# 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

## 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

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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

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