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# Exam 1 - 1 Exam 1Equations gi = Vi Vj(Gij cos(i j Bij sin(i...

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1 Exam 1Equations POWER FLOW EQUATIONS FORMULATION Admittance Matrix Y bus = G + jB = Y ij Power flow equations P i = f i ( δ , V ) = V i n j =1 V j ( G ij cos( δ i δ j )+ B ij sin( δ i δ j )) Q i = g i ( δ , V ) = V i n j =1 V j ( G ij sin( δ i δ j ) B ij cos( δ i δ j )) NUMERICAL ITERATION General form update = old value + iteration matrix*error x ( k +1) = x ( k ) + A 1 [ y f ( x ( k ) )] Gauss A = diag { a i } Newton-Raphson A = J = jacobian = [ f i x j ] | x ( k ) GAUSS-SEIDEL ITERATION V i ( k +1) = V i ( k ) + Y ii 1 S i V i ( k ) i 1 j =1 Y ij V j ( k +1) + . . . . . . Y ii 1 n j = i Y ij V j ( k ) Notes: 1) At slack bus simply calculate S after solution found. 2) At PV bus, calculate Q from most recent voltage and angle updates; and update only the voltage angle. NEWTON-RAPHSON LOAD FLOW Jacobian i = j f i ∂δ j = V i V j ( G ij sin( δ i δ j ) B ij cos( δ i δ j )) V j f i V j = V i V j ( G ij cos( δ i δ j ) + B ij sin( δ i δ j )) g i ∂δ j = V i V j ( G ij cos( δ i δ j ) + B ij sin( δ i

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Exam 1 - 1 Exam 1Equations gi = Vi Vj(Gij cos(i j Bij sin(i...

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