A single phase voltage source of magnitude $${V_s}$$ and frequency $$\omega \,\,\left( {rad\,/\,\sec } \right)$$ is connected to an inductance $$L$$ through an antiparallel back-to-back pair of thyristors. The forward and reverse conducting thyristors are fired at an angle of $$\alpha \ge \pi /2$$ from the positive going and negative going zer crossings of the supply voltage respectively, in each cycle. Obtain an expression for the inductor current in each cycle for a given value of $$\alpha .$$ The voltage drop across the thyristors, when either of them is in conduction, may be assumed to be negligible.

The incremental cost characteristic of two generators delivering $$200$$ $$MW$$ are as follows $$\,\,\,{{d{F_1}} \over {d{P_1}}} = 20 + 0.1{P_1},\,\,{{d{F_2}} \over {d{P_2}}} = 16 + 0.2{P_2}$$
For economic operation, the generations $${P_1}$$ and $${P_2}$$ should be

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.

The corona loss on a particular system at 50 Hz is 1 kW/km per phase. The corona loss at 60 Hz would be