$(2)$ During a short circuit test, a Y$-$connected synchronous generator produces $100$ A of short$-$circuit armature current per phase at a field current of $2\mathrm{.}5$ A $.$ At the same field current, the open$-$circuit line voltage is measured to be $440$ V $.$

$($a$)$ Calculate the saturated synchronous reactance under these conditions.

$($b$)$ If the armature resistance is $0\mathrm{.}3$ per phase, and the generator supplies $60$ A to a purely resistive $Y-$connected load of $3$ per phase at this field current setting, determine the voltage regulation under these load conditions.

Open circutit

$E_1=490V$

Sonat Cireui

$=\frac{E_A}{x_S}$

$t_{}=\frac{440v}{1001}=4\mathrm{.}4$

$I_A=\frac{{}_A}{R_A+j_S}$

ismor; RA$...$ I

$vv+60A(0\mathrm{.}3+j4\mathrm{.}45)+V_p$

$440V-60A(4\mathrm{.}91s)=v_{6}175\mathrm{.}3$