Problem $2$: Synchronous generator

A $3-$phase, $2000$ kV A$,11kV,1800rpm$ synchronous generator has a resistance of $1\mathrm{.}5$ ohms and synchronous reactance of $15$ ohms per phase. The synchronous machine is connected to an infinite bus. The generator is made to deliver the rated current at $0\mathrm{.}8$ power factor lagging.

$($i$)$ Determine the excitation voltage Ef and power angle. Draw the phasor diagram for this condition.

$($ii$)$ If the field excitation is increased by $10\%($without change in prime mover power$),$ find the stator current, power factor, and reactive KVA supplied by machine.

$($iii$)$ For the excitation in $($i$),$ what is the steady$-$state stability limit$?$