(a) The bus impedance matrix for a three-bus power system is [boldsymbol{Z}_{text {bus }}=jleft[begin{array}{ccc}0.12&0.08&0.040.08&0.12&0.060.04&0.06& 0.08end{array} ight] text...

(a) The bus impedance matrix for a three-bus power system is

\[\boldsymbol{Z}_{\text {bus }}=j\left[\begin{array}{ccc}0.12&0.08&0.04\\0.08&0.12&0.06\\0.04&0.06& 0.08\end{array}\right] \text { per unit }\]

where subtransient reactances were used to compute \(\boldsymbol{Z}_{\text {bus }}\). Prefault voltage is 1.0 per unit and prefault current is neglected.

• Draw the bus impedance matrix equivalent circuit (rake equivalent). Identify the per-unit self- and mutual impedances as well as the prefault voltage in the circuit.

• A three-phase short circuit occurs at bus 2. Determine the sub transient fault current and the voltages at buses 1, 2, and 3 during the fault.

(b) For 7.18 Repeat for the case of  

\[\boldsymbol{Z}_{\text {bus }}=j\left[\begin{array}{lll}0.4&0.1&0.3\\0.1&0.8&0.5\\0.3&0.5& 1.2\end{array}\right] \text { per unit }\]