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1 Load Flow Equations POWER FLOW FORMULATION Admittance Matrix Y bus = G + jB = Y ij Power fow 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 ±orm 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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