Consider a round$-$rotor $($Xd $=$ Xq$)$ synchronous generator in the steady state with r $=$ b$.$ Assume that rs $=0.$ Prove that, in per unit, P $=$ Q $+$ V $2$ s Xq $$ tan $,$ where P and Q are the real and reactive power output of the generator. $2$ Hint: Recall that S $=$ P $+$ jQ $=$ V$$ as $$I $$ as $($in per unit$).$ Eliminate the current from this expression using the steady$-$state phasor equation