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lecture13

# lecture13 - EE 740 Professor Ali Keyhani Lecture#13...

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EE 740 Professor Ali Keyhani Lecture #13 Symmetrical Components

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Operator Positive Sequence Voltage (1 = ‘+’) Vc 1 Va 1 =V 1 Vb 1 Va = Va 1 = V 0 ° = V 1 0 ° Vb = Vb 1 = V 1 240 ° Vc = Vc 1 = V 1 120 ° Let a = 1 120 ° a 2 = 1 240 ° Va 1 = V 1 Vb 1 = a 2 V 1 Vc 1 = aV 1 Va 1 1 Vb 1 = a 2 V 1 Vc 1 a
Negative Sequence Voltage (2 = ‘-‘) Vb 2 Va 2 =V 2 Vc 2 Va 2 = V 2 Va 2 1 Vb 2 = aV 2 Vb 2 = a V 2 Vc 2 = a 2 V 2 Vc 2 a 2 Zero Sequence Voltage (“0”) Va 0 = V 0 Vb 0 = V 0 Vc 0 = V 0 We will show that a set of unbalanced voltages Va,Vb,Vc can be written as: Va = Va 0 + Va 1 + Va 2 Va = V 0 + V 1 + V 2 Vb = Vb 0 + Vb 1 + Vb 2 Vb = V 0 + a 2 V 1 + aV 2 Vc = Vc 0 + Vc 1 + Vc 2 Vc = V 0 + aV 1 + a 2 V 2

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Compact Form: Va 1 1 1 V 0 Vb = 1 a 2 a V 1 Vc 1 a a 2 V 2 Vabc = T V 012 T -1 Vabc = T -1 T V 012 V 012 = T -1 Vabc T -1 = 1/3 1 1 1 1 a a 2 1 a 2 a V0 = 1/3(Va + Vb + Vc) V1 = 1/3(Va + aVb + a 2 Vc) V2 = 1/3(Va + a 2 Vb + aVc) Similarly: Iabc = T I 012 I 012 = T -1 Iabc
Problem: Consider a balanced, Y-connected, 460 Volt generator. Compute the positive, negative and zero sequence voltages.

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lecture13 - EE 740 Professor Ali Keyhani Lecture#13...

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