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Questão de Engenharia Elétrica — Fluxo de Potência — FGV 2024

Engenharia ElétricaFluxo de Potência
Código
fg163049
Banca
FGV
Órgão
EPE
Ano
2024
Cargo
APE ( )
O sistema elétrico a seguir tem a Barra 1 definida como barra de referência, a Barra 2 é do tipo barra de geração, e a Barra 3, do tipo barra de carga. Considere que a Barra 3 tem a tensão controlada pelo gerador da Barra 2. Dessa forma, o problema de fluxo de potência linearizado pelo método de Newton-Raphson é dado porImagem associada para resolução da questão
  1. A{ [△P2△P3]\begin{bmatrix} \triangle P_2\\ \triangle P_3 \end{bmatrix}} = { [∂P2∂θ2  ∂P2∂θ3∂P3∂θ2  ∂P3∂θ3]\begin{bmatrix} \frac{ \partial P_2} { \partial \theta_2}\,\,\frac{ \partial P_2} { \partial \theta_3}\\\frac{ \partial P_3} { \partial \theta_2}\,\,\frac{ \partial P_3} { \partial \theta_3} \end{bmatrix}} .{ [△θ2△θ3]\begin{bmatrix} \triangle \theta_2\\ \triangle \theta_3 \end{bmatrix}}
  2. B{ [△P1△P2△Q3]\begin{bmatrix} \triangle P_1\\ \triangle P_2\\\triangle Q_3 \end{bmatrix}} = { [∂P1∂θ1  ∂P1∂θ2∂P1∂V3∂P2∂θ1  ∂P2∂θ2∂P2∂V3∂Q3∂θ1∂Q3∂θ2∂Q3∂V3]\begin{bmatrix} \frac{ \partial P_1} { \partial \theta_1}\,\,\frac{ \partial P_1} { \partial \theta_2} \frac{ \partial P_1} { \partial V_3} \\\frac{ \partial P_2} { \partial \theta_1}\,\,\frac{ \partial P_2} { \partial \theta_2} \frac{ \partial P_2} { \partial V_3}\\ \frac{ \partial Q_3} { \partial \theta_1} \frac{ \partial Q_3} { \partial \theta_2} \frac{ \partial Q_3} { \partial V_3}\end{bmatrix}} .{ [△θ1△θ2△V3]\begin{bmatrix} \triangle \theta_1\\ \triangle \theta_2\\ \triangle V_3 \end{bmatrix}}
  3. C{ [△P2△P3△Q3]\begin{bmatrix} \triangle P_2\\ \triangle P_3\\\triangle Q_3 \end{bmatrix}} = { [∂P2∂θ2  ∂P2∂θ3∂P2∂V3∂P3∂θ2  ∂P3∂θ3∂P3∂V3∂Q3∂θ2∂Q3∂θ3∂Q3∂V3]\begin{bmatrix} \frac{ \partial P_2} { \partial \theta_2}\,\,\frac{ \partial P_2} { \partial \theta_3} \frac{ \partial P_2} { \partial V_3} \\\frac{ \partial P_3} { \partial \theta_2}\,\,\frac{ \partial P_3} { \partial \theta_3} \frac{ \partial P_3} { \partial V_3}\\ \frac{ \partial Q_3} { \partial \theta_2} \frac{ \partial Q_3} { \partial \theta_3} \frac{ \partial Q_3} { \partial V_3}\end{bmatrix}} .{ [△θ2△θ3△V3]\begin{bmatrix} \triangle \theta_2\\ \triangle \theta_3\\ \triangle V_3 \end{bmatrix}}
  4. D{ [△P2△P3△Q3]\begin{bmatrix} \triangle P_2\\ \triangle P_3\\ \triangle Q_3 \end{bmatrix}} = { [∂P2∂θ2  ∂P2∂θ3∂P2∂V2∂P3∂θ2  ∂P3∂θ3∂P3∂V2∂Q3∂θ2∂Q3∂θ3∂Q3∂V2]\begin{bmatrix} \frac{ \partial P_2} { \partial \theta_2}\,\,\frac{ \partial P_2} { \partial \theta_3} \frac{ \partial P_2} { \partial V_2} \\\frac{ \partial P_3} { \partial \theta_2}\,\,\frac{ \partial P_3} { \partial \theta_3} \frac{ \partial P_3} { \partial V_2}\\ \frac{ \partial Q_3} { \partial \theta_2} \frac{ \partial Q_3} { \partial \theta_3} \frac{ \partial Q_3} { \partial V_2}\end{bmatrix}}.{ [△θ2△θ3△V2]\begin{bmatrix} \triangle \theta_2\\ \triangle \theta_3\\ \triangle V_2 \end{bmatrix}}
  5. E{ [△P2△P3△Q2△Q3]\begin{bmatrix} \triangle P_2\\ \triangle P_3 \\\triangle Q_2\\\triangle Q_3 \end{bmatrix}} = { [∂P2∂θ2  ∂P2∂θ3∂P2∂V2∂P2∂V3∂P3∂θ2  ∂P3∂θ3∂P3∂V2∂P3∂V3∂Q2∂θ2∂Q2∂θ3∂Q2∂V2∂Q2∂V3∂Q3∂θ2∂Q3∂θ3∂Q3∂V2∂Q3∂V3]\begin{bmatrix} \frac{ \partial P_2} { \partial \theta_2}\,\,\frac{ \partial P_2} { \partial \theta_3} \frac{ \partial P_2} { \partial V_2} \frac{ \partial P_2} { \partial V_3} \\\frac{ \partial P_3} { \partial \theta_2}\,\,\frac{ \partial P_3} { \partial \theta_3} \frac{ \partial P_3} { \partial V_2} \frac{ \partial P_3} { \partial V_3}\\ \frac{ \partial Q_2} { \partial \theta_2} \frac{ \partial Q_2} { \partial \theta_3} \frac{ \partial Q_2} { \partial V_2} \frac{ \partial Q_2} { \partial V_3}\\ \frac{ \partial Q_3} { \partial \theta_2} \frac{ \partial Q_3} { \partial \theta_3} \frac{ \partial Q_3} { \partial V_2} \frac{ \partial Q_3} { \partial V_3}\end{bmatrix}} .{ [△θ2△θ3△V2△V3]\begin{bmatrix} \triangle \theta_2\\ \triangle \theta_3 \\ \triangle V_2\\\triangle V_3 \end{bmatrix}}
Revelar gabarito e comentário

GabaritoD — { \begin{bmatrix} \triangle P_2\\ \triangle P_3\\ \triangle Q_3 \end{bmatrix}} = { \begin{bmatrix} \frac{ \partial P_2} { \partial \theta_2}\,\,\frac{ \partial P_2} { \partial \theta_3} \frac{ \partial P_2} { \partial V_2} \\\frac{ \partial P_3} { \partial \theta_2}\,\,\frac{ \partial P_3} { \partial \theta_3} \frac{ \partial P_3} { \partial V_2}\\ \frac{ \partial Q_3} { \partial \theta_2} \frac{ \partial Q_3} { \partial \theta_3} \frac{ \partial Q_3} { \partial V_2}\end{bmatrix}}.{ \begin{bmatrix} \triangle \theta_2\\ \triangle \theta_3\\ \triangle V_2 \end{bmatrix}}

Link permanente: /questoes/fg163049