A $33kV,50$ MVA three$-$phase network synchronous generator is operating at $90\%$ of its rated current value with a power factor of $0\mathrm{.}9$ lagging. The synchronous reactance $x_s$ of the machine is $13.$

Draw the phasor diagram of the generator and use it to determine the level of excitation needed to achieve this operating point. What are the corresponding values of $($i$)$ the generator load angle, $($ii$)$ the power injected into the network by the generator, and $($iii$)$ the reactive power injected into the network by the generator?

Maintaining the same level of excitation, the power flowing through the machine is now reduced by $50\%.$

What is the new value of the stator current and what is the corresponding operating power factor of the generator?