lecture14 - EE740 Professor Ali Keyhani Lecture#14 Sequence...

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Unformatted text preview: EE740 Professor Ali Keyhani Lecture #14 Sequence Impedances of 3-Phase Balanced Transmission Lines jXm jXm jXs Ia Va jXm Va’ Vb jXs Ib Vb’ Vc Vc’ jXs Ic Ia+Ib+Ic Ground Va = jXsIa + jXmIb + jXmIc + Va’ Vb = jXsIb + jXmIa + jXmIc + Vb’ Vc = jXsIc + jXmIa + jXmIc + Vc’ Put into Matrix Notation: Va Va’ Xs Xm Xm Ia Vb - Vb’ = j Xm Xs Xm Ib Vc Vc’ Xm Xm Xs Ic Combined Matrix Notation: Vabc - Vabc’ = j Zabc Iabc 1 R e c a l l : V a b c = T s V 0 1 2 2 I a b c = T s I 0 1 2 3 R e p l a c e V a b c w i t h e q u a t i o n ( 2 ) a n d I a b c w i t h e q u a t i o n ( 3 ) t o g e t : T s V 0 1 2 - T s V ’ 0 1 2 = Z a b c T s I 0 1 2 4 M u l t i p l y ( 4 ) b y T s- 1 : T s - 1 T s V 0 1 2- T s - 1 T s V ’ 0 1 2 = T s - 1 T s Z a b c I 0 1 2 ( N o t e : T s - 1 T s = I d e n t i t y M a t r i x ) S o w e h a v e : V 0 1 2- V ’ 0 1 2 = Z 0 1 2 I 0 1 2 o r Z 0 1 2 = T s - 1 Z a b c T s 1 1 1 X s X m X m 1 1 1 Z 0 1 2 = 1 / 3 1 a a 2 j X m X s X m 1 a 2 a 1 a 2 a X m X m X s 1 a a 2 T h i s c a n b e w r i t t e n a s : (X s+2X m )...
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lecture14 - EE740 Professor Ali Keyhani Lecture#14 Sequence...

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