In the $$3$$-phase inverter circuit shown, the load is balanced and the gating scheme is $${180^ \circ }$$ -conduction mode. All the switching devices are ideal.

The $$rms$$ value of load phase voltage is

The bus admittance matrix of a three-bus three-line system is
$$y = j\left[ {\matrix{ { - 13} & {10} & 5 \cr {10} & { - 18} & {10} \cr 5 & {10} & { - 13} \cr } } \right]$$
If each transmission line between the two buses is represented by an equivalent $$\pi \,$$ network, the magnitude of the shunt susceptance of the line connecting bus $$1$$ and $$2$$ is

The figure shows a two-generator system supplying a load of $${P_D} = 40\,MW,$$ connected at bus $$2.$$

The fuel cost of generators $${G_1}$$ and $${G_2}$$ are: $${C_1}\left( {{P_{G1}}} \right) = 10,000\,\,Rs/MWhr$$ and $${C_2}\left( {{P_{G2}}} \right) = 12,500\,\,Rs/MWhr$$ and the loss in the line is $$\,{P_{loss(pu)}} = 0.5\,\,P_{G1\left( {pu} \right),}^2\,\,\,\,$$ where the loss coefficient is specified in pu on a $$100$$ $$MVA$$ base. The most economic power generation schedule in $$MW$$ is

For the system shown below, S_D1 and S_D2 are complex power demands at bus $$1$$ and bus $$2$$ respectively. If $$\left| {{V_2}} \right| = 1$$ pu, the VAR rating of the capacitor (Q_G2) connected at bus $$2$$ is