsup><mi>x</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>d</mi></msub><mo>−</mo><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><msubsup><mi>T</mi><mrow><mi>d</mi><mn>0</mn></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mfrac><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>+</mo><mrow><mo fence="true">(</mo><msubsup><mi>x</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup><mo>−</mo><msubsup><mi>x</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup><mo fence="true">)</mo></mrow><msub><mi>I</mi><mi>q</mi></msub><mo>−</mo><msub><mi>s</mi><mi>d</mi></msub><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><msubsup><mi>T</mi><mrow><mi>q</mi><mn>0</mn></mrow><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mfrac><mspace linebreak="newline"></mspace><mtext> </mtext><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><mi>ω</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><msub><mi>ω</mi><mi>r</mi></msub><mrow><mn>2</mn><mi>H</mi></mrow></mfrac><mrow><mo fence="true">[</mo><msub><mi>P</mi><mi>m</mi></msub><mo>−</mo><msub><mi>P</mi><mi>e</mi></msub><mo>−</mo><msub><mi>D</mi><mi>a</mi></msub><mrow><mo fence="true">(</mo><mi>ω</mi><mo>−</mo><msub><mi>ω</mi><mi>r</mi></msub><mo fence="true">)</mo></mrow><mo fence="true">]</mo></mrow><mspace linebreak="newline"></mspace><mfrac><mrow><mi>d</mi><mi>δ</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><mrow><mo fence="true">(</mo><mi>ω</mi><mo>−</mo><msub><mi>ω</mi><mi>r</mi></msub><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">E_{q}&#x27; - V_q = r_aI_q - x_{ds}&#x27;Id\\ E_{d}&#x27; - V_d = r_aI_d - x_{qs}&#x27;Iq\\ E_{q}&#x27;&#x27; - V_q = r_aI_q - x_{ds}&#x27;&#x27;Id\\ E_{d}&#x27;&#x27; - V_d = r_aI_d - x_{qs}&#x27;&#x27;Iq\\ ~\\ \frac{dE_{q}&#x27;}{dt} = \frac{V_{fd} + \left( x_d - x_{d}&#x27; \right)I_d - s_d E_{q}&#x27;}{T_{d0}&#x27;}\\ \frac{dE_{d}&#x27;}{dt} = \frac{- \left( x_q - x_{q}&#x27; \right)I_q - s_q E_{d}&#x27;}{T_{q0}&#x27;}\\ \frac{dE_{q}&#x27;&#x27;}{dt} = \frac{s_dE_{q}&#x27; + \left( x_{d}&#x27; - x_{d}&#x27;&#x27; \right)I_d - s_d E_{q}&#x27;&#x27;}{T_{d0}&#x27;&#x27;}\\ \frac{dE_{d}&#x27;&#x27;}{dt} = \frac{s_dE_{d}&#x27; + \left( x_{q}&#x27; - x_{q}&#x27;&#x27; \right)I_q - s_d E_{d}&#x27;&#x27;}{T_{q0}&#x27;&#x27;}\\ ~\\ \frac{d\omega}{dt} = \frac{\omega_r}{2H} \left[ P_m - P_e - D_a \left( \omega - \omega_r \right) \right]\\ \frac{d\delta}{dt} = \Omega_b\left( \omega - \omega_r \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.185em;vertical-align:-0.383108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span 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style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="mord mathdefault">d</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.185em;vertical-align:-0.383108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="mord mathdefault" style="margin-right:0.03588em">q</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.185em;vertical-align:-0.383108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="mord mathdefault">d</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.048892em;vertical-align:-0.247em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8018919999999999em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.113em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.185em;vertical-align:-0.383108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.801892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mathdefault mtight">s</span></span></span></span><span style="top:-3.1130000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="mord mathdefault" style="margin-right:0.03588em">q</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0em;vertical-align:0em"></span><span class="mspace nobreak"> </span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.211em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.525em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.512308em;vertical-align:-0.9873080000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.525em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.398692em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.30130799999999996em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em">f</span><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9873080000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.114892em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.7115240000000003em;vertical-align:-1.088416em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6231080000000002em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.4336920000000006em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4024159999999999em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">−</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.088416em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.211em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.525em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.512308em;vertical-align:-0.9873080000000001em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.525em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.398692em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.30130799999999996em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9873080000000001em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.114892em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.7115240000000003em;vertical-align:-1.088416em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6231080000000002em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.733692em"><span style="top:-2.4336920000000006em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4024159999999999em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.773108em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">(</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.383108em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.088416em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0em;vertical-align:0em"></span><span class="mspace nobreak"> </span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.05744em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.7935599999999998em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1075599999999999em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">2</span><span class="mord mathdefault" style="margin-right:0.08125em">H</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">[</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span><span class="mclose delimcenter" style="top:0em">]</span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:2.05744em;vertical-align:-0.686em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault">t</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">d</span><span class="mord mathdefault" style="margin-right:0.03785em">δ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span></span></div><p>As duas últimas equações diferenciais são as equações mecânicas da máquina; e as demais são equações elétricas (consulte essa <a href="https://dx.doi.org/10.14393/ufu.te.2019.2444" target="_blank" rel="noopener noreferrer">tese</a> para maiores detalhes acerca dos parâmetros dessas equações).</p><p>Utilizando as equações transitórias e subtransitórias podem-se definir cinco modelos de distintas complexidades.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>O modelo da máquina síncrona é <strong>selecionado automaticamente</strong> de acordo com os dados fornecidos ao programa.</p></div></div><p>Na sequência são apresentados tais modelos, incluídos os efeitos da saturação magnética, em conjunto com seus diagramas de blocos:</p><ul><li><strong>Modelo 1</strong>: Corresponde a uma tensão constante atrás de uma reatância transitória de eixo direto (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>x</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><annotation encoding="application/x-tex">x_{d}&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.035em;vertical-align:-0.2831079999999999em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span></span>), não exigindo equações diferenciais;</li><li><strong>Modelo 2</strong>: São representados os efeitos transitórios de eixo direto, sendo necessária a solução de uma equação diferencial (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>), cujo diagrama de blocos é apresentado na figura abaixo:</li></ul><div><center><img src="/PSP/images/model2SyncGenerator.svg" alt="Diagrama de blocos do Modelo 2 das máquinas síncronas" title="Diagrama de blocos do Modelo 2 das máquinas síncronas"></center></div><ul><li><strong>Modelo 3</strong>: São representados os efeitos transitórios de eixo direto e em quadratura, exigindo duas equações diferenciais (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{d}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.43468em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.08968em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.5102em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>), cujo diagrama de blocos é apresentado na figura abaixo:</li></ul><div><center><img src="/PSP/images/model3SyncGenerator.svg" alt="Diagrama de blocos do Modelo 3 das máquinas síncronas" title="Diagrama de blocos do Modelo 3 das máquinas síncronas"></center></div><ul><li><strong>Modelo 4</strong>: São representados os efeitos subtransitórios de eixo direto e em quadratura, sendo necessária a solução de três equações diferenciais (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{d}&#x27;&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.43468em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.08968em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.5102em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>), cujo diagrama de blocos é apresentado na figura abaixo:</li></ul><div><center><img src="/PSP/images/model4SyncGenerator.svg" alt="Diagrama de blocos do Modelo 4 das máquinas síncronas" title="Diagrama de blocos do Modelo 4 das máquinas síncronas"></center></div><ul><li><strong>Modelo 5</strong>: São representados os efeitos subtransitórios de eixo direto e em quadratura, sendo necessária a solução de quatro equações diferenciais (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{d}&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.43468em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.08968em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.5102em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>q</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{q}&#x27;&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5319em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1869em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.60742em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.42488571428571426em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>d</mi><msubsup><mi>E</mi><mi>d</mi><mrow><mo mathvariant="normal">′</mo><mo mathvariant="normal">′</mo></mrow></msubsup></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{dE_{d}&#x27;&#x27;}{dt}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.43468em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.08968em"><span style="top:-2.6550000000000002em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">t</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.5102em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8278285714285715em"><span style="top:-2.214em;margin-left:-0.05764em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-2.931em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>), cujo diagrama de blocos é apresentado na figura abaixo:</li></ul><div><center><img src="/PSP/images/model5SyncGenerator.svg" alt="Diagrama de blocos do Modelo 4 das máquinas síncronas" title="Diagrama de blocos do Modelo 4 das máquinas síncronas"></center></div><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Em todos os modelos as equações diferenciais mecânicas são solucionadas.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="saturação"></a>Saturação<a aria-hidden="true" tabindex="-1" class="hash-link" href="#saturação" title="Direct link to heading">#</a></h4><p>Para representar matematicamente o efeito da saturação nas equações das máquinas síncronas são introduzidos “fatores de saturação” que modificam as impedâncias do circuito equivalente, os quais dependem de uma reatância de dispersão efetiva, chamada de reatância de Potier (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">x_p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>).</p><p>Tal reatância pode ser obtida por meio de ensaios (utilizando curvas de saturação de circuito aberto e carga de fator de potência zero) ou estimadas de forma aproximada por outros parâmetros da máquina. A reatância de dispersão (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>l</mi></msub></mrow><annotation encoding="application/x-tex">x_l</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>), aqui substituída de forma aproximada por <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">x_p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>, representa a parcela da reatância da máquina originados do fluxo magnético que percorrem o ar na maioria de seu caminho e, portanto, é independente da saturação.</p><p>O método implementado no programa permite reproduzir a saturação em ambos os eixos (direto e em quadratura), diferindo entre si devido à divergência no tamanho do entreferro. É assumido que a soma vetorial das duas componentes do fluxo magnético saturado está em fase com a f.m.m. e proporcional à Tensão de Potier (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>E</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">E_p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.969438em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.05764em">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:-0.05764em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>, a qual é a tensão atrás da reatância de Potier).</p><p>Para isso, são utilizados internamente dois fatores de saturação, sendo um no eixo direto (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>s</mi><mi>d</mi></msub></mrow><annotation encoding="application/x-tex">s_d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>) e outro no eixo em quadratura (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>s</mi><mi>q</mi></msub></mrow><annotation encoding="application/x-tex">s_q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span></span>). Esses fatores de saturação são <strong>automaticamente calculados</strong> a cada passo de integração e dependem da curva de saturação da máquina definida pelo <a href="/PSP/docs/syncGenerator#fator-de-satura%C3%A7%C3%A3o">fator de saturação inserido no formulário de edição de dados</a>.</p><p>Portanto as reatâncias saturadas, que devem ser inseridas nas equações algébricas da máquina, são definidas pelas seguintes equações:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mrow><mi>d</mi><mi>s</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>x</mi><mi>d</mi></msub><mo>−</mo><msub><mi>x</mi><mi>p</mi></msub></mrow><mrow><msub><mi>s</mi><mi>d</mi></msub><mo>+</mo><msub><mi>x</mi><mi>p</mi></msub></mrow></mfrac><mspace linebreak="newline"></mspace><msub><mi>x</mi><mrow><mi>q</mi><mi>s</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>x</mi><mi>q</mi></msub><mo>−</mo><msub><mi>x</mi><mi>p</mi></msub></mrow><mrow><msub><mi>s</mi><mi>q</mi></msub><mo>+</mo><msub><mi>x</mi><mi>p</mi></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">x_{ds}=\frac{x_d-x_p}{s_d +x_p}\\ x_{qs}=\frac{x_q-x_p}{s_q +x_p}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">s</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.232438em;vertical-align:-0.972108em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.26033em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.972108em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span><span class="mord mathdefault mtight">s</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.232438em;vertical-align:-0.972108em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.26033em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em">q</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.972108em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Essas equações também são utilizadas para as reatâncias transitórias e subtransitórias, visto que o valor da reatância de Potier (ou de dispersão) não é alterada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="barramento-infinito"></a>Barramento infinito<a aria-hidden="true" tabindex="-1" class="hash-link" href="#barramento-infinito" title="Direct link to heading">#</a></h4><p>Algumas referências incluem um modelo sem equações diferenciais, em que a máquina é somente representada por uma tensão constante atrás de uma reatância transitória de eixo direto. Tal é utilizado na representação de um <strong>barramento infinito</strong>, o qual é normalmente constituído de um subsistema muito maior àquele simulado.</p><p>No PSP-UFU a <strong>representação de um barramento infinito</strong> pode ser obtido por meio da utilização de uma máquina representada pelo Modelo 1 cujo valor da constante de inércia (H) é infinito ou muito grande (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>9999</mn><mtext> </mtext><mi>s</mi></mrow><annotation encoding="application/x-tex">9999~s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mord">9</span><span class="mspace nobreak"> </span><span class="mord mathdefault">s</span></span></span></span></span>, por exemplo) em relação às demais máquinas do sistema, e o valor de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>x</mi><mi>d</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msubsup></mrow><annotation encoding="application/x-tex">x_{d}&#x27;</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.035em;vertical-align:-0.2831079999999999em"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.751892em"><span style="top:-2.4168920000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">d</span></span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2831079999999999em"><span></span></span></span></span></span></span></span></span></span></span> deve ser um valor muito pequeno (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><msup><mn>0</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mtext> </mtext><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">10^{-3}~p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.008548em;vertical-align:-0.19444em"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">3</span></span></span></span></span></span></span></span></span><span class="mspace nobreak"> </span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, por exemplo).</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="centro-de-inércia"></a>Centro de inércia<a aria-hidden="true" tabindex="-1" class="hash-link" href="#centro-de-inércia" title="Direct link to heading">#</a></h4><p>Normalmente utiliza-se a velocidade de referência como sendo a síncrona e portanto, nesse caso, <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ω</mi><mi>r</mi></msub><mo>=</mo><msub><mi>ω</mi><mi>b</mi></msub><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>0</mn><mtext> </mtext><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">\omega_r = \omega_b = 1,0~p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord">0</span><span class="mspace nobreak"> </span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> Essa abordagem, adotada por vários livros de estabilidade, considera como referência uma máquina fictícia girando sempre na velocidade síncrona independente das perturbações aplicadas no sistema. No PSP-UFU foi implementado o conceito de centro de inércia (COI, do inglês, <em>Center of Inertia</em>), que constitui uma soma ponderada das velocidades das máquinas presentes no sistema:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ω</mi><mi>r</mi></msub><mo>=</mo><mfrac><mrow><mo fence="true">(</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>H</mi><mi>i</mi></msub><msub><mi>ω</mi><mi>i</mi></msub><mo fence="true">)</mo></mrow><mrow><mo fence="true">(</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>H</mi><mi>i</mi></msub><mo fence="true">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">\omega_r=\frac{\left( \sum_{i=1}^{n} H_i \omega_i \right)}{\left( \sum_{i=1}^{n} H_i \right)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.488004em;vertical-align:-0.994002em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.494002em"><span style="top:-2.305708em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.804292em"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6897100000000003em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.804292em"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.994002em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>Em que:
 <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">n</span></span></span></span></span>	é o número de máquinas síncronas <strong>conectadas</strong> no sistema.</p><p>A aplicação do COI resulta em dados de saída, como o ângulo do rotor, mais fáceis de serem analisados. Na implementação realizada no programa a utilização ou não desse recurso é opcional e pode ser <a href="/PSP/docs/simulationConfig">definida pelo usuário</a>.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-dos-geradores-síncronos"></a>Formulário de edição dos geradores síncronos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-geradores-síncronos" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos geradores síncronos:</p><div><center><img src="/PSP/images/syncGeneratorForm.png" alt="Formulário dos geradores síncronos no PSP-UFU" title="Formulário dos geradores síncronos no PSP-UFU"></center></div><p>Um segundo pelos dados de estabilidade, como mostra a figura abaixo, acessado ao clicar no botão &quot;Estabilidade&quot; do formulário principal. Nele é possível também acessar aos controles das máquinas síncronas manipulados pelo <a href="/PSP/docs/controlEditor">editor de controle</a>.</p><div><center><img src="/PSP/images/syncGeneratorStabForm.png" alt="Formulário de estabilidade dos geradores síncronos no PSP-UFU" title="Formulário de estabilidade dos geradores síncronos no PSP-UFU"></center></div><p>No formulário de estabilidade pode ser observado o botão &quot;Chaveamento&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do gerador durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/syncGeneratorSw.png" alt="Formulário de chaveamento do gerador síncrono" title="Formulário de chaveamento do gerador síncrono"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_1w39 tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Falta</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Botão Estabilidade</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Botão Chaveamento</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal do gerador, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potências-ativa-e-reativa"></a>Potências ativa e reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potências-ativa-e-reativa" title="Direct link to heading">#</a></h4><p>Potências ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do gerador.</p><p>Caso a barra conectada seja PV o valor de potência reativa será ignorado e caso seja de referência ambos os valores inseridos serão desprezados.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Caso mais de um gerador esteja conectado na mesma barra, os valores de potência reativa (nas barras de referência e PV) e ativa (nas barras de referência) são igualmente distribuídas, respeitando os limites individuais de potência reativa.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potências-reativas-máxima-e-mínima"></a>Potências reativas máxima e mínima<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potências-reativas-máxima-e-mínima" title="Direct link to heading">#</a></h4><p>Limites de potência reativa máxima e mínima do gerador para controle de tensão em barras PV. Caso esses valores sejam ultrapassados, o reativo gerado pela unidade será limitado ao valor inserido e a barra conectada será transformada em PQ, não controlando a tensão estabelecida.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="utilizar-potência-nominal-como-base"></a>Utilizar potência nominal como base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-potência-nominal-como-base" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar a potência nominal do gerador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a <a href="/PSP/docs/simulationConfig">potência base do sistema</a>.</p></div></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="acesso-aos-controles-da-máquina-síncrona"></a>Acesso aos controles da máquina síncrona<a aria-hidden="true" tabindex="-1" class="hash-link" href="#acesso-aos-controles-da-máquina-síncrona" title="Direct link to heading">#</a></h2><p>Como já <a href="/PSP/docs/syncGenerator#utilizar-avr-e-regulador-de-velocidade">mencionado anteriormente</a>, os reguladores de velocidade e tensão da máquina síncrona podem ser acionados ou inibidos por meio das caixas de seleção &quot;<a href="/PSP/docs/syncGenerator#utilizar-avr-e-regulador-de-velocidade">Utilizar AVR e regulador de velocidade</a>&quot;. Ambas as opções irão acessar o <a href="/PSP/docs/controlEditor">editor de controles</a>.</p><p>O acesso aos controles do <strong>AVR</strong> poderão então ser criados e manipulados ao clicar no botão &quot;Editar AVR&quot;, assim como o <strong>Regulador de Velocidade</strong> é acessado no botão &quot;Editar regulador de velocidade&quot;.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>No PSP-UFU a opção de editar o <strong>AVR</strong> engloba mais que somente o controle de tensão da máquina. Nele <strong>deve</strong> ser inserida a malha de controle da máquina assim como a <strong>excitatriz da máquina síncrona</strong>. Outras estratégias de controle (opcionais), como PSS (<em>Power System Stabilizer</em>) e/ou controles de sobre e sub excitação, são também implementadas em conjunto.</p></div></div><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Assim como no AVR, o <strong>Regulador de Velocidade</strong> engloba mais que a regulação primária da máquina. Nessa opção <strong>deve</strong> ser inserida ao menos a malha de controle da regulação primária de velocidade, assim como o <strong>modelo da turbina</strong>. Estratégias opcionais de controle da velocidade também são inseridas nessa opção.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="referências"></a>Referências<a aria-hidden="true" tabindex="-1" class="hash-link" href="#referências" title="Direct link to heading">#</a></h2><ol><li>MILANO, F. Power System Modelling and Scripting. London: Springer, 2010. doi: <a href="https://doi.org/10.1007/978-3-642-13669-6" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/978-3-642-13669-6</a></li><li>ARRILLAGA, J.; WATSON, N. R. Computer Modelling of Electrical Power Systems. Wiley &amp; Sons, New York, 2001. doi: <a href="https://doi.org/10.1002/9781118878286" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/9781118878286</a></li><li>KUNDUR, P. Power System Stability and Control. McGraw-Hill, New York, 1994.</li><li>DOMMEL, H. W.; SATO, N. Fast Transient Stability Solutions. IEEE Transactions on Power Aparatus and Systems, v. PAS-91, n. 4, jul 1972, p. 1643-1650. doi: <a href="https://doi.org/10.1109/TPAS.1972.293341" target="_blank" rel="noopener noreferrer">https://doi.org/10.1109/TPAS.1972.293341</a></li><li>IEEE Std 1110-2002 IEEE Guide for Synchronous Generator Modeling Practices and Applications in Power System Stability Analyses. IEEE, New York, nov. 2003. doi: <a href="https://doi.org/10.1109/IEEESTD.2003.94408" target="_blank" rel="noopener noreferrer">https://doi.org/10.1109/IEEESTD.2003.94408</a></li><li>KIMBARK, E. W. Power System Stability: Volume III – Synchronous Machine. New York: Wiley-IEEE Press, 1995.</li></ol></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/syncGenerator.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/harmSource"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Fonte de Corrente Harmônica</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/syncMotor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Compensador Síncrono »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#gerador-síncrono-no-psp-ufu" class="table-of-contents__link">Gerador Síncrono no PSP-UFU</a><ul><li><a href="#gerador-síncrono-no-fluxo-de-carga" class="table-of-contents__link">Gerador Síncrono no fluxo de carga</a></li><li><a href="#gerador-síncrono-no-estudo-de-curto-circuito" class="table-of-contents__link">Gerador Síncrono no estudo de curto-circuito</a></li><li><a href="#gerador-síncrono-no-estudo-de-estabilidade" class="table-of-contents__link">Gerador Síncrono no estudo de estabilidade</a></li></ul></li><li><a href="#formulário-de-edição-dos-geradores-síncronos" class="table-of-contents__link">Formulário de edição dos geradores síncronos</a></li><li><a href="#acesso-aos-controles-da-máquina-síncrona" class="table-of-contents__link">Acesso aos controles da máquina síncrona</a></li><li><a href="#referências" class="table-of-contents__link">Referências</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Compensador Síncrono</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Uma máquina síncrona operando sem carga mecânica e fornecendo ou absorvendo energia reativa. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=411-34-03" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="compensador-síncrono-no-psp-ufu"></a>Compensador Síncrono no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#compensador-síncrono-no-psp-ufu" title="Direct link to heading">#</a></h2><p>O compensador síncrono nada mais é que um motor síncrono operando sem carga em seu eixo com o intuito de fornecer ou absorver potência reativa na rede. Em relação ao <a href="/PSP/docs/powerFlow">fluxo de carga</a>, no PSP-UFU esse elemento tem comportamento idêntico ao <a href="/PSP/docs/syncGenerator">gerador síncrono</a>, porém a sua potência ativa é inserida nos algoritmos de solução com sinal negativo.</p><p>Sua parametrização para o estudo de <a href="/PSP/docs/powerFlow">fluxo de carga</a>, <a href="/PSP/docs/fault">falta</a> e <a href="/PSP/docs/harmonics">harmônicos</a> é idêntica ao <a href="/PSP/docs/syncGenerator">gerador síncrono</a>.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>O compensador síncrono <strong>não foi implementado no estudo de <a href="/PSP/docs/stability">estabilidade</a></strong> e sua presença no circuito pode causar erros durante os cálculos.</p><p>Não inclua esse elemento para os estudos de <a href="/PSP/docs/stability">estabilidade</a>. Versões futuras do PSP-UFU irão contemplar esse elemento para esse estudo.</p></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>É possível utilizar um <a href="/PSP/docs/syncGenerator">gerador síncrono</a> com potência ativa <em>nula</em> ou <em>negativa</em> para representar o compensador síncrono nos estudos de <a href="/PSP/docs/stability">estabilidade</a>.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-dos-compensadores-síncronos"></a>Formulário de edição dos compensadores síncronos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-compensadores-síncronos" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos compensadores síncronos:</p><div><center><img src="/PSP/images/syncMotorForm.png" alt="Formulário dos compensadores síncronos no PSP-UFU" title="Formulário dos compensadores síncronos no PSP-UFU"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_1w39 tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Falta</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal do compensador, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potências-ativa-e-reativa"></a>Potências ativa e reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potências-ativa-e-reativa" title="Direct link to heading">#</a></h4><p>Potências ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do compensador.</p><p>Caso a barra conectada seja PV o valor de potência reativa será ignorado e caso seja de referência ambos os valores inseridos serão desprezados.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Caso mais de um compensador esteja conectado na mesma barra, os valores de potência reativa (nas barras de referência e PV) e ativa (nas barras de referência) são igualmente distribuídas, respeitando os limites individuais de potência reativa.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potências-reativas-máxima-e-mínima"></a>Potências reativas máxima e mínima<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potências-reativas-máxima-e-mínima" title="Direct link to heading">#</a></h4><p>Limites de potência reativa máxima e mínima do compensador para controle de tensão em barras PV. Caso esses valores sejam ultrapassados, o reativo gerado pela unidade será limitado ao valor inserido e a barra conectada será transformada em PQ, não controlando a tensão estabelecida.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="utilizar-potência-nominal-como-base"></a>Utilizar potência nominal como base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-potência-nominal-como-base" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar a potência nominal do compensador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a <a href="/PSP/docs/simulationConfig">potência base do sistema</a>.</p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/syncMotor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/syncGenerator"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Gerador Síncrono</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/indMotor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Motor de Indução »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#compensador-síncrono-no-psp-ufu" class="table-of-contents__link">Compensador Síncrono no PSP-UFU</a></li><li><a href="#formulário-de-edição-dos-compensadores-síncronos" class="table-of-contents__link">Formulário de edição dos compensadores síncronos</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Compensador Síncrono</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Uma máquina síncrona operando sem carga mecânica e fornecendo ou absorvendo energia reativa. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=411-34-03" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="compensador-síncrono-no-psp-ufu"></a>Compensador Síncrono no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#compensador-síncrono-no-psp-ufu" title="Direct link to heading">#</a></h2><p>O compensador síncrono nada mais é que um motor síncrono operando sem carga em seu eixo com o intuito de fornecer ou absorver potência reativa na rede. Em relação ao <a href="/PSP/docs/powerFlow">fluxo de carga</a>, no PSP-UFU esse elemento tem comportamento idêntico ao <a href="/PSP/docs/syncGenerator">gerador síncrono</a>, porém a sua potência ativa é inserida nos algoritmos de solução com sinal negativo.</p><p>Sua parametrização para o estudo de <a href="/PSP/docs/powerFlow">fluxo de carga</a>, <a href="/PSP/docs/fault">falta</a> e <a href="/PSP/docs/harmonics">harmônicos</a> é idêntica ao <a href="/PSP/docs/syncGenerator">gerador síncrono</a>.</p><div class="admonition admonition-warning alert alert--danger"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M5.05.31c.81 2.17.41 3.38-.52 4.31C3.55 5.67 1.98 6.45.9 7.98c-1.45 2.05-1.7 6.53 3.53 7.7-2.2-1.16-2.67-4.52-.3-6.61-.61 2.03.53 3.33 1.94 2.86 1.39-.47 2.3.53 2.27 1.67-.02.78-.31 1.44-1.13 1.81 3.42-.59 4.78-3.42 4.78-5.56 0-2.84-2.53-3.22-1.25-5.61-1.52.13-2.03 1.13-1.89 2.75.09 1.08-1.02 1.8-1.86 1.33-.67-.41-.66-1.19-.06-1.78C8.18 5.31 8.68 2.45 5.05.32L5.03.3l.02.01z"></path></svg></span>Cuidado!</h5></div><div class="admonition-content"><p>O compensador síncrono <strong>não foi implementado no estudo de <a href="/PSP/docs/stability">estabilidade</a></strong> e sua presença no circuito pode causar erros durante os cálculos.</p><p>Não inclua esse elemento para os estudos de <a href="/PSP/docs/stability">estabilidade</a>. Versões futuras do PSP-UFU irão contemplar esse elemento para esse estudo.</p></div></div><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>É possível utilizar um <a href="/PSP/docs/syncGenerator">gerador síncrono</a> com potência ativa <em>nula</em> ou <em>negativa</em> para representar o compensador síncrono nos estudos de <a href="/PSP/docs/stability">estabilidade</a>.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-dos-compensadores-síncronos"></a>Formulário de edição dos compensadores síncronos<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-compensadores-síncronos" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos compensadores síncronos:</p><div><center><img src="/PSP/images/syncMotorForm.png" alt="Formulário dos compensadores síncronos no PSP-UFU" title="Formulário dos compensadores síncronos no PSP-UFU"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_1w39 tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Falta</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal do compensador, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potências-ativa-e-reativa"></a>Potências ativa e reativa<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potências-ativa-e-reativa" title="Direct link to heading">#</a></h4><p>Potências ativa (inserida em W, kW, MW ou p.u.) e reativa (inserida em var, kvar, Mvar ou p.u.) do compensador.</p><p>Caso a barra conectada seja PV o valor de potência reativa será ignorado e caso seja de referência ambos os valores inseridos serão desprezados.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Caso mais de um compensador esteja conectado na mesma barra, os valores de potência reativa (nas barras de referência e PV) e ativa (nas barras de referência) são igualmente distribuídas, respeitando os limites individuais de potência reativa.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potências-reativas-máxima-e-mínima"></a>Potências reativas máxima e mínima<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potências-reativas-máxima-e-mínima" title="Direct link to heading">#</a></h4><p>Limites de potência reativa máxima e mínima do compensador para controle de tensão em barras PV. Caso esses valores sejam ultrapassados, o reativo gerado pela unidade será limitado ao valor inserido e a barra conectada será transformada em PQ, não controlando a tensão estabelecida.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="utilizar-potência-nominal-como-base"></a>Utilizar potência nominal como base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-potência-nominal-como-base" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar a potência nominal do compensador como base para a conversão das unidades, inclusive aqueles no formulário de estabilidade, caso contrário será usada a <a href="/PSP/docs/simulationConfig">potência base do sistema</a>.</p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/syncMotor.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/syncGenerator"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Gerador Síncrono</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/indMotor"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Motor de Indução »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#compensador-síncrono-no-psp-ufu" class="table-of-contents__link">Compensador Síncrono no PSP-UFU</a></li><li><a href="#formulário-de-edição-dos-compensadores-síncronos" class="table-of-contents__link">Formulário de edição dos compensadores síncronos</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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Principal</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/cadTools">Ferramentas CAD</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Editor de Elementos de Potência</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/powerEditor">Editor de Potência</a></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!" tabindex="-1">Elementos de Potência</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/bus">Barramento</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/line">Linha</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/transformer">Transformador</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/load">Carga</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/capacitor">Capacitor</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/inductor">Indutor</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/harmSource">Fonte de Corrente Harmônica</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/syncGenerator">Gerador Síncrono</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/syncMotor">Compensador Síncrono</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/indMotor">Motor de Indução</a></li></ul></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu__link--sublist" href="#!">Editor de Elementos de Controle</a><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="-1" 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docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Relatórios Tabulares</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>Para visualização de todos os resultados dos cálculos de <a href="/PSP/docs/powerFlow">fluxo de carga</a> e <a href="/PSP/docs/fault">curto-circuito</a>, desenvolveu-se um visualizador de relatórios tabulares:</p><div><center><img src="/PSP/images/tabReport.png" alt="Visualizador de dados tabulados no PSP-UFU" title="Visualizador de dados tabulados no PSP-UFU"></center></div><p>Tal visualizador pode ser acessado no <a href="/PSP/docs/mainScreen#menu-ribbon">submenu Ribbon</a> <strong>Ferramentas</strong> e então no botão <strong>Relatório de dados</strong>, sendo exibido o formulário organizado em abas.</p><p>As grandezas de alguns dados desse relatório podem ser modificadas, sendo selecionadas no cabeçalho da tabela, como mostra a figura acima.</p><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Os valores podem ser exportados para editores de texto e tabelas externos, selecionando e copiando (Ctrl+C) para a área de transferência.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/tabularReport.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/text"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Texto Vinculado</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/graphViewer"><div 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docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Texto Vinculado</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>O elemento de texto vinculado (ao elemento de potência) pode ser inserido no editor de <a href="/PSP/docs/powerEditor">elementos de potência</a>. Esse elemento de texto pode ser vinculado a inúmeros resultados e parâmetros do sistema de potência.</p><p>Esse elemento é útil para identificação e análise dos resultados de elementos de potência.</p><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Outra aplicação importante é a atualização de seu valor ao aplicar a “solução contínua” no projeto, auxiliando na visualização das mudanças de estado da rede elétrica.</p><p>Também pode-se utilizar os resultados apresentados por esses elementos juntamente com o diagrama unifilar na criação de relatórios do projeto.</p></div></div><div><center><img src="/PSP/images/textExp.png" alt="Exemplo de elemento de texto no PSP-UFU" title="Exemplo de elemento de texto no PSP-UFU"></center></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-de-dados-do-elemento-de-texto"></a>Formulário de edição de dados do elemento de texto<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-de-dados-do-elemento-de-texto" title="Direct link to heading">#</a></h2><p>A figura abaixo apresenta o formulário de edição de dados desse componente gráfico.</p><div><center><img src="/PSP/images/textForm.png" alt="Formulário do elemento de texto no PSP-UFU" title="Formulário do elemento de texto no PSP-UFU"></center></div><p>Sua parametrização é realizada por campos que associam o componente aos elementos elétricos de potência, além do formato dos resultados numéricos. Os campos são liberados a medida que os dados anteriores são inseridos e uma mensagem de erro é apresentada ao usuário caso algum parâmetro necessário não seja preenchido.</p><p>O processo de associação se inicia na escolha do tipo de elemento de potência será vinculado ao texto. Em seguida é exibida uma lista com o nome de todos os componentes previamente inseridos no editor de elementos de potência do tipo definido no campo anterior, associando, assim, o texto ao elemento.</p><p>Em “Tipo de texto” define-se qual será a saída apresentada. Tal campo depende do tipo de elemento selecionado, como mostra a tabela abaixo. Alguns outros dados são necessários para os elementos de ramo, como barra de origem e destino, com o intuito de representar o fluxo correto de potência e corrente. Finalmente o usuário deve inserir a quantidade de casas decimais para dados numéricos. A pré-visualização pode ser observada no formulário.</p><table><thead><tr><th align="center">Elemento de potência</th><th>Tipo de texto</th><th>Unidades disponíveis</th></tr></thead><tbody><tr><td align="center"><a href="/PSP/docs/bus">Barra</a></td><td>Nome<br>Tensão<br>Ângulo<br>Corrente de falta<br>Tensão de falta<br>Nível de curto-circuito<br>THD de tensão</td><td>-<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, V, kV<br>Graus, Radianos<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, A, kA<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, V, kV<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, VA, kVA, MVA<br>%</td></tr><tr><td align="center"><a href="/PSP/docs/syncGenerator">Gerador</a></td><td>Nome<br>Potência ativa<br>Potência reativa<br>Corrente de falta</td><td>-<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, W, kW, MW<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, var, kvar, Mvar<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, A, kA</td></tr><tr><td align="center"><a href="/PSP/docs/line">Linha</a> e <a href="/PSP/docs/transformer">transformador</a></td><td>Nome<br>Fluxo de potência ativo<br>Fluxo de potência reativo<br>Perdas<br>Corrente<br>Corrente de falta</td><td>-<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, W, kW, MW<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, var, kvar, Mvar<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, W, kW, MW<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, A, kA<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, A, kA</td></tr><tr><td align="center"><a href="/PSP/docs/load">Carga</a>, <a href="/PSP/docs/indMotor">Motor de indução</a><br>e <a href="/PSP/docs/syncMotor">Compensador síncrono</a></td><td>Nome<br>Potência ativa<br>Potência reativa</td><td>-<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, W, kW, MW<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, var, kvar, Mvar</td></tr><tr><td align="center"><a href="/PSP/docs/capacitor">Capacitor</a> e <a href="/PSP/docs/inductor">Indutor</a></td><td>Nome<br>Potência reativa</td><td>-<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, var, kvar, Mvar</td></tr></tbody></table><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Uma vez inseridos, esses elementos de texto podem ser manipulados da <a href="/PSP/docs/cadTools">mesma forma que os elementos de potência</a>.