For a power system the admittance and impedance matrices for the fault studies are as follows. $$$\eqalign{ & {Y_{bus}} = \left[ {\matrix{ { - j8.75} & {j1.25} & {j2.50} \cr {j1.25} & { - j6.25} & {j2.50} \cr {j2.50} & {j2.50} & { - j5.00} \cr } } \right] \cr & {Z_{bus}} = \left[ {\matrix{ {j0.16} & {j0.08} & {j0.12} \cr {j0.08} & {j0.24} & {j0.16} \cr {j0.12} & {j0.16} & {j0.34} \cr } } \right] \cr} $$$

The pre-fault voltages are $$1.0$$ $$p.u.$$ at all the buses. The system was unloaded prior to the fault. A solid $$3$$ phase fault takes place at bus $$2.$$

The post fault voltages at buses $$1$$ and $$3$$ in per unit respectively are

For a power system the admittance and impedance matrices for the fault studies are as follows. $$$\eqalign{ & {Y_{bus}} = \left[ {\matrix{ { - j8.75} & {j1.25} & {j2.50} \cr {j1.25} & { - j6.25} & {j2.50} \cr {j2.50} & {j2.50} & { - j5.00} \cr } } \right] \cr & {Z_{bus}} = \left[ {\matrix{ {j0.16} & {j0.08} & {j0.12} \cr {j0.08} & {j0.24} & {j0.16} \cr {j0.12} & {j0.16} & {j0.34} \cr } } \right] \cr} $$$

The pre-fault voltages are $$1.0$$ $$p.u.$$ at all the buses. The system was unloaded prior to the fault. A solid $$3$$ phase fault takes place at bus $$2.$$

The per unit fault feeds from generators connected to buses $$1$$ and $$2$$ respectively are

The network shown in the given figure has impedances in p.u. as indicated. The diagonal element $$Y22$$ of the bus admittance matrix $${Y_{BUS}}$$ of the network is

The bus impedance matrix of a $$4$$-bus power system is given by $$${Z_{bus}} = \left[ {\matrix{ {j0.3435} & {j0.2860} & {j0.2723} & {j0.277} \cr {j0.2860} & {j0.3408} & {j0.2586} & {j0.2414} \cr {j0.2723} & {j0.2586} & {j0.2791} & {j0.2209} \cr {j0.2277} & {j0.2414} & {j0.2209} & {j0.2791} \cr } } \right]$$$

A branch having an impedance of $$j0.2\Omega $$ is connected between bus $$2$$ and the reference. Then the values of $${Z_{22,new}}$$ and $${Z_{23,new}}$$ of the bus impedance matrix of the modified network are respectively