An $11kV,10$ MVA three$-$phase network synchronous generator is operating with an excitation level $($stator induced emf$)$ of $16$ kV with a lagging power factor of $0\mathrm{.}86.$ The synchronous reactance $x_s$ of the machine is $10.$

Draw the phasor diagram of the generator and use it to determine the stator rms current at 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 power through the machine, the excitation is now reduced by $20\%.$

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