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/text.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 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class="menu__link" tabindex="-1" href="/PSP/docs/stability">Estabilidade</a></li><li class="menu__list-item"><a class="menu__link" tabindex="-1" href="/PSP/docs/simulationConfig">Configurações da Simulação</a></li></ul></li><li class="menu__list-item"><a class="menu__link menu__link--sublist menu__link--active" href="#!">Visualização dos Dados</a><ul class="menu__list"><li class="menu__list-item"><a aria-current="page" class="menu__link menu__link--active active" tabindex="0" href="/PSP/docs/text">Texto Vinculado</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/tabularReport">Relatórios Tabulares</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/graphViewer">Visualizador de Gráficos</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/PSP/docs/heatmap">Mapa de Tensão</a></li></ul></li></ul></div></div></div><main class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Texto Vinculado</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>O elemento de texto vinculado (ao elemento de potência) pode ser inserido no editor de <a href="/PSP/docs/powerEditor">elementos de potência</a>. Esse elemento de texto pode ser vinculado a inúmeros resultados e parâmetros do sistema de potência.</p><p>Esse elemento é útil para identificação e análise dos resultados de elementos de potência.</p><div class="admonition admonition-tip alert alert--success"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="12" height="16" viewBox="0 0 12 16"><path fill-rule="evenodd" d="M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z"></path></svg></span>Dica</h5></div><div class="admonition-content"><p>Outra aplicação importante é a atualização de seu valor ao aplicar a “solução contínua” no projeto, auxiliando na visualização das mudanças de estado da rede elétrica.</p><p>Também pode-se utilizar os resultados apresentados por esses elementos juntamente com o diagrama unifilar na criação de relatórios do projeto.</p></div></div><div><center><img src="/PSP/images/textExp.png" alt="Exemplo do elemento de texto no PSP-UFU" title="Exemplo de elemento de texto no PSP-UFU"></center></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="inserindo-elementos-de-texto-no-psp-ufu"></a>Inserindo elementos de texto no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#inserindo-elementos-de-texto-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Por meio do submenu <strong>Ferramentas</strong> pode-se inserir os elementos de texto, como é apresentado na imagem abaixo.</p><div><center><img src="/PSP/images/addTextElement.svg" alt="Adicionar elementos de texto" title="Adicionar elementos de texto"></center></div><p>Ao selecionar o botão &quot;Texto&quot; ou utilizar a <strong>tecla de atalho &quot;A&quot;</strong>, o usuário deve clicar na posição desejada da <a href="/PSP/docs/powerEditor">área de trabalho</a>. Com isso, será adicionado um elemento temporário com o valor &quot;Texto&quot;. Para parametrizar esse elemento clique duas vezes sobre ele.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>O elemento de texto, assim como os <a href="/PSP/docs/controlEditor">elementos de controle</a> não exibem automaticamente o formulário de edição de dados ao inseri-lo pela primeira vez.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-de-dados-do-elemento-de-texto"></a>Formulário de edição de dados do elemento de texto<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-de-dados-do-elemento-de-texto" title="Direct link to heading">#</a></h2><p>A figura abaixo apresenta o formulário de edição de dados desse componente gráfico.</p><div><center><img src="/PSP/images/textForm.png" alt="Formulário do elemento de texto no PSP-UFU" title="Formulário do elemento de texto no PSP-UFU"></center></div><p>Sua parametrização é realizada por campos que associam o componente aos elementos elétricos de potência, além do formato dos resultados numéricos. Os campos são liberados a medida que os dados anteriores são inseridos e uma mensagem de erro é apresentada ao usuário caso algum parâmetro necessário não seja preenchido.</p><p>O processo de associação se inicia na escolha do tipo de elemento de potência será vinculado ao texto. Em seguida é exibida uma lista com o nome de todos os componentes previamente inseridos no editor de elementos de potência do tipo definido no campo anterior, associando, assim, o texto ao elemento.</p><p>Em “Tipo de texto” define-se qual será a saída apresentada. Tal campo depende do tipo de elemento selecionado, como mostra a tabela abaixo. Alguns outros dados são necessários para os elementos de ramo, como barra de origem e destino, com o intuito de representar o fluxo correto de potência e corrente. Finalmente o usuário deve inserir a quantidade de casas decimais para dados numéricos. A pré-visualização pode ser observada no formulário.</p><table><thead><tr><th align="center">Elemento de potência</th><th>Tipo de texto</th><th>Unidades disponíveis</th></tr></thead><tbody><tr><td align="center"><a href="/PSP/docs/bus">Barra</a></td><td>Nome<br>Tensão<br>Ângulo<br>Corrente de falta<br>Tensão de falta<br>Nível de curto-circuito<br>THD de tensão</td><td>-<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, V, kV<br>Graus, Radianos<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, A, kA<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, V, kV<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, VA, kVA, MVA<br>%</td></tr><tr><td align="center"><a href="/PSP/docs/syncGenerator">Gerador</a></td><td>Nome<br>Potência ativa<br>Potência reativa<br>Corrente de falta</td><td>-<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, W, kW, MW<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, var, kvar, Mvar<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, A, kA</td></tr><tr><td align="center"><a href="/PSP/docs/line">Linha</a> e <a href="/PSP/docs/transformer">transformador</a></td><td>Nome<br>Fluxo de potência ativo<br>Fluxo de potência reativo<br>Perdas<br>Corrente<br>Corrente de falta</td><td>-<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, W, kW, MW<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, var, kvar, Mvar<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, W, kW, MW<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, A, kA<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, A, kA</td></tr><tr><td align="center"><a href="/PSP/docs/load">Carga</a>, <a href="/PSP/docs/indMotor">Motor de indução</a><br>e <a href="/PSP/docs/syncMotor">Compensador síncrono</a></td><td>Nome<br>Potência ativa<br>Potência reativa</td><td>-<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, W, kW, MW<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, var, kvar, Mvar</td></tr><tr><td align="center"><a href="/PSP/docs/capacitor">Capacitor</a> e <a href="/PSP/docs/inductor">Indutor</a></td><td>Nome<br>Potência reativa</td><td>-<br><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span>, var, kvar, Mvar</td></tr></tbody></table><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Uma vez inseridos, esses elementos de texto podem ser manipulados da <a href="/PSP/docs/cadTools">mesma forma que os elementos de potência</a>.</p></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/text.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 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class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Função Transferência</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>A Função Transferência é um importante bloco elementar e essencial em um sistema de controle, visto que esse componente possibilita a representação de sistemas dinâmicos por meio de equações algébricas no domínio da frequência.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Nesses blocos é utilizado a letra “<strong>s</strong>” para representação no domínio da frequência, pois essa é a terminologia mais utilizada em sistemas de controle.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="função-transferência-no-psp-ufu"></a>Função Transferência no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#função-transferência-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Após a inserção da função transferência, o programa a transforma na representação em espaço de estado, visto que sua solução é sistemática tornando-a, assim, mais eficiente computacionalmente.</p><p>Dada uma função transferência genérica abaixo:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>Y</mi><mo stretchy="false">(</mo><mi mathvariant="bold">s</mi><mo stretchy="false">)</mo></mrow><mrow><mi>U</mi><mo stretchy="false">(</mo><mi mathvariant="bold">s</mi><mo stretchy="false">)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>b</mi><mn>0</mn></msub><msup><mi mathvariant="bold">s</mi><mi>k</mi></msup><mo>+</mo><msub><mi>b</mi><mn>1</mn></msub><msup><mi mathvariant="bold">s</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mi>b</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub><mi mathvariant="bold">s</mi><mo>+</mo><msub><mi>b</mi><mi>k</mi></msub></mrow><mrow><msup><mi mathvariant="bold">s</mi><mi>k</mi></msup><mo>+</mo><msub><mi>a</mi><mn>1</mn></msub><msup><mi mathvariant="bold">s</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mi>a</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub><mi mathvariant="bold">s</mi><mo>+</mo><msub><mi>a</mi><mi>k</mi></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{Y(\bold{s})}{U(\bold{s})} = \frac{b_0 \bold{s}^k + b_1 \bold{s}^{k-1} + \cdots + b_{k-1} \bold{s} + b_k}{\bold{s}^k + a_1 \bold{s}^{k-1} + \cdots + a_{k-1} \bold{s} + a_k}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10903em">U</span><span class="mopen">(</span><span class="mord"><span class="mord mathbf">s</span></span><span class="mclose">)</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mopen">(</span><span class="mord"><span class="mord mathbf">s</span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.420439em;vertical-align:-0.894331em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.526108em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7751079999999999em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7751079999999999em"><span style="top:-2.989em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathbf">s</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathbf">s</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.894331em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>A transformação em espaço de estado na <em>forma canônica controlável</em> ficará da seguinte forma:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="bold">s</mi><msub><mi>x</mi><mn>1</mn></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="bold">s</mi><msub><mi>x</mi><mn>2</mn></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="bold">s</mi><msub><mi>x</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="bold">s</mi><msub><mi>x</mi><mi>k</mi></msub></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋱</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><msub><mi>a</mi><mi>k</mi></msub></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><msub><mi>a</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><msub><mi>a</mi><mrow><mi>k</mi><mo>−</mo><mn>2</mn></mrow></msub></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><msub><mi>a</mi><mn>1</mn></msub></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mn>1</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mn>2</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mi>k</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>+</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><msub><mi>u</mi><mi>n</mi></msub><mspace linebreak="newline"></mspace><msub><mi>y</mi><mi>n</mi></msub><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo fence="true">(</mo><msub><mi>b</mi><mi>n</mi></msub><mo>−</mo><msub><mi>a</mi><mi>n</mi></msub><msub><mi>b</mi><mn>0</mn></msub><mo fence="true">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo fence="true">(</mo><msub><mi>b</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>−</mo><msub><mi>a</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><msub><mi>b</mi><mn>0</mn></msub><mo fence="true">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo fence="true">(</mo><msub><mi>b</mi><mn>1</mn></msub><mo>−</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>b</mi><mn>0</mn></msub><mo fence="true">)</mo></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mn>1</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mn>2</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mi>k</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>+</mo><msub><mi>b</mi><mn>0</mn></msub><msub><mi>u</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\begin{bmatrix} \bold{s}x_1\\ \bold{s}x_2\\ \vdots\\ \bold{s}x_{k-1}\\ \bold{s}x_k \end{bmatrix} = \begin{bmatrix} 0 &amp; 1 &amp; 0 &amp; \cdots &amp; 0\\ 0 &amp; 0 &amp; 1 &amp; \cdots &amp; 0\\ \vdots &amp; \vdots &amp; \vdots &amp; \ddots &amp; \vdots\\ 0 &amp; 0 &amp; 0 &amp; \cdots &amp; 1\\ -a_k &amp; -a_{k-1} &amp; -a_{k-2} &amp; \cdots &amp; -a_1 \end{bmatrix} \begin{bmatrix} x_1\\ x_2\\ \vdots\\ x_{k-1}\\ x_k \end{bmatrix} + \begin{bmatrix} 0\\ 0\\ \vdots\\ 0\\ 1 \end{bmatrix} u_n\\ y_n = \begin{bmatrix} \left( b_n - a_n b_0 \right) &amp; \left( b_{n-1} - a_{n-1} b_0 \right) &amp; \cdots &amp; \left( b_1 - a_1 b_0 \right) \end{bmatrix} \begin{bmatrix} x_1\\ x_2\\ \vdots\\ x_k \end{bmatrix} + b_0 u_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:6.66em;vertical-align:-3.079999999999999em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:6.66em;vertical-align:-3.079999999999999em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.240000000000001em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋯</span></span></span><span style="top:-5.04em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋯</span></span></span><span style="top:-3.18em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋱</span></span></span><span style="top:-1.9800000000000009em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋯</span></span></span><span style="top:-0.7800000000000009em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋯</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:6.66em;vertical-align:-3.079999999999999em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:5.459999999999999em;vertical-align:-2.4799999999999995em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner">⋯</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.953995em"><span style="top:-1.3499850000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-2.4999850000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0959850000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6919850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.712975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.953995em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.4500349999999997em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.9799999999999995em"><span style="top:-5.8275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-4.6275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.7674999999999996em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-1.5675000000000006em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.4799999999999995em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.953995em"><span style="top:-1.3499850000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-2.4999850000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0959850000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6919850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.712975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.953995em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.4500349999999997em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>A equação diferencial matricial é resolvida pelo método <strong>Trapezoidal Implícito</strong>. Um processo iterativo é realizado até que o erro entre os cálculos se torne menor que uma tolerância pré-estipulada e caso as iterações se tornem excessivas, ultrapassando um número máximo definido pelo usuário, o processo é interrompido com erro. Com os valores do vetor de estado (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">x</span></span></span></span></span>) calculados obtém-se o valor da saída do bloco (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">y_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>).</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-de-dados-da-função-transferência"></a>Formulário de edição de dados da Função Transferência<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-de-dados-da-função-transferência" title="Direct link to heading">#</a></h2><p>A figura abaixo apresenta o formulário de edição de dados da função transferência.</p><div><center><img src="/PSP/images/transferFunctionForm.png" alt="Formulário de edição de dados da função transferência no PSP-UFU" title="Formulário de edição de dados da função transferência no PSP-UFU"></center></div><p>A função transferência é definida pelos coeficientes do numerador e denominador, <strong>separados por espaço</strong>.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Os elementos não presentes são representados como coeficientes de valor zero.</p><p>Por exemplo, um parâmetro inserido igual a “<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mn>0</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>5</mn></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>2</mn></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{matrix} 1 &amp; 0{,}5 &amp; 0 &amp; 2 \end{matrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2000000000000002em;vertical-align:-0.35000000000000003em"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span></span></span></span></span></span></span>” irá gerar: “<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>s</mi><mn>3</mn></msup><mo>+</mo><mn>0</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>5</mn><msup><mi>s</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">s^3+0{,}5s^2+2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.897438em;vertical-align:-0.08333em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.008548em;vertical-align:-0.19444em"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">2</span></span></span></span></span>”.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="referências"></a>Referências<a aria-hidden="true" tabindex="-1" class="hash-link" href="#referências" title="Direct link to heading">#</a></h2><ol><li>OGATA, K. Modern Control Engineering. Prentice Hall Inc., New Jersey, 2004.</li></ol></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/transferFunction.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/io"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Entrada / Saída</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/sum"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Somador »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#função-transferência-no-psp-ufu" class="table-of-contents__link">Função Transferência no PSP-UFU</a></li><li><a href="#formulário-de-edição-de-dados-da-função-transferência" class="table-of-contents__link">Formulário de edição de dados da Função Transferência</a></li><li><a href="#referências" class="table-of-contents__link">Referências</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="docMainContainer_3EyW"><div class="container padding-vert--lg docItemWrapper_1EkI"><div class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Função Transferência</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><p>A Função Transferência é um importante bloco elementar e essencial em um sistema de controle, visto que esse componente possibilita a representação de sistemas dinâmicos por meio de equações algébricas no domínio da frequência.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>Nesses blocos é utilizado a letra “<strong>s</strong>” para representação no domínio da frequência, pois essa é a terminologia mais utilizada em sistemas de controle.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="função-transferência-no-psp-ufu"></a>Função Transferência no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#função-transferência-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Após a inserção da função transferência, o programa a transforma na representação em espaço de estado, visto que sua solução é sistemática tornando-a, assim, mais eficiente computacionalmente.</p><p>Dada uma função transferência genérica abaixo:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mrow><mi>Y</mi><mo stretchy="false">(</mo><mi mathvariant="bold">s</mi><mo stretchy="false">)</mo></mrow><mrow><mi>U</mi><mo stretchy="false">(</mo><mi mathvariant="bold">s</mi><mo stretchy="false">)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>b</mi><mn>0</mn></msub><msup><mi mathvariant="bold">s</mi><mi>k</mi></msup><mo>+</mo><msub><mi>b</mi><mn>1</mn></msub><msup><mi mathvariant="bold">s</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mi>b</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub><mi mathvariant="bold">s</mi><mo>+</mo><msub><mi>b</mi><mi>k</mi></msub></mrow><mrow><msup><mi mathvariant="bold">s</mi><mi>k</mi></msup><mo>+</mo><msub><mi>a</mi><mn>1</mn></msub><msup><mi mathvariant="bold">s</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mi>a</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub><mi mathvariant="bold">s</mi><mo>+</mo><msub><mi>a</mi><mi>k</mi></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{Y(\bold{s})}{U(\bold{s})} = \frac{b_0 \bold{s}^k + b_1 \bold{s}^{k-1} + \cdots + b_{k-1} \bold{s} + b_k}{\bold{s}^k + a_1 \bold{s}^{k-1} + \cdots + a_{k-1} \bold{s} + a_k}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10903em">U</span><span class="mopen">(</span><span class="mord"><span class="mord mathbf">s</span></span><span class="mclose">)</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mopen">(</span><span class="mord"><span class="mord mathbf">s</span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:2.420439em;vertical-align:-0.894331em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.526108em"><span style="top:-2.3139999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7751079999999999em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7751079999999999em"><span style="top:-2.989em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathbf">s</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathbf">s</span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.894331em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></div><p>A transformação em espaço de estado na <em>forma canônica controlável</em> ficará da seguinte forma:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="bold">s</mi><msub><mi>x</mi><mn>1</mn></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="bold">s</mi><msub><mi>x</mi><mn>2</mn></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="bold">s</mi><msub><mi>x</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="bold">s</mi><msub><mi>x</mi><mi>k</mi></msub></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋱</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><msub><mi>a</mi><mi>k</mi></msub></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><msub><mi>a</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><msub><mi>a</mi><mrow><mi>k</mi><mo>−</mo><mn>2</mn></mrow></msub></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><msub><mi>a</mi><mn>1</mn></msub></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mn>1</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mn>2</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mi>k</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>+</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><msub><mi>u</mi><mi>n</mi></msub><mspace linebreak="newline"></mspace><msub><mi>y</mi><mi>n</mi></msub><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo fence="true">(</mo><msub><mi>b</mi><mi>n</mi></msub><mo>−</mo><msub><mi>a</mi><mi>n</mi></msub><msub><mi>b</mi><mn>0</mn></msub><mo fence="true">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo fence="true">(</mo><msub><mi>b</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>−</mo><msub><mi>a</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><msub><mi>b</mi><mn>0</mn></msub><mo fence="true">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">⋯</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo fence="true">(</mo><msub><mi>b</mi><mn>1</mn></msub><mo>−</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>b</mi><mn>0</mn></msub><mo fence="true">)</mo></mrow></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mn>1</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mn>2</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi><mi mathvariant="normal">⋮</mi><mpadded height="+0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>x</mi><mi>k</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>+</mo><msub><mi>b</mi><mn>0</mn></msub><msub><mi>u</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\begin{bmatrix} \bold{s}x_1\\ \bold{s}x_2\\ \vdots\\ \bold{s}x_{k-1}\\ \bold{s}x_k \end{bmatrix} = \begin{bmatrix} 0 &amp; 1 &amp; 0 &amp; \cdots &amp; 0\\ 0 &amp; 0 &amp; 1 &amp; \cdots &amp; 0\\ \vdots &amp; \vdots &amp; \vdots &amp; \ddots &amp; \vdots\\ 0 &amp; 0 &amp; 0 &amp; \cdots &amp; 1\\ -a_k &amp; -a_{k-1} &amp; -a_{k-2} &amp; \cdots &amp; -a_1 \end{bmatrix} \begin{bmatrix} x_1\\ x_2\\ \vdots\\ x_{k-1}\\ x_k \end{bmatrix} + \begin{bmatrix} 0\\ 0\\ \vdots\\ 0\\ 1 \end{bmatrix} u_n\\ y_n = \begin{bmatrix} \left( b_n - a_n b_0 \right) &amp; \left( b_{n-1} - a_{n-1} b_0 \right) &amp; \cdots &amp; \left( b_1 - a_1 b_0 \right) \end{bmatrix} \begin{bmatrix} x_1\\ x_2\\ \vdots\\ x_k \end{bmatrix} + b_0 u_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:6.66em;vertical-align:-3.079999999999999em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:6.66em;vertical-align:-3.079999999999999em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.240000000000001em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋯</span></span></span><span style="top:-5.04em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋯</span></span></span><span style="top:-3.18em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋱</span></span></span><span style="top:-1.9800000000000009em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋯</span></span></span><span style="top:-0.7800000000000009em"><span class="pstrut" style="height:3.5em"></span><span class="mord"><span class="minner">⋯</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">1</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:6.66em;vertical-align:-3.079999999999999em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.5800000000000005em"><span style="top:-6.427500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-5.2275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-3.3675em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-2.167500000000001em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-0.9675000000000009em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.079999999999999em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.555985em"><span style="top:-0.7499750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-1.8999750000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-2.4959750000000005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0919750000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6879750000000002em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.283975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.314965000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-5.555985000000001em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:3.050045em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:5.459999999999999em;vertical-align:-2.4799999999999995em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size1">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner">⋯</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em">(</span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size1">]</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.953995em"><span style="top:-1.3499850000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-2.4999850000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.0959850000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.6919850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.712975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.953995em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.4500349999999997em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.9799999999999995em"><span style="top:-5.8275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-4.6275em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.7674999999999996em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em"></span></span></span></span><span style="top:-1.5675000000000006em"><span class="pstrut" style="height:3.6875em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.4799999999999995em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.953995em"><span style="top:-1.3499850000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-2.4999850000000006em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.0959850000000007em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.6919850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.712975em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.953995em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.4500349999999997em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">u</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></div><p>A equação diferencial matricial é resolvida pelo método <strong>Trapezoidal Implícito</strong>. Um processo iterativo é realizado até que o erro entre os cálculos se torne menor que uma tolerância pré-estipulada e caso as iterações se tornem excessivas, ultrapassando um número máximo definido pelo usuário, o processo é interrompido com erro. Com os valores do vetor de estado (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em"></span><span class="mord mathdefault">x</span></span></span></span></span>) calculados obtém-se o valor da saída do bloco (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>y</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">y_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>).</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-de-dados-da-função-transferência"></a>Formulário de edição de dados da Função Transferência<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-de-dados-da-função-transferência" title="Direct link to heading">#</a></h2><p>A figura abaixo apresenta o formulário de edição de dados da função transferência.</p><div><center><img src="/PSP/images/transferFunctionForm.png" alt="Formulário de edição de dados da função transferência no PSP-UFU" title="Formulário de edição de dados da função transferência no PSP-UFU"></center></div><p>A função transferência é definida pelos coeficientes do numerador e denominador, <strong>separados por espaço</strong>.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>Os elementos não presentes são representados como coeficientes de valor zero.</p><p>Por exemplo, um parâmetro inserido igual a “<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mn>0</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>5</mn></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>2</mn></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{matrix} 1 &amp; 0{,}5 &amp; 0 &amp; 2 \end{matrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2000000000000002em;vertical-align:-0.35000000000000003em"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8500000000000001em"><span style="top:-3.01em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35000000000000003em"><span></span></span></span></span></span></span></span></span></span></span></span>” irá gerar: “<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>s</mi><mn>3</mn></msup><mo>+</mo><mn>0</mn><mo separator="true" lspace="0em" rspace="0em">,</mo><mn>5</mn><msup><mi>s</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">s^3+0{,}5s^2+2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.897438em;vertical-align:-0.08333em"></span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.008548em;vertical-align:-0.19444em"></span><span class="mord">0</span><span class="mord"><span class="mpunct">,</span></span><span class="mord">5</span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">2</span></span></span></span></span>”.</p></div></div><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="referências"></a>Referências<a aria-hidden="true" tabindex="-1" class="hash-link" href="#referências" title="Direct link to heading">#</a></h2><ol><li>OGATA, K. Modern Control Engineering. Prentice Hall Inc., New Jersey, 2004.</li></ol></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/transferFunction.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog list page navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/PSP/docs/io"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« Entrada / Saída</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/PSP/docs/sum"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Somador »</div></a></div></nav></div></div></div><div class="col col--3"><div class="tableOfContents_3klQ"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#função-transferência-no-psp-ufu" class="table-of-contents__link">Função Transferência no PSP-UFU</a></li><li><a href="#formulário-de-edição-de-dados-da-função-transferência" class="table-of-contents__link">Formulário de edição de dados da Função Transferência</a></li><li><a href="#referências" class="table-of-contents__link">Referências</a></li></ul></div></div></div></div></main></div></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Transformador</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Aparelho estático com dois ou mais enrolamentos que, por indução eletromagnética, transforma um sistema de tensão e corrente alternada em outro sistema de tensão e corrente geralmente de valores diferentes e na mesma frequência com o objetivo de transmitir energia elétrica. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=421-01-01" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="transformador-no-psp-ufu"></a>Transformador no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#transformador-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Transformadores com quaisquer conexões e defasagens entre as tensões primárias e secundárias podem ser inseridos no PSP-UFU. Para isso, os transformadores devem ser modelados representando seu tape (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi></mrow><annotation encoding="application/x-tex">t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.61508em;vertical-align:0em"></span><span class="mord mathdefault">t</span></span></span></span></span>) e defasagem (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϕ</mi></mrow><annotation encoding="application/x-tex">\phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">ϕ</span></span></span></span></span>), utilizando um transformador ideal de relação de transformação <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover><mo>:</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\overline{t}:1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.81508em;vertical-align:0em"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span></span></span></span></span> em série com sua impedância (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><mo>=</mo><msub><mi>r</mi><mi>T</mi></msub><mo>+</mo><mi>j</mi><msub><mi>x</mi><mi>T</mi></msub></mrow><annotation encoding="application/x-tex">\overline{y}_T = r_T + jx_T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8747em;vertical-align:-0.24414em"></span><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>), em que <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">\overline{t}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.81508em;vertical-align:0em"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span></span></span> é um número complexo (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi><mi mathvariant="normal">∠</mi><mi>ϕ</mi></mrow><annotation encoding="application/x-tex">t\angle\phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">t</span><span class="mord">∠</span><span class="mord mathdefault">ϕ</span></span></span></span></span>)</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>O modelo utilizado no PSP-UFU <strong>não considera</strong> o ramo magnetizante ou impedâncias mútuas entre as fases.</p></div></div><p>A figura abaixo mostra o modelo do transformador implementado no PSP-UFU:</p><div><center><img src="/PSP/images/transformerModel.svg" alt="Modelo PI da linha" title="Modelo PI da linha"></center></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold">r</mi><mi mathvariant="bold">T</mi></msub></mrow><annotation encoding="application/x-tex">\bold{r_T}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.59444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord"><span class="mord mathbf">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33027699999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathbf mtight">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a resistência total do transformador;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold">x</mi><mi mathvariant="bold">T</mi></msub></mrow><annotation encoding="application/x-tex">\bold{x_T}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.59444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33027699999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathbf mtight">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a reatância indutiva total do transformador;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi mathvariant="bold">t</mi><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">\bold{\overline{t}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8349200000000001em;vertical-align:0em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8349200000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathbf">t</span></span></span><span style="top:-3.7549200000000003em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span></span></span></span>	é a o tape complexo do transformador.</li></ul><p>A relação entre as tensões e correntes das barras genéricas <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em"></span><span class="mord mathdefault">i</span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span></span></span></span></span> é obtida pela equação matricial:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>i</mi><mi>j</mi></mrow></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>j</mi><mi>i</mi></mrow></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><msup><mi>t</mi><mn>2</mn></msup></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><msup><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover><mo>∗</mo></msup></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover></mfrac></mstyle></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>×</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>i</mi></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>j</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">\begin{bmatrix} \dot{I}_{ij}\\ \dot{I}_{ji} \end{bmatrix} = \begin{bmatrix} \displaystyle \frac{\overline{y}_T}{t^2} &amp; -\displaystyle \frac{\overline{y}_T}{\overline{t}^*}\\ -\displaystyle \frac{\overline{y}_T}{\overline{t}} &amp; \overline{y}_T \end{bmatrix} \times \begin{bmatrix} \dot{V}_{i}\\ \dot{V}_{j} \end{bmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.5603800000000003em;vertical-align:-1.0301900000000004em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.53019em"><span style="top:-3.61em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-2.3298099999999997em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.0301900000000004em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">]</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:4.202030000000001em;vertical-align:-1.850025em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.352005em"><span style="top:-1.9499950000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-3.0999950000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.1109850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.352005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.850025em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.3019380000000007em"><span style="top:-4.301938em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.2107020000000004em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.29492em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.70508em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8019379999999998em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.3019380000000007em"><span style="top:-4.301938em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.216324em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.893676em"><span style="top:-3.26798em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.783676em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.2107020000000004em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8019379999999998em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.352005em"><span style="top:-1.9499950000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-3.0999950000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.1109850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.352005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.850025em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.5603800000000003em;vertical-align:-1.0301900000000004em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.53019em"><span style="top:-3.61em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.3298099999999997em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.0301900000000004em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">]</span></span></span></span></span></span></span></div><p>Assim como nas <a href="/PSP/docs/line">linhas</a>, o transformador de dois enrolamentos deve ser inserido entre barras, porém não há a necessidade das tensões nominais desses barramentos serem idênticas.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>A primeira barra selecionada será o lado <strong>primário</strong>, o qual é indicado por um círculo. Para alterar o lado primário após a inserção basta desconectar os nós dos transformadores e reconectá-los alternando as barras, utilizando as <a href="/PSP/docs/cadTools#conex%C3%A3o-e-desconex%C3%A3o-de-elemetos-na-barra">ferramentas CAD</a>.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="transformadores-no-estudo-de-curto-circuito"></a>Transformadores no estudo de curto-circuito<a aria-hidden="true" tabindex="-1" class="hash-link" href="#transformadores-no-estudo-de-curto-circuito" title="Direct link to heading">#</a></h3><p>Da mesma forma que no estudo de fluxo de carga, a representação dos elementos do sistema para o estudo de curto-circuito é realizada por meio de circuitos equivalentes inseridos na matriz admitância de barras. Nas <a href="/PSP/docs/fault">faltas desbalanceadas</a> é necessário formar três matrizes admitância de sequência: positiva, negativa e zero.</p><p>A matriz admitância de sequência positiva é construída da mesma forma que os estudos de fluxo de carga. Na sequência negativa o ângulo de defasagem entre tensões primária e secundária (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϕ</mi></mrow><annotation encoding="application/x-tex">\phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">ϕ</span></span></span></span></span>) deve ser invertido, uma vez que os fasores da sequência negativa <strong>são deslocados na direção oposta</strong>. Com isso, a matriz que representa as admitâncias da equação anterior deve ser substituída pela seguinte expressão:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>Y</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>Y</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>j</mi></mrow></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>Y</mi><mo stretchy="true">‾</mo></mover><mrow><mi>j</mi><mi>i</mi></mrow></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>Y</mi><mo stretchy="true">‾</mo></mover><mrow><mi>j</mi><mi>j</mi></mrow></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><msup><mi>t</mi><mn>2</mn></msup></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><msup><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover><mo>∗</mo></msup></mfrac></mstyle></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">\begin{bmatrix} \overline{Y}_{ii} &amp; \overline{Y}_{ij}\\ \overline{Y}_{ji} &amp; \overline{Y}_{jj} \end{bmatrix} = \begin{bmatrix} \displaystyle \frac{\overline{y}_T}{t^2} &amp; -\displaystyle \frac{\overline{y}_T}{\overline{t}}\\ -\displaystyle \frac{\overline{y}_T}{\overline{t}^*} &amp; \overline{y}_T \end{bmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.4866600000000005em;vertical-align:-0.9933300000000005em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.49333em"><span style="top:-3.61em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span><span style="top:-3.80333em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.3666699999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span><span style="top:-3.80333em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9933300000000005em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.49333em"><span style="top:-3.61em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span><span style="top:-3.80333em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-2.3666699999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span><span style="top:-3.80333em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9933300000000005em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">]</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:4.202030000000001em;vertical-align:-1.850025em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.352005em"><span style="top:-1.9499950000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-3.0999950000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.1109850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.352005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.850025em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.3019380000000003em"><span style="top:-4.301938em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.2892979999999996em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.216324em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.893676em"><span style="top:-3.26798em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.783676em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8019380000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.3019380000000003em"><span style="top:-4.301938em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.29492em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.70508em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.2892979999999996em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8019380000000003em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.352005em"><span style="top:-1.9499950000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-3.0999950000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.1109850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.352005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.850025em"><span></span></span></span></span></span></span></span></span></span></span></span></div><p>A impedância de sequência negativa nos transformadores deve ser tratada de maneira específica devido aos diferentes tipos de conexão. Na figura abaixo são mostrados os circuitos equivalentes para cada tipo de conexão de transformadores de dois enrolamentos. As setas indicam os caminhos possíveis para circulação da corrente de sequência zero.