Spectral method of electrical circuits accelerated simulation with thyristors

Authors

  • S.M. Tykhovod National University "Zaporizhzhia Polytechnic", Ukraine
  • T.YE. Dyvchuk National University "Zaporizhzhia Polytechnic",National University Zaporizhzhia Polytechnic , Ukraine
  • T.P. Solodovnikova National University "Zaporizhzhia Polytechnic",National University Zaporizhzhia Polytechnic , Ukraine
  • O.V. Sytik National University "Zaporizhzhia Polytechnic",National University Zaporizhzhia Polytechnic , Ukraine

DOI:

https://doi.org/10.15588/1607-6761-2023-02-03

Keywords:

electric circuits, orthogonal polynomials, differential equations, numerical methods, spectral methods, approximation, Chebyshev polynomials, transient processes, schematic model

Abstract

Purpose. The development of transient processes calculation method in electric circuits with thyristors based on the use of functions approximation by orthogonal polynomials.

Methodology. Functions approximation by orthogonal polynomials, numerical methods of differential equations integration, matrix methods, programming, theory of electric circuits.

Obtained results. The method of solution function polynomial approximation of integro-differential equations of state, which describes the transient processes of an electric circuit with thyristors, is used in this paper. The used method showed the advantages over other known methods in increasing the accuracy and reducing the simulation time of transient electrical processes by more than 6 times.

Findings. The solution is approximated by a series of Chebyshev polynomials. The integro-differential equations of state are transformed into linear algebraic equations for special depiction of the solution functions. The depiction of functions of true currents in the equivalent circuit is interpreted as direct currents. Such a schematic model creates visibility for a researcher performing simulation of transient electrical processes.

Practical value. The proposed methods discover the possibility of using the apparatus of direct current electric circuits’ theory for transient processes in complex schemes modeling with thyristors.

Author Biographies

S.M. Tykhovod, National University "Zaporizhzhia Polytechnic"

Dr. Sc. (Tech.), Associate Professor, Professor of the Electrical Machines Department, National University "Zaporizhzhia Polytechnic", Zaporizhzhia

T.YE. Dyvchuk, National University "Zaporizhzhia Polytechnic",National University Zaporizhzhia Polytechnic

PhD, Associate Professor of the Electrical Machines Department, National University "Zaporizhzhia Polytechnic", Zaporizhzhia

T.P. Solodovnikova, National University "Zaporizhzhia Polytechnic",National University Zaporizhzhia Polytechnic

Senior teacher of the Electrical Machines Department, National University "Zaporizhzhia Polytechnic", Zaporizhzhia

O.V. Sytik, National University "Zaporizhzhia Polytechnic",National University Zaporizhzhia Polytechnic

Senior teacher of the Electrical Machines Department, National University "Zaporizhzhia Polytechnic", Zaporizhzhia, Ukraine

References

Zhuikov V.Ya and others. (1988) Automated design of power electronic circuits

Yagup V.G. (1968) Automated design of thyristor cir-cuits

Boyd, J. P. (2001). Chebyshev and Fourier spectral methods. Courier Corporation.

Epperson, James F., (2013). An introduction to numerical methods and analysis / James F. Epperson, Mathematical Reviews. ISBN 978-1-118-36759-9

Gourgoulhon, E., Bonazzola, S., Grandclément, P., Marck, J. A., & Novak, J. (2002, September). Intro-duction to spectral methods. In 4th EU Network meeting, Palma de Mallorca (Vol. 175, p. 176).

Costa, B. (2004). Spectral Methods for Partial Differential Equations. CUBO, A Mathematical Journal, 6(4), 1–32. Retrieved from https://cubo.ufro.cl/ojs/index.php/cubo/article/view/1552

Kopriva, D. A. (2009). Implementing spectral methods for partial differential equations: Algorithms for scientists and engineers. Springer Science & Business Media.

Trefethen, L. N. (2000). Spectral methods in MATLAB. Society for industrial and applied mathematics.

Tykhovod, S., & Patalakh, D. (2019, September). Cal-culation of Transients in Electrical Circuits at the Use of Solution Approximation by Tchebyshev's Poly-nomials. In 2019 IEEE 20th International Confer-ence on Computational Problems of Electrical Engi-neering (CPEE) (pp. 1-4). IEEE. DOI: https://doi.org/10.1109/CPEE47179.2019.8949129

Boyd, J. P., & Petschek, R. (2014). The relationships between Chebyshev, Legendre and Jacobi polynomials: the generic superiority of Chebyshev polynomials and three important exceptions. Journal of Scientific Computing, 59, 1-27. DOI: https://doi.org/10.1007/s10915-013-9751-7

Tykhovod, S., & Orlovskyi, I. (2022). Development and Research of Method in the Calculation of Tran-sients in Electrical Circuits Based on Polynomials. Energies, 15(22), 8550. DOI: https://doi.org/10.3390/en15228550

Program for calculating the transient process by the special method in the RLCe circuit. Retrieved from: https://drive.google.com/file/d/1PVHWp9caGdHy_L8AMR39VTtogw0ylcGY/view?usp=sharing

Tykhovod S.M. Afanasieva I.O., Kornus T.M. (2009) Development of a computer program for the simula-tion of magnetoelectric circuits with thyristors. Tech-nical electrodynamics. 3(9-14)

Tykhovod S.M. (2000) Methodology for computer simulation of electrical circuits containing semicon-ductor valves. Electrical engineering and power engi-neering. 2(50-52).

Downloads

Published

2023-09-15

How to Cite

Tykhovod, S., Dyvchuk, T., Solodovnikova, T., & Sytik, O. (2023). Spectral method of electrical circuits accelerated simulation with thyristors. Electrical Engineering and Power Engineering, (2), 27–31. https://doi.org/10.15588/1607-6761-2023-02-03