Q$2.$

A $50-$MVA,$12\mathrm{.}5kV$ generator has a direct$-$axis sub$-$transient reactance of $0\mathrm{.}25$ per unit. The negative$-$ and zero$-$sequence reactances are, respectively, $0\mathrm{.}35$ and $0\mathrm{.}10$ per unit. The neutral of the generator is solidly grounded. When a single line$-$toground fault occurs at the generator terminals with the generator operating unloaded at rated voltage, determine

$($a$)$ the sub$-$transient current $($in amperes$)$ in the generator, and

$($b$)$ the line$-$to$-$line voltages $($in kV $)$ for sub$-$transient conditions.

$(8$ marks$)$

$(12$ marks$)$