Mathematical modeling of wave processes in two-winding transformers taking into account the main magnetic flux

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Authors:


M.S.Seheda, orcid.org/0000-0001-8459-5758, Lviv Polytechnic National University, Lviv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Ye.V.Cheremnykh, orcid.org/0000-0002-4621-2426, Lviv Polytechnic National University, Lviv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

P.F.Gogolyuk, orcid.org/0000-0003-0002-4638, Lviv Polytechnic National University, Lviv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Yu.V.Blyznak, orcid.org/0000-0002-4914-2283, Lviv Polytechnic National University, Lviv, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.


повний текст / full article



Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2021, (5): 080 - 086

https://doi.org/10.33271/nvngu/2021-5/080



Abstract:



Purpose.
To create a method for mathematical modeling of wave processes in power two-winding transformers based on a substitute scheme, which takes into account the design features of power transformers.


Methodology.
Formation of mathematical models for the research on wave processes in power two-winding transformers and further development of the analytical method for solving the system of partial differential equations.


Findings.
A mathematical model for the research on wave processes in power two-winding transformers based on a substitution scheme, witch adequately takes into account both electrical and magnetic connections, is created and an improved analytical method is proposed for solving a system of partial differential equations which allows taking into account the interval time of propagation of electromagnetic waves along the entire length of the windings and the time interval, during which the voltage changes significantly from its complete change during the wave processes,.


Originality.
The paper proposes a mathematical model for the research on wave processes in the windings of power two-winding transformers based on its alternative scheme, which takes into account electrical and magnetic connections, and improves the Fourier method for solving a system of differential equations with partial derivatives.


Practical value.
A mathematical model is created for calculating wave processes in transformers, which allows analyzing the voltage distribution in the transformer windings during the action of pulse voltage on them and adjusting their insulating abilities, given that the operation of power transformers is subject to high requirements for the reliability of their work.



Keywords:
wave process, mathematical model, transformer, differential equations in partial derivatives, boundary value problem

References.


1. Seheda, M.S., Cheremnykh, Y.V., Chimjk, .V., Mazur, T.A., & Kurylyshyn, .M. (2015). Mathematical modelling of stress distribution along the winding transformers under impulse surges. Tekhnichna Elektrodynamika, (6), 8-11. ISSN:1607-7970. E-ISSN:2218-1903.

2. Seheda, M.S., Cheremnykh, Y.V., Gogolyuk, P.F., & Blyznak,Y.V. (2020). Mathematical model of wave processes in two-winding transformers. Tekhnichna Elektrodynamika, (6), 63-67. https://doi.org/10.15407/techned2020.06.005.

3. Beshta, O., Kuvaiev, V., Mladetskyi, I., & Kuvaiev, M. (2020). Ulpa particle separation model in a spiral classifier. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, (1), 31-35. https://doi.org/10.33271/nvngu/2020-1/031.

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5. CIGRE Brochure 577A, Electrical Transient Interaction between Transformers and the Power System. Part 1: Expertise. Joint Working Group A2/C4.39 (2014). Retrieved from http://www.http//xmlopez.webs.uvigo.es/Html/Info/2014_Electrical_Transients_Part1_Expertise.pdf.

6. CIGRE Brochure 577B, Electrical Transient Interaction between Transformers and the Power System. Part 2: Case Studies. Joint Working Group A2/C4.39 (2014). Retrieved from http://www.http//xmlopez.webs.uvigo.es/Html/Info/2014_Electrical_Transients_Part2_Expertise.pdf.

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11. Mikulovi, J.., & ekara, T.B. (2014). The Numerical Method of Inverse Laplace Transform for Calculation of Overvoltages in Power Transformers and Test Results. Serbian Journal of Electrical Engineering, 11(2), 243-256.

12. Isaev, Y.N., Startseva, E.V., & Schekotuev, A.V. (2015). Investigation of wave processes of transformer windings as electric circuit with distributed parameters. Izvestiya Tomskogo Politechnicheskogo Universiteta. Inzhiniering energoresursov, 326(8), 29-35.

 

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ISSN (print) 2071-2227,
ISSN (online) 2223-2362.
Journal was registered by Ministry of Justice of Ukraine.
Registration number КВ No.17742-6592PR dated April 27, 2011.

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