A$3$ $,10$ kVA, $220$ V$,$ four$-$pole, $60$ Hz$,$ star$-$connected synchronous machine has negligible stator winding resistance and a synchronous reactance of $6$ ohms per phase at rated terminal voltage. The machine is $$rst operated as a generator in parallel with a $3$$,220$ V$,60$ Hz power supply.

$($a$)$ Determine the excitation voltage and the power angle when the machine is delivering rated kVA at $0\mathrm{.}8$ PF lagging.

$($b$)$ If the $$eld excitation current is now increased by $20$ percent $($without changing the prime mover power$),$nd the stator current, power factor, and reactive kVA supplied by the machine.