In the converter circuit shown below, the switches are controlled such that the load voltage $${v_0}\left( t \right)$$ is a $$400$$ $$Hz$$ square wave.

The RMS value of the fundamental component of $${v_0}\left( t \right)$$ in volts is ___________.

A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L1, L2, L3, L4, L5, L6. The generator bus G1 is considered as slack bus, and the load buses L3 and L4 are voltage controlled buses. The generator at bus G2 cannot supply the required reactive power demand, and hence it is operating at its maximum reactive power limit. The number of non-linear equations required for solving the load flow problem using Newton-Raphson method in polar form is ____________.

The bus admittance matrix for a power system network is $$$\left[ {\matrix{ { - j39.9} & {j20} & {j20} \cr {j20} & { - j39.9} & {j20} \cr {j20} & {j20} & { - j39.9} \cr } } \right]\,pu.$$$
There is a transmission line connected between buses $$1$$ and $$3,$$ which is represented by the circuit shown in figure.

If this transmission line is removed from service what is the modified bus admittance matrix?

A $$3$$-bus power system is shown in the figure below, where the diagonal elements of $$Y$$-bus matrix are: $${Y_{11}} = - j12\,pu,\,\,\,{Y_{22}} = - j15\,pu\,\,$$ and $$\,{Y_{33}} = - j7\,pu.$$

The per unit values of the line reactance's $$p, q$$ and $$r$$ shown in the figure are