Question

The positive, negative and zero sequence bus impedance and admittance matrices of a system are given as follows:

\(Z^{+}=Z^{-}=j\left[\begin{array}{ccc}0.14 & 0.11 & 0.125 \\ 0.11 & 0.14 & 0.125 \\ 0.125 & 0.125 & 0.175\end{array}\right] \quad Y^{+}=Y^{-}=j\left[\begin{array}{ccc}-24 & 10 & 10 \\ 10 & -24 & 10 \\ 10 & 10 & -20\end{array}\right]\)

\(Z^{0}=j\left[\begin{array}{ccc}0.10 & 0.10 & 0.10 \\ 0.10 & 0.30 & 0.20 \\ 0.10 & 0.20 & 0.30\end{array}\right] \quad Y^{0}=j\left[\begin{array}{ccc}-16.66 & 3.33 & 3.33 \\ 3.33 & -6.66 & 3.33 \\ 3.33 & 3.33 & -6.66\end{array}\right]\)

Assuming no-load conditions and assuming all bus voltages to be at \(1 / 0\) pu in steady-state, apply a solid, single-line-to-ground fault at phase 'a' of bus 3 and find:

(i) [10 marks] The phase 'a' voltage at Bus 1 during the fault

(ii) [15 marks] The phase 'a' current in the line between Bus 1 and Bus 2 during the fault.