Phase Coordinates Method: Power Line Model

In almost any simulated circuit there is a power line. The phase coordinate method allows you to simulate the power line, including with distributed parameters, taking into account the longitudinal active and capacitive conductivity.

Fig. 1 shows a line equivalent circuit with distributed parameters.

phcoor4_1

Fig. 1. The equivalent circuit of a power line with distributed parameters

In addition to longitudinal resistivities in both positive phcoor4_1 and zero sequence phcoor4_2, due to the material and location of the wires of the power line, the phase coordinate method takes into account specific conductivities phcoor4_3 and phcoor4_4 (positive and zero sequence, respectively). The active component of conductivity takes into account losses on the corona, losses on melting ice and losses on leakage currents; capacitive occurs due to the charging currents of the power line.

To calculate the direct transmission matrix phcoor2_f9 of the power line, an auxiliary matrix is first compiled according to the expression

phcoor4_5,

where

phcoor3_f8,

phcoor4_6,

Матрица проводимостей ЛЭП.

The direct transmission matrix is determined by the expression

phcoor4_8,

where phcoor4_9 is the length of the power line. The exp function in this case denotes the matrix exponential.

The attached file contains the calculation of the matrix phcoor2_f9 of the power line in Matlab: A_line.m

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