A synchronous generator is to be connected to an infinite bus through a transmission line of reactance X = 0.2 pu, as shown in figure the generator data is as follows:

X¹ = 0.1 pu, E¹ = 1.0 pu, H = 5 MJ/MVA, mechanical power P_m = 0.0 pu, $$\omega $$_B = 2 $$\pi \times $$50 rad/sec. All quantities are expressed on a common base.

The generator is initially running on open circuit with the frequency of the open circuit voltage slightly higher than that of the infinite bus. If at the instant of switch closure $$\delta = 0$$ and $$\omega = {{d\delta } \over {dt}} = {\omega _{init}},$$ compute the maximum value of $${\omega _{init}}$$ so that the generator pulls into synchronism.

$$\int {\left( {{{2H} \over {{\omega _B}}}} \right)\omega d\omega + {P_e}d\delta = 0} $$

A generator is connected to a transformer which feeds another transformer through a short feeder. The zero sequence impedance values are expressed in pu on a common base and are indicated in figure. The Thevenin equivalent zero sequence impedance at point B is

Consider the problem of relay co-ordination for the distance relays $$R1$$ and $$R2$$ on adjacent lines of a transmission system figure. The Zone $$1$$
and Zone $$2$$ settings for both the relays are indicated on the diagram. Which of the following indicates the correct time setting for the Zone $$2$$ of relays $$R1$$ and $$R2.$$

Consider a power system with three identical generators. The transmission losses are negligible. One generator ($$G1$$) has a speed governor which maintains its speed constant at the rated value, while the other generators ($$G2$$ and $$G3$$) have governors with a droop of $$5$$%. If the load of the system is increased, then in steady state.