A small load flow problem, similar to the one in the text, is shown in Figure $11\mathrm{.}11.$ Note the voltages, impedances and flows are all noted in per$-$unit

$($a$)$ Write a Gauss$-$Seidel based program to solve for the voltage magnitudes and angles that result in the power flows described in the figure. Note that bus $4$ here is the 'swing bus', which means its angle is the reference point.

$($b$)$ Note the voltage source at bus $3$ is producing quite a lot of reactive power. How does this change if you inject $Q=0\mathrm{.}5$ per$-$unit into bus $S?$

$($c$)$ What happens to the line flows if line IIs removed?