$(1)$ At steady state, $10$MVA,$5$kV generator shown in Figure $1$ operates at internal voltage $($V$\_($G$))/(\_(\backslash$delta $)\_($G$))=1\mathrm{.}1$p$($u$)/(\_(\backslash$delta $)\_($G$))$

delivering its rated power to a load P$\_($L$)$ thru a reactance x$\_($L$).$ The load voltage $($V$\_($L$))/(\_(\backslash$delta $)\_($L$))$ is always held at $1\mathrm{.}0$ pu $()/(\_(0))\backslash$deg $.$

$($a$)$ What is the angle $\backslash$delta $\_($G$)$ at steady state.

$($b$)$ Due to an error in fuel supply system, the mechanical power P$\_($M$)$ to the generator instantly doubles causing

rotor to accelerate, thereby increasing $\backslash$delta $\_($G$).$ When $\backslash$delta $\_($G$)$ increases to $\backslash$delta $\_($GC$),$ the P$\_($M$)$ is instantly corrected back to its

original value and the generator stabilizes again. What is the maximum value of $\backslash$delta $\_($GC$).$

$($c$)$ If the P$\_($M$)$ is corrected to its original value before $\backslash$delta $\_($G$)$ reaches maximum $\backslash$delta $\_($GC$)$ found in $($b$),$ what is the angle $\backslash$delta $\_($G$)$ at

which the generator stabilizes again.

$($d$)$ Instead P$\_($M$)$ had doubled, if P$\_($M$)$ had tripled, speculate whether the maximum $\backslash$delta $\_($GC$)$ will be more than or less than

the value found in $($b$).$

REactance in PER Unts on GENERator MVA and

Generator Rated Voltage as base Values

x$\_($G$)=0\mathrm{.}1,$x$\_($L$)=0\mathrm{.}55$