Improvement of modeling techniques of transients in transformers based on magnetoelectric equivalent schemes

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Authors:


D.Patalakh, orcid.org/0000-0001-8264-8625, Zaporizhzhia Polytechnic National University, Zaporizhzhia, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

A.Prykhodko, orcid.org/0000-0001-6258-6826, Zaporizhzhia Polytechnic National University, Zaporizhzhia, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

K.Lut, orcid.org/0000-0002-9842-3540, Zaporizhzhia Polytechnic National University, Zaporizhzhia, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

S.Tykhovod, orcid.org/0000-0003-0748-1735, Zaporizhzhia Polytechnic National University, Zaporizhzhia, 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, (6): 107 - 112

https://doi.org/10.33271/nvngu/2021-6/107



Abstract:



Purpose.
Use of an improved numerical method of calculating transient processes in electrical circuits for modeling electromagnetic processes in nonlinear magneto-electric circuits, and also development of a circuit model based on this method, which leads to the convenience of calculation.


Methodology.
Approximation of functions by Chebyshevs polynomials, numerical methods of differential equations integrating, matrix methods, spline interpolation, programming, theory of electric and magnetic circuits.


Findings.
On the base of the well-known method of transient process analysis in linear electric circuits, the method of numerical calculation of transient processes in nonlinear magneto-electric equivalent circuits of transformer has been developed. By the help of the proposed method it is possible to reduce processing time for modeling electromagnetic processes in transformers. The example of using the developed method is shown. The computer program for modeling of electromagnetic transient in a single-phase transformer based on the described method has been developed. This example shows reduction of processor time by more than four times compared to examples of calculations based on other known methods.


Originality.
The method in which the solution of state differential equations is presented in the form of decomposition into a series along orthogonal Chebyshevs polynomials is used in this work. The polynomial approximation applied in this work is not corresponding to the solution function itself, but its derivative, which significantly reduces the error of integration of differential equations. Differential equations of state are transformed into linear algebraic equations for special images of solution functions. A principle is developed of constructing magneto-electric substitution circuits in which images of solution functions appear. Images of true dynamic currents and magnetic fluxes in the proposed equivalent scheme are interpreted as direct currents and direct magnetic fluxes. The used method has shown advantages in accuracy and time of simulation of electromagnetic transient over other known methods based on application of magneto-electric substitution circuits.


Practical value.
The developed method opens up the possibility of using the apparatus of the theory of electric and magnetic circuits to work with images of currents and magnetic fluxes. Based on this, a universal software complex is being developed to calculate transients in transformers of various constructions.



Keywords:
transient electromagnetic process, differential equations, circuit model, polynomial approximation, Chebyshevs polynomials, transformer

References.


1. Eiichi, H., Tadashi, K., Junichi, A., & Hisatochi, I. (2016). Power System Transient Analysis: Theory and Practice using Simulation Programs (ATP-EMTP). ISBN: 978-1-118-73749-1. 280 p.

2. Akulin, A., & Suponin, A. (2017). Modeling and Advanced Circuit Analysis in PSpice. Electronics Science. Technology. Business, 82-91. https://doi.org/10.22184/1992-4178.2017.171.10.82.91.

3. Chernykh, I.V. (2014). Modeling of electrical devices in MATLAB, SimPowerSystems and Simulink. Moscow: DMK Press. St. Petersburg: Peter. Publ. SBN 5-94074-395-1 (DMK Press). ISBN 978-5-388-00020- (Peter).

4. Bansal, R.K. (2018). Fundamentals of Numerical Methods. Oxford: Alpha Science International Ltd. ISBN 1783323604.

5. Smancer, D.S. (2019). Simulation of transients in electrical circuits of periodic non-sinusoidal current. Scientific and Practical Conference Issues of Technical and Physical and Mathematical Sciences in the Light of Modern Studies, 8-9(15), 5-11. Retrieved from: https://libeldoc.bsuir.by/bitstream/123456789/37109/1/Smantser_Modelirovaniye.pdf.

6. Tikhovod, S.M. (2014). Modification of magnetoelectric substitution circuits of electromagnetic devices for analysis of transient processes. Elektrichestvo, (2), 53-60. ISSN: 0013-5380. eISSN: 2411-1333.

7. Guadalupe, G. Gonzalez, & Mehrdad Ehsani (2018). Power-Invariant Magnetic System Modeling. International Journal of Magnetics and Electromagnetism, 4(1). https://doi.org/10.35840/2631-5068/6512.

8. Lambert, M., Mahseredjian, J., Martnez-Dur, M., & Siroi, F. (2015). Magnetic Circuits within Electric Circuits: Critical Review of Existing Methods and New Mutator Implementations. IEEE Transactions on Power Delivery. 30(6), 2427-2434. https://doi.org/10.1109/TPWRD.2015.2391231.

9. Arushanyan, O., Volchenskova, N., & Zaletkin, S. (2013). Amethod for solving the auchy problem for ordinary differential equations using Chebyshevs series. Computational methods and programming, 14, 203-214.

10. Katrich, S.A. (2015). Computing features of minimization of the error in the approximation of functions on chebyshev interpolation units. Vectnik Taganrogckogo inctituta imeni A. P. Chehova. Fiziko-matematicheckie i ectectvennie nauki, (1), 67-72. ISSN 2225-501X. eISSN: 2306-2037.

11. Tokmakov, I. (2015). Modeling of electromechanical transients in asynchronous motors based on the use of Chebyshevs polynomials. Electrical Engineering and Power Engineering, (2), 35-41. https://doi.org/10.15588/1607-6761-2015-2-5.

12. Trigub, R. (2016). Polynomials with integer coefficients and Chebyshev polynomials. Ukrainian mathematical news, 13(3), 421-448.

13. Khovanskii, A. (2013). Chebyshevs polynomials and their appeals. Matematicheskoye Prosveshcheniye, 17, 93-106. Retrieved from: https://www.math.toronto.edu/askold/2013%20Mat-Prosv-17%2093-106.pdf.

14. Tykhovod, S., & Patalakh, D. (2019). Calculation of Transients in Electrical Circuits at the Use of Solution Approximation by Chebyshevs Polynomials. IEEE 20th International Conference on Computational Problems of Electrical Engineering (CPEE). ISBN Information: INSPEC Accession Number: 19247158. https://doi.org/10.1109/CPEE47179.2019.8949129.

15. Patalakh, D. (2019). Modification of numeral calculation of transients in electric circuits on basis of Chebyshevs polynomials. Electrical Engineering and Power Engineering, (4), 11-24. https://doi.org/10.15588/1607-6761-2019-4-2.

16. Boor, C., de Hllig, K., & Riemenschneider, S. (2013). Box splines. Springer Science & Business Media. https://doi.org/10.1007/978-1-4757-2244-4_1.

17. Pankiv, V.I., Tankevich, Ye.M., & Lutchin, M.M. (2014). Approximation of the characteristics of the magnitisation of current transformers. Works of the Institute of Electrodynamics of the National Academy of Sciences of Ukraine, 37, 82-90.

 

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