A $$dc$$ motor with armature resistance $${R_a}$$ is fed from a step down chopper in the continuous mode, and operates at some known speed and known excitation current. The motor current rises from $${I_{\min }}\,\,$$ to $${I_{\max }}\,\,$$ in the $${T_{on}}$$ period Ton of the chopper; and drops from $${I_{\max }}\,\,$$ to $${I_{\min }}\,\,$$ in the $${T_{off}}$$ period Toff of the same circuit. Both the rise and fall of the current may be assumed to be approximately linear. What is the average power loss in the machine armature?

A transmission line has equal voltages at the two ends, maintained constant by two sources. A third source is to be provided to maintain constant voltage (equal to end voltages) at either the midpoint of the line or at $$75$$% of the distance from the sending end. Then the maximum power transfer capabilities of the line in the original case and the other two cases respectively will be in the following ratios.

A $$275$$ $$kV,$$ $$3$$-phase, $$50$$ $$Hz,$$ $$400$$ $$km$$ lossless line has following parameters:
$$x=0.05$$ $$ohms/km,$$ line charging susceptance $$y=3.0$$ micro-Siemens/k.

(a) Calculate the receiving end voltage on open circuit using justifiable assumptions.

(b) What load at the receiving end will result in a flat voltage profile on the line?

(c) If the flat voltage profile is to be achieved at $$1.2$$ times the loading in (b), what will be the nature and quantum of uniformly distributed compensation required?

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.