# Answer Question

### Series impedance matrix format

Hello

I'm trying to transpose a transmission line with delta, vertical and horizontal subsections with different crossarm configurations in it's full lenght. In order to achieve the minimal imbalance factor (optimal transposition) throughout the line, the differences in conductors mutual-impedances must be minimal. I have created the possible transposition scenarios and now i would like to test them and select the best one. My question is how the series impedance matrix is constructed/formated? For example I use the General Line Geometry Data Input, which allows to insert custom tower configuration. In this model (for simplified example, lets take a horizontal layout of conductors) i define the conductors from left to right C1, C2 and C3 (phase 1, 2, 3). It generates the following matrix:

C11, C12, C13

C21, C22, C23

C31, C32, C33

Where self-impedances are indexed 11, 22, 33 and mutual-impedances are all other combinations.

In case of untransposed line (depends on how the conductor positions are defined initially) i can sum up the output impedance matrixes and calculate the imbalance factors for this case, because the conductor number correlates to the phase number.

Question becomes harder, when i try to make a transposition in the next section.

The General Line Geometry Data Input block allows to change connection phasing. Conductor configuration remains the same, but the phase is changed. For example C1 is now phase 2. Then the conductor definition remains the same, but the phasing is different: C1, C2, C3 (phase 2, 1, 3). How is it manifested in impedance matrix? How does changing the phasing influence the matrix? Does the matrix become phase based instead of condctor based?

PSCAD help provides the following sentence:

The positions of elements in this matrix are dependent on the manner in which the conductors/ground wires have been numbered. The type of ideal transposition that has been selected will also affect this matrix.

How do they depend on numbering?

Hope you understood my problem and help me solve this question.

Best Regards

RK