</p><div><center><img src="/PSP/images/seqZeroTrafo.svg" alt="Circuitos equivalentes de sequência zero dos transformadores" title="Circuitos equivalentes de sequência zero dos transformadores"></center></div><p>Para os transformadores com conexão estrela aterrado, se a ligação do neutro para a terra apresentar uma impedância <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\overline{z}_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.78056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>, o circuito equivalente de sequência zero deve ter impedância de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">3\overline{z}_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.79444em;vertical-align:-0.15em"></span><span class="mord">3</span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> em série com a resistência e reatância equivalentes do transformador.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-dos-transformadores"></a>Formulário de edição dos transformadores<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-transformadores" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos transformadores:</p><div><center><img src="/PSP/images/trafoForm.png" alt="Formulário dos transformadores no PSP-UFU" title="Formulário dos transformadores no PSP-UFU"></center></div><p>Esse formulário é subdividido em dois contextos distintos:</p><ul><li><strong>Geral</strong>: no qual são inseridas informações gerais dos transformadores, informações do fluxo de carga, sua conexão e defasagem;</li><li><strong>Falta</strong>: local onde as impedâncias de sequência zero e impedâncias de aterramento são inseridas.</li></ul><p>Além desses dois contextos, pode ser observado o botão &quot;Estabilidade&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do transformador durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/trafoSw.png" alt="Formulário de chaveamento do transformador" title="Formulário de chaveamento do transformador"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_1w39 tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Falta</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Botão Estabilidade</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="tensão-nominal"></a>Tensão nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tensão-nominal" title="Direct link to heading">#</a></h4><p>Campo de informação <em>não editável</em> que apresenta a tensão primária e secundária do transformador. Para alterar esse campo é necessário editar o campo correspondente dos <a href="/PSP/docs/bus#geral">barramento</a> conectados.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="tensão-base"></a>Tensão base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tensão-base" title="Direct link to heading">#</a></h4><p>Tensão utilizada para converter os parâmetros de impedância inseridos em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Ω</span></span></span></span></span> para <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> As tensões selecionadas por uma caixa de escolha são editadas nos formulários dos <a href="/PSP/docs/bus#geral">barramentos</a> conectados.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>A tensão base é ignorada caso os dados inseridos estejam em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal do transformador, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="impedância-do-transformador"></a>Impedância do transformador<a aria-hidden="true" tabindex="-1" class="hash-link" href="#impedância-do-transformador" title="Direct link to heading">#</a></h4><p>Impedância série do transformador (resistência e reatância indutiva), inserida em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Ω</span></span></span></span></span>. Caso as impedâncias sejam inseridas em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Ω</span></span></span></span></span> será utilizada a tensão base selecionada para conversão para <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="conexão"></a>Conexão<a aria-hidden="true" tabindex="-1" class="hash-link" href="#conexão" title="Direct link to heading">#</a></h4><p>Conexão do transformador utilizada para cálculo das correntes de sequência zero nas faltas desbalanceadas com presença de terra (fase-terra e fase-fase-terra).</p><p>As seguintes conexões estão disponíveis:</p><ol><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub><mo>−</mo><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub></mrow><annotation encoding="application/x-tex">Y_{aterrado}-Y_{aterrado}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi><mo>−</mo><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub></mrow><annotation encoding="application/x-tex">Y-Y_{aterrado}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub><mo>−</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y_{aterrado}-Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi><mo>−</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y-Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mo>−</mo><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub></mrow><annotation encoding="application/x-tex">\Delta-Y_{aterrado}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord">Δ</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mo>−</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">\Delta-Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord">Δ</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub><mo>−</mo><mi mathvariant="normal">Δ</mi></mrow><annotation encoding="application/x-tex">Y_{aterrado}-\Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi><mo>−</mo><mi mathvariant="normal">Δ</mi></mrow><annotation encoding="application/x-tex">Y-\Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mo>−</mo><mi mathvariant="normal">Δ</mi></mrow><annotation encoding="application/x-tex">\Delta-\Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord">Δ</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span></span></span></span></span></li></ol><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="tap"></a>TAP<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tap" title="Direct link to heading">#</a></h4><p>Tape do transformador <strong>em relação ao primário</strong>.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>O tape no PSP-UFU deve ser inserido pela relação entre a tensão primária nominal e a tensão de tape <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">(</mo><mtext>TAP</mtext><mo>=</mo><mfrac><msub><mi>V</mi><mrow><mi>n</mi><mi>o</mi><mi>m</mi><mi>i</mi><mi>n</mi><mi>a</mi><mi>l</mi></mrow></msub><msub><mi>V</mi><mrow><mi>t</mi><mi>a</mi><mi>p</mi><mi>e</mi></mrow></msub></mfrac><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(\text{TAP} = \frac{V_{nominal}}{V_{tape}}\right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.80002em;vertical-align:-0.65002em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">(</span></span><span class="mord text"><span class="mord">TAP</span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.894191em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.29634285714285713em"><span style="top:-2.357em;margin-left:-0.22222em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">p</span><span class="mord mathdefault mtight">e</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2818857142857143em"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.41586em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em"><span style="top:-2.3487714285714287em;margin-left:-0.22222em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">m</span><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5423199999999999em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">)</span></span></span></span></span></span></span>.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="defasagem"></a>Defasagem<a aria-hidden="true" tabindex="-1" class="hash-link" href="#defasagem" title="Direct link to heading">#</a></h4><p>Defasagem do transformador em relação ao primário, em graus. Esse valor independe do tipo de conexão, portanto para conexões diferentes de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi><mo>−</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y-Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span></span></span>(aterrado ou não) e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mo>−</mo><mi mathvariant="normal">Δ</mi></mrow><annotation encoding="application/x-tex">\Delta-\Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord">Δ</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span></span></span></span></span>, deve-se inserir o ângulo de defasagem correto.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="utilizar-potência-nominal-como-base"></a>Utilizar potência nominal como base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-potência-nominal-como-base" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar a potência nominal do transformador como base para a conversão das unidades, caso contrário será usada a <a href="/PSP/docs/simulationConfig">potência base do sistema</a>.</p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/transformer.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog 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class="row"><div class="col docItemCol_2ASc"><div class="docItemContainer_3QWW"><article><header><h1 class="docTitle_1Lrw">Transformador</h1></header><div class="markdown"><link rel="stylesheet" href="/PSP/katex/katex.min.css"><blockquote><p>Aparelho estático com dois ou mais enrolamentos que, por indução eletromagnética, transforma um sistema de tensão e corrente alternada em outro sistema de tensão e corrente geralmente de valores diferentes e na mesma frequência com o objetivo de transmitir energia elétrica. <a href="http://www.electropedia.org/iev/iev.nsf/display?openform&amp;ievref=421-01-01" target="_blank" rel="noopener noreferrer"><em>tradução livre</em> - IEC 60050</a>.</p></blockquote><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="transformador-no-psp-ufu"></a>Transformador no PSP-UFU<a aria-hidden="true" tabindex="-1" class="hash-link" href="#transformador-no-psp-ufu" title="Direct link to heading">#</a></h2><p>Transformadores com quaisquer conexões e defasagens entre as tensões primárias e secundárias podem ser inseridos no PSP-UFU. Para isso, os transformadores devem ser modelados representando seu tape (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi></mrow><annotation encoding="application/x-tex">t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.61508em;vertical-align:0em"></span><span class="mord mathdefault">t</span></span></span></span></span>) e defasagem (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϕ</mi></mrow><annotation encoding="application/x-tex">\phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">ϕ</span></span></span></span></span>), utilizando um transformador ideal de relação de transformação <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover><mo>:</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\overline{t}:1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.81508em;vertical-align:0em"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em"></span><span class="mord">1</span></span></span></span></span> em série com sua impedância (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><mo>=</mo><msub><mi>r</mi><mi>T</mi></msub><mo>+</mo><mi>j</mi><msub><mi>x</mi><mi>T</mi></msub></mrow><annotation encoding="application/x-tex">\overline{y}_T = r_T + jx_T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8747em;vertical-align:-0.24414em"></span><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:-0.02778em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>), em que <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">\overline{t}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.81508em;vertical-align:0em"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span></span></span> é um número complexo (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi><mi mathvariant="normal">∠</mi><mi>ϕ</mi></mrow><annotation encoding="application/x-tex">t\angle\phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">t</span><span class="mord">∠</span><span class="mord mathdefault">ϕ</span></span></span></span></span>)</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção</h5></div><div class="admonition-content"><p>O modelo utilizado no PSP-UFU <strong>não considera</strong> o ramo magnetizante ou impedâncias mútuas entre as fases.</p></div></div><p>A figura abaixo mostra o modelo do transformador implementado no PSP-UFU:</p><div><center><img src="/PSP/images/transformerModel.svg" alt="Modelo PI da linha" title="Modelo PI da linha"></center></div><p>Em que:</p><ul><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold">r</mi><mi mathvariant="bold">T</mi></msub></mrow><annotation encoding="application/x-tex">\bold{r_T}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.59444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord"><span class="mord mathbf">r</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33027699999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathbf mtight">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a resistência total do transformador;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold">x</mi><mi mathvariant="bold">T</mi></msub></mrow><annotation encoding="application/x-tex">\bold{x_T}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.59444em;vertical-align:-0.15em"></span><span class="mord"><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33027699999999993em"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathbf mtight">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></span>	é a reatância indutiva total do transformador;</li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi mathvariant="bold">t</mi><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">\bold{\overline{t}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8349200000000001em;vertical-align:0em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8349200000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathbf">t</span></span></span><span style="top:-3.7549200000000003em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span></span></span></span>	é a o tape complexo do transformador.</li></ul><p>A relação entre as tensões e correntes das barras genéricas <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em"></span><span class="mord mathdefault">i</span></span></span></span></span> e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em"></span><span class="mord mathdefault" style="margin-right:0.05724em">j</span></span></span></span></span> é obtida pela equação matricial:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>i</mi><mi>j</mi></mrow></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>I</mi><mo>˙</mo></mover><mrow><mi>j</mi><mi>i</mi></mrow></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><msup><mi>t</mi><mn>2</mn></msup></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><msup><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover><mo>∗</mo></msup></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover></mfrac></mstyle></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>×</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>i</mi></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>V</mi><mo>˙</mo></mover><mi>j</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">\begin{bmatrix} \dot{I}_{ij}\\ \dot{I}_{ji} \end{bmatrix} = \begin{bmatrix} \displaystyle \frac{\overline{y}_T}{t^2} &amp; -\displaystyle \frac{\overline{y}_T}{\overline{t}^*}\\ -\displaystyle \frac{\overline{y}_T}{\overline{t}} &amp; \overline{y}_T \end{bmatrix} \times \begin{bmatrix} \dot{V}_{i}\\ \dot{V}_{j} \end{bmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.5603800000000003em;vertical-align:-1.0301900000000004em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.53019em"><span style="top:-3.61em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-2.3298099999999997em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em">I</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.027780000000000013em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.0301900000000004em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">]</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:4.202030000000001em;vertical-align:-1.850025em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.352005em"><span style="top:-1.9499950000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-3.0999950000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.1109850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.352005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.850025em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.3019380000000007em"><span style="top:-4.301938em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.2107020000000004em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.29492em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.70508em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8019379999999998em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.3019380000000007em"><span style="top:-4.301938em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.216324em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.893676em"><span style="top:-3.26798em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.783676em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.2107020000000004em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8019379999999998em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.352005em"><span style="top:-1.9499950000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-3.0999950000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.1109850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.352005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.850025em"><span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:2.5603800000000003em;vertical-align:-1.0301900000000004em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.53019em"><span style="top:-3.61em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.3298099999999997em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">V</span></span></span><span style="top:-3.25233em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.13889em"><span class="mord">˙</span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.0301900000000004em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">]</span></span></span></span></span></span></span></div><p>Assim como nas <a href="/PSP/docs/line">linhas</a>, o transformador de dois enrolamentos deve ser inserido entre barras, porém não há a necessidade das tensões nominais desses barramentos serem idênticas.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>A primeira barra selecionada será o lado <strong>primário</strong>, o qual é indicado por um círculo. Para alterar o lado primário após a inserção basta desconectar os nós dos transformadores e reconectá-los alternando as barras, utilizando as <a href="/PSP/docs/cadTools#conex%C3%A3o-e-desconex%C3%A3o-de-elemetos-na-barra">ferramentas CAD</a>.</p></div></div><h3><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="transformadores-no-estudo-de-curto-circuito"></a>Transformadores no estudo de curto-circuito<a aria-hidden="true" tabindex="-1" class="hash-link" href="#transformadores-no-estudo-de-curto-circuito" title="Direct link to heading">#</a></h3><p>Da mesma forma que no estudo de fluxo de carga, a representação dos elementos do sistema para o estudo de curto-circuito é realizada por meio de circuitos equivalentes inseridos na matriz admitância de barras. Nas <a href="/PSP/docs/fault">faltas desbalanceadas</a> é necessário formar três matrizes admitância de sequência: positiva, negativa e zero.</p><p>A matriz admitância de sequência positiva é construída da mesma forma que os estudos de fluxo de carga. Na sequência negativa o ângulo de defasagem entre tensões primária e secundária (<span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϕ</mi></mrow><annotation encoding="application/x-tex">\phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em"></span><span class="mord mathdefault">ϕ</span></span></span></span></span>) deve ser invertido, uma vez que os fasores da sequência negativa <strong>são deslocados na direção oposta</strong>. Com isso, a matriz que representa as admitâncias da equação anterior deve ser substituída pela seguinte expressão:</p><div class="math math-display"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>Y</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>i</mi></mrow></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>Y</mi><mo stretchy="true">‾</mo></mover><mrow><mi>i</mi><mi>j</mi></mrow></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>Y</mi><mo stretchy="true">‾</mo></mover><mrow><mi>j</mi><mi>i</mi></mrow></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>Y</mi><mo stretchy="true">‾</mo></mover><mrow><mi>j</mi><mi>j</mi></mrow></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><msup><mi>t</mi><mn>2</mn></msup></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover></mfrac></mstyle></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub><msup><mover accent="true"><mi>t</mi><mo stretchy="true">‾</mo></mover><mo>∗</mo></msup></mfrac></mstyle></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mover accent="true"><mi>y</mi><mo stretchy="true">‾</mo></mover><mi>T</mi></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">\begin{bmatrix} \overline{Y}_{ii} &amp; \overline{Y}_{ij}\\ \overline{Y}_{ji} &amp; \overline{Y}_{jj} \end{bmatrix} = \begin{bmatrix} \displaystyle \frac{\overline{y}_T}{t^2} &amp; -\displaystyle \frac{\overline{y}_T}{\overline{t}}\\ -\displaystyle \frac{\overline{y}_T}{\overline{t}^*} &amp; \overline{y}_T \end{bmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.4866600000000005em;vertical-align:-0.9933300000000005em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.49333em"><span style="top:-3.61em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span><span style="top:-3.80333em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-2.3666699999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span><span style="top:-3.80333em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span><span class="mord mathdefault mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9933300000000005em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.49333em"><span style="top:-3.61em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span><span style="top:-3.80333em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span><span style="top:-2.3666699999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833300000000001em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span><span style="top:-3.80333em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span><span class="mord mathdefault mtight" style="margin-right:0.05724em">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9933300000000005em"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">]</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:4.202030000000001em;vertical-align:-1.850025em"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.352005em"><span style="top:-1.9499950000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎣</span></span></span><span style="top:-3.0999950000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-3.1109850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎢</span></span></span><span style="top:-4.352005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎡</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.850025em"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.3019380000000003em"><span style="top:-4.301938em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em"><span style="top:-2.9890000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.2892979999999996em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.216324em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.893676em"><span style="top:-3.26798em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∗</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.783676em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8019380000000003em"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em"></span><span class="arraycolsep" style="width:0.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.3019380000000003em"><span style="top:-4.301938em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord">−</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.30756em"><span style="top:-2.29492em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.81508em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault">t</span></span></span><span style="top:-3.73508em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.6769999999999996em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.70508em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.2892979999999996em"><span class="pstrut" style="height:3.30756em"></span><span class="mord"><span class="mord"><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em">y</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.23419099999999995em"><span style="top:-2.4558600000000004em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em">T</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.24414em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.8019380000000003em"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.352005em"><span style="top:-1.9499950000000004em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎦</span></span></span><span style="top:-3.0999950000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-3.1109850000000003em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎥</span></span></span><span style="top:-4.352005em"><span class="pstrut" style="height:3.1550000000000002em"></span><span class="delimsizinginner delim-size4"><span>⎤</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.850025em"><span></span></span></span></span></span></span></span></span></span></span></span></div><p>A impedância de sequência negativa nos transformadores deve ser tratada de maneira específica devido aos diferentes tipos de conexão. Na figura abaixo são mostrados os circuitos equivalentes para cada tipo de conexão de transformadores de dois enrolamentos. As setas indicam os caminhos possíveis para circulação da corrente de sequência zero.</p><div><center><img src="/PSP/images/seqZeroTrafo.svg" alt="Circuitos equivalentes de sequência zero dos transformadores" title="Circuitos equivalentes de sequência zero dos transformadores"></center></div><p>Para os transformadores com conexão estrela aterrado, se a ligação do neutro para a terra apresentar uma impedância <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\overline{z}_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.78056em;vertical-align:-0.15em"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>, o circuito equivalente de sequência zero deve ter impedância de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><msub><mover accent="true"><mi>z</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">3\overline{z}_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.79444em;vertical-align:-0.15em"></span><span class="mord">3</span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.63056em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.04398em">z</span></span></span><span style="top:-3.55056em"><span class="pstrut" style="height:3em"></span><span class="overline-line" style="border-bottom-width:0.04em"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em"><span style="top:-2.5500000000000003em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span> em série com a resistência e reatância equivalentes do transformador.</p><h2><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="formulário-de-edição-dos-transformadores"></a>Formulário de edição dos transformadores<a aria-hidden="true" tabindex="-1" class="hash-link" href="#formulário-de-edição-dos-transformadores" title="Direct link to heading">#</a></h2><p>A imagem abaixo apresenta o formulário de inserção/alteração de dados dos transformadores:</p><div><center><img src="/PSP/images/trafoForm.png" alt="Formulário dos transformadores no PSP-UFU" title="Formulário dos transformadores no PSP-UFU"></center></div><p>Esse formulário é subdividido em dois contextos distintos:</p><ul><li><strong>Geral</strong>: no qual são inseridas informações gerais dos transformadores, informações do fluxo de carga, sua conexão e defasagem;</li><li><strong>Falta</strong>: local onde as impedâncias de sequência zero e impedâncias de aterramento são inseridas.</li></ul><p>Além desses dois contextos, pode ser observado o botão &quot;Estabilidade&quot; na parte inferior esquerda do formulário. Esse formulário, comum a vários outros elementos, permite a inserção e/ou remoção do transformador durante o estudo de <a href="/PSP/docs/stability">estabilidade</a>.</p><div><center><img src="/PSP/images/trafoSw.png" alt="Formulário de chaveamento do transformador" title="Formulário de chaveamento do transformador"></center></div><div><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_1w39 tabs__item--active">Geral</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Falta</li><li role="tab" tabindex="0" aria-selected="false" class="tabs__item tabItem_1w39">Botão Estabilidade</li></ul><div role="tabpanel" class="margin-vert--md"><div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="nome"></a>Nome<a aria-hidden="true" tabindex="-1" class="hash-link" href="#nome" title="Direct link to heading">#</a></h4><p>Identificação do elemento elétrico. Podem ser inseridos quaisquer números de caracteres no padrão <a href="https://pt.wikipedia.org/wiki/Unicode" target="_blank" rel="noopener noreferrer">Unicode</a>.</p><p>Todos os componentes de potência do PSP-UFU possuem esse campo.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="tensão-nominal"></a>Tensão nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tensão-nominal" title="Direct link to heading">#</a></h4><p>Campo de informação <em>não editável</em> que apresenta a tensão primária e secundária do transformador. Para alterar esse campo é necessário editar o campo correspondente dos <a href="/PSP/docs/bus#geral">barramento</a> conectados.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="tensão-base"></a>Tensão base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tensão-base" title="Direct link to heading">#</a></h4><p>Tensão utilizada para converter os parâmetros de impedância inseridos em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Ω</span></span></span></span></span> para <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> As tensões selecionadas por uma caixa de escolha são editadas nos formulários dos <a href="/PSP/docs/bus#geral">barramentos</a> conectados.</p><div class="admonition admonition-info alert alert--info"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="16" viewBox="0 0 14 16"><path fill-rule="evenodd" d="M7 2.3c3.14 0 5.7 2.56 5.7 5.7s-2.56 5.7-5.7 5.7A5.71 5.71 0 0 1 1.3 8c0-3.14 2.56-5.7 5.7-5.7zM7 1C3.14 1 0 4.14 0 8s3.14 7 7 7 7-3.14 7-7-3.14-7-7-7zm1 3H6v5h2V4zm0 6H6v2h2v-2z"></path></svg></span>Informação</h5></div><div class="admonition-content"><p>A tensão base é ignorada caso os dados inseridos estejam em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="potência-nominal"></a>Potência nominal<a aria-hidden="true" tabindex="-1" class="hash-link" href="#potência-nominal" title="Direct link to heading">#</a></h4><p>Potência nominal do transformador, inserida em MVA, kVA ou VA.</p><p>Esse campo é especialmente importante caso a opção &quot;Utilizar a potência nominal como base&quot; esteja marcada.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="impedância-do-transformador"></a>Impedância do transformador<a aria-hidden="true" tabindex="-1" class="hash-link" href="#impedância-do-transformador" title="Direct link to heading">#</a></h4><p>Impedância série do transformador (resistência e reatância indutiva), inserida em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span> ou <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Ω</span></span></span></span></span>. Caso as impedâncias sejam inseridas em <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Ω</span></span></span></span></span> será utilizada a tensão base selecionada para conversão para <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi mathvariant="normal">.</mi><mi>u</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">p.u.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em"></span><span class="mord mathdefault">p</span><span class="mord">.</span><span class="mord mathdefault">u</span><span class="mord">.</span></span></span></span></span></p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="conexão"></a>Conexão<a aria-hidden="true" tabindex="-1" class="hash-link" href="#conexão" title="Direct link to heading">#</a></h4><p>Conexão do transformador utilizada para cálculo das correntes de sequência zero nas faltas desbalanceadas com presença de terra (fase-terra e fase-fase-terra).</p><p>As seguintes conexões estão disponíveis:</p><ol><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub><mo>−</mo><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub></mrow><annotation encoding="application/x-tex">Y_{aterrado}-Y_{aterrado}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi><mo>−</mo><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub></mrow><annotation encoding="application/x-tex">Y-Y_{aterrado}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub><mo>−</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y_{aterrado}-Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi><mo>−</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y-Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mo>−</mo><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub></mrow><annotation encoding="application/x-tex">\Delta-Y_{aterrado}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord">Δ</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mo>−</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">\Delta-Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord">Δ</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Y</mi><mrow><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>d</mi><mi>o</mi></mrow></msub><mo>−</mo><mi mathvariant="normal">Δ</mi></mrow><annotation encoding="application/x-tex">Y_{aterrado}-\Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">e</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight" style="margin-right:0.02778em">r</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">d</span><span class="mord mathdefault mtight">o</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi><mo>−</mo><mi mathvariant="normal">Δ</mi></mrow><annotation encoding="application/x-tex">Y-\Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span></span></span></span></span></li><li><span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mo>−</mo><mi mathvariant="normal">Δ</mi></mrow><annotation encoding="application/x-tex">\Delta-\Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord">Δ</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span></span></span></span></span></li></ol><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="tap"></a>TAP<a aria-hidden="true" tabindex="-1" class="hash-link" href="#tap" title="Direct link to heading">#</a></h4><p>Tape do transformador <strong>em relação ao primário</strong>.</p><div class="admonition admonition-caution alert alert--warning"><div class="admonition-heading"><h5><span class="admonition-icon"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"></path></svg></span>Atenção!</h5></div><div class="admonition-content"><p>O tape no PSP-UFU deve ser inserido pela relação entre a tensão primária nominal e a tensão de tape <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">(</mo><mtext>TAP</mtext><mo>=</mo><mfrac><msub><mi>V</mi><mrow><mi>n</mi><mi>o</mi><mi>m</mi><mi>i</mi><mi>n</mi><mi>a</mi><mi>l</mi></mrow></msub><msub><mi>V</mi><mrow><mi>t</mi><mi>a</mi><mi>p</mi><mi>e</mi></mrow></msub></mfrac><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(\text{TAP} = \frac{V_{nominal}}{V_{tape}}\right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.80002em;vertical-align:-0.65002em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size2">(</span></span><span class="mord text"><span class="mord">TAP</span></span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.894191em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.29634285714285713em"><span style="top:-2.357em;margin-left:-0.22222em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">t</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">p</span><span class="mord mathdefault mtight">e</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2818857142857143em"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.41586em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em"><span style="top:-2.3487714285714287em;margin-left:-0.22222em;margin-right:0.07142857142857144em"><span class="pstrut" style="height:2.5em"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">m</span><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight" style="margin-right:0.01968em">l</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5423199999999999em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size2">)</span></span></span></span></span></span></span>.</p></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="defasagem"></a>Defasagem<a aria-hidden="true" tabindex="-1" class="hash-link" href="#defasagem" title="Direct link to heading">#</a></h4><p>Defasagem do transformador em relação ao primário, em graus. Esse valor independe do tipo de conexão, portanto para conexões diferentes de <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi><mo>−</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y-Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord mathdefault" style="margin-right:0.22222em">Y</span></span></span></span></span>(aterrado ou não) e <span class="math math-inline"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mo>−</mo><mi mathvariant="normal">Δ</mi></mrow><annotation encoding="application/x-tex">\Delta-\Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.76666em;vertical-align:-0.08333em"></span><span class="mord">Δ</span><span class="mspace" style="margin-right:0.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em"></span><span class="mord">Δ</span></span></span></span></span>, deve-se inserir o ângulo de defasagem correto.</p><h4><a aria-hidden="true" tabindex="-1" class="anchor enhancedAnchor_2cZh" id="utilizar-potência-nominal-como-base"></a>Utilizar potência nominal como base<a aria-hidden="true" tabindex="-1" class="hash-link" href="#utilizar-potência-nominal-como-base" title="Direct link to heading">#</a></h4><p>Caso essa opção seja marcada, o programa irá utilizar a potência nominal do transformador como base para a conversão das unidades, caso contrário será usada a <a href="/PSP/docs/simulationConfig">potência base do sistema</a>.</p></div></div></div></div></article><div class="margin-vert--xl"><div class="row"><div class="col"><a href="https://github.com/Thales1330/PSP/tree/master/docusaurus/docs/transformer.md" target="_blank" rel="noreferrer noopener"><svg fill="currentColor" height="1.2em" width="1.2em" preserveAspectRatio="xMidYMid meet" viewBox="0 0 40 40" style="margin-right:0.3em;vertical-align:sub"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div></div></div><div class="margin-vert--lg"><nav class="pagination-nav" aria-label="Blog 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Um processo iterativo \xe9 realizado at\xe9 que o erro entre os c\xe1lculos se torne menor que uma toler\xe2ncia pr\xe9-estipulada e caso as itera\xe7\xf5es se tornem excessivas, ultrapassando um n\xfamero m\xe1ximo definido pelo usu\xe1rio, o processo \xe9 interrompido com erro. 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Um processo iterativo \xe9 realizado at\xe9 que o erro entre os c\xe1lculos se torne menor que uma toler\xe2ncia pr\xe9-estipulada e caso as itera\xe7\xf5es se tornem excessivas, ultrapassando um n\xfamero m\xe1ximo definido pelo usu\xe1rio, o processo \xe9 interrompido com erro. 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",Object(m.b)("strong",{parentName:"p"},"harm\xf4nicos")," as cargas s\xe3o modeladas como imped\xe2ncia constante, independentemente da sinaliza\xe7\xe3o indicada em seu formul\xe1rio de edi\xe7\xe3o de dados."))),Object(m.b)("h3",{id:"carga-no-estudo-de-estabilidade"},"Carga no estudo de estabilidade"),Object(m.b)("p",null,"A modelagem das cargas do sistema de forma exata se torna impratic\xe1vel em um problemas de estabilidade, visto \xe0 grande quantidade e variedade dos componentes envolvidos, al\xe9m de apresentar modifica\xe7\xf5es em suas composi\xe7\xf5es causado por v\xe1rios fatores, como tempo, condi\xe7\xf5es clim\xe1ticas e economia. 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diff --git a/docs/ece76bd1.a4744b55.js b/docs/ece76bd1.cf058485.js
similarity index 98%
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Podem ser inseridos quaisquer n\xfameros de caracteres no padr\xe3o ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Unicode"}),"Unicode"),"."),Object(n.b)("p",null,"Todos os componentes de pot\xeancia do PSP-UFU possuem esse campo."),Object(n.b)("h4",{id:"pot\xeancia-nominal"},"Pot\xeancia nominal"),Object(n.b)("p",null,"Pot\xeancia nominal do gerador, inserida em MVA, kVA ou VA."),Object(n.b)("p",null,'Esse campo \xe9 especialmente importante caso a op\xe7\xe3o "Utilizar a pot\xeancia nominal como base" esteja marcada.'),Object(n.b)("h4",{id:"pot\xeancias-ativa-e-reativa"},"Pot\xeancias ativa e reativa"),Object(n.b)("p",null,"Pot\xeancias ativa (inserida em W, kW, MW ou ",Object(n.b)("span",Object(s.a)({parentName:"p"},{className:"math 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Tal fator eleva o valor da resist\xeancia do rotor em condi\xe7\xf5es de grande escorregamento, como ocorre em motores de gaiola dupla ou gaiola profunda. 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Podem ser inseridos quaisquer n\xfameros de caracteres no padr\xe3o ",Object(n.b)("a",Object(s.a)({parentName:"p"},{href:"https://pt.wikipedia.org/wiki/Unicode"}),"Unicode"),"."),Object(n.b)("p",null,"Todos os componentes de pot\xeancia do PSP-UFU possuem esse campo."),Object(n.b)("h4",{id:"pot\xeancia-nominal"},"Pot\xeancia nominal"),Object(n.b)("p",null,"Pot\xeancia nominal do gerador, inserida em MVA, kVA ou VA."),Object(n.b)("p",null,'Esse campo \xe9 especialmente importante caso a op\xe7\xe3o "Utilizar a pot\xeancia nominal como base" esteja marcada.'),Object(n.b)("h4",{id:"pot\xeancias-ativa-e-reativa"},"Pot\xeancias ativa e reativa"),Object(n.b)("p",null,"Pot\xeancias ativa (inserida em W, kW, MW ou ",Object(n.b)("span",Object(s.a)({parentName:"p"},{className:"math 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Tal fator eleva o valor da resist\xeancia do rotor em condi\xe7\xf5es de grande escorregamento, como ocorre em motores de gaiola dupla ou gaiola profunda. 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diff --git a/docs/images/stabInit.svg b/docs/images/stabInit.svg
index 032c2358..8b8035eb 100644
