For a 3-Phase fault at Bus 3, find (see attachment) the post fault bus voltages for each bus, and the currents to all busses. Show your work, including the Y & Z matrices. Explain your method of matrix inversion.
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Please see attached.
Use the Delta-Y transformation to convert the Delta formed by buses 1,2 and 3 to a Y and then we end up with a simple series-parallel network, which can be easily solved.
If Z12, Z13, and Z23 are the impedances across buses 1-2, 1-3 and 2-3, we get the Y network with,
Z1 = Z12*Z13/ZSum, Z2 = Z12*Z23/ZSum, Z3 = Z23*Z31/ZSum, where
ZSum = Z12+ Z13+Z23
Z12 = j0.25, Z13 = j0.5, Z23 = ...
The solution is given in an attachment step-by-step with short explanation.