# Power Systems Problem (3-Phase Fault; Matrices; Matrix Inversion)

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.

**Please see attachment for complete question and diagram.

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#### Solution Preview

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 = ...

#### Solution Summary

The solution is given in an attachment step-by-step with short explanation.

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