The network shown in Figure $157$ represents the connection of a single$-$phase wind turbine driving an active load. The Thevenin's equivalent for the generator is shown in the 'wind turbine' box. The time$-$domain expression for the generator voltage source is written as

$E_{WT}(t)=50cos(4t)V$

The RLC network connected at A$-$B to the right of the turbine is a model of a known active load network with zero initial conditions. You are asked to calculate values for the following:

$($a$)$ the complex power hat$(S)$ in volt$-$amperes $($va$),$ the average power $P_{\text{a}\text{v}\text{g}}$ in Watts, the reactive power Q in vars, and the power factor pf $,$ and

$($b$)$ the type, value, and the connection at terminals $A-B$ of the component that will correct the power factor to unity.

Wind turbine network