The single-phase full-bridge voltage source inverter $$(VSI),$$ shown in figure, has an output frequency of $$50$$ $$Hz$$. It uses unipolar pulse width modulation with switching frequency of $$50$$ $$kHz$$ and modulation index of $$0.7.$$ For
$${V_{in}} = 100\,V\,\,DC,\,\,L = 9.55\,\,mH,\,C = 63.66\,\,\mu F,$$ and $$R = 5\,\Omega ,$$ the amplitude of

A 50 Hz generating unit has H-constant of 2 MJ/MVA. The machine is initially operating in steady state at synchronous speed, and producing 1 pu of real power. The initial value of the rotor angle $$\delta $$ is $${5^ \circ }$$, when a bolted three phase to ground short circuit fault occurs at the terminal of the generator. Assuming the input mechanical power to remain at 1 pu, the value of $$\delta $$ in degrees, 0.02 second after the fault is _____________

A sustained three phase fault occurs in the power system shown in the figure. The current and voltage phasors during the fault (on a common reference), after the natural transients have died down, are also shown. Where is the fault located?

Consider the economic dispatch problem for a power plant having two generating units. The fuel costs in $$Rs/MWh$$ along with the generation limits for the two units are given below:
$$\eqalign{ & {C_1}\left( {{P_1}} \right) = 0.01\,P_1^2 + 30{P_1} + 10; \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,100\,MW \le {P_1} \le 150\,MW \cr} $$
$$\eqalign{ & {C_2}\left( {{P_2}} \right) = 0.05\,P_2^2 + 10{P_2} + 10; \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,100\,MW \le {P_2} \le 180\,MW \cr} $$

The incremental cost (in $$Rs/MWh$$) of the power plant when it supplies $$200$$ $$MW$$ is __________.