Determine the initial Jacobian matrix for the power system described in Problem 6.34.

Problem 6.34

For the three-bus system whose \(\boldsymbol{Y}_{\text {bus }}\) is given, calculate the second iteration value of \(\mathrm{V}_{3}\) using the Gauss-Seidel method. Assume bus 1 as the slack (with \(V_{1}=1.0 / 0^{\circ}\) ), and buses 2 and 3 are load buses with a per-unit load of \(S_{2}=1+j 0.5 \) and \(S_{3}=1.5+j 0.75 \). Use voltage guesses of \(1.0 \angle 0^{\circ}\) at both buses 2 and 3 . The bus admittance matrix for a three-bus system is

Yb bus -j10 j5 j5 j5 -j10 j5 j5 j5 -j10