Phase Coordinates Method: Equivalent Power System Model

The part of the network diagram, about which only general parameters are known, is modeled using an equivalent power system. In the phase coordinate method, the equivalent power system is modeled by the resistances in the direct and zero sequence and by the voltage source.

The equivalent circuit of the three-phase power system is shown in Fig. 1. It is given by the resistances along the straight and zero sequences, as well as the equivalent voltage source.

phcoor3_1

Fig. 1. Equivalent power system equivalent circuit

In a symmetric three-phase system, the phase emf vectors are displaced relative to each other by 120 °. Taking into account possible regulation, the equivalent voltage source matrix phcoor3_f1 by the phase coordinate method will be determined by the expression

phcoor3_f2,

where phcoor3_f4 is the rated voltage of the network (linear or phase, acting or amplitude); phcoor3_f3 – voltage regulation coefficient; phcoor3_f5 – angle of power transmission.

The equivalent direct transmission matrix of the equivalent power system is determined based on the resistance in the direct and zero sequence according to the following expressions

phcoor3_f6,

where

phcoor3_f7, phcoor3_f8, phcoor3_f9,

phcoor3_f10, phcoor3_f11 – resistance of the equivalent system in a direct and zero sequence, respectively.

The attached file contains the calculation of the matrix formphcoor2_f9 and voltage of the equivalent power system in Matlab: A_eqsys.m

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