Example $3\mathrm{.}1$

A $50-$MVA, $30-kV,$ three$-$phase, $60-Hz$ synchronous generator has a synchronous reactance of $9$ per phase and a negligible resistance. The generator is delivering rated power at a $0\mathrm{.}8$ power factor lagging at the rated terminal voltage to an infinite bus.

$($a$)$ Determine the excitation voltage per phase $E$ and the power angle $.$

$($b$)$ With the 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.

Example $3\mathrm{.}3$

For the generator of Example $3\mathrm{.}1,$ construct the V curve for the rated power of $40$ MW with varying field excitation from $0\mathrm{.}4$ power factor leading to $0\mathrm{.}4$ power factor lagging. Assume the open$-$circuit characteristic in the operating region is given by $E=2000I_{f}V$