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Uberlândia</p><p><center><iframe src="https://ghbtns.com/github-btn.html?user=thales1330&amp;repo=psp&amp;type=star&amp;count=true&amp;size=large" frameborder="0" scrolling="0" width="130" height="30" title="GitHub"></iframe></center></p><div class="buttons_1Wc3"><a href="https://github.com/Thales1330/PSP/releases/latest" target="_blank" rel="noopener noreferrer" class="button button--outline button--secondary button--lg">Download</a></div><div class="buttons_1Wc3"><a class="button button--outline button--secondary button--lg" href="/PSP/docs/">User Guide</a></div><div class="buttons_1Wc3"><a href="https://minhaskamal.github.io/DownGit/#/home?url=https://github.com/Thales1330/PSP/tree/master/Project/data/samples" target="_blank" rel="noopener noreferrer" class="button button--outline button--secondary button--lg">Samples</a></div></div></header><main><section class="features_P2SU"><div class="container"><div class="row"><div class="col col--4"><div class="text--center"><img class="featureImage_3Xqx" src="/PSP/img/complete-platform.svg" alt="[object Object]"></div><h3>Complete Platform</h3><p>PSP-UFU is a <b>cross-platform</b>, <b>multilingual</b>, <b>Free and Open-Source Software (FOSS)</b> with <b>advanced GUI (Graphical User Interface)</b> features and <b>CAD (Computer-Aided Design) tools</b> for electrical power system studies.</p></div><div class="col col--4"><div class="text--center"><img class="featureImage_3Xqx" src="/PSP/img/advanced-cad.svg" alt="[object Object]"></div><h3>Advanced CAD Features</h3><p>The software allows the construction of any electric <b>transmission network</b> and <b>control systems</b> through the deployment of visual elements.</p></div><div class="col col--4"><div class="text--center"><img class="featureImage_3Xqx" src="/PSP/img/visualization.svg" alt="[object Object]"></div><h3>Easy Visualization</h3><p>For the visualization of results, the program offers linked text elements in the main screen, voltage heatmap display, and also table and graph editors.</p></div><div class="col col--4"><div class="text--center"><img class="featureImage_3Xqx" src="/PSP/img/application.svg" alt="[object Object]"></div><h3>Application</h3><p>The PSP-UFU aims to provide efficient computer simulation tools for <b>research</b> and <b>education</b> purposes, in addition to <b>industrial applications</b> in electrical power systems.</p></div></div></div></section><div class="container"><h2>Studies Performed</h2></div><section class="features_P2SU"><div class="container"><div class="row"><div class="col col--4"><h3>Power Flow</h3><ul><li>Newton-Raphson</li><li>Gauss-Seidel</li><li>Hybrid Newton-Gauss</li><li>Three-phase induction motors included</li></ul></div><div class="col col--4"><h3>Short-Circuit calculation</h3><ul><li>Balanced</li><li>Unbalanced</li><li>Short-Circuit power in all system buses</li></ul></div><div class="col col--4"><h3>Harmonics</h3><ul><li>Harmonic voltages and THD (Total Harmonic Distortion) calculation</li><li>Frequency scan</li></ul></div><div class="col col--4"><h3>Transient and Dynamic Stability</h3><ul><li>Several synchronous machine models automatically selected</li><li>Three-phase induction motors</li><li>User-defined machine controls, exciters and prime moves created using block diagrams (Exciters, AVR, PSS, Hydro and Thermal turbines, Speed Governor, etc.)</li></ul></div></div></div></section><div class="container"><h2>Published Papers</h2>Further details can be found in the published papers:<blockquote cite="https://doi.org/10.1002/2050-7038.12185">Oliveira, T. L., Guimarães, G. C., &amp; Silva, L. R. C. (2019). PSP-UFU: An open-source, graphical, and multiplatform software for power system studies. <i>International Transactions on Electrical Energy Systems</i>, e12185. doi: <a href="https://doi.org/10.1002/2050-7038.12185">10.1002/2050-7038.12185</a></blockquote><blockquote cite="https://doi.org/10.1177/0020720919879058">Oliveira, T. L., Guimarães, G. C., Silva, L. R., &amp; Rezende, J. O. (2019). Power system education and research applications using free and open-source, graphical and multiplatform PSP-UFU software. <i>The International Journal of Electrical Engineering &amp; Education</i>, 0020720919879058. doi: <a href="https://doi.org/10.1177/0020720919879058">10.1177/0020720919879058</a></blockquote></div><div class="container"><h2>Code Documentation</h2><p>All detailed descriptions of the source-code can be found at <b><a href="https://thales1330.github.io/PSP/doxygen/html/index.html">Online Documentation</a></b>, generated by <a href="http://www.doxygen.org/">Doxygen</a>.</p></div><div class="container"><h2>Screenshots</h2><center><iframe src="gallery.html" style="position:relative;width:100%;height:56.25vw;display:block;overflow:hidden;border:none">Your browser doesn’t support the this feature.</iframe></center></div></main></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. 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Uberlândia</p><p><center><iframe src="https://ghbtns.com/github-btn.html?user=thales1330&amp;repo=psp&amp;type=star&amp;count=true&amp;size=large" frameborder="0" scrolling="0" width="130" height="30" title="GitHub"></iframe></center></p><div class="buttons_1Wc3"><a href="https://github.com/Thales1330/PSP/releases/latest" target="_blank" rel="noopener noreferrer" class="button button--outline button--secondary button--lg">Download</a></div><div class="buttons_1Wc3"><a class="button button--outline button--secondary button--lg" href="/PSP/docs/">User Guide</a></div><div class="buttons_1Wc3"><a href="https://minhaskamal.github.io/DownGit/#/home?url=https://github.com/Thales1330/PSP/tree/master/Project/data/samples" target="_blank" rel="noopener noreferrer" class="button button--outline button--secondary button--lg">Samples</a></div></div></header><main><section class="features_P2SU"><div class="container"><div class="row"><div class="col col--4"><div class="text--center"><img class="featureImage_3Xqx" src="/PSP/img/complete-platform.svg" alt="[object Object]"></div><h3>Complete Platform</h3><p>PSP-UFU is a <b>cross-platform</b>, <b>multilingual</b>, <b>Free and Open-Source Software (FOSS)</b> with <b>advanced GUI (Graphical User Interface)</b> features and <b>CAD (Computer-Aided Design) tools</b> for electrical power system studies.</p></div><div class="col col--4"><div class="text--center"><img class="featureImage_3Xqx" src="/PSP/img/advanced-cad.svg" alt="[object Object]"></div><h3>Advanced CAD Features</h3><p>The software allows the construction of any electric <b>transmission network</b> and <b>control systems</b> through the deployment of visual elements.</p></div><div class="col col--4"><div class="text--center"><img class="featureImage_3Xqx" src="/PSP/img/visualization.svg" alt="[object Object]"></div><h3>Easy Visualization</h3><p>For the visualization of results, the program offers linked text elements in the main screen, voltage heatmap display, and also table and graph editors.</p></div><div class="col col--4"><div class="text--center"><img class="featureImage_3Xqx" src="/PSP/img/application.svg" alt="[object Object]"></div><h3>Application</h3><p>The PSP-UFU aims to provide efficient computer simulation tools for <b>research</b> and <b>education</b> purposes, in addition to <b>industrial applications</b> in electrical power systems.</p></div></div></div></section><div class="container"><h2>Studies Performed</h2></div><section class="features_P2SU"><div class="container"><div class="row"><div class="col col--4"><h3>Power Flow</h3><ul><li>Newton-Raphson</li><li>Gauss-Seidel</li><li>Hybrid Newton-Gauss</li><li>Three-phase induction motors included</li></ul></div><div class="col col--4"><h3>Short-Circuit calculation</h3><ul><li>Balanced</li><li>Unbalanced</li><li>Short-Circuit power in all system buses</li></ul></div><div class="col col--4"><h3>Harmonics</h3><ul><li>Harmonic voltages and THD (Total Harmonic Distortion) calculation</li><li>Frequency scan</li></ul></div><div class="col col--4"><h3>Transient and Dynamic Stability</h3><ul><li>Several synchronous machine models automatically selected</li><li>Three-phase induction motors</li><li>User-defined machine controls, exciters and prime moves created using block diagrams (Exciters, AVR, PSS, Hydro and Thermal turbines, Speed Governor, etc.)</li></ul></div></div></div></section><div class="container"><h2>Published Papers</h2>Further details can be found in the published papers:<blockquote cite="https://doi.org/10.1002/2050-7038.12185">Oliveira, T. L., Guimarães, G. C., &amp; Silva, L. R. C. (2019). PSP-UFU: An open-source, graphical, and multiplatform software for power system studies. <i>International Transactions on Electrical Energy Systems</i>, e12185. doi: <a href="https://doi.org/10.1002/2050-7038.12185">10.1002/2050-7038.12185</a></blockquote><blockquote cite="https://doi.org/10.1177/0020720919879058">Oliveira, T. L., Guimarães, G. C., Silva, L. R., &amp; Rezende, J. O. (2019). Power system education and research applications using free and open-source, graphical and multiplatform PSP-UFU software. <i>The International Journal of Electrical Engineering &amp; Education</i>, 0020720919879058. doi: <a href="https://doi.org/10.1177/0020720919879058">10.1177/0020720919879058</a></blockquote></div><div class="container"><h2>Code Documentation</h2><p>All detailed descriptions of the source-code can be found at <b><a href="https://thales1330.github.io/PSP/doxygen/html/index.html">Online Documentation</a></b>, generated by <a href="http://www.doxygen.org/">Doxygen</a>.</p></div><div class="container"><h2>Screenshots</h2><center><iframe src="gallery.html" style="position:relative;width:100%;height:56.25vw;display:block;overflow:hidden;border:none">Your browser doesn’t support the this feature.</iframe></center></div></main></div><footer class="footer footer--dark"><div class="container"><div class="row footer__links"><div class="col footer__col"><h4 class="footer__title">Guide</h4><ul class="footer__items"><li class="footer__item"><a class="footer__link-item" href="/PSP/docs/">PSP-UFU Guide</a></li><li class="footer__item"><a href="https://thales1330.github.io/PSP/doxygen/html/index.html" target="_blank" rel="noopener noreferrer" class="footer__link-item">Code Documentation</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Community</h4><ul class="footer__items"><li class="footer__item"><a href="https://github.com/Thales1330/PSP/issues" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ask a question</a></li><li class="footer__item"><a href="https://twitter.com/PspUfu" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter</a></li></ul></div><div class="col footer__col"><h4 class="footer__title">Site Image Credit</h4><ul class="footer__items"><li class="footer__item"><a href="http://www.freepik.com/" target="_blank" rel="noopener noreferrer" class="footer__link-item">Images designed by upklyak / slidesgo / macrovector / Freepik</a></li></ul></div></div><div class="text--center"><div>Copyright © 2020 Thales Lima Oliveira. Built with Docusaurus.</div></div></div></footer></div>
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t={pattern:/{\$(?:{(?:{[^{}]+}|[^{}]+)}|[^{}])+}|(^|[^\\{])\$+(?:\w+(?:\[.+?]|->\w+)*)/,lookbehind:!0,inside:{rest:e.languages.php}};e.languages.insertBefore("php","string",{"nowdoc-string":{pattern:/<<<'([^']+)'(?:\r\n?|\n)(?:.*(?:\r\n?|\n))*?\1;/,greedy:!0,alias:"string",inside:{delimiter:{pattern:/^<<<'[^']+'|[a-z_]\w*;$/i,alias:"symbol",inside:{punctuation:/^<<<'?|[';]$/}}}},"heredoc-string":{pattern:/<<<(?:"([^"]+)"(?:\r\n?|\n)(?:.*(?:\r\n?|\n))*?\1;|([a-z_]\w*)(?:\r\n?|\n)(?:.*(?:\r\n?|\n))*?\2;)/i,greedy:!0,alias:"string",inside:{delimiter:{pattern:/^<<<(?:"[^"]+"|[a-z_]\w*)|[a-z_]\w*;$/i,alias:"symbol",inside:{punctuation:/^<<<"?|[";]$/}},interpolation:t}},"single-quoted-string":{pattern:/'(?:\\[\s\S]|[^\\'])*'/,greedy:!0,alias:"string"},"double-quoted-string":{pattern:/"(?:\\[\s\S]|[^\\"])*"/,greedy:!0,alias:"string",inside:{interpolation:t}}}),delete 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t={pattern:/{\$(?:{(?:{[^{}]+}|[^{}]+)}|[^{}])+}|(^|[^\\{])\$+(?:\w+(?:\[.+?]|->\w+)*)/,lookbehind:!0,inside:{rest:e.languages.php}};e.languages.insertBefore("php","string",{"nowdoc-string":{pattern:/<<<'([^']+)'(?:\r\n?|\n)(?:.*(?:\r\n?|\n))*?\1;/,greedy:!0,alias:"string",inside:{delimiter:{pattern:/^<<<'[^']+'|[a-z_]\w*;$/i,alias:"symbol",inside:{punctuation:/^<<<'?|[';]$/}}}},"heredoc-string":{pattern:/<<<(?:"([^"]+)"(?:\r\n?|\n)(?:.*(?:\r\n?|\n))*?\1;|([a-z_]\w*)(?:\r\n?|\n)(?:.*(?:\r\n?|\n))*?\2;)/i,greedy:!0,alias:"string",inside:{delimiter:{pattern:/^<<<(?:"[^"]+"|[a-z_]\w*)|[a-z_]\w*;$/i,alias:"symbol",inside:{punctuation:/^<<<"?|[";]$/}},interpolation:t}},"single-quoted-string":{pattern:/'(?:\\[\s\S]|[^\\'])*'/,greedy:!0,alias:"string"},"double-quoted-string":{pattern:/"(?:\\[\s\S]|[^\\"])*"/,greedy:!0,alias:"string",inside:{interpolation:t}}}),delete 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class="DocSearch-Button-Key">K</span></button></div></div><div role="presentation" class="navbar-sidebar__backdrop"></div><div class="navbar-sidebar"><div class="navbar-sidebar__brand"><a class="navbar__brand" href="/PSP/"><img class="navbar__logo" src="/PSP/img/logo.svg" alt="PSP-UFU logo"><strong class="navbar__title">PSP-UFU</strong></a></div><div class="navbar-sidebar__items"><div class="menu"><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" href="/PSP/docs/">User Guide</a></li><li class="menu__list-item"><a class="menu__link" href="/PSP/blog">Changelog</a></li><li class="menu__list-item"><a href="https://github.com/Thales1330/PSP" target="_blank" rel="noopener noreferrer" class="menu__link">PSP-UFU Source Code</a></li></ul></div></div></div></nav><div class="main-wrapper"><div class="container margin-vert--lg"><h1>Search the documentation</h1><form class="row"><div class="col searchQueryColumn_Sxqm col--12"><input type="search" name="q" 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diff --git a/docs/styles.187818cc.css b/docs/styles.1ab9c66d.css
similarity index 73%
rename from docs/styles.187818cc.css
rename to docs/styles.1ab9c66d.css
index 9d0591cc..30bd8d94 100644
--- a/docs/styles.187818cc.css
+++ b/docs/styles.1ab9c66d.css
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svg,.DocSearch-MagnifierLabel svg{height:24px;width:24px}.DocSearch-Cancel{display:none}.DocSearch-Dropdown{min-height:12px;min-height:var(--docsearch-spacing);max-height:488px;max-height:calc(var(--docsearch-modal-height) - var(--docsearch-searchbox-height) - var(--docsearch-spacing) - var(--docsearch-footer-height));overflow-y:auto;overflow-y:overlay;padding:0 12px;padding:0 var(--docsearch-spacing);scrollbar-color:#969faf #f5f6f7;scrollbar-color:var(--docsearch-muted-color) var(--docsearch-modal-background);scrollbar-width:thin}.DocSearch-Dropdown::-webkit-scrollbar{width:12px}.DocSearch-Dropdown::-webkit-scrollbar-track{background:transparent}.DocSearch-Dropdown::-webkit-scrollbar-thumb{background-color:#969faf;background-color:var(--docsearch-muted-color);border:3px solid #f5f6f7;border:3px solid var(--docsearch-modal-background);border-radius:20px}.DocSearch-Dropdown ul{list-style:none;margin:0;padding:0}.DocSearch-Label{font-size:.75em;line-height:1.6em}.DocSearch-Help,.DocSearch-Label{color:#969faf;color:var(--docsearch-muted-color)}.DocSearch-Help{font-size:.9em;margin:0;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none}.DocSearch-Title{font-size:1.2em}.DocSearch-Logo a{display:flex}.DocSearch-Logo svg{color:#5468ff;color:var(--docsearch-logo-color);margin-left:8px}.DocSearch-Hits:last-of-type{margin-bottom:24px}.DocSearch-Hits mark{background:none;color:#5468ff;color:var(--docsearch-highlight-color)}.DocSearch-HitsFooter{color:#969faf;color:var(--docsearch-muted-color);display:flex;font-size:.85em;justify-content:center;margin-bottom:12px;margin-bottom:var(--docsearch-spacing);padding:12px;padding:var(--docsearch-spacing)}.DocSearch-HitsFooter a{border-bottom:1px solid;color:inherit}.DocSearch-Hit{border-radius:4px;display:flex;padding-bottom:4px;position:relative}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit--deleting{transition:none}}.DocSearch-Hit--deleting{opacity:0;transition:all .25s linear}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit--favoriting{transition:none}}.DocSearch-Hit--favoriting{transform:scale(0);transform-origin:top center;transition:all .25s linear;transition-delay:.25s}.DocSearch-Hit a{background:#fff;background:var(--docsearch-hit-background);border-radius:4px;box-shadow:0 1px 3px 0 #d4d9e1;box-shadow:var(--docsearch-hit-shadow);display:block;padding-left:12px;padding-left:var(--docsearch-spacing);width:100%}.DocSearch-Hit-source{background:#f5f6f7;background:var(--docsearch-modal-background);color:#5468ff;color:var(--docsearch-highlight-color);font-size:.85em;font-weight:600;line-height:32px;margin:0 -4px;padding:8px 4px 0;position:-webkit-sticky;position:sticky;top:0;z-index:10}.DocSearch-Hit-Tree{color:#969faf;color:var(--docsearch-muted-color);height:56px;height:var(--docsearch-hit-height);opacity:.5;stroke-width:1.4;stroke-width:var(--docsearch-icon-stroke-width);width:24px}.DocSearch-Hit[aria-selected=true] a{background-color:#5468ff;background-color:var(--docsearch-highlight-color)}.DocSearch-Hit[aria-selected=true] mark{text-decoration:underline}.DocSearch-Hit-Container{align-items:center;color:#444950;color:var(--docsearch-hit-color);display:flex;flex-direction:row;height:56px;height:var(--docsearch-hit-height);padding:0 12px 0 0;padding:0 var(--docsearch-spacing) 0 0}.DocSearch-Hit-icon{height:20px;width:20px}.DocSearch-Hit-action,.DocSearch-Hit-icon{color:#969faf;color:var(--docsearch-muted-color);stroke-width:1.4;stroke-width:var(--docsearch-icon-stroke-width)}.DocSearch-Hit-action{align-items:center;display:flex;height:22px;width:22px}.DocSearch-Hit-action svg{display:block;height:18px;width:18px}.DocSearch-Hit-action+.DocSearch-Hit-action{margin-left:6px}.DocSearch-Hit-action-button{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;border-radius:50%;color:inherit;cursor:pointer;padding:2px}svg.DocSearch-Hit-Select-Icon{display:none}.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-Select-Icon{display:block}.DocSearch-Hit-action-button:focus,.DocSearch-Hit-action-button:hover{background:rgba(0,0,0,.2);transition:background-color .1s ease-in}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit-action-button:focus,.DocSearch-Hit-action-button:hover{transition:none}}.DocSearch-Hit-action-button:focus path,.DocSearch-Hit-action-button:hover path{fill:#fff}.DocSearch-Hit-content-wrapper{display:flex;flex:1 1 auto;flex-direction:column;font-weight:500;justify-content:center;line-height:1.2em;margin:0 8px;overflow-x:hidden;position:relative;text-overflow:ellipsis;white-space:nowrap;width:80%}.DocSearch-Hit-title{font-size:.9em}.DocSearch-Hit-path{color:#969faf;color:var(--docsearch-muted-color);font-size:.75em}.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-action,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-icon,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-path,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-text,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-title,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-Tree,.DocSearch-Hit[aria-selected=true] mark{color:#fff!important;color:var(--docsearch-hit-active-color)!important}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit-action-button:focus,.DocSearch-Hit-action-button:hover{background:rgba(0,0,0,.2);transition:none}}.DocSearch-ErrorScreen,.DocSearch-NoResults,.DocSearch-StartScreen{font-size:.9em;margin:0 auto;padding:36px 0;text-align:center;width:80%}.DocSearch-Screen-Icon{color:#969faf;color:var(--docsearch-muted-color);padding-bottom:12px}.DocSearch-NoResults-Prefill-List{display:inline-block;padding-bottom:24px;text-align:left}.DocSearch-NoResults-Prefill-List ul{display:inline-block;padding:8px 0 0}.DocSearch-NoResults-Prefill-List li{list-style-position:inside;list-style-type:"» "}.DocSearch-Prefill{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;border-radius:1em;color:#5468ff;color:var(--docsearch-highlight-color);cursor:pointer;display:inline-block;font-size:1em;font-weight:700;padding:0}.DocSearch-Prefill:focus,.DocSearch-Prefill:hover{outline:none;text-decoration:underline}.DocSearch-Footer{align-items:center;background:#fff;background:var(--docsearch-footer-background);border-radius:0 0 8px 8px;box-shadow:0 -1px 0 0 #e0e3e8,0 -3px 6px 0 rgba(69,98,155,.12);box-shadow:var(--docsearch-footer-shadow);display:flex;flex-direction:row-reverse;flex-shrink:0;height:44px;height:var(--docsearch-footer-height);justify-content:space-between;padding:0 12px;padding:0 var(--docsearch-spacing);position:relative;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;width:100%;z-index:300}.DocSearch-Commands{color:#969faf;color:var(--docsearch-muted-color);display:flex;list-style:none;margin:0;padding:0}.DocSearch-Commands li{align-items:center;display:flex}.DocSearch-Commands li:not(:last-of-type){margin-right:.8em}.DocSearch-Commands-Key{align-items:center;background:linear-gradient(-225deg,#d5dbe4,#f8f8f8);background:var(--docsearch-key-gradient);border-radius:2px;box-shadow:inset 0 -2px 0 0 #cdcde6,inset 0 0 1px 1px #fff,0 1px 2px 1px rgba(30,35,90,.4);box-shadow:var(--docsearch-key-shadow);display:flex;height:18px;justify-content:center;margin-right:.4em;padding-bottom:2px;width:20px}@media (max-width:750px){:root{--docsearch-spacing:10px;--docsearch-footer-height:40px}.DocSearch--active #__docusaurus{display:none}.DocSearch-Dropdown{height:100%}.DocSearch-Container{height:100vh;height:-webkit-fill-available;position:absolute}.DocSearch-Footer{border-radius:0;bottom:0;position:absolute}.DocSearch-Hit-content-wrapper{display:flex;position:relative;width:80%}.DocSearch-Modal{border-radius:0;box-shadow:none;height:100vh;height:-webkit-fill-available;margin:0;max-width:100%;width:100%}.DocSearch-Cancel{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;color:#5468ff;color:var(--docsearch-highlight-color);cursor:pointer;display:inline-block;flex:none;font:inherit;font-size:1em;font-weight:500;margin-left:12px;margin-left:var(--docsearch-spacing);outline:none;overflow:hidden;padding:0;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;white-space:nowrap}.DocSearch-Commands,.DocSearch-Hit-Tree{display:none}}@-webkit-keyframes fade-in{0%{opacity:0}to{opacity:1}}@keyframes fade-in{0%{opacity:0}to{opacity:1}}:root{--docsearch-primary-color:var(--ifm-color-primary);--docsearch-text-color:var(--ifm-font-color-base)}
\ No newline at end of file
diff --git a/docs/styles.b40f6121.js b/docs/styles.b40f6121.js
deleted file mode 100644
index a4d691a9..00000000
--- a/docs/styles.b40f6121.js
+++ /dev/null
@@ -1 +0,0 @@
-(window.webpackJsonp=window.webpackJsonp||[]).push([[0],{111:function(e,o,n){e.exports={heroBanner:"heroBanner_2Ftp",buttons:"buttons_1Wc3",features:"features_P2SU",featureImage:"featureImage_3Xqx"}},120:function(e,o,n){},25:function(e,o,n){},39:function(e,o,n){},43:function(e,o,n){},44:function(e,o,n){},47:function(e,o,n){e.exports={tabItem:"tabItem_1w39"}},48:function(e,o,n){e.exports={codeBlockContent:"codeBlockContent_1u-d",codeBlockTitle:"codeBlockTitle_3nn1",codeBlock:"codeBlock_3iAC",codeBlockWithTitle:"codeBlockWithTitle_3QsD",copyButton:"copyButton_10dd",codeBlockLines:"codeBlockLines_b7E3"}},49:function(e,o,n){},50:function(e,o,n){e.exports={enhancedAnchor:"enhancedAnchor_2cZh"}},51:function(e,o,n){e.exports={mdxCodeBlock:"mdxCodeBlock_1XEh"}},52:function(e,o,n){},53:function(e,o,n){e.exports={announcementBar:"announcementBar_1l0Z",announcementBarClose:"announcementBarClose_21wD",announcementBarContent:"announcementBarContent_1xni"}},54:function(e,o,n){e.exports={toggle:"toggle_BsTx",moon:"moon_6SPT",sun:"sun_152_"}},55:function(e,o,n){e.exports={displayOnlyInLargeViewport:"displayOnlyInLargeViewport_2aTZ",hideLogoText:"hideLogoText_GP-Q",navbarHideable:"navbarHideable_3046",navbarHidden:"navbarHidden_1Uo_"}},56:function(e,o,n){e.exports={footerLogoLink:"footerLogoLink_1zJy"}},57:function(e,o,n){},62:function(e,o,n){e.exports={searchQueryInput:"searchQueryInput_2wzZ",searchVersionInput:"searchVersionInput_onPS",searchResultsColumn:"searchResultsColumn_gCu4",searchLogoColumn:"searchLogoColumn_3CX6",algoliaLogo:"algoliaLogo_2w8o",algoliaLogoPathFill:"algoliaLogoPathFill_2lQN",searchResultItem:"searchResultItem_2Ox1",searchResultItemHeading:"searchResultItemHeading_E89F",searchResultItemPath:"searchResultItemPath_W0N5",searchResultItemSummary:"searchResultItemSummary_2EZC",searchQueryColumn:"searchQueryColumn_Sxqm",searchVersionColumn:"searchVersionColumn_2cau",loadingSpinner:"loadingSpinner_My1l",loadingspin:"loadingspin_XSpe",loader:"loader_15BX"}},65:function(e,o,n){e.exports={docTitle:"docTitle_1Lrw",docItemContainer:"docItemContainer_3QWW",docItemCol:"docItemCol_2ASc",docItemWrapper:"docItemWrapper_1EkI",tableOfContents:"tableOfContents_3klQ",docLastUpdatedAt:"docLastUpdatedAt_217_"}},66:function(e,o,n){e.exports={sidebar:"sidebar_2urC",sidebarWithHideableNavbar:"sidebarWithHideableNavbar_2IoJ",sidebarLogo:"sidebarLogo_Snse",menu:"menu_5FrY",menuLinkText:"menuLinkText_2zSB",menuWithAnnouncementBar:"menuWithAnnouncementBar_18ic",sidebarMenuIcon:"sidebarMenuIcon_Dm3K",sidebarMenuCloseIcon:"sidebarMenuCloseIcon_hir9"}},67:function(e,o,n){e.exports={docPage:"docPage_2gpo",docSidebarContainer:"docSidebarContainer_3_JD",docMainContainer:"docMainContainer_3EyW"}},84:function(e,o,n){e.exports={blogPostTitle:"blogPostTitle_1mse",blogPostDate:"blogPostDate_3bQP"}}}]);
\ No newline at end of file
diff --git a/docs/styles.f1364c44.js b/docs/styles.f1364c44.js
new file mode 100644
index 00000000..e2c34707
--- /dev/null
+++ b/docs/styles.f1364c44.js
@@ -0,0 +1 @@
+(window.webpackJsonp=window.webpackJsonp||[]).push([[0],{113:function(e,o,n){e.exports={heroBanner:"heroBanner_2Ftp",buttons:"buttons_1Wc3",features:"features_P2SU",featureImage:"featureImage_3Xqx"}},122:function(e,o,n){},15:function(e,o,n){},39:function(e,o,n){},43:function(e,o,n){},44:function(e,o,n){},47:function(e,o,n){e.exports={tabItem:"tabItem_1w39"}},48:function(e,o,n){e.exports={codeBlockContent:"codeBlockContent_1u-d",codeBlockTitle:"codeBlockTitle_3nn1",codeBlock:"codeBlock_3iAC",codeBlockWithTitle:"codeBlockWithTitle_3QsD",copyButton:"copyButton_10dd",codeBlockLines:"codeBlockLines_b7E3"}},49:function(e,o,n){},50:function(e,o,n){e.exports={enhancedAnchor:"enhancedAnchor_2cZh"}},51:function(e,o,n){e.exports={mdxCodeBlock:"mdxCodeBlock_1XEh"}},52:function(e,o,n){},53:function(e,o,n){e.exports={announcementBar:"announcementBar_1l0Z",announcementBarClose:"announcementBarClose_21wD",announcementBarContent:"announcementBarContent_1xni"}},54:function(e,o,n){e.exports={toggle:"toggle_BsTx"}},55:function(e,o,n){e.exports={displayOnlyInLargeViewport:"displayOnlyInLargeViewport_2aTZ",hideLogoText:"hideLogoText_GP-Q",navbarHideable:"navbarHideable_3046",navbarHidden:"navbarHidden_1Uo_"}},56:function(e,o,n){e.exports={footerLogoLink:"footerLogoLink_1zJy"}},57:function(e,o,n){},62:function(e,o,n){e.exports={searchQueryInput:"searchQueryInput_2wzZ",searchVersionInput:"searchVersionInput_onPS",searchResultsColumn:"searchResultsColumn_gCu4",searchLogoColumn:"searchLogoColumn_3CX6",algoliaLogo:"algoliaLogo_2w8o",algoliaLogoPathFill:"algoliaLogoPathFill_2lQN",searchResultItem:"searchResultItem_2Ox1",searchResultItemHeading:"searchResultItemHeading_E89F",searchResultItemPath:"searchResultItemPath_W0N5",searchResultItemSummary:"searchResultItemSummary_2EZC",searchQueryColumn:"searchQueryColumn_Sxqm",searchVersionColumn:"searchVersionColumn_2cau",loadingSpinner:"loadingSpinner_My1l",loadingspin:"loadingspin_XSpe",loader:"loader_15BX"}},65:function(e,o,n){e.exports={docTitle:"docTitle_1Lrw",docItemContainer:"docItemContainer_3QWW",docItemCol:"docItemCol_2ASc",docItemWrapper:"docItemWrapper_1EkI",tableOfContents:"tableOfContents_3klQ",docLastUpdatedAt:"docLastUpdatedAt_217_"}},66:function(e,o,n){e.exports={sidebar:"sidebar_2urC",sidebarWithHideableNavbar:"sidebarWithHideableNavbar_2IoJ",sidebarLogo:"sidebarLogo_Snse",menu:"menu_5FrY",menuLinkText:"menuLinkText_2zSB",menuWithAnnouncementBar:"menuWithAnnouncementBar_18ic",sidebarMenuIcon:"sidebarMenuIcon_Dm3K",sidebarMenuCloseIcon:"sidebarMenuCloseIcon_hir9"}},67:function(e,o,n){e.exports={docPage:"docPage_2gpo",docSidebarContainer:"docSidebarContainer_3_JD",docMainContainer:"docMainContainer_3EyW"}},85:function(e,o,n){e.exports={blogPostTitle:"blogPostTitle_1mse",blogPostDate:"blogPostDate_3bQP"}}}]);
\ No newline at end of file
diff --git a/docs/videos/heatmap.kdenlive b/docs/videos/heatmap.kdenlive
new file mode 100644
index 00000000..79fe2ca6
--- /dev/null
+++ b/docs/videos/heatmap.kdenlive
@@ -0,0 +1,406 @@
+<?xml version='1.0' encoding='utf-8'?>
+<mlt LC_NUMERIC="pt_BR" producer="main_bin" version="6.21.0" root="C:/Users/thale/Documents/GitHub/PSP/docusaurus/static/videos">
+ <profile frame_rate_num="30" sample_aspect_num="1" display_aspect_den="1080" colorspace="601" progressive="1" description="1920x1080 30.00fps" display_aspect_num="1920" frame_rate_den="1" width="1920" height="1080" sample_aspect_den="1"/>
+ <producer id="producer0" in="00:00:00,000" out="00:00:22,000">
+  <property name="length">661</property>
+  <property name="eof">pause</property>
+  <property name="resource">C:/Users/thale/Videos/2020-08-01 17-10-55.mkv</property>
+  <property name="audio_index">1</property>
+  <property name="video_index">0</property>
+  <property name="mute_on_pause">0</property>
+  <property name="mlt_service">avformat-novalidate</property>
+  <property name="seekable">1</property>
+  <property name="aspect_ratio">1</property>
+  <property name="kdenlive:clipname"/>
+  <property name="kdenlive:folderid">-1</property>
+  <property name="kdenlive:id">2</property>
+  <property name="kdenlive:file_size">6998585</property>
+  <property name="kdenlive:file_hash">ae822e60d4e2248265daaa3d21841b38</property>
+  <property name="global_feed">1</property>
+  <property name="meta.media.nb_streams">2</property>
+  <property name="meta.media.0.stream.type">video</property>
+  <property name="meta.media.0.stream.frame_rate">30</property>
+  <property name="meta.media.0.stream.sample_aspect_ratio">0</property>
+  <property name="meta.media.0.codec.width">1920</property>
+  <property name="meta.media.0.codec.height">1080</property>
+  <property name="meta.media.0.codec.rotate">0</property>
+  <property name="meta.media.0.codec.frame_rate">30</property>
+  <property name="meta.media.0.codec.pix_fmt">yuv420p</property>
+  <property name="meta.media.0.codec.sample_aspect_ratio">1</property>
+  <property name="meta.media.0.codec.colorspace">601</property>
+  <property name="meta.media.0.codec.name">h264</property>
+  <property name="meta.media.0.codec.long_name">H.264 / AVC / MPEG-4 AVC / MPEG-4 part 10</property>
+  <property name="meta.media.0.codec.bit_rate">0</property>
+  <property name="meta.attr.0.stream.DURATION.markup">00:00:22.033000000</property>
+  <property name="meta.media.1.stream.type">audio</property>
+  <property name="meta.media.1.codec.sample_fmt">fltp</property>
+  <property name="meta.media.1.codec.sample_rate">44100</property>
+  <property name="meta.media.1.codec.channels">2</property>
+  <property name="meta.media.1.codec.name">aac</property>
+  <property name="meta.media.1.codec.long_name">AAC (Advanced Audio Coding)</property>
+  <property name="meta.media.1.codec.bit_rate">0</property>
+  <property name="meta.attr.1.stream.title.markup">simple_aac</property>
+  <property name="meta.attr.1.stream.DURATION.markup">00:00:21.989000000</property>
+  <property name="meta.attr.ENCODER.markup">Lavf58.29.100</property>
+  <property name="meta.media.sample_aspect_num">1</property>
+  <property name="meta.media.sample_aspect_den">1</property>
+  <property name="meta.media.frame_rate_num">30</property>
+  <property name="meta.media.frame_rate_den">1</property>
+  <property name="meta.media.colorspace">601</property>
+  <property name="meta.media.color_trc">2</property>
+  <property name="meta.media.width">1920</property>
+  <property name="meta.media.height">1080</property>
+  <property name="meta.media.color_range">mpeg</property>
+  <property name="meta.media.top_field_first">0</property>
+  <property name="meta.media.progressive">1</property>
+ </producer>
+ <playlist id="main_bin">
+  <property name="kdenlive:docproperties.activeTrack">2</property>
+  <property name="kdenlive:docproperties.audioTarget">1</property>
+  <property name="kdenlive:docproperties.decimalPoint">,</property>
+  <property name="kdenlive:docproperties.disablepreview">0</property>
+  <property name="kdenlive:docproperties.documentid">1596312714884</property>
+  <property name="kdenlive:docproperties.enableTimelineZone">0</property>
+  <property name="kdenlive:docproperties.enableexternalproxy">0</property>
+  <property name="kdenlive:docproperties.enableproxy">0</property>
+  <property name="kdenlive:docproperties.externalproxyparams">../Sub;;S03.MP4;../Clip;;.MXF</property>
+  <property name="kdenlive:docproperties.generateimageproxy">0</property>
+  <property name="kdenlive:docproperties.generateproxy">0</property>
+  <property name="kdenlive:docproperties.kdenliveversion">20.04.1</property>
+  <property name="kdenlive:docproperties.position">321</property>
+  <property name="kdenlive:docproperties.previewextension"/>
+  <property name="kdenlive:docproperties.previewparameters"/>
+  <property name="kdenlive:docproperties.profile">C:/Users/thale/AppData/Roaming/kdenlive/profiles/customprofile0</property>
+  <property name="kdenlive:docproperties.proxyextension"/>
+  <property name="kdenlive:docproperties.proxyimageminsize">2000</property>
+  <property name="kdenlive:docproperties.proxyimagesize">800</property>
+  <property name="kdenlive:docproperties.proxyminsize">1000</property>
+  <property name="kdenlive:docproperties.proxyparams"/>
+  <property name="kdenlive:docproperties.scrollPos">0</property>
+  <property name="kdenlive:docproperties.seekOffset">30000</property>
+  <property name="kdenlive:docproperties.version">0.99</property>
+  <property name="kdenlive:docproperties.verticalzoom">1</property>
+  <property name="kdenlive:docproperties.videoTarget">2</property>
+  <property name="kdenlive:docproperties.zonein">0</property>
+  <property name="kdenlive:docproperties.zoneout">75</property>
+  <property name="kdenlive:docproperties.zoom">8</property>
+  <property name="kdenlive:documentnotes"/>
+  <property name="kdenlive:docproperties.groups">[
+    {
+        "children": [
+            {
+                "data": "2:0",
+                "leaf": "clip",
+                "type": "Leaf"
+            },
+            {
+                "data": "1:0",
+                "leaf": "clip",
+                "type": "Leaf"
+            }
+        ],
+        "type": "AVSplit"
+    }
+]
+</property>
+  <property name="kdenlive:docproperties.renderaudioquality">192</property>
+  <property name="kdenlive:docproperties.rendercategory">Generic (HD for web, mobile devices...)</property>
+  <property name="kdenlive:docproperties.renderendguide">-1</property>
+  <property name="kdenlive:docproperties.renderexportaudio">0</property>
+  <property name="kdenlive:docproperties.renderfield">0</property>
+  <property name="kdenlive:docproperties.renderguide">0</property>
+  <property name="kdenlive:docproperties.renderplay">0</property>
+  <property name="kdenlive:docproperties.renderprofile">MP4 - the dominating format (H264/AAC)</property>
+  <property name="kdenlive:docproperties.renderquality">23</property>
+  <property name="kdenlive:docproperties.renderratio">1</property>
+  <property name="kdenlive:docproperties.renderrescale">0</property>
+  <property name="kdenlive:docproperties.renderrescaleheight">540</property>
+  <property name="kdenlive:docproperties.renderrescalewidth">960</property>
+  <property name="kdenlive:docproperties.renderscanning">0</property>
+  <property name="kdenlive:docproperties.renderspeed">2</property>
+  <property name="kdenlive:docproperties.renderstartguide">-1</property>
+  <property name="kdenlive:docproperties.rendertcoverlay">0</property>
+  <property name="kdenlive:docproperties.rendertctype">0</property>
+  <property name="kdenlive:docproperties.rendertwopass">0</property>
+  <property name="kdenlive:docproperties.renderurl">heatmap.mp4</property>
+  <property name="kdenlive:docproperties.renderzone">0</property>
+  <property name="xml_retain">1</property>
+  <entry producer="producer0" in="00:00:00,000" out="00:00:22,000"/>
+ </playlist>
+ <producer id="black_track" in="00:00:00,000" out="00:16:50,700">
+  <property name="length">2147483647</property>
+  <property name="eof">continue</property>
+  <property name="resource">black</property>
+  <property name="aspect_ratio">1</property>
+  <property name="mlt_service">color</property>
+  <property name="mlt_image_format">rgb24a</property>
+  <property name="set.test_audio">0</property>
+ </producer>
+ <playlist id="playlist0">
+  <property name="kdenlive:audio_track">1</property>
+ </playlist>
+ <playlist id="playlist1">
+  <property name="kdenlive:audio_track">1</property>
+ </playlist>
+ <tractor id="tractor0" in="00:00:00,000">
+  <property name="kdenlive:audio_track">1</property>
+  <property name="kdenlive:trackheight">67</property>
+  <property name="kdenlive:collapsed">0</property>
+  <property name="kdenlive:thumbs_format"/>
+  <property name="kdenlive:audio_rec"/>
+  <property name="kdenlive:timeline_active">1</property>
+  <track hide="video" producer="playlist0"/>
+  <track hide="video" producer="playlist1"/>
+  <filter id="filter0">
+   <property name="window">75</property>
+   <property name="max_gain">20dB</property>
+   <property name="mlt_service">volume</property>
+   <property name="internal_added">237</property>
+   <property name="disable">1</property>
+  </filter>
+  <filter id="filter1">
+   <property name="channel">-1</property>
+   <property name="mlt_service">panner</property>
+   <property name="internal_added">237</property>
+   <property name="start">0,5</property>
+   <property name="disable">1</property>
+  </filter>
+  <filter id="filter2">
+   <property name="iec_scale">0</property>
+   <property name="mlt_service">audiolevel</property>
+   <property name="disable">1</property>
+  </filter>
+ </tractor>
+ <producer id="producer1" in="00:00:00,000" out="00:00:10,967">
+  <property name="length">331</property>
+  <property name="eof">pause</property>
+  <property name="resource">2,000000:C:/Users/thale/Videos/2020-08-01 17-10-55.mkv</property>
+  <property name="aspect_ratio">1</property>
+  <property name="meta.media.nb_streams">2</property>
+  <property name="meta.media.0.stream.type">video</property>
+  <property name="meta.media.0.stream.frame_rate">30</property>
+  <property name="meta.media.0.stream.sample_aspect_ratio">0</property>
+  <property name="meta.media.0.codec.width">1920</property>
+  <property name="meta.media.0.codec.height">1080</property>
+  <property name="meta.media.0.codec.rotate">0</property>
+  <property name="meta.media.0.codec.frame_rate">30</property>
+  <property name="meta.media.0.codec.pix_fmt">yuv420p</property>
+  <property name="meta.media.0.codec.sample_aspect_ratio">1</property>
+  <property name="meta.media.0.codec.colorspace">601</property>
+  <property name="meta.media.0.codec.name">h264</property>
+  <property name="meta.media.0.codec.long_name">H.264 / AVC / MPEG-4 AVC / MPEG-4 part 10</property>
+  <property name="meta.media.0.codec.bit_rate">0</property>
+  <property name="meta.attr.0.stream.DURATION.markup">00:00:22.033000000</property>
+  <property name="meta.media.1.stream.type">audio</property>
+  <property name="meta.media.1.codec.sample_fmt">fltp</property>
+  <property name="meta.media.1.codec.sample_rate">44100</property>
+  <property name="meta.media.1.codec.channels">2</property>
+  <property name="meta.media.1.codec.name">aac</property>
+  <property name="meta.media.1.codec.long_name">AAC (Advanced Audio Coding)</property>
+  <property name="meta.media.1.codec.bit_rate">0</property>
+  <property name="meta.attr.1.stream.title.markup">simple_aac</property>
+  <property name="meta.attr.1.stream.DURATION.markup">00:00:21.989000000</property>
+  <property name="meta.attr.ENCODER.markup">Lavf58.29.100</property>
+  <property name="seekable">1</property>
+  <property name="meta.media.sample_aspect_num">1</property>
+  <property name="meta.media.sample_aspect_den">1</property>
+  <property name="audio_index">1</property>
+  <property name="video_index">0</property>
+  <property name="mute_on_pause">1</property>
+  <property name="warp_speed">2</property>
+  <property name="warp_resource">C:/Users/thale/Videos/2020-08-01 17-10-55.mkv</property>
+  <property name="mlt_service">timewarp</property>
+  <property name="set.test_audio">0</property>
+  <property name="set.test_image">1</property>
+  <property name="warp_pitch">0</property>
+  <property name="meta.media.frame_rate_num">30</property>
+  <property name="meta.media.frame_rate_den">1</property>
+  <property name="meta.media.colorspace">601</property>
+  <property name="meta.media.color_trc">2</property>
+  <property name="meta.media.width">1920</property>
+  <property name="meta.media.height">1080</property>
+  <property name="meta.media.color_range">mpeg</property>
+ </producer>
+ <playlist id="playlist2">
+  <property name="kdenlive:audio_track">1</property>
+  <entry producer="producer1" in="00:00:00,000" out="00:00:10,667">
+   <property name="kdenlive:id">2</property>
+  </entry>
+ </playlist>
+ <playlist id="playlist3">
+  <property name="kdenlive:audio_track">1</property>
+ </playlist>
+ <tractor id="tractor1" in="00:00:00,000" out="00:00:10,667">
+  <property name="kdenlive:audio_track">1</property>
+  <property name="kdenlive:trackheight">67</property>
+  <property name="kdenlive:collapsed">0</property>
+  <property name="kdenlive:thumbs_format"/>
+  <property name="kdenlive:audio_rec"/>
+  <property name="kdenlive:timeline_active">1</property>
+  <track hide="video" producer="playlist2"/>
+  <track hide="video" producer="playlist3"/>
+  <filter id="filter3">
+   <property name="window">75</property>
+   <property name="max_gain">20dB</property>
+   <property name="mlt_service">volume</property>
+   <property name="internal_added">237</property>
+   <property name="disable">1</property>
+  </filter>
+  <filter id="filter4">
+   <property name="channel">-1</property>
+   <property name="mlt_service">panner</property>
+   <property name="internal_added">237</property>
+   <property name="start">0,5</property>
+   <property name="disable">1</property>
+  </filter>
+  <filter id="filter5">
+   <property name="iec_scale">0</property>
+   <property name="mlt_service">audiolevel</property>
+   <property name="disable">1</property>
+  </filter>
+ </tractor>
+ <producer id="producer2" in="00:00:00,000" out="00:00:10,967">
+  <property name="length">331</property>
+  <property name="eof">pause</property>
+  <property name="resource">2,000000:C:/Users/thale/Videos/2020-08-01 17-10-55.mkv</property>
+  <property name="aspect_ratio">1</property>
+  <property name="meta.media.nb_streams">2</property>
+  <property name="meta.media.0.stream.type">video</property>
+  <property name="meta.media.0.stream.frame_rate">30</property>
+  <property name="meta.media.0.stream.sample_aspect_ratio">0</property>
+  <property name="meta.media.0.codec.width">1920</property>
+  <property name="meta.media.0.codec.height">1080</property>
+  <property name="meta.media.0.codec.rotate">0</property>
+  <property name="meta.media.0.codec.frame_rate">30</property>
+  <property name="meta.media.0.codec.pix_fmt">yuv420p</property>
+  <property name="meta.media.0.codec.sample_aspect_ratio">1</property>
+  <property name="meta.media.0.codec.colorspace">601</property>
+  <property name="meta.media.0.codec.name">h264</property>
+  <property name="meta.media.0.codec.long_name">H.264 / AVC / MPEG-4 AVC / MPEG-4 part 10</property>
+  <property name="meta.media.0.codec.bit_rate">0</property>
+  <property name="meta.attr.0.stream.DURATION.markup">00:00:22.033000000</property>
+  <property name="meta.media.1.stream.type">audio</property>
+  <property name="meta.media.1.codec.sample_fmt">fltp</property>
+  <property name="meta.media.1.codec.sample_rate">44100</property>
+  <property name="meta.media.1.codec.channels">2</property>
+  <property name="meta.media.1.codec.name">aac</property>
+  <property name="meta.media.1.codec.long_name">AAC (Advanced Audio Coding)</property>
+  <property name="meta.media.1.codec.bit_rate">0</property>
+  <property name="meta.attr.1.stream.title.markup">simple_aac</property>
+  <property name="meta.attr.1.stream.DURATION.markup">00:00:21.989000000</property>
+  <property name="meta.attr.ENCODER.markup">Lavf58.29.100</property>
+  <property name="seekable">1</property>
+  <property name="meta.media.sample_aspect_num">1</property>
+  <property name="meta.media.sample_aspect_den">1</property>
+  <property name="audio_index">1</property>
+  <property name="video_index">0</property>
+  <property name="mute_on_pause">1</property>
+  <property name="warp_speed">2</property>
+  <property name="warp_resource">C:/Users/thale/Videos/2020-08-01 17-10-55.mkv</property>
+  <property name="mlt_service">timewarp</property>
+  <property name="set.test_audio">1</property>
+  <property name="set.test_image">0</property>
+  <property name="warp_pitch">0</property>
+  <property name="meta.media.frame_rate_num">30</property>
+  <property name="meta.media.frame_rate_den">1</property>
+  <property name="meta.media.colorspace">601</property>
+  <property name="meta.media.color_trc">2</property>
+  <property name="meta.media.width">1920</property>
+  <property name="meta.media.height">1080</property>
+  <property name="meta.media.color_range">mpeg</property>
+  <property name="meta.media.top_field_first">0</property>
+  <property name="meta.media.progressive">1</property>
+ </producer>
+ <playlist id="playlist4">
+  <entry producer="producer2" in="00:00:00,000" out="00:00:10,667">
+   <property name="kdenlive:id">2</property>
+  </entry>
+ </playlist>
+ <playlist id="playlist5"/>
+ <tractor id="tractor2" in="00:00:00,000" out="00:00:10,667">
+  <property name="kdenlive:trackheight">67</property>
+  <property name="kdenlive:collapsed">0</property>
+  <property name="kdenlive:thumbs_format"/>
+  <property name="kdenlive:audio_rec"/>
+  <property name="kdenlive:timeline_active">1</property>
+  <track hide="audio" producer="playlist4"/>
+  <track hide="audio" producer="playlist5"/>
+ </tractor>
+ <playlist id="playlist6"/>
+ <playlist id="playlist7"/>
+ <tractor id="tractor3" in="00:00:00,000">
+  <property name="kdenlive:trackheight">67</property>
+  <property name="kdenlive:collapsed">0</property>
+  <property name="kdenlive:thumbs_format"/>
+  <property name="kdenlive:audio_rec"/>
+  <property name="kdenlive:timeline_active">1</property>
+  <track hide="audio" producer="playlist6"/>
+  <track hide="audio" producer="playlist7"/>
+ </tractor>
+ <tractor id="tractor4" global_feed="1" in="00:00:00,000" out="00:16:50,700">
+  <track producer="black_track"/>
+  <track producer="tractor0"/>
+  <track producer="tractor1"/>
+  <track producer="tractor2"/>
+  <track producer="tractor3"/>
+  <transition id="transition0">
+   <property name="a_track">0</property>
+   <property name="b_track">1</property>
+   <property name="mlt_service">mix</property>
+   <property name="kdenlive_id">mix</property>
+   <property name="internal_added">237</property>
+   <property name="always_active">1</property>
+   <property name="sum">1</property>
+  </transition>
+  <transition id="transition1">
+   <property name="a_track">0</property>
+   <property name="b_track">2</property>
+   <property name="mlt_service">mix</property>
+   <property name="kdenlive_id">mix</property>
+   <property name="internal_added">237</property>
+   <property name="always_active">1</property>
+   <property name="sum">1</property>
+  </transition>
+  <transition id="transition2">
+   <property name="a_track">0</property>
+   <property name="b_track">3</property>
+   <property name="compositing">0</property>
+   <property name="distort">0</property>
+   <property name="rotate_center">0</property>
+   <property name="mlt_service">qtblend</property>
+   <property name="kdenlive_id">qtblend</property>
+   <property name="internal_added">237</property>
+   <property name="always_active">1</property>
+  </transition>
+  <transition id="transition3">
+   <property name="a_track">0</property>
+   <property name="b_track">4</property>
+   <property name="compositing">0</property>
+   <property name="distort">0</property>
+   <property name="rotate_center">0</property>
+   <property name="mlt_service">qtblend</property>
+   <property name="kdenlive_id">qtblend</property>
+   <property name="internal_added">237</property>
+   <property name="always_active">1</property>
+  </transition>
+  <filter id="filter6">
+   <property name="window">75</property>
+   <property name="max_gain">20dB</property>
+   <property name="mlt_service">volume</property>
+   <property name="internal_added">237</property>
+   <property name="disable">1</property>
+  </filter>
+  <filter id="filter7">
+   <property name="channel">-1</property>
+   <property name="mlt_service">panner</property>
+   <property name="internal_added">237</property>
+   <property name="start">0,5</property>
+   <property name="disable">1</property>
+  </filter>
+  <filter id="filter8">
+   <property name="iec_scale">0</property>
+   <property name="mlt_service">audiolevel</property>
+   <property name="disable">1</property>
+  </filter>
+ </tractor>
+</mlt>
diff --git a/docs/videos/heatmap.mp4 b/docs/videos/heatmap.mp4
new file mode 100644
index 00000000..b5dd309c
Binary files /dev/null and b/docs/videos/heatmap.mp4 differ
diff --git a/docs/videos/heatmap.webm b/docs/videos/heatmap.webm
new file mode 100644
index 00000000..e3186c55
Binary files /dev/null and b/docs/videos/heatmap.webm differ
diff --git a/docusaurus/blog/2019-10-13-2019w42a-beta.md b/docusaurus/blog/2019-10-13-2019w42a-beta.md
index 201d25e9..6fd385b9 100644
--- a/docusaurus/blog/2019-10-13-2019w42a-beta.md
+++ b/docusaurus/blog/2019-10-13-2019w42a-beta.md
@@ -8,7 +8,7 @@ author_image_url: https://avatars0.githubusercontent.com/u/16141330?s=460&v=4
 tags: [psp-ufu]
 ---
 
