Question

For the Y-bus matrix of a 4-bus system given in per unit , the buses having shunt elements are
$Y_{BUS}=j\left[\begin{array}{cccc}-5& 2& 2.5& 0\\ 2& -10& 2.5& 4\\ 2.5& 2.5& -9& 4\\ 0& 4& 4& -8\end{array}\right]$

• A. 3 adn 4
• B. 2 and 3
• C. 1 and 2
• D. 1,2 and 4

Answer 1

The correct option is C 1 and 2

Method 1
$\left[\begin{array}{cccc}{Y}_{11}& Y_{12}& Y_{13}& Y_{14}\\ Y_{21}& Y_{22}& Y_{23}& Y_{24}\\ Y_{31}& Y_{32}& Y_{33}& Y_{34}\\ Y_{41}& Y_{42}& Y_{43}& Y_{44}\end{array}\right]$
Here,
$Y_{11}=y_{10}+y_{12}+y_{13}+y_{14}=-5j...\left(i\right)$
$Y_{22}=y_{20}+y_{22}+y_{23}+y_{24}=-10j...\left(ii\right)$
$Y_{33}=y_{30}+y_{32}+y_{33}+y_{34}=-10j...\left(iiI\right)$
$Y_{42}=y_{40}+y_{42}+y_{43}+y_{44}=-10j...\left(iv\right)$
$Y_{12}=Y_{21}=-y_{12}=2j$
$Y_{13}=Y_{31}=-y_{13}=2.5j$
$Y_{14}=Y_{41}=-y_{14}=0j$
$Y_{23}=Y_{32}=y_{23}=2.5j$
$Y_{24}=Y_{42}=-y_{24}=4j$
$Y_{34}=Y_{43}=-y_{34}=4j$
From equation (i),
$y_{10}=Y_{11}-Y_{12}-y_{13}-y_{14}$
$=-5j+2j+2.5j+0j=-0.5j$
Form equation (ii),
$y_{20}=Y_{22}-y_{12}-y_{23}-y_{24}$
$=-10j+2j+2.5j+4j$
$=-1.5j$
From equation (iii),
$y_{30}=Y_{33}-y_{31}-y_{32}-y_{34}$
$=-9j+2.5j+2.5j+4j$
$=0$
From equation (iv),
$y_{40}=Y_{44}-y_{41}-y_{42}-y_{43}$
$=-8j-0+4j+4j=0$
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Method 2
If sum of all the elements in a row is zero, then there is no shunt element at that bus. If sum of elements in the row is non zero, then there is a shunt element.
Hence, at bus 1 and 2, there are shunt elements. ​​​​​​​
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