Question

A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the uncompensated system is
$=\left[\begin{array}{ccc}-j6& j3& j4\\ j3& -j7& j5\\ j4& j5& -j8\end{array}\right]$pu
if the shunt capacitance of all transmission lines is 50% compensated, the imaginary part of the $3^{rd}$row $3^{rd}$ column element (in pu) of the bus admittance matrix after compensation is

• A. $-j7.0$
• B. -j8.5
• C. -j7.5
• D. -j9.0

Answer 1

The correct option is B -j8.5

$Y_{BUS}=\left[\begin{array}{ccc}{y}_{11}+y_{12}+y_{13}& -y_{12}& -y_{13}\\ y_{21}& y_{21}+y_{22}+y_{23}& -y_{23}\\ -y_{31}& -y_{32}& y_{31}+y_{32}+y_{33}\end{array}\right]$

$=\left[\begin{array}{ccc}-j6& j3& j4\\ j3& -j7& j5\\ j4& j5& -j8\end{array}\right]$

By comparing for $Y_{33}$element
$y_{31}+y_{32}+y_{30}=-j8$

$(-j4)+(-j5)+j_{30}=-j8$

$y_{30}=j1$

After compensating with 50% of shunt capacitance
$j1\times 0.5=j0.5$

Hence, new value$=-j8-j0.5$

$=-j8.5$