-- Harmonic study implemented;
-- Autolayout from importation implemented;
-- Importation of Matpower files;
-- Several minor bugfixes.
\ No newline at end of file
+- 🔥 Harmonic study implemented;
+- 🔥 Autolayout from importation implemented;
+- 🔥 Importation of Matpower files;
+- 🐛 Several minor bugfixes.
\ No newline at end of file
diff --git a/docusaurus/blog/2019-11-01-2019w44a-beta.md b/docusaurus/blog/2019-11-01-2019w44a-beta.md
index 3e0b3a9f..5e38a3d5 100644
--- a/docusaurus/blog/2019-11-01-2019w44a-beta.md
+++ b/docusaurus/blog/2019-11-01-2019w44a-beta.md
@@ -8,5 +8,5 @@ author_image_url: https://avatars0.githubusercontent.com/u/16141330?s=460&v=4
 tags: [psp-ufu]
 ---
 
-- Minor changes to 32bit MSW version for compatibility;
-- Travis CI (Continuous Integration) implemented (Linux).
\ No newline at end of file
+- ✔️ Minor changes to 32bit MSW version for compatibility;
+- ✔️ Travis CI (Continuous Integration) implemented (Linux).
\ No newline at end of file
diff --git a/docusaurus/blog/2020-06-13-2020w24a-beta.md b/docusaurus/blog/2020-06-13-2020w24a-beta.md
index e06e0bfa..4511f206 100644
--- a/docusaurus/blog/2020-06-13-2020w24a-beta.md
+++ b/docusaurus/blog/2020-06-13-2020w24a-beta.md
@@ -8,6 +8,6 @@ author_image_url: https://avatars0.githubusercontent.com/u/16141330?s=460&v=4
 tags: [psp-ufu]
 ---
 
