Машинный расчет несимметричных режимов трехфазных цепей с динамической нагрузкой

Татьяна [Tatyana] Александровна [A.] Васьковская [Vaskovskaya]; Марина [Marina] Павловна [P.] Жохова [Zhokhova]; Кристина [Kristina] Сергеевна [S.] Рослова [Roslova]

doi:10.24160/1993-6982-2021-1-62-69

Татьяна [Tatyana] Александровна [A.] Васьковская [Vaskovskaya]
Марина [Marina] Павловна [P.] Жохова [Zhokhova]
Кристина [Kristina] Сергеевна [S.] Рослова [Roslova]

DOI: https://doi.org/10.24160/1993-6982-2021-1-62-69

Keywords: three-phase circuit, phase coordinates, static load, dynamic load, unbalanced and emergency operating conditions

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.

Information about authors

Татьяна [Tatyana] Александровна [A.] Васьковская [Vaskovskaya]

Dr.Sci. (Techn.), Assistant Professor of Theoretical Fundamentals of Electrical Engineering Dept., NRU MPEI, e-mail: tatiana.vaskovskaya@gmail.com

Марина [Marina] Павловна [P.] Жохова [Zhokhova]

Ph.D. (Techn.), Assistant Professor of Theoretical Fundamentals of Electrical Engineering Dept., NRU MPEI, e-mail: ZhokhovaMP@mail.ru

Кристина [Kristina] Сергеевна [S.] Рослова [Roslova]

Student of Relay Protection and Automation of Energy Systems Dept., NRU MPEI, e-mail: Roslovaks@mpei.ru

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Для цитирования: Васьковская Т.А., Жохова М.П., Рослова К.С. Машинный расчет несимметричных режимов трехфазных цепей с динамической нагрузкой // Вестник МЭИ. 2021. № 1.
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For citation: Vaskovskaya T.A., Zhokhova M.P., Roslova K.S. Computer-Aided Analysis of Unbalanced Operating Conditions in Three-Phase Circuits Containing a Dynamic Load. Bulletin of MPEI. 2021;1:62—69. (in Russian).