A$3$$,1$ MVA, $2300$ V$,60$ Hz synchronous machine has negligible stator resistance and a satu$-$rated synchronous reactance Xs $=1$:$25$ at rated terminal voltage. The efficiency of the machine is $0\mathrm{.}95$ at rated speed. The machine is connected to an infinite bus.

$($a$)$

Determine Xs in pu$.$

$($b$)$

Determine the excitation voltage and the power angle when the machine operates as a synchronous motor at $0\mathrm{.}85$ lagging power factor and delivers $500$ hp$.$

$($c$)$ The field current is now reduced by $40\%,$ keeping the power output the same as in $($b$).$ Find the stator current and the power factor. Will the motor lose synchronism?