A synchronous machine is connected to an infinite bus through a transformer having a reactance of 0.1 pu and a double-circuit transmission line with 0.45 pu reactance for each circuit to an infinite bus. The system is shown in Figure. All reactances are given in per-unit on a common system base. If the infinite bus receives 1.0 per unit real power at 0.95 p.f. lagging, H = 3.0 p.u.-s, Pm = 1.0 per unit and ωp.u= 1.0 in the swing equation.
Determine:
1. The internal voltage of the generator and The equation for the electrical power delivered by the generator versus its power angle δ.
2. If the synchronous generator is initially operating in the steady state condition given in 1 when a permanent three-phase-to-ground bolted short circuit occurs in the middle of line 2. The fault is cleared by opening the circuit breakers at both ends. These circuit breakers then remain open. Calculate the critical clearing angle. Assume the same source voltage E is maintained as before.
Bus1
Line 1
Bus 2
T1
Line 2
Vbus=1.0
X'd = j0.15 p.u.
XTr = j0.1 p.u.
XTL1 = XTL2 = j0.45 p.u.