$7.$ Consider a system with the single line diagram shown in Fig. $3.$ The three phase transformer name plate ratings are listed. The transformer reactances are given in percent; $\backslash (10\backslash \%=0\mathrm{.}1\backslash )$ p$.$u$.$ The transmission line impedance $\backslash ($ Z$\_\{$L$\}\backslash )$ is $\backslash (10+\backslash$mathrm$\{$j$\}100\backslash )$ ohms and load impedance $\backslash ($ Z$\_\{\backslash$text $\{$load $\}\}\backslash )$ is $440$ ohms. The generator has a terminal voltage $($magnitude$)$ of $13\mathrm{.}2$ kV $($line$-$line$).$ Find the power delivered to the load, the power supplied by the generator and the efficiency.

$[$Suggestions: In your calculation, use the $3-$phase complex power base value of $10$ MVA for the entire system and a base line$-$to$-$line voltage value of $138$ kV for the transmission section. What about the phase$-$shift induced by the two transformers?$]$

$(1)$

$(2)$

$(3)$

$13\mathrm{.}2$ kV

Fig. $3$

$($Answer: $8\mathrm{.}78$ MW$,8\mathrm{.}83$ MW$,99\mathrm{.}4\backslash \%)$