The circuit shown in the figure has reached steady state with thyristor 'T' in OFF condition. Assume that the latching and holding currents of the thyristor are zero. The thyristor is turned ON at $$t=0$$ sec. The duration in microseconds for which the thyristor would conduct, before it turns off, is _________ (Round off to 2 decimal places).

The single phase rectifier consisting of three thyristors $$T_1,T_2,T_3$$ and a diode $$D_1$$ feed power to a 10 A constant current load. $$T_1$$ and $$T_3$$ are fired at $$\alpha=60^\circ$$ and $$T_2$$ is fired at $$\alpha=240^\circ$$. The reference for $$\alpha$$ is the positive zero crossing of $$V_{in}$$. The average voltage $$V_0$$ across the load in volts is __________ (Round off to 2 decimal places).

For the three-bus power system shown in the figure, the trip signals to the circuit breakers B$$_1$$ to B$$_9$$ are provided by overcurrent relays R$$_1$$ to R$$_9$$, respectively, some of which have directional properties also. The necessary condition for the system to be protected for short circuit fault at any part of the system between bus 1 and the R-L loads with isolation of minimum portion of the network using minimum number of directional relays is

The expressions of fuel cost of two thermal generating units as a function of the respective power generation $${P_{G1}}$$ and $${P_{G2}}$$ are given as

$$\matrix{ {{F_1}({P_{G1}}) = 0.1aP_{G1}^2 + 40{P_{G1}} + 120\,Rs/hour} & {0\,MW \le {P_{G1}} \le 350\,MW} \cr {{F_2}({P_{G2}}) = 0.2P_{G2}^2 + 30{P_{G2}} + 100\,Rs/hour} & {0\,MW \le {P_{G2}} \le 300\,MW} \cr } $$

where $$a$$ is a constant. For a given value of $$a$$, optimal dispatch requires the total load of 290 MW to be shared as $${P_{G1}} = 175\,MW$$ and $${P_{G2}} = 115\,MW$$. With the load remaining unchanged, the value of $$a$$ is increased by 10% and optimal dispatch is carried out. The changes in $${P_{G1}}$$ and the total cost of generation, $$F( = {F_1} + {F_2})$$ in Rs/hour will be as follows