$(10$ points$)$ A three$-$phase round$-$rotor synchronous generator, rated $15$ kV and $150$ MVA $,$ has negligible internal losses and synchronous reactance of $2$ per unit. It is operated on an infinite bus having a voltage of $18$ kV $.$ The internal emf, $\backslash ($ E$\_\{$i$\}\backslash )$ and the power angle, $\backslash (\backslash$delta $\backslash )$ of the machine are found to be $25$ kV $($line$-$to$-$line$)$ and $\backslash (27\mathrm{.}2^\{\backslash$circ$\}\backslash )$ respectively.

a$)$ Determine the line current, kA and the three$-$phase real power MW and reactive power Mvar, being delivered to the system. help $($numbers$)$

b$)$ If the mechanical power input and the field current of the generator are now changed so that the line current of the machine is reduced by $\backslash (29\backslash \%\backslash )$ at the power factor of $($a$),$ find the new internal emf $\backslash ($ E$\_\{$i$\}\backslash )$ :

kV and the power angle, $\backslash (\backslash$delta $\backslash )$ : $\backslash (\{\}^\{\backslash$circ$\}\backslash ).$ help $($numbers$)$

c$)$ While delivering the reduced line current of $($b$),$ the mechanical power input and the excitation are further adjusted so that the machine operates at unity power factor at its terminals. Calculate the new values of$,\backslash ($ E$\_\{$i$\}\backslash )$ : kV and the power angle, $\backslash (\backslash$delta $\backslash )$ : $\backslash (\{\}^\{\backslash$circ$\}\backslash ).$ help $($numbers$)$

Note: You can earn partial credit on this problem.