-- Device context render implemented (to avoid use OpenGL - some machines can't use it properly);
-- Added Visual Studio solution to the GitHub project;
-- Several major and minor bugfixes.
\ No newline at end of file
+- ✔️ Device context render implemented (to avoid use OpenGL - some machines can't use it properly);
+- ✔️ Added Visual Studio solution to the GitHub project;
+- 🐛 Several major and minor bugfixes.
\ No newline at end of file
diff --git a/docusaurus/blog/2020-07-09-2020w28a-beta.md b/docusaurus/blog/2020-07-09-2020w28a-beta.md
index b74d4c62..2440de49 100644
--- a/docusaurus/blog/2020-07-09-2020w28a-beta.md
+++ b/docusaurus/blog/2020-07-09-2020w28a-beta.md
@@ -8,5 +8,5 @@ author_image_url: https://avatars0.githubusercontent.com/u/16141330?s=460&v=4
 tags: [psp-ufu]
 ---
 
-- Voltage heatmap implemented (OpenGL enabled);
-- Several major and minor bugfixes.
\ No newline at end of file
+- 🔥 Voltage heatmap implemented (OpenGL enabled);
+- 🐛 Several major and minor bugfixes.
\ No newline at end of file
diff --git a/docusaurus/blog/2020-08-01-2020w31a-beta.md b/docusaurus/blog/2020-08-01-2020w31a-beta.md
new file mode 100644
index 00000000..1f10f66b
--- /dev/null
+++ b/docusaurus/blog/2020-08-01-2020w31a-beta.md
@@ -0,0 +1,14 @@
+---
+id: 2020w31a-beta
+title: 2020w31a-beta
+author: Thales
+author_title: PhD
+author_url: https://github.com/thales1330
+author_image_url: https://avatars0.githubusercontent.com/u/16141330?s=460&v=4
+tags: [psp-ufu]
+---
+
+- 🔥 PSP-UFU online user guide finally written (only in Brazilian Portuguese, if you want to help me translate this guide, contact-me on [GitHub](https://github.com/Thales1330/PSP/issues) or [Twitter](https://twitter.com/PspUfu));
+- ✔️ New fancy [PSP-UFU website](https://thales1330.github.io/PSP/) and [changelog](https://thales1330.github.io/PSP/blog) using [docusaurus](https://v2.docusaurus.io/);
+- ✔️ Text element performance improved for OpenGL render;
+- 🐛 Several major and minor bug fixes.
\ No newline at end of file
diff --git a/docusaurus/docs/cadTools.md b/docusaurus/docs/cadTools.md
index c741ba8c..e26737bc 100644
--- a/docusaurus/docs/cadTools.md
+++ b/docusaurus/docs/cadTools.md
@@ -31,7 +31,7 @@ Mantendo pressionado a tecla Control (Ctrl) do teclado pode-se manter seleções
 
