$(4)$ A $30-$kV$.3-$phase, $50.$Hz synchronous generator has a synchronous reactance of $9/$ phase and a $3/$ phase resistance. The generator is delivering $50$ MVA at a $0\mathrm{.}8$ power factor lagging at the rated terminal voltage to an infinite bus. $($a$)$ Determine the excitation voltage E$$ per phase and the power angle $.($b$)$ With excitation held constant at the value found in $($a$),$ the driving torque is reduced until the generator is delivering $25$MW$.$ Determine the armature current and the power factor. $($c$)$ If the generator is operating at the excitation voltage of part $($a$)$ what is the steady state maximum power the machine can deliver before losing synchronism? Also, find the armature current corresponding to this maximum power. $($d$)$ The excitation voltage is decreased to $79\mathrm{.}2\%$ of the value in part $($a$).$ The generator is delivering $40$MW$.$ Compute the power angle, armature current and power factor. $($e$)$ Construct the V$-$curve if the generator is delivering $40$MW varying field excitation from $0\mathrm{.}4$ pf leading to $0\mathrm{.}4$ pf laging Assume the open$-$circuit characteristic in the operating region is given by E$=3464\mathrm{.}1$Tf$$