$(4)$ A $\backslash (30-\backslash$mathrm$\{$kV$\},3\backslash )-$phase, $\backslash (50\backslash$cdot $\backslash$mathrm$\{$~Hz$\}\backslash )$ synchronous generator has a synchronous reactance of $\backslash (9\backslash$Omega $/\backslash )$ phase and $\backslash (03\mathrm{.}5\backslash$Omega $/\backslash )$ phresistance. The generator is delivering $50$ MVA at a $0\mathrm{.}8$ power factor lagging at the rated terminal voltage to an inferite bus.

$($a$)$ Determine the excitation voltage $\backslash (\backslash$bar$\{$E$\}\backslash )$ per phase and the power angle $\backslash (\backslash$delta $\backslash ).$

$($b$)$ With excitation held constant at the value found in $($a$),$ the driving torque is reduced until the generator is delivering $25$ MW $.$ Determine the armature current and the power factor.

$($c$)$ If the generator is operating at the excitation voltage of part $($a$)$ what is the steady state maximum power the machine can deliver before losing synchronism? Also, find the armature current corresponding to this maximum power.

$($d$)$ The excitation voltage is decreased to $\backslash (79\mathrm{.}2\backslash \%\backslash )$ of the value in part $($a$).$ The generator is delivering $40$ MW $.$ Compute the power angle, armature current and power factor.

$($e$)$ Construct the V$-$curve if the generator is delivering $40$ MW varying field excitation from $0\mathrm{.}4$ pf leading to $0\mathrm{.}4$ pf lagging Assume the open.circuit characteristic in the operating region is given by $\backslash ($ E$=3464\mathrm{.}1$ T$\_\{$F$\}\backslash )$