The input voltage $${V_{DC}}$$ of the buck-boost converter shown below varies from $$32$$ $$V$$ to $$72$$ $$V.$$ Assume that all components are ideal, inductor current is continuous, and output voltage is ripple free. The range of duty ratio $$D$$ of the converter for which the magnitude of the steady state output voltage remains constant at $$48$$ $$V$$ is

A $$3$$-phase voltage source inverter is supplied from a $$600V$$ $$DC$$ source as shown in the figure below. For a star connected resistive load of $$20\,\,\Omega $$per phase, the load power for $${120^ \circ }$$ device conduction, in $$kW,$$ is ___________.

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 ____________.