Машинный расчет несимметричных режимов трехфазных цепей с динамической нагрузкой

Abstract

A new approach to analyzing three-phase circuits in the phase coordinates under unbalanced normal and emergency operating conditions is proposed, in which the information about the three-phase circuit to be analyzed by means of software is entered in a simplified manner. The equivalent circuits of three-phase generators, power lines, and static and dynamic loads are aggregated and considered in a generalized form. With such presentation, the work with a three-phase circuit diagram is significantly simplified even if it contains unbalanced loads, a few faulty sections, and control links in the equivalent circuits of electrical machines. The labeling of three-phase circuit nodes is proposed that allows three-phase and single-phase parts of the circuit to be distinguished. The topologic list of branches intended for computer-aided calculations of currents and voltages and currents is compiled for three-phase branches in a generalized form. The obtained list is compact and retains a clear representation of the three-phase circuit. The analogy between the basic electrical equations written for electrical circuit three-phase and single-phase branches is shown. Thus, the voltages and currents in a three-phase element are interrelated by equations similar to the generalized Ohm’s law, while Kirchhoff's current law is written for three-phase nodes and has the same form as for single-phase circuits. The analogy of drawing up the incidence matrix and the matrix of nodal equations is shown. Submatrices of dimensions 3 × 3, 1 × 3, or 1 × 1 depending on the node label appear as entries in the incidence matrices and nodal admittance matrices of a three-phase circuit. The nodal equations used for carrying out the subsequent analysis of the circuit in the phase coordinates are written in a standard way as in single-phase circuits. In analyzing emergency operating conditions, it is proposed to keep the simplicity and clarity of the approach by representing the circuit faulty section of as a corresponding branch embedded into the three-phase circuit. The developed approach is illustrated by calculation of unbalanced and emergency operating conditions in a complex three-phase unbalanced circuit containing two synchronous generators, one dynamic load, and one static load. The calculation has been carried for four- and three-wire three-phase circuits.