Answer to Question #130959 in Electrical Engineering for Muchindu Titus

Question

30mva 13.8kv 3-phase alternator has subtransient of 15% and negative and zero sequence reactances of 15% and 5%. The alternator supplies two motors over a transmission line having transformers.Motors rated inputs 20mva & 10mva both at 12.5kv with 20% subtransient reactances and negative & zero sequence reactances are 20% & 5% respectively. Current limiting reactors of 2ohm each in neutral of alternator of large motor.3 phase transformers are rated 35mva 21/132 kV delta/star with leakage reactance of 10%, series reactance of the line is 100ohm & zero sequence reactance of the line is 175 ohms. Use a base of 30mva and 22kv and determine the fault current when an L-L-G fault occurs at point P. Assume a prefault voltage of 138 kv

Answer 1

Solution

The base voltage on the line side of the transformer = 13.8*132/21 =86.742 kV

The base voltage on the motor side of the transformer = 86.742 *21/132 = 13.8 kV

The per cent reactance of transformer = 10 * (21/13.8)² *30/35 = 19.8%

The per cent reactance of motor 20 * (12.5/13.8)² *30/20 = 24.6 %

Zero sequence network

The neutral reactance = 2*3 * 30/13.8² *100 = 94.5%

The zero sequence reactance of line = 200* 30/138² *100 = 31.5%

L-L-G fault

I_a1 = (1+j0.0)/(j0.19224) = -j5.2 p.u

I_a2 = (+j5.2*j0.06767)/j0.21367 = j1.647

I_a0 = j3.553

The fault current is

I_b + I_c = 3l_a0 = 3 * j3.553 p.u

Therefore the fault current = 3*3.553*114.3 = 1538 amps