## Weightage of Bus Admittance Matrix

Total 3 Questions have been asked from Bus Admittance Matrix topic of Power Systems subject in previous GATE papers. Average marks 1.33.

$A\;3$-bus power system is shown in the figure below, where the diagonal elements of $Y$-bus matrix are: $Y_{11}=-j12\;pu,\;Y_{22}=-j15\;pu$ and $Y_{33}=-j7\;pu.$

The per unit values of the lines reactances $p,q$ and $r$ shown in the figure are

The bus admittance matrix for a power system network is

$\begin{bmatrix}j39.9&j20&j20\\j20&-j39.9&j20\\j20&j20&j39.9\end{bmatrix}pu$

There is a transmission line, connected between buses 1 and 3, which is represent by the circuit shown in figure.

If this transmission line is removed from service, what is the modified bus admittance matrix?

$\left[\begin{array}{ccc}-j6& j3& j4\\ j3& -j7& j5\\ j4& j5& -j8\end{array}\right]\mathrm{pu}.$
If the shunt capacitance of all transmission line is 50% compensated, the imaginary part of the ${3}^{\mathrm{rd}}$row${3}^{\mathrm{rd}}$column element (in pu) of the bus admittance matrix after compensation is