$3.$ The open$-$circuit characteristic $($occ$)$ for a $3$phase, $195$ MVA, I$6$ KV$,60$ Hz$.$ synchronous machine is attached. The short$-$circuit test gives IA $=6000$ A$.$ at If $=650$ A$.$ Neglect the armature resistance, Ra$.$

a$)$ Determine the unsaturated and saturated synchronous reactances: Xs $($unsat$),$ Xs $($sat$).$

b$)$ Find the required If if the synchronous machine is to deliver $180$ MVA at rated. voltage at a power factor of $0\mathrm{.}85$ lagging.