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.

If the $$dc$$ bus voltage $${V_d} = 300\,\,V,$$ the power consumed by $$3$$-phase load 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 sequence components of the fault current are as follows:
$${{\rm I}_{positive}} = j1.5\,pu,\,\,{{\rm I}_{negative}} = - j0.5\,\,pu,$$
$${{\rm I}_{zero}} = - j1\,\,pu.$$ The typeof fault in the system 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