Consider a $20$MVA, $11$ kV $($line$,$ rms$),$ Y$-$connected synchronous machine. The excitation current $\backslash ($ I$\_\{$f$\}\backslash )$ of the machine is adjusted so that machine terminal voltage $($bus voltage$)$ is always at $11$ kV $.$ The synchronous reactance of the machine is $\backslash ($ X$\_\{$s$\}=5\backslash$Omega $\backslash ).$ Assume that stator resistance is negligible compared to the synchronous reactance. Find the per phase excitation voltage of the machine, and draw the phasor diagram for each case, when it delivers:

$($a$)$ Resistive load of $20$ MW $,$

$($b$)$ Inductive load of $14$ MW at $0\mathrm{.}9$ power factor lagging,

$($c$)$ No load,

$($d$)$ Capacitive load of $13$ MVAR, $\backslash (90^\{\backslash$circ$\}\backslash )$ leading.