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.

The severity of line-to-ground and three phase faults at the terminals of an unloaded synchronous generator is to be same. If the terminal voltage is
$$1.0$$ p.u. and $${Z_1} = {Z_2} = j0.1\,\,$$ p.u.,
$$\,{Z_0} = j0.05\,\,\,\,\,$$ p.u., for the alternator, then the required inductive reacttance for neutral grounding is

For the configuration shown in figure, the breaker connecting a large system to bus $$2$$ is initially open. The system $$3$$-phase fault level at bus $$3$$ under this condition is not known. After closing the system breaker, the $$3$$-phase fault level at bus $$1$$ was found to be $$5.0$$ p.u. What will be the new $$3$$-phase fault level at system bus $$3,$$ after the interconnection? All per unit values are on common base. Prefault load currents are neglected and prefault voltages are assumed to be $$1.0$$ p.u. at all buses.

In an inverse definite minimum time, electromagnetic type over-current relay, the minimum time feature is achieved because of