Consider the $4-$node network shown in figure Q$4.$ Generator $\backslash (\backslash$mathbf$\{$G $1\}\backslash )$ is connected to the swing bus at Node $1.$

Figure Q$4$

a$)$ Develop the bus admittance matrix $\backslash ($ Y$\_\{\backslash$text $\{$bus $\}\}\backslash )$ for this network.

b$)$ Generator $\backslash (\backslash$mathbf$\{$G $2\}\backslash )$ is an embedded distributed $"$PQ$"$ generator producing a set power input of $\backslash (\backslash$mathrm$\{$S$\}\_\{\backslash$mathrm$\{$G$\}2\}=0\mathrm{.}5\backslash )$ pu$.$ at Angle $0$ degrees $($i$.$e$.,$ unity power factor$).$ How much real power has to be supplied to this network from the swing generator G$1?$ The network loads $\backslash (\backslash$mathbf$\{$S $1\}\backslash )$ to $\backslash (\backslash$mathbf$\{$S $4\}\backslash )$ at nodes $1$ to $4$ respectively are shown on the diagram.

Note: Line resistances and ohmic losses are being ignored.