 Para desmarcar todos os objetos basta clicar em uma área sem objetos.
 
-<video autoPlay loop muted controls>
+<video autoPlay loop muted playsInline controls>
   <source src= {useBaseUrl("videos/select.mp4")} type="video/mp4" />
   <source src= {useBaseUrl("videos/select.webm")} type="video/webm" />
 </video>
@@ -41,7 +41,7 @@ Um elemento poderá ser movido para qualquer local por meio da ação *drag-and-
 
 Ao habilitar o “modo mover”, movendo todos os componentes selecionados à medida que a posição do mouse é alterada. Para desabilitar esse modo basta pressionar a tecla Escape do teclado.
 
-<video autoPlay loop muted controls>
+<video autoPlay loop muted playsInline controls>
   <source src= {useBaseUrl("videos/move.mp4")} type="video/mp4" />
   <source src= {useBaseUrl("videos/move.webm")} type="video/webm" />
 </video>
@@ -55,7 +55,7 @@ O menu de contexto somente será exibido se o elemento estiver selecionado.
 
 Ao utilizar essa ferramenta os objetos irão girar 45º a partir do seu ponto de origem. Para atingir a angulação pretendida basta repetir o processo de rotação.
 
-<video autoPlay loop muted controls>
+<video autoPlay loop muted playsInline controls>
   <source src= {useBaseUrl("videos/rotate.mp4")} type="video/mp4" />
   <source src= {useBaseUrl("videos/rotate.webm")} type="video/webm" />
 </video>
@@ -67,7 +67,7 @@ A ferramenta arrastar possibilita mover todo o circuito **preservando as posiç
 
 Para sair do “modo arrastar” basta pressionar a tecla Escape do teclado.
 
-<video autoPlay loop muted controls>
+<video autoPlay loop muted playsInline controls>
   <source src= {useBaseUrl("videos/drag.mp4")} type="video/mp4" />
   <source src= {useBaseUrl("videos/drag.webm")} type="video/webm" />
 </video>
@@ -75,7 +75,7 @@ Para sair do “modo arrastar” basta pressionar a tecla Escape do teclado.
 ### Zoom
 O zoom será aplicado ao utilizar o **scroll do mouse** para mais ou menos zoom. A ferramenta zoom irá aproximar ou distanciar o circuito a partir da posição do ponteiro do mouse na tela para encontrar objetos ou destaca-los.
 
-<video autoPlay loop muted controls>
+<video autoPlay loop muted playsInline controls>
   <source src= {useBaseUrl("videos/zoom.mp4")} type="video/mp4" />
   <source src= {useBaseUrl("videos/zoom.webm")} type="video/webm" />
 </video>
@@ -83,7 +83,7 @@ O zoom será aplicado ao utilizar o **scroll do mouse** para mais ou menos zoom.
 ### Encaixar
 A ferramenta encaixar irá mover o circuito e aplicar o zoom necessário para que todos os componentes da rede sejam exibidos na tela. Esta ferramenta pode ser acessada através do submenu “Ferramentas” ou pela combinação de teclas “Shift + F”.
 
-<video autoPlay loop muted controls>
+<video autoPlay loop muted playsInline controls>
   <source src= {useBaseUrl("videos/fit.mp4")} type="video/mp4" />
   <source src= {useBaseUrl("videos/fit.webm")} type="video/webm" />
 </video>
@@ -93,7 +93,7 @@ Duas ferramentas importantes durante o processo de criação da rede elétrica d
 
 Para copiar basta selecionar os elementos que se deseja duplicar e acessar a ferramenta no submenu “Ferramentas” ou pressionando a combinação das teclas “Ctrl + C”, então os dados do circuito serão copiados para a área de transferência. Ao copiar um circuito ele poderá ser colado no mesmo projeto ou em um projeto distinto, utilizando o mesmo submenu ou pressionando a combinação das teclas “Ctrl + V”.
 
-<video autoPlay loop muted controls>
+<video autoPlay loop muted playsInline controls>
   <source src= {useBaseUrl("videos/copyPaste.mp4")} type="video/mp4" />
   <source src= {useBaseUrl("videos/copyPaste.webm")} type="video/webm" />
 </video>
@@ -101,7 +101,7 @@ Para copiar basta selecionar os elementos que se deseja duplicar e acessar a fer
 ### Excluir
 Qualquer objeto poderá ser excluído do projeto por meio da ferramenta deletar, presente no menu Ribbon, pela tecla de atalho Delete ou pelo acesso ao menu de contexto clicando com o botão direito sobre o elemento selecionado.
 
-<video autoPlay loop muted controls>
+<video autoPlay loop muted playsInline controls>
   <source src= {useBaseUrl("videos/delete.mp4")} type="video/mp4" />
   <source src= {useBaseUrl("videos/delete.webm")} type="video/webm" />
 </video>
@@ -120,7 +120,7 @@ Após a sua inserção, novos nós podem ser anexados pelo menu de contexto aces
 
 Assim como nos barramentos, a alteração da posição dos nós é obtida clicando e arrastando o *pickbox* exibido ao posicionar o ponteiro do mouse sobre esse elemento selecionado.
 
-<video autoPlay loop muted controls>
+<video autoPlay loop muted playsInline controls>
   <source src= {useBaseUrl("videos/graphicPropsChange.mp4")} type="video/mp4" />
   <source src= {useBaseUrl("videos/graphicPropsChange.webm")} type="video/webm" />
 </video>
@@ -138,7 +138,7 @@ No caso de desconexão, o elemento será automaticamente removido da simulação
 Ao reconectar o elemento ao circuito, deve-se **atentar para estado do seu "disjuntor"**, indicado por um quadrado próximo ao seu nó de conexão. Um elemento reconectado volta ao circuito com seu disjuntor aberto (<Highlight color="#ff1919">vermelho</Highlight>), sendo necessário clicar sobre o mesmo a fim de inserir o elemento no circuito.
 :::
 
-<video autoPlay loop muted controls>
+<video autoPlay loop muted playsInline controls>
   <source src= {useBaseUrl("videos/disconnect.mp4")} type="video/mp4" />
   <source src= {useBaseUrl("videos/disconnect.webm")} type="video/webm" />
 </video>
\ No newline at end of file
diff --git a/docusaurus/docs/controlEditor.md b/docusaurus/docs/controlEditor.md
index c27ac87b..6be6e71a 100644
--- a/docusaurus/docs/controlEditor.md
+++ b/docusaurus/docs/controlEditor.md
@@ -30,7 +30,7 @@ Uma vez que o usuário clicar no ícone desejado, o elemento de controle acompan
 
 As ferramentas de manipulação e navegação, como arrastar, mover e excluir são [herdadas](cadTools) do [editor de elementos de potência](powerEditor), possuindo comportamento idêntico. A **edição dos dados** dos componentes inseridos também é realizada com **duplo clique** sobre o elemento inserido, exibindo um formulário de edição de dados.
 
-<video autoPlay loop muted controls>
+<video autoPlay loop muted playsInline controls>
   <source src= "/PSP/videos/timelapseControlEditor.mp4" type="video/mp4" />
   <source src= "/PSP/videos/timelapseControlEditor.webm" type="video/webm" />
 </video>
diff --git a/docusaurus/docs/graphViewer.md b/docusaurus/docs/graphViewer.md
index 5498f9a3..952e2522 100644
--- a/docusaurus/docs/graphViewer.md
+++ b/docusaurus/docs/graphViewer.md
@@ -5,4 +5,39 @@ sidebar_label: Visualizador de Gráficos
 ---
 import useBaseUrl from "@docusaurus/useBaseUrl";
 
-<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
\ No newline at end of file
+<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
+
+Para exibição dos resultados originados dos cálculos de [estabilidade](stability) e [varredura de frequências](harmonics), desenvolveu-se um visualizador de gráficos, como mostra a figura abaixo:
+
+<div><center><img src={useBaseUrl("images/graphViewer.png")} alt="Visualizador de gráficos do PSP-UFU" title="Visualizador de gráficos do PSP-UFU" /></center></div>
+
+## Criação, manipulação e navegação de curvas
+Tal visualizador utiliza a biblioteca [wxMathPlot](https://wxmathplot.sourceforge.io/), e permite ao usuário imprimir todas as curvas no tempo originadas dos resultados de [estabilidade](stability) e [varredura de frequências](harmonics), acessados em dados hierárquicos em forma de árvore, identificados pelo tipo e nome do elemento de potência, além do tipo de curva.
+
+:::info Informação
+As curvas podem ser plotadas com **clique duplo** sobre ela ou ao selecionar a caixa "Plotar" nas propriedades do traço.
+:::
+
+Os gráficos impressos podem ser caracterizados pela edição de suas propriedades do traço, ou seja, pode-se alterar a cor, espessura e tipo de traço (seis tipos disponíveis). Por padrão o eixo vertical é o tempo (em estabilidade) ou frequência (varredura de frequências), porém o usuário pode alterar para qualquer curva disponível.
+
+Várias propriedades gerais do gráfico podem ser editadas: título do gráfico, rótulos dos eixos x e y, margens e limites inferiores e superiores de ambos os eixos.
+
+O menu **Visualização** permite a inserção de exibição de legenda, linhas de grade e coordenadas do ponteiro do mouse (utilizada para destacar pontos na curva), além da possibilidade de alternar o tema de impressão entre escuro e claro, facilitando a visualização ou exportação do gráfico.
+
+No menu **Arquivo**, pode-se salvar o gráfico na forma de imagem (*.png*, *.jpg* ou *.bmp*) ou enviá-lo diretamente para a área de transferência. No mesmo menu também é permitido a exportação no formato *[CSV (Comma-separated Values)](https://en.wikipedia.org/wiki/Comma-separated_values)*, o qual poderá ser utilizado em outros visualizadores de gráficos, como o Excel ou o [gnuplot](http://www.gnuplot.info/).
+
+A área de plotagem permite a navegação utilizando ferramentas de zoom, por área de seleção e comandos de mouse, e arrasto das curvas impressas.
+
+:::tip Dica
+Ao clicar com o botão direito sobre a área de plotagem as opções de manipulação são exibidas por meio de um menu de contexto.
+:::
+
+Os seguintes **comandos de mouse** são utilizados para navegação das curvas:
+
+|Comando|Ação|
+|-------|----|
+|Botão esquerdo pressionado + Selecionar área|Seleciona a área de zoom|
+|Botão direito pressionado + Mover mouse|Arrasta a curva|
+|Roda do mouse|Arrasto vertical|
+|Roda do mouse + Shift|Arrasto horizontal|
+|Roda do mouse + Ctrl|Mais/menos zoom|
\ No newline at end of file
diff --git a/docusaurus/docs/heatmap.md b/docusaurus/docs/heatmap.md
index 30ea55f2..a16995c3 100644
--- a/docusaurus/docs/heatmap.md
+++ b/docusaurus/docs/heatmap.md
@@ -5,4 +5,37 @@ sidebar_label: Mapa de Tensão
 ---
 import useBaseUrl from "@docusaurus/useBaseUrl";
 
-<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
\ No newline at end of file
+<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
+
+A ferramenta Mapa de Tensão utiliza o concento de [mapa de calor](https://en.wikipedia.org/wiki/Heat_map) para exibir os valores de tensão de todas as barras do sistema por meio de cores.
+
+<video autoPlay loop muted playsInline controls>
+  <source src= {useBaseUrl("videos/heatmap.mp4")} type="video/mp4" />
+  <source src= {useBaseUrl("videos/heatmap.webm")} type="video/webm" />
+</video>
+
+:::tip Dica
+Essa ferramenta é útil para identificação de barras com sub e sobretensões no sistema de potência, assim como o efeito da inserção / remoção de elementos do sistema.
+:::
+
+A legenda que correlaciona os valores do módulo da tensão com as cores são exibidas à esquerda da área de trabalho.
+
+## Habilitando a ferramenta Mapa de Tensão
+
+A ferramenta pode ser habilitada ou desabilitada no [submenu Ribbon **Ferramentas**](mainScreen#menu-ribbon) clicando no botão **Mapa de tensão** ou pela tecla de atalho "Ctrl + Shift + H".
+
+As configurações da ferramenta podem ser também acessadas no [submenu Ribbon **Ferramentas**](mainScreen#menu-ribbon) clicando no botão **Configurações do projeto**
+
+<div><center><img src={useBaseUrl("images/heatmapForm.png")} alt="Configurações da ferramenta Mapa de Tensão" title="Configurações da ferramenta Mapa de Tensão" /></center></div>
+
+:::info Informação
+Na versão atual do programa, somente as opções do mapa de tensão são exibidas nas configurações de projeto.
+:::
+
+Os limites superiores e inferiores, em $p.u.$ são editados nesse formulário.
+
+Alternativamente, o programa pode calcular automaticamente os limites. Nesse caso, o limite superior será a maior tensão do circuito e o limite inferior será a menor tensão do circuito.
+
+:::warning Cuidado!
+O cálculo automático dos limites pode prejudicar a identificação de barras com sub e sobretensões no sistema.
+:::
\ No newline at end of file
diff --git a/docusaurus/docs/powerEditor.md b/docusaurus/docs/powerEditor.md
index d47fef21..f7dc3d12 100644
--- a/docusaurus/docs/powerEditor.md
+++ b/docusaurus/docs/powerEditor.md
@@ -49,7 +49,7 @@ Sempre que são inseridos novos elementos, um formulário de dados é exibido e
 O primeiro elemento que a ser inserido no projeto **deve** ser um barramento. Os demais elementos elétricos devem ser conectados em uma ou mais barras.
 :::
 
-Além dos elementos de potência pode-se inserir os elementos de *texto vinculado*, os quais estão associados a uma grandeza que se deseja vizualizar diretamente na [Área de Trabalho](mainScreen#área-de-trabalho).
+Além dos elementos de potência pode-se inserir os elementos de *[texto vinculado](text)*, os quais estão associados a uma grandeza que se deseja vizualizar diretamente na [Área de Trabalho](mainScreen#área-de-trabalho).
 
