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In an unbalanced three phase system, phase current Iₐ = 1∠(-90°) pu, negative sequence current I_b2 = 4∠(-150°) pu, zero sequence current I_c0 = 3∠90° pu. The magnitude of phase current I_b in pu is

1. 1.00
2. 7.81
3. 11.53
4. 13.00

Correct answer: 11.53

Solution

From the given quantities the zero, positive and negative sequence components of phase a are I0=3<90, I1=8<-90, I2=4<90. Then Ib = I0 + a^2 I1 + a I2 evaluates to about -10.39 + j5.0, whose magnitude is 11.53 pu, not 7.81 pu.

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