$3.$ The open$-$circuit characteristic $($occ$)$ for a $3$phase $,195$ MVA, IL KV$,60$ Hz synchronous machine is attached. The short$-$circuit. test gives IA $=4000$ A$.$ at It $=650$ 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.