Solve $4-13.$ A $\backslash (25-\backslash$mathrm$\{$MVA$\},12\mathrm{.}2-\backslash$mathrm$\{$kV$\},0\mathrm{.}9-\backslash$mathrm$\{$PF$\}-\backslash$mathrm$\{$lag$\}\backslash )$ ging, three$-$phase, two$-$pole, Y$-$connected, $\backslash (60-\backslash$mathrm$\{$Hz$\}\backslash )$ synchronous generator was tested by the open$-$circuit test, and its air$-$gap voltage was extrapolated with the following results:

Open$-$circuit test

The short$-$circuit test was then performed with the following results:

Short$-$circuit test

The armature resistance is $\backslash (0\mathrm{.}6\backslash$Omega $\backslash )$ per phase,

$($a$)$ Find the unsaturated synchronous reactance of this generator in ohms per phase

$($b$)$ Find the approximate saturated synchronous reactance $\backslash ($ X$\_\{5\}\backslash )$ at a field current of $380$ A $.$ Express the answer both in ohms per phase

$($c$)$ Find the approximate saturated synchronous reactance at a field current of $475$ A $.$ Express the answer both in ohms per phase

$($e$)$ What is the internal generated voltage of this generator at rated conditions?

$($f$)$ What field current is required to achieve rated voltage at rated load?