Question

Fault at bus -$1$ and $2$ are of interest. The prefault voltage is $1.05p.u$ and prefault load current is neglected. The $2\times 2$ positive sequence bus impedance matrix is given by

• A. $-j\left[\begin{array}{cc}9.9454& -3.2787\\ -3.2787& 8.2787\end{array}\right]p.u$
• B. +j$\left[\begin{array}{cc}0.11565& 0.04580\\ 0.04580& 0.13893\end{array}\right]p.u$
• C. +j$\left[\begin{array}{cc}0.11565& 0\\ 0& 0.13893\end{array}\right]p.u$
• D. -j$\left[\begin{array}{cc}9.9454& 0\\ 0& 8.2787\end{array}\right]p.u$

Answer 1

The correct option is B +j$\left[\begin{array}{cc}0.11565& 0.04580\\ 0.04580& 0.13893\end{array}\right]p.u$

$\left(b\right)$


Above circuit is redrawn as in form of admittances as

Neglecting prefault load current,
$E_q^{{}^{\prime \prime }}$ = $E_m^{{}^{\prime \prime }}=V_F=1.05<0^0$
$Y_{bus}=-j\left[\begin{array}{cc}9.9454& -3.2787\\ -3.2787& 8.2787\end{array}\right]p.u$
Inverting $Y_{bus},Z_{bus}=[Y_{bus}{]}^{-1}$= +j$\left[\begin{array}{cc}0.11565& 0.04580\\ 0.04580& 0.13893\end{array}\right]p.u$