A $3-$phase, $125$hp$,460$Vrms $($line$-$to$-$line$),60$Hz$,0\mathrm{.}85$ PF leading, $4-$pole star$-$connected

synchronous motor has Ls $=3\mathrm{.}5$mH with negligible Rs$.$ The speed of this motor is controlled

over the range from $300$ to $1800$ rpm$.$

a$)$ b$)$ c$)$ Determine the range of supply frequency variation.

Determine the excitation voltage at the rated condition.

Determine the maximum power the motor can deliver at:

I. Rated speed

II$.$ Lowest speed