According to the “Electrical Installation Rules”, one full transposition cycle should be performed on overhead power transmission lines with a voltage of 110-500 kV and a length of more than 100 km to limit asymmetry of currents and voltages.

Transposition is an artificial change in the sequence of phases of a power line (Fig. 1).

Fig. 1. Transposition of wires

In the phase coordinates method, wire transposition is taken into account by adding an additional direct transfer matrix. Consider the calculation of this matrix. In fig. 2 shows a diagram of the transposition of wires with the indicated currents and voltages.

Fig. 2. Transposition of wires

Given that there are no resistances between the input and output, we compose the equations for the circuit in Fig. 2:

.

The presented system of equations can be described by the matrix equation

.

As you know, a direct-transfer matrix connects currents and voltages to the inputs and outputs of a multipole. Thus, the direct transfer matrix of the wire transposition model is described by the equation

,

where , .

The attached file contains the calculation of the matrix form of the model of wire transposition in Matlab: A_transposition.m