$($a$)$ In the power system network shown in Figure Q$4($a$),$ bus $1$ is a slack bus with $V_1=\frac{1\mathrm{.}0}{0}$ per unit and bus $2$ is a load bus with $S_2=50MW+j100$MVar. Capacitor of $Q_{g2}=j1$ is connected to bus $2.$ The line impedance on a base of $100$ MVA is $Z=j0\mathrm{.}5pu.$ Using Gauss$-$Siedal method, determine the voltage $V_2.$ Use an initial estimate of $V_2^{(0)}=1+j0\mathrm{.}0$ and perform $2$ iterations.

$[13$ marks$]$