A $33kV,30$ MVA three$-$phase network synchronous generator is operating at its rated current value with a leading power factor of $0\mathrm{.}922.$ The generator has a synchronous reactance $x_s$ of $12$ and negligible winding resistance.

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, and $($ii$)$ the power injected into the network by the generator?

Maintaining the same level of power flow through the generator, the excitation is now increased by $20\%.$

Draw the phasor diagram of the generator for this new operating point and use it to obtain $($i$)$ the new value of the stator current and $($ii$)$ the corresponding power factor of the generator?