Question

A 3-bus power system is shown in the figure below, where the diagonal elements of Y-bus matrix are:$Y_{11}=-j12pu,Y_{22}=-j15puand{Y}_{33}=-j7pu.$

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

• A. p = -0.2, q = -0.1, r = -0.5
• B. p = 0.2, q = 0.1, r = 0.5
• C. p = -5, q = -10, r = -2
• D. p = 5, q = 10, r = 2

Answer 1

The correct option is B p = 0.2, q = 0.1, r = 0.5

Given,
$Y_{11}=-j12p.u.$
$Y_{22}=-j15p.u.$
$Y_{33}=-j7p.u.$

We know that,
$Y_{11}=y_{12}+y_{13}=-j13p.u...\left(i\right)$
$Y_{22}=y_{12}+y_{23}=-j15p.u...\left(ii\right)$
$Y_{33}=y_{13}+y_{23}=-j7p.u...\left(iii\right)$

Form equation (i) and (ii),

$y_{13}-y_{23}=j3p.u$

$y_{13}+y_{23}=-j7p.u...\left(iv\right)$

$y_{13}=-j2p.u$

$y_{23}=-j5p.u$

$y_{12}=-j10p.u$

The p.u. values of line reactances p, q and r are

$jr=\frac{1}{-j2}=j0.5p.u$

$jp=\frac{1}{-j5}=j0.2p.u.$

$jq=\frac{1}{-j10}=j0.1p.u.$

$\therefore p=0.2,q=0.1,r=0.5$