$4-2$ A $13\mathrm{.}8-$kV$,50-$MVA, $0\mathrm{.}9-$power$-$factor$-$lagging, $60-Hz,$ four$-$pole Y$-$connected syndronous generator has a synchronous reactance of $25$ and an armature row tunce of $0\mathrm{.}2.$ At $60$ Hz $,$ its friction and windage losses are $1$ MW $,$ and its cones losses are $1\mathrm{.}5$ MW $.$ The field circuit has a de voltage of $120$ V $,$ and the maximum i$,$ is $10$ A $.$ The current of the field circuit is adjustable over the range from $0$ to $10.$ A$.$ The OCC of this generator is shown in Figure P$4-1.$

Open$-$circuit characteristic