DETERMINATION OF THE PERMISSIBLE LONG-TERM LOAD FOR POWER TRANSFORMERS

DOI: 10.47026/1810-1909-2025-2-97-111

УДК 621.31

ББК 31.2

Alexander I. ORLOV, Denis V. BORTNIK, Ilya A. KARPOV

Key words

power transformer, permissible long-term load, thermal regime, Newton-Richmann equation, heat transfer coefficient.

Abstract

The article addresses the problem of determining the permissible long-term load for power transformers while considering their thermal regime. The relevance of this work is due to the high level of physical wear and tear on transformer equipment and the need to improve its operational reliability. Exceeding the temperature of windings and oil accelerates insulation aging, necessitating the development of methods to predict the thermal state of transformers.

The purpose of this work is to develop a methodology for determining the permissible long-term load of a transformer depending on ambient temperature. The scientific novelty lies in the development of an approximate model of the thermal operating mode of a power transformer, allowing for the prediction of element temperatures and permissible loads.

Materials and methods. Research methods include mathematical modeling using Newton – Rikhman equations to describe heat exchange between thermally homogeneous elements of the transformer. The fourth-order Runge – Kutta method with a time step of 30 seconds was used for numerical solution of the system of differential equations. Calculations were performed using author-developed programs in Python with Numpy and Matplotlib libraries. A comparative analysis of simulation results with experimental data from open sources and GOST 14209-85 requirements was conducted.

Results. A mathematical model is proposed, treating the transformer as a system of three thermally homogeneous elements – the core, windings, and oil – with heat exchange described by Newton – Rikhman equations. Equations are obtained that make it possible to determine the steady-state temperature of transformer elements and the maximum allowable load factor, taking into account the limitation of the temperature of the winding and oil, the set ambient temperature and the load factor. Approximate formulas were obtained for determining the volumes and contact surface areas of transformer elements based on a calculation scheme. Ratios are presented that allow these values to be estimated approximately depending on the rated power for geometrically similar transformers. It was shown that the heat transfer coefficient between the oil and the environment has the greatest impact on the thermal regime. A condition for the permissible operation of the transformer was formulated, taking into account the required load level and ambient temperature. Simulation results were validated by comparison with experimental data.

Conclusions. A mathematical model of the transformer’s thermal regime has been proposed, taking into account the inertia of temperature changes in its thermally homogeneous elements. The influence of the load factor and ambient temperature on the steady-state temperature values of the elements has been determined. A condition for the permissible operation of the transformer has been obtained, ensuring the limitation of winding and oil temperatures.

