How to obtain the sequence impedances from the Z matrix

To obtain the sequence impedance from the Z matrix, transpose the impedance matrix (Z) first:

Impedance Matrix:


Symmetrical Component Matrix:


Then the sequence impedances are as follows:



Example:

Given the impedance matrix of a cable:



Zs = 0.064143 + j0.010117
Zm = 0.010583 + j0.003438

Thus,
Z0 = (0.064143 + j0.010117) + 2*(0.010583 + j0.003438)
Z0 = 0.0853 + j0.017

Z0 = R0 + jX0


Z1 = (0.064143 + j0.010117) - (0.010583 + j0.003438)
Z1 = 0.0536 + j0.0067

Z1 = R1 + jX1


These are the same results shown on the cable datablock: