(Solved): The one-line diagram of a simple four-bus power system is shown below. Each generator is represent ...

The one-line diagram of a simple four-bus power system is shown below. Each generator is represented by an emf behind the transient reactance. All impedances are expressed in per unit on a common 100 MVA base, and for simplicity, all resistances and shunt capacitances are neglected. The generators are operating at no load at their rated voltage with their emf's in phase, and transformers phase shifts are neglected. Assume pre-fault voltage value of \( 1.0 \) per unit at all buses. (a) Using Thevenin's theorem, determine the fault current when a balanced three-phase fault occurs on bus 2 . (b) The per unit bus impedance matrix of the four-bus power system is: \[ \boldsymbol{Z}_{b u s}=\left[\begin{array}{cccc} j 0.240 & j 0.140 & j 0.200 & j 0.200 \\ j 0.140 & j 0.2275 & j 0.175 & j 0.175 \\ j 0.200 & j 0.175 & j 0.310 & j 0.310 \\ j 0.200 & j 0.175 & j 0.310 & j 0.500 \end{array}\right] \] Using the bus impedance matrix method, compute the fault current, the bus voltages, and line currents during the fault when a balanced three-phase fault occurs on bus 2 . [30 points]