Q1Power System - I
Question
Q.1. A balanced star connected load takes 150 A from a balanced 3-phase, 4-wire supply. If the fuses in two of the lines are removed, find the symmetrical components of the line current before and after the fuses are removed.
Answer
In a balanced 3-phase, 4-wire system, before the fuses are removed all currents are purely positive-sequence (150 A) with zero negative and zero-sequence components; after two line fuses (say B and C) blow, only line A carries 150 A, giving equal positive, negative and zero-sequence components of 50 A each.
Before the fuses are removed: the load is a balanced star-connected load fed from a balanced 3-phase, 4-wire supply, so the line currents are perfectly balanced: Ia = 150∠0° A, Ib = 150∠-120° A, Ic = 150∠120° A.
Using the symmetrical component transformation (with operator a = 1∠120°):
Since Ia, Ib, Ic form a perfectly balanced positive-sequence set, Ia0 = 0, Ia2 = 0, and Ia1 = Ia = 150∠0° A. Thus, before the fuses are removed: zero-sequence current = 0 A, negative-sequence current = 0 A, positive-sequence current = 150 A.
After two fuses (in lines B and C) are removed: Line A alone continues carrying current (since it is a 4-wire system with a neutral return, an open circuit in two of the three lines does not by itself force zero current in the remaining line — the load impedance and the neutral wire complete the circuit for line A alone). Assuming the source maintains the same phase-A voltage and the star load, the current in the surviving line A remains Ia = 150∠0° A, while Ib = Ic = 0 (since lines B and C are physically open).
Applying the symmetrical component equations with Ia = 150∠0°, Ib = 0, Ic = 0:
Thus, after the two line fuses are removed, the symmetrical components of the line current become equal: zero-sequence = 50 A, positive-sequence = 50 A, negative-sequence = 50 A (all in phase, 50∠0° A each), verifying that Ia0 + Ia1 + Ia2 = 150∠0° A = Ia, and Ib = Ic = 0 is satisfied by the vector sum of the sequence components with the a, a² rotation operators applied to phases B and C.