Triangular $$PWM$$ control, when applied to a $$BJT$$ based three phase voltage source inverter, introduces.

A three phase voltage source inverter supplies a purely inductive three phase load. Upon Fourier analysis, the output voltage waveform is found to have an $${h^{th}}$$ order harmonic of magnitude α h times that of the fundamental frequency component $$\left( {{\alpha _h} < 1} \right),$$ the load current would then have an $${h^{th}}$$ order harmonic of magnitude

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