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The Use of Hypergeometric Functions in Hysteresis Modeling

Author

Listed:
  • Dejana Herceg

    (Department of Power, Electronic and Telecommunication Engineering, Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia)

  • Krzysztof Chwastek

    (Faculty of Electrical Engineering, Częstochowa University of Technology, Al. Armii Krajowej 17, 42-201 Częstochowa, Poland)

  • Đorđe Herceg

    (Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia)

Abstract

Accurate hysteresis models are necessary for modeling of magnetic components of devices such as transformers and motors. This study presents a hysteresis model with a convenient analytical form, based on hypergeometric functions with one free parameter, built upon a class of parameterized curves. The aim of this work is to explore suitability of the presented model for describing major and minor loops, as well as to demonstrate improved agreement between experimental and modeled hysteresis loops. The procedure for generating first order reversal curves is also discussed. The added parameter, introduced into the model, controls the shape of the model curve, especially near saturation. It can be adjusted to provide better agreement between measured and model curves. The model parameters are nonlinearly dependent; therefore, they are determined in a nonlinear curve fitting procedure. The choice of the initial approximation and a suitable set of constraints for the optimization procedure are discussed. The inverse of the model function, required to generate first order reversal curves, cannot be obtained in analytical form. The procedure to calculate the inverse numerically is presented. Performance of the model is demonstrated and verified on experimental data obtained from measurements on construction steel sheets and grain-oriented electrical steel samples.

Suggested Citation

  • Dejana Herceg & Krzysztof Chwastek & Đorđe Herceg, 2020. "The Use of Hypergeometric Functions in Hysteresis Modeling," Energies, MDPI, vol. 13(24), pages 1-14, December.
    • Handle: RePEc:gam:jeners:v:13:y:2020:i:24:p:6500-:d:459270
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    References listed on IDEAS

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    1. Sarah Saeed & Ramy Georgious & