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When a 50 MVA, 11 kV, 3-phase generator is subjected to a three phase fault, the fault current is -j5 pu. When it is subjected to a line to line fault, positive sequence current is -j4 pu. Positive sequence and negative sequence reactances are respectively
j0.2 pu and j0.05 pu
j0.2 pu and j0.25 pu
j0.25 pu and j0.25 pu
j0.05 pu and j0.05 pu
j0.2 pu and j0.05 pu
Quick Trick: For 3-phase fault, X1 = 1/If3ph; for L-L fault, X1 + X2 = V/If_pos_seq. Use reciprocals to find reactances instantly.
For 3-phase fault, X1 = 1/If3ph; for L-L fault, X1 + X2 = V/If_pos_seq. Use reciprocals to find reactances instantly.
Calculate Positive Sequence Reactance
For a 3-phase fault, the fault current If3ph = 1/X1. Given If3ph = 5 pu, then X1 = 1 / 5 = 0.2 pu.
Calculate Negative Sequence Reactance
For a line-to-line fault, the positive sequence current I1 = 1 / (X1 + X2). Given I1 = 4 pu, then X1 + X2 = 1 / 4 = 0.25 pu.
Solve for X2
Substitute X1 = 0.2 into X1 + X2 = 0.25, giving 0.2 + X2 = 0.25, so X2 = 0.05 pu.
B: Incorrect, sums to 0.45; C: Incorrect, sums to 0.50; D: Incorrect, X1 value is 0.05 instead of 0.2.
A is correct because the 3-phase fault current defines the positive sequence reactance as 0.2 pu, and the line-to-line fault sequence network determines the negative sequence reactance as 0.05 pu.
Always remember that in power systems, the positive sequence reactance is simply the reciprocal of the 3-phase fault current in pu.