lecture9 - EE 740 Professor Ali Keyhani Lecture #9 Z Bus...

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EE 740 Professor Ali Keyhani Lecture #9 Z Bus Matrices
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Algorithm for the construction of Z Bus impedance matrix. [Y Bus ][ V Bus ] = [I Bus ] [V Bus ] = [Y Bus ] -1 [I Bus ] [Z Bus ] = [Y Bus ] -1 Ex: Z 11 Z 12 Z 13 I 1 V 1 Z 21 Z 22 Z 23 I 2 = V 2 Z 31 Z 32 Z 33 I 3 V 3 Suppose C-B A is closed and C-B B is open then: I 1 0 I 2 = 0 I 3 = 0 Z 11 Z 12 Z 13 I 1 V 1 Z 21 Z 22 Z 23 0 = V 2 Z 31 Z 32 Z 33 0 V 3 Z 11 I 1 = V 1 Z 11 = V 1 / I 1 = Zth between bus 1 and ground Z 21 I 1 = V 2 Z 21 = V 2 / I 1 Z 31 I 1 = V 3 Z 31 = V 3 / I 1 Suppose I 1 = 1A then: Z 11 = V 1 Z 21 = V 2 and Z 31 = V 3 z 12 z 13 z 23 z 1 C-B C-B A C-B B V 1 1 2 3
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We conclude that by injecting 1 amp at bus (1) and calculating the voltage rise, then: Z 11 = V 1 Z 21 = V 2 Z 31 = V 3 Suppose that C-B A is open and we inject 1 amp into bus (3), then: I 3 = 1 I 2 = 0 and I 1 = 0 Z 11 Z 12 Z 13 0 V 1 Z 21 Z 22 Z 23 0 = V 2 Z 31 Z 32 Z 33 I 3 V 3 Z 13 I 3 = V 1 Z 13 = V 1 / I 3 Z 23 I 3 = V 2 Z 23 = V 2 / I 3 Z 33 I 3 = V 3 Z 33
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lecture9 - EE 740 Professor Ali Keyhani Lecture #9 Z Bus...

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