A $3-$phase, $22$ kV $($phase$),500$ MVA star$-$connected synchronous generator has a per phase reactance of $1\mathrm{.}8$ pu and supplies $0\mathrm{.}8$ pu per phase real power P at the rated voltage,

with a lagging power factor of $0\mathrm{.}8,$ to the load. The per$-$unit bases are the rated voltage and apparent power of the generator. Calculate the actual excitation voltage V$\_(0)($in kV $)$

$[$line value$].$

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