$6\mathrm{.}38$

A generator bus $($with a $1\mathrm{.}0$ per unit voltage$)$ supplies a $180$ MW$,60$ Mvar load through a lossless transmission line with per unit $(100$ MVA base$)$ impedance of j$0\mathrm{.}1$ and no line charging. Starting with an initial voltage guess of $,$ iterate until converged using the Newton$-$Raphson power flow method. For convergence criteria, use a maximum power flow mismatch of $0\mathrm{.}1$ MVA.

For the three bus$-$system whose

$$

bus

is given, calculate the second iteration value of

V

$3$

using the Gauss$-$Seidel method. Assume bus $1$ as the slack $($with $),$ and buses $2$ and $3$ are load buses with a per$-$unit load of

$$

$2$

$=$

$1$

$+$

$$

$0\mathrm{.}5$

and

$$

$3$

$=$

$1\mathrm{.}5$

$+$

$$

$0\mathrm{.}75$

$.$ Use voltage guesses of at both buses $2$ and $3.$ The bus admittance matrix for a three$-$bus system is