Question

The bus admittance matrix of a three-bus thee line system is
$Y=j\left[\begin{array}{ccc}-13& 10& 5\\ 10& -18& 10\\ 5& 10& -13\end{array}\right]$
If each transmission line between the two buses is represented by an equivalent $\pi$-network, the magnitude of the shunt susceptance of the line connecting bus 1 and 2 is

• A. 4
• B. 2
• C. 1
• D. 0

Answer 1

The correct option is B 2

$y_{ik}=$ Series admittance of the line connecting buses i and k
$\frac{y_{ik}^{{}^{\prime }}}{2}=$Half line charging admittance in bus admittance matrix

$Y_{11}=\frac{y_{12}^{{}^{\prime }}}{2}+\frac{y_{31}^{{}^{\prime }}}{2}+y_{12}+y_{31}=-j13$
$y_{12}=-y_{12}=j10$
$y_{23}=-y_{23}=j10$
$y_{31}=-y_{31}=j5$
$\therefore y_{12}^{{}^{\prime }}+y_{31}^{{}^{\prime }}=2[-j13+j10+j5]$
$=j4$
Similarly,
$y_{12}^{{}^{\prime }}+y_{23}^{{}^{\prime }}=2[-j18+j10+j10]$
$=j4$
$y_{23}^{{}^{\prime }}+y_{31}^{{}^{\prime }}=2[-j13+j10+j5]$
$=j4$
$\Rightarrow y_{12}^{{}^{\prime }}=j6-j4=j2$