Calculation of power transformer inductance matrix

DOI: 10.47026/1810-1909-2023-4-120-129

УДК 621.31

ББК 31.2

Aleksandr I. ORLOV, Sergei V. VOLKOV, Ilsur kh. GARIPOV

Key words

inductance, inductance matrix, magnetic core, winding, transformer, modified nodal analysis

Abstract

Practical calculations of electric equipment and electric networks are performed using equivalent circuits. Without taking into account saturation phenomena, electromagnetic processes in a power transformer are described by a system of linear equations, which can be represented in matrix form. The transformer inductance matrix contains self and mutual winding inductances, whose values for one phase are determined directly from the passport data containing the results of no-load and short circuit experiments. Mutual inductances between phases depending on the type and size of the magnetic core are not usually given in the transformer documentation. It does not allow to simulate the operating modes that differ from the steady state with uniform phase load.

The purpose of the work is to develop an algorithm for calculating elements of the power transformer inductance matrix according to its passport data and magnetic circuit parameters.

The scientific novelty lies in use of information about magnetic circuit type and size to determine elements of the inductance matrix.

Materials and methods. Methods of linear electric and magnetic circuit theory are used in the work.

Results. The proposed algorithm for calculation of power transformer inductance matrix includes three stages: calculation of self and mutual inductances for one phase; construction of an equivalent circuit for a magnetic circuit and calculation of magnetic fluxes in order to take into account the mutual influence of windings on various phases; assembly of the inductance matrix of three-phase transformer. A method is proposed for constructing the transformer inductance matrix with an arbitrary type of magnetic circuit, phases and windings quantity. The method involves preliminary calculation of the coefficient matrix that characterizes the magnetic circuit and depends mainly on its type and, to a less, on the ratio of geometric dimensions in rods and yokes. The coefficient matrix can be calculated in advance and used to determine the inductance matrix of a wide range of transformers.

Conclusions. 1. The passport data of the transformer do not allow to model transformer operation at unbalanced load validly. 2. An algorithm for determining the inductance matrix of transformers has been developed. 3. A method for compilation of a transformer inductance matrix with an arbitrary type of magnetic circuit, the number of phases and windings is introduced. The practical significance of the algorithm is determined by the simplicity of algorithmizing, as well as by the possibility of using it in computer simulation of electrical circuits with transformers, for example, using the modified nodal analysis method.

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Information about the authors

Aleksandr I. Orlov – Candidate of Technical Sciences, Head of the Department of Electromechanics, Mari State University, Russia, Yoshkar-Ola (a.i.orlov@yandex.ru; ORCID: https://orcid.org/0000-0003-1152-6668).

Sergei V. Volkov – Candidate of Technical Sciences, Associate Professor, Dean of the Electroenergy Faculty, Mari State University, Russia, Yoshkar-Ola (svedin2011@mail.ru; ORCID: https://orcid.org/0000-0003-1152-6668).

Ilsur Kh. Garipov – Candidate of Technical Sciences, Head of the Department of Power Supply and Technical Diagnostics, Mari State University, Russia, Yoshkar-Ola (ilsur@bk.ru; ORCID: https://orcid.org/0000-0002-3037-7365).

For citations

Orlov A.I., Volkov S.V., Garipov I.Kh.  CALCULATION OF POWER TRANSFORMER INDUCTANCE MATRIX. Vestnik Chuvashskogo universiteta, 2023, no. 4, pp. 120–129. DOI: 10.47026/1810-1909-2023-4-120-129 (in Russian).

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