Question

For the Y-bus matrix of a 4-bus system given in per unit, which of the following buses will have shunt elements?

$Y_{BUS}=j\left[\begin{array}{cccc}-5& 2.5& 2& 0\\ 2.5& -9& 1& 5\\ 2& 1& -9& 4\\ 0& 5& 4& -9\end{array}\right]$

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (A), (B), (C)

3

To have a shunt element i.e. $y_{10},y_{20},y_{30},or{y}_{40}$

$Y_{11}=y_{10}+y_{12}+y_{13}+y_{14}$

$y_{10}=y_{11}+y_{12}+y_{13}+y_{14}$

$y_{10}=-5+2.5+2+0=-0.5\ne 0$\)

$y_{10}=-0.5$

$\therefore$ shunt element is present

$y_{20}=Y_{22}-y_{12}-y_{23}-y_{24}$

$=-9+2.5+1+5=-0.5$

$y_{20}=-0.5$

$y_{30}=y_{33}-y_{13}-y_{23}-y_{43}$

$=-9+2+1+4=-2$

$y_{30}=-2$

$y_{40}=Y_{44}-y_{14}-y_{24}-y_{34}$

$=-9+0+5+4$

$y_{40}=0$

$\therefore$ Only bus 4 is not having shunt element.