A synchronous generator is connected to an infinite bus through a lossless double circuit transmission line. The generator is delivering 1.0 per unit power at a load angle of $${30^0}$$ when a sudden fault reduces the peak power that can be transmitted to 0.5 per unit. After clearance of fault, the peak power that can be transmitted becomes 1.5 per unit. Find the critical clearing angle.

A synchronous generator, having a reactance of 0.15 p.u., is connected to an infinite bus through two identical parallel transmission lines having reactance of 0.3 p.u. each. In steady state, the generator is delivering 1 p.u. Power to the infinite bus. For a three phase fault at the receiving end of one line, calculate the rotor angle at the end of first time step of 0.05 seconds. Assume the voltage behind transient reactance for the generator as 1.1 p.u. and infinite bus voltage as 1.0 p.u. Also indicate how the accelerating powers will be evaluated for the next time step if the breaker clears the fault.

(i) at the end of an interval
(ii) at the middle of an interval.

An alternator is connected to an infinite bus as shown in figure. It delivers 1.0 p.u. current at 0.8 p.f lagging at V = 1.0 p.u.. The reactance X_d of the alternator is 1.2 p.u. Determine the active power output and the steady state power limit. Keeping the active power fixed, if the excitation is reduced, find the critical excitation corresponding to operation at stability limit.

A synchronous motor is receiving 50% of the power it is cable to receiving from an infinite bus. If the load on the motor is suddenly reduced to 80% of the previous value, swing of the motor around is new equilibrium position.