 :::warning Cuidado!
 Ao inserir um barramento, a mesma irá acompanhar o ponteiro do mouse até que você clique na posição desejada. Para os demais elementos **deve-se clicar em uma mais barras** para exibir o elemento inserido.
@@ -57,7 +57,7 @@ Ao inserir um barramento, a mesma irá acompanhar o ponteiro do mouse até que v
 **Sempre fique atento às instruções da [Barra de Status](mainScreen#barra-de-status).**
 :::
 
-<video autoPlay loop muted controls>
+<video autoPlay loop muted playsInline controls>
   <source src= "/PSP/videos/timelapseBuild.mp4" type="video/mp4" />
 </video>
 
diff --git a/docusaurus/docs/tabularReport.md b/docusaurus/docs/tabularReport.md
index b59ad780..abef142e 100644
--- a/docusaurus/docs/tabularReport.md
+++ b/docusaurus/docs/tabularReport.md
@@ -5,4 +5,16 @@ sidebar_label: Relatórios Tabulares
 ---
 import useBaseUrl from "@docusaurus/useBaseUrl";
 
-<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
\ No newline at end of file
+<link rel="stylesheet" href={useBaseUrl("katex/katex.min.css")} />
+
+Para visualização de todos os resultados dos cálculos de [fluxo de carga](powerFlow) e [curto-circuito](fault), desenvolveu-se um visualizador de relatórios tabulares:
+
+<div><center><img src={useBaseUrl("images/tabReport.png")} alt="Visualizador de dados tabulados no PSP-UFU" title="Visualizador de dados tabulados no PSP-UFU" /></center></div>
+
+Tal visualizador pode ser acessado no [submenu Ribbon](mainScreen#menu-ribbon) **Ferramentas** e então no botão **Relatório de dados**, sendo exibido o formulário organizado em abas.
+
+As grandezas de alguns dados desse relatório podem ser modificadas, sendo selecionadas no cabeçalho da tabela, como mostra a figura acima.
+
+:::tip Dica
+Os valores podem ser exportados para editores de texto e tabelas externos, selecionando e copiando (Ctrl+C) para a área de transferência.
+:::
\ No newline at end of file
diff --git a/docusaurus/docs/text.md b/docusaurus/docs/text.md
index 0e89104b..54079a41 100644
--- a/docusaurus/docs/text.md
+++ b/docusaurus/docs/text.md
@@ -20,7 +20,18 @@ Outra aplicação importante é a atualização de seu valor ao aplicar a “sol
 Também pode-se utilizar os resultados apresentados por esses elementos juntamente com o diagrama unifilar na criação de relatórios do projeto.
 :::
 
-<div><center><img src={useBaseUrl("images/textExp.png")} alt="Exemplo de elemento de texto no PSP-UFU" title="Exemplo de elemento de texto no PSP-UFU" /></center></div>
+<div><center><img src={useBaseUrl("images/textExp.png")} alt="Exemplo do elemento de texto no PSP-UFU" title="Exemplo de elemento de texto no PSP-UFU" /></center></div>
+
+## Inserindo elementos de texto no PSP-UFU
+Por meio do submenu **Ferramentas** pode-se inserir os elementos de texto, como é apresentado na imagem abaixo.
+
+<div><center><img src={useBaseUrl("images/addTextElement.svg")} alt="Adicionar elementos de texto" title="Adicionar elementos de texto" /></center></div>
+
+Ao selecionar o botão "Texto" ou utilizar a **tecla de atalho "A"**, o usuário deve clicar na posição desejada da [área de trabalho](powerEditor). Com isso, será adicionado um elemento temporário com o valor "Texto". Para parametrizar esse elemento clique duas vezes sobre ele.
+
+:::caution Atenção
+O elemento de texto, assim como os [elementos de controle](controlEditor) não exibem automaticamente o formulário de edição de dados ao inseri-lo pela primeira vez.
+:::
 
 ## Formulário de edição de dados do elemento de texto
 A figura abaixo apresenta o formulário de edição de dados desse componente gráfico.
diff --git a/docusaurus/docusaurus.config.js b/docusaurus/docusaurus.config.js
index cd743641..798ba61b 100644
--- a/docusaurus/docusaurus.config.js
+++ b/docusaurus/docusaurus.config.js
@@ -10,6 +10,23 @@ module.exports = {
   organizationName: 'thales1330', // Usually your GitHub org/user name.
   projectName: 'PSP', // Usually your repo name.
   themeConfig: {
+    colorMode: {
+      defaultMode: 'dark',
+      disableSwitch: false,
+      respectPrefersColorScheme: true,
+      switchConfig: {
+        darkIcon: '🌙',
+        darkIconStyle: {
+          // Style object passed to inline CSS
+          // For more information about styling options visit: https://reactjs.org/docs/dom-elements.html#style
+          marginLeft: '2px',
+        },
+        lightIcon: '\u2600',
+        lightIconStyle: {
+          marginLeft: '1px',
+        },
+      },
+    },
     navbar: {
       title: 'PSP-UFU',
       logo: {
diff --git a/docusaurus/package-lock.json b/docusaurus/package-lock.json
index 6c802161..3f8be4ff 100644
--- a/docusaurus/package-lock.json
+++ b/docusaurus/package-lock.json
@@ -128,9 +128,9 @@
       }
     },
     "@babel/compat-data": {
-      "version": "7.10.5",
-      "resolved": "https://registry.npmjs.org/@babel/compat-data/-/compat-data-7.10.5.tgz",
-      "integrity": "sha512-mPVoWNzIpYJHbWje0if7Ck36bpbtTvIxOi9+6WSK9wjGEXearAqlwBoTQvVjsAY2VIwgcs8V940geY3okzRCEw==",
+      "version": "7.11.0",
+      "resolved": "https://registry.npmjs.org/@babel/compat-data/-/compat-data-7.11.0.tgz",
+      "integrity": "sha512-TPSvJfv73ng0pfnEOh17bYMPQbI95+nGWc71Ss4vZdRBHTDqmM9Z8ZV4rYz8Ks7sfzc95n30k6ODIq5UGnXcYQ==",
       "requires": {
         "browserslist": "^4.12.0",
         "invariant": "^2.2.4",
@@ -145,18 +145,18 @@
       }
     },
     "@babel/core": {
-      "version": "7.10.5",
-      "resolved": "https://registry.npmjs.org/@babel/core/-/core-7.10.5.tgz",
-      "integrity": "sha512-O34LQooYVDXPl7QWCdW9p4NR+QlzOr7xShPPJz8GsuCU3/8ua/wqTr7gmnxXv+WBESiGU/G5s16i6tUvHkNb+w==",
+      "version": "7.11.0",
+      "resolved": "https://registry.npmjs.org/@babel/core/-/core-7.11.0.tgz",
+      "integrity": "sha512-mkLq8nwaXmDtFmRkQ8ED/eA2CnVw4zr7dCztKalZXBvdK5EeNUAesrrwUqjQEzFgomJssayzB0aqlOsP1vGLqg==",
       "requires": {
         "@babel/code-frame": "^7.10.4",
-        "@babel/generator": "^7.10.5",
-        "@babel/helper-module-transforms": "^7.10.5",
+        "@babel/generator": "^7.11.0",
+        "@babel/helper-module-transforms": "^7.11.0",
         "@babel/helpers": "^7.10.4",
-        "@babel/parser": "^7.10.5",
+        "@babel/parser": "^7.11.0",
         "@babel/template": "^7.10.4",
-        "@babel/traverse": "^7.10.5",
-        "@babel/types": "^7.10.5",
+        "@babel/traverse": "^7.11.0",
+        "@babel/types": "^7.11.0",
         "convert-source-map": "^1.7.0",
         "debug": "^4.1.0",
         "gensync": "^1.0.0-beta.1",
@@ -175,11 +175,11 @@
       }
     },
     "@babel/generator": {
-      "version": "7.10.5",
-      "resolved": "https://registry.npmjs.org/@babel/generator/-/generator-7.10.5.tgz",
-      "integrity": "sha512-3vXxr3FEW7E7lJZiWQ3bM4+v/Vyr9C+hpolQ8BGFr9Y8Ri2tFLWTixmwKBafDujO1WVah4fhZBeU1bieKdghig==",
+      "version": "7.11.0",
+      "resolved": "https://registry.npmjs.org/@babel/generator/-/generator-7.11.0.tgz",
+      "integrity": "sha512-fEm3Uzw7Mc9Xi//qU20cBKatTfs2aOtKqmvy/Vm7RkJEGFQ4xc9myCfbXxqK//ZS8MR/ciOHw6meGASJuKmDfQ==",
       "requires": {
-        "@babel/types": "^7.10.5",
+        "@babel/types": "^7.11.0",
         "jsesc": "^2.5.1",
         "source-map": "^0.5.0"
       }
@@ -308,11 +308,11 @@
       }
     },
     "@babel/helper-member-expression-to-functions": {
-      "version": "7.10.5",
-      "resolved": "https://registry.npmjs.org/@babel/helper-member-expression-to-functions/-/helper-member-expression-to-functions-7.10.5.tgz",
-      "integrity": "sha512-HiqJpYD5+WopCXIAbQDG0zye5XYVvcO9w/DHp5GsaGkRUaamLj2bEtu6i8rnGGprAhHM3qidCMgp71HF4endhA==",
+      "version": "7.11.0",
+      "resolved": "https://registry.npmjs.org/@babel/helper-member-expression-to-functions/-/helper-member-expression-to-functions-7.11.0.tgz",
+      "integrity": "sha512-JbFlKHFntRV5qKw3YC0CvQnDZ4XMwgzzBbld7Ly4Mj4cbFy3KywcR8NtNctRToMWJOVvLINJv525Gd6wwVEx/Q==",
       "requires": {
-        "@babel/types": "^7.10.5"
+        "@babel/types": "^7.11.0"
       }
     },
     "@babel/helper-module-imports": {
@@ -324,16 +324,16 @@
       }
     },
     "@babel/helper-module-transforms": {
-      "version": "7.10.5",
-      "resolved": "https://registry.npmjs.org/@babel/helper-module-transforms/-/helper-module-transforms-7.10.5.tgz",
-      "integrity": "sha512-4P+CWMJ6/j1W915ITJaUkadLObmCRRSC234uctJfn/vHrsLNxsR8dwlcXv9ZhJWzl77awf+mWXSZEKt5t0OnlA==",
+      "version": "7.11.0",
+      "resolved": "https://registry.npmjs.org/@babel/helper-module-transforms/-/helper-module-transforms-7.11.0.tgz",
+      "integrity": "sha512-02EVu8COMuTRO1TAzdMtpBPbe6aQ1w/8fePD2YgQmxZU4gpNWaL9gK3Jp7dxlkUlUCJOTaSeA+Hrm1BRQwqIhg==",
       "requires": {
         "@babel/helper-module-imports": "^7.10.4",
         "@babel/helper-replace-supers": "^7.10.4",
         "@babel/helper-simple-access": "^7.10.4",
-        "@babel/helper-split-export-declaration": "^7.10.4",
+        "@babel/helper-split-export-declaration": "^7.11.0",
         "@babel/template": "^7.10.4",
-        "@babel/types": "^7.10.5",
+        "@babel/types": "^7.11.0",
         "lodash": "^4.17.19"
       }
     },
@@ -391,11 +391,11 @@
       }
     },
     "@babel/helper-split-export-declaration": {
-      "version": "7.10.4",
-      "resolved": "https://registry.npmjs.org/@babel/helper-split-export-declaration/-/helper-split-export-declaration-7.10.4.tgz",
-      "integrity": "sha512-pySBTeoUff56fL5CBU2hWm9TesA4r/rOkI9DyJLvvgz09MB9YtfIYe3iBriVaYNaPe+Alua0vBIOVOLs2buWhg==",
+      "version": "7.11.0",
+      "resolved": "https://registry.npmjs.org/@babel/helper-split-export-declaration/-/helper-split-export-declaration-7.11.0.tgz",
+      "integrity": "sha512-74Vejvp6mHkGE+m+k5vHY93FX2cAtrw1zXrZXRlG4l410Nm9PxfEiVTn1PjDPV5SnmieiueY4AFg2xqhNFuuZg==",
       "requires": {
-        "@babel/types": "^7.10.4"
+        "@babel/types": "^7.11.0"
       }
     },
     "@babel/helper-validator-identifier": {
@@ -447,9 +447,9 @@
       }
     },
     "@babel/parser": {
-      "version": "7.10.5",
-      "resolved": "https://registry.npmjs.org/@babel/parser/-/parser-7.10.5.tgz",
-      "integrity": "sha512-wfryxy4bE1UivvQKSQDU4/X6dr+i8bctjUjj8Zyt3DQy7NtPizJXT8M52nqpNKL+nq2PW8lxk4ZqLj0fD4B4hQ=="
+      "version": "7.11.0",
+      "resolved": "https://registry.npmjs.org/@babel/parser/-/parser-7.11.0.tgz",
+      "integrity": "sha512-qvRvi4oI8xii8NllyEc4MDJjuZiNaRzyb7Y7lup1NqJV8TZHF4O27CcP+72WPn/k1zkgJ6WJfnIbk4jTsVAZHw=="
     },
     "@babel/plugin-proposal-async-generator-functions": {
       "version": "7.10.5",
@@ -936,9 +936,9 @@
       }
     },
     "@babel/plugin-transform-runtime": {
-      "version": "7.10.5",
-      "resolved": "https://registry.npmjs.org/@babel/plugin-transform-runtime/-/plugin-transform-runtime-7.10.5.tgz",
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+      "resolved": "https://registry.npmjs.org/@docusaurus/theme-search-algolia/-/theme-search-algolia-2.0.0-alpha.61.tgz",
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+        "@docsearch/react": "^1.0.0-alpha.25",
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         "algoliasearch": "^4.0.0",
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+      "resolved": "https://registry.npmjs.org/@docusaurus/types/-/types-2.0.0-alpha.61.tgz",
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@@ -1553,9 +1583,9 @@
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+      "version": "2.0.0-alpha.61",
+      "resolved": "https://registry.npmjs.org/@docusaurus/utils/-/utils-2.0.0-alpha.61.tgz",
+      "integrity": "sha512-MHvR3Rq8Kk9W6skBR3x7mLsDaNrnp6Mmobyc0ZVql+eiLrjiN7SPunvrVJDE90bQ50HZFLLoAkfgfrvbX5mecg==",
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         "fs-extra": "^8.1.0",
@@ -1572,6 +1602,14 @@
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+    "@docusaurus/utils-validation": {
+      "version": "2.0.0-alpha.61",
+      "resolved": "https://registry.npmjs.org/@docusaurus/utils-validation/-/utils-validation-2.0.0-alpha.61.tgz",
+      "integrity": "sha512-3QrJqZoR5eBz2XG0ijuTIp5AEOe1OHtuv7nkKArOCzFmjuBJLhUTRcECf0K+lcmdJ25zrRAWAYNgTvpVpBjaNg==",
+      "requires": {
+        "@hapi/joi": "17.1.1"
+      }
+    },
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       "resolved": "https://registry.npmjs.org/@endiliey/static-site-generator-webpack-plugin/-/static-site-generator-webpack-plugin-4.0.0.tgz",
@@ -1666,6 +1704,36 @@
         "unified": "9.1.0",
         "unist-builder": "2.0.3",
         "unist-util-visit": "2.0.3"
+      },
+      "dependencies": {
+        "@babel/core": {
+          "version": "7.10.5",
+          "resolved": "https://registry.npmjs.org/@babel/core/-/core-7.10.5.tgz",
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+          "requires": {
+            "@babel/code-frame": "^7.10.4",
+            "@babel/generator": "^7.10.5",
+            "@babel/helper-module-transforms": "^7.10.5",
+            "@babel/helpers": "^7.10.4",
+            "@babel/parser": "^7.10.5",
+            "@babel/template": "^7.10.4",
+            "@babel/traverse": "^7.10.5",
+            "@babel/types": "^7.10.5",
+            "convert-source-map": "^1.7.0",
+            "debug": "^4.1.0",
+            "gensync": "^1.0.0-beta.1",
+            "json5": "^2.1.2",
+            "lodash": "^4.17.19",
+            "resolve": "^1.3.2",
+            "semver": "^5.4.1",
+            "source-map": "^0.5.0"
+          }
+        },
+        "semver": {
+          "version": "5.7.1",
+          "resolved": "https://registry.npmjs.org/semver/-/semver-5.7.1.tgz",
+          "integrity": "sha512-sauaDf/PZdVgrLTNYHRtpXa1iRiKcaebiKQ1BJdpQlWH2lCvexQdX55snPFyK7QzpudqbCI0qXFfOasHdyNDGQ=="
+        }
       }
     },
     "@mdx-js/react": {
@@ -2424,13 +2492,13 @@
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+      "version": "9.8.6",
+      "resolved": "https://registry.npmjs.org/autoprefixer/-/autoprefixer-9.8.6.tgz",
+      "integrity": "sha512-XrvP4VVHdRBCdX1S3WXVD8+RyG9qeb1D5Sn1DeLiG2xfSpzellk5k54xbUERJ3M5DggQxes39UGOTP8CFrEGbg==",
       "requires": {
         "browserslist": "^4.12.0",
-        "caniuse-lite": "^1.0.30001097",
-        "colorette": "^1.2.0",
+        "caniuse-lite": "^1.0.30001109",
+        "colorette": "^1.2.1",
         "normalize-range": "^0.1.2",
         "num2fraction": "^1.2.2",
         "postcss": "^7.0.32",
@@ -4524,9 +4592,9 @@
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-      "resolved": "https://registry.npmjs.org/electron-to-chromium/-/electron-to-chromium-1.3.514.tgz",
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+      "version": "1.3.516",
+      "resolved": "https://registry.npmjs.org/electron-to-chromium/-/electron-to-chromium-1.3.516.tgz",
+      "integrity": "sha512-WDM5AAQdOrvLqSX8g3Zd5AujBXfMxf96oeZkff0U2HF5op3tjShE+on2yay3r1UD4M9I3p0iHpAS4+yV8U8A9A=="
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@@ -10347,6 +10415,36 @@
         "is-alphabetical": "1.0.4",
         "remark-parse": "8.0.3",
         "unified": "9.1.0"
+      },
+      "dependencies": {
+        "@babel/core": {
+          "version": "7.10.5",
+          "resolved": "https://registry.npmjs.org/@babel/core/-/core-7.10.5.tgz",
+          "integrity": "sha512-O34LQooYVDXPl7QWCdW9p4NR+QlzOr7xShPPJz8GsuCU3/8ua/wqTr7gmnxXv+WBESiGU/G5s16i6tUvHkNb+w==",
+          "requires": {
+            "@babel/code-frame": "^7.10.4",
+            "@babel/generator": "^7.10.5",
+            "@babel/helper-module-transforms": "^7.10.5",
+            "@babel/helpers": "^7.10.4",
+            "@babel/parser": "^7.10.5",
+            "@babel/template": "^7.10.4",
+            "@babel/traverse": "^7.10.5",
+            "@babel/types": "^7.10.5",
+            "convert-source-map": "^1.7.0",
+            "debug": "^4.1.0",
+            "gensync": "^1.0.0-beta.1",
+            "json5": "^2.1.2",
+            "lodash": "^4.17.19",
+            "resolve": "^1.3.2",
+            "semver": "^5.4.1",
+            "source-map": "^0.5.0"
+          }
+        },
+        "semver": {
+          "version": "5.7.1",
+          "resolved": "https://registry.npmjs.org/semver/-/semver-5.7.1.tgz",
+          "integrity": "sha512-sauaDf/PZdVgrLTNYHRtpXa1iRiKcaebiKQ1BJdpQlWH2lCvexQdX55snPFyK7QzpudqbCI0qXFfOasHdyNDGQ=="
+        }
       }
     },
     "remark-parse": {
diff --git a/docusaurus/package.json b/docusaurus/package.json
index 4a650368..9a6e00d7 100644
--- a/docusaurus/package.json
+++ b/docusaurus/package.json
@@ -9,8 +9,8 @@
     "deploy": "docusaurus deploy"
   },
   "dependencies": {
-    "@docusaurus/core": "^2.0.0-alpha.60",
-    "@docusaurus/preset-classic": "^2.0.0-alpha.60",
+    "@docusaurus/core": "^2.0.0-alpha.61",
+    "@docusaurus/preset-classic": "^2.0.0-alpha.61",
     "clsx": "^1.1.1",
     "galleria": "^1.6.1",
     "react": "^16.8.4",
diff --git a/docusaurus/static/images/addTextElement.svg b/docusaurus/static/images/addTextElement.svg
new file mode 100644
index 00000000..2a590662
--- /dev/null
+++ b/docusaurus/static/images/addTextElement.svg
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+   xmlns:xlink="http://www.w3.org/1999/xlink"
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+   width="565"
+   id="svg1088"
+   version="1.1">
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diff --git a/docusaurus/static/videos/heatmap.mp4 b/docusaurus/static/videos/heatmap.mp4
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index 00000000..b5dd309c
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diff --git a/docusaurus/static/videos/heatmap.webm b/docusaurus/static/videos/heatmap.webm
new file mode 100644
index 00000000..e3186c55
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