I posted this on /sqt/ but got no answers and can't find an answer anywhere else so in making a thread.

Where doing asymetric fault analysis and there's something that doesn't add up.

By definition, the impedance matrix of a system is the inverse of its admittance matrix, this is:
$$Z_{bus} = Y_{bus}^{-1}$$

Because of this fact, whenever we've had to use the impedance matrix, for example to get the thevenin impedance a bar "sees", we simply construct $Y_{bus}$ and then invert it.

The problem is, now that we're doing asymmetric faults, You need to know the thevenin impedance each bar sees in every sequence in order to compute the fault voltages and currents for each bar. basically we need $Z_{bus}^{(0)},Z_{bus}^{(1)}$ and $Z_{bus}^{(2)}$

Now, the book were using (Stevenson, Grainger) uses an algorithm to build the $Z_{bus}$ of a system directly from its diagram and this works just fine, but if you construct $Y_{bus}$ for lets say the zero sequence network and then invert it, you get a $completely$ different matrix from the $Z_{bus}$ that was built directly using the algortihm.

This is a major issue because we don't know how to use that algorithm (prof didn't teach it) and we have no time to learn it.

Tl;dr why does constructing $Y_{bus}$ and inverting it does not yield $Z_{bus}$ when dealing with sequence networks?

(Is coffee good for you?)