Problem $1.$ A $300-$MVA, $13\mathrm{.}8-$kV$,$ three$-$phase, $60-Hz,$ Y$-$connected synchronous generator is adjusted to produce rated voltage on open circuit. A balanced threephase fault is applied to the terminals at $t=0.$ After analyzing the raw data, the symmetrical transient current is obtained as

$i_{ac}(t)={10}^4(1+e^{-\frac{t}{{}_1}}+6e^{-\frac{t}{{}_2}})A$

where ${}_1=200ms$ and ${}_2=15ms.$ Determine $x_d^{\text{'}\text{'}}$ and $x_d$ in per unit based on the machine ratings.