Accelerated Modeling of Transients in Electromagnetic Devices Based on Magnetoelectric Substitution Circuits

Sergii Tykhovod () and Ihor Orlovskyi ()
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Sergii Tykhovod: Department of Electrical Machines, Electrical Engineering Faculty, National University “Zaporizhzhia Polytechnic”, 69063 Zaporizhzhia, Ukraine
Ihor Orlovskyi: Department of Power Electronics, Electrical Machines and Drives, Bydgoszcz University of Science and Technology, 85796 Bydgoszcz, Poland

Energies, 2025, vol. 18, issue 2, 1-20

Abstract: During switching in electrical systems, transient electromagnetic processes occur. The resulting dangerous current surges are best studied by computer simulation. However, the time required for computer simulation of such processes is significant for complex electromagnetic devices, which is undesirable. The use of spectral methods can significantly speed up the calculation of transient processes and ensure high accuracy. At present, we are not aware of publications showing the use of spectral methods for calculating transient processes in electromagnetic devices containing ferromagnetic cores. The purpose of the work: The objective of this work is to develop a highly effective method for calculating electromagnetic transient processes in a coil with a ferromagnetic magnetic core connected to a voltage source. The method involves the use of nonlinear magnetoelectric substitution circuits for electromagnetic devices and a spectral method for representing solution functions using orthogonal polynomials. Additionally, a schematic model for applying the spectral method is developed. Obtained Results: A method for calculating transients in magnetoelectric circuits based on approximating solution functions with algebraic orthogonal polynomial series is proposed and studied. This helps to transform integro-differential state equations into linear algebraic equations for the representations of the solution functions. The developed schematic model simplifies the use of the calculation method. Representations of true electric and magnetic current functions are interpreted as direct currents in the proposed substitution circuit. Based on these methods, a computer program is created to simulate transient processes in a magnetoelectric circuit. Comparing the application of various polynomials enables the selection of the optimal polynomial type. The proposed method has advantages over other known methods. These advantages include reducing the simulation time for electromagnetic transient processes (in the examples considered, by more than 12 times than calculations using the implicit Euler method) while ensuring the same level of accuracy. The simulation of processes over a long time interval demonstrate error reduction and stabilization. This indicates the potential of the proposed method for simulating processes in more complex electromagnetic devices, (for example, transformers).

Keywords: electrical circuits; orthogonal polynomials; differential equations; numerical methods; spectral methods; approximation; collocation; algebraic polynomials; Chebyshev; hermit and Legendre polynomials; transients; magnetoelectric substitution circuits (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2025
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