$6\mathrm{.}12.$ Figure $60$ shows the one$-$line diagram of a simple three$-$bus power system with generation at buses $1$ and $2.$ The voltage at bus $1$ is $V=\frac{1\mathrm{.}0}{{?}_0}$ per unit. Voltage magnitude at bus $2$ is fixed at $1\mathrm{.}05$ pu with a real power generation of $400$ MW $.$ A load consisting of $500$ MW and $400$ Mvar is taken from bus $3.$ Line admittances are marked in per unit on a $100$ MVA base. For the purpose of hand calculations, line resistances and line charging susceptances are neglected.

$($b$)$ Using Newton$-$Raphson method, start with the initial estimates of $V_2^{(0)}=1\mathrm{.}05+j0$ and $V_3^{(0)}=1\mathrm{.}0+j0,$ and keeping $|V_2|=1\mathrm{.}05pu,$ determine the phasor values of $V_2$ and $V_3.$ Perform two iterations.