$3.$ The open$-$circuit characteristic $($oce$)$ for a $36,195$ MVA, IL KV$,40$ He 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 $($unent$),$ Xs $($sat$).$

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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.