References

1. Anishchenko V.A., Gorokhovik I.V. Vliyanie peregruzochnoi sposobnosti maslonapolnennykh transformatorov na propusknuyu sposobnost’ elektricheskoi seti [Influence of overload capacity of oil-filled transformers on the throughput of electric network]. Izvestiya vysshikh uchebnykh zavedenii i energeticheskikh ob”edinenii SNG, 2018, vol. 61, no. 4, pp. 310–320.
2. Anishchenko V.A., Ivanov V.V. Opredelenie dopustimykh sistematicheskikh peregruzok raspredelitel’nykh maslyanykh transformatorov [Determination of permissible systematic overloads of distribution oil transformers]. Izvestiya vysshikh uchebnykh zavedenii i energeticheskikh ob”edinenii SNG, 2015, no. 3, pp. 5–15.
3. Zaliznyi D.I. Ispol’zovanie teplovoi modeli dlya teoreticheskikh issledovanii teplovykh protsessov v maslyanykh transformatorakh 10/0,4 kV [Using a thermal model for theoretical studies of thermal processes in oil transformers 10/0.4 kV]. Vestnik Gomel’skogo gosudarstvennogo tekhnicheskogo universiteta im. P.O. Sukhogo, 2001, no. 3–4 (6), pp. 51–60.
4. Zaliznyi D.I., Shirokov O.G. Raschet temperatury osnovnykh elementov silovogo maslyanogo transformatora na osnove analiza temperatury poverkhnosti ego baka [Calculation of the temperature of the main elements of a power oil transformer based on the analysis of the surface temperature of its tank]. Izvestiya vysshikh uchebnykh zavedenii i energeticheskikh ob”edinenii SNG, 2012, no. 4, pp. 18–28.
5. Ivanov-Smolenskii A.V. Elektricheskie mashiny: v 2 t. [Electrical Machines. 2 vols.]. Moscow, MEI Publishing House Publ., 2006, vol. 1, 652 p.
6. Kish L. Nagytranszformatorok. Müszaki Könyvkiadó, Budapest, 1973. (Russ. ed.: Nagrev i okhlazhdenie transformatorov. Moscow, Energiya Publ., 1980, 208 p.)
7. Pokazateli deyatel’nosti. Proizvodstvennyi potentsial. PAO «Rosseti Tsentr» [Performance indicators. Production potential. PJSC “Rosseti Centre”]. Available at: https://www.mrsk-1.ru/investors/indicators/production-potential/ (Accessed Date: 2024, Dec. 6).
8. Soldatov V.I., Zaichikov I.V., Lavrov I.V. Metod prognozirovaniya teplovogo sostoyaniya silovykh maslonapolnennykh transformatorov v zavisimosti ot temperatury okruzhayushchei sredy pri postoyannoi ekspluatatsionnoi nagruzke [Method for predicting the thermal state of power oil-filled transformers depending on ambient temperature at constant operational load]. Izvestiya Tul’skogo gosudarstvennogo universiteta. Tekhnicheskie nauki, 2013, no. 9–1, pp. 159–164.
9. Soldatov V.I., Zaichikov I.V., Lavrov I.V. Rasshirenie metoda prognozirovaniya teplovogo sostoyaniya silovykh maslonapolnennykh transformatorov v zavisimosti ot temperatury okruzhayushchei sredy i povysheniya nagruzki [Expansion of the method for predicting the thermal state of power oil-filled transformers depending on ambient temperature and increased load]. Izvestiya Tul’skogo gosudarstvennogo universiteta. Tekhnicheskie nauki, 2013, no. 9–1, pp. 165–170.
10. Tikhomirov P.M. Raschet transformatorov [Transformer Calculations]. Moscow, Energoatomizdat Publ., 1986, 528 p.
11. Snit’ko I.S., Tikhonov A.I., Stulov A.V., Tumakov N.Yu. Faktory, vliyayushchie na srok sluzhby energoeffektivnykh transformatorov [Factors affecting the service life of energy-efficient transformers]. Energiya edinoi seti, 2024, no. 2(73), pp. 54–60.
12. Shirokov O.G., Zaliznyi D.I., Los’ D.M. Parametricheskaya identifikatsiya matematicheskoi teplovoi modeli silovogo maslyanogo transformatora [Parametric identification of the mathematical thermal model of a power oil transformer]. Vestnik Gomel’skogo gosudarstvennogo tekhnicheskogo universiteta im. P.O. Sukhogo, 2005, no. 1(26), pp. 35–42.

Information about the authors

Alexander I. Orlov – Candidate of Technical Sciences, Associate Professor, 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).

Denis V. Bortnik – Assistant Lecturer, Department of Electromechanics, Post-Graduate Student, Department of Power Supply and Technical Diagnostics, Mari State University, Russia, Yoshkar-Ola (bortnik_denis16@mail.ru; ORCID: https://orcid.org/0009-0002-7010-8271).

Ilya A. Karpov – Post-Graduate Student, Department of Power Supply and Technical Diagnostics, Mari State University, Russia, Yoshkar-Ola (ShumkenRP@yandex.ru; ORCID: https://orcid.org/0000-0002-9768-9574).

For citations

Orlov A.I., Bortnik D.V., Karpov I.A. Determination of the permissible long-term load for power transformers. Vestnik Chuvashskogo universiteta, 2025, no. 2, pp. 97–111. DOI: 10.47026/1810-1909-2025-2-97-111 (in Russian).

Download the full article