contraction - DERIVATION OF ITERATION SCHEME FOR 3 BUS...

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DERIVATION OF ITERATION SCHEME FOR 3 BUS SYSTEM Overall Decoupled Iterative Form δ 2 δ 3 V 2 k +1 = φ ( x k )= δ 2 δ 3 V 2 k - ± ( B ± ) - 1 0 0( B ± ) - 1 ² ( f 2 ( δ k 2 k 3 ,V k 2 ) - P 2 ) /V k 2 ( f 3 ( δ k 2 k 3 k 2 ) - P 3 ) /V k 3 ( g 2 ( δ k 2 k 3 k 2 ) - Q 2 ) /V k 2 with f 2 ( δ k 2 k 3 k 2 V k 2 V X (sin( δ k 2 ) + sin( δ k 2 - δ k 3 )) f 3 ( δ k 2 k 3 k 2 V k s V X (sin( δ k 3 - δ k 2 )) g 2 ( δ k 2 k 3 k 2 - V k 2 V X (cos( δ k 2 ) + cos( δ k 2 - δ k 3 )) - BX - 2 X ( V k 2 ) 2 B ± = 1 X ± 2 - 1 - 11 ² B ± = 2 X - B = 2 - X after substitution δ 2 δ 3 V 2 k +1 = φ ( x k δ 2 δ 3 V 2 k - ± 1 1 1 2 ² ³ 00 ´ 0 0 1 2 - V (sin( δ k 2 ) + sin( δ k 2 - δ k 3 )) V k 2 sin( δ k 3 - δ k 2 ) - PX V - V (cos( δ k 2 ) + cos( δ k 2 - δ k 3 )) - ( - 2) V k 2 = δ 2 δ 3 V 2 k - V (sin( δ k 2 ) + sin( δ k 2 - δ k 3 )) + V k 2 sin( δ k 3 - δ k 2 ) - V V (sin( δ k 2 ) + sin( δ k 2 - δ k 3 )) + 2 V k 2 sin( δ k 3 - δ k 2 ) - 2 V ) - V 2 - (cos( δ k 2 ) + cos( δ k 2 - δ k 3 )) + V k 2 Simpli±ed Form
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This note was uploaded on 07/14/2011 for the course ECE 522 taught by Professor Tomsovic during the Summer '10 term at University of Florida.

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contraction - DERIVATION OF ITERATION SCHEME FOR 3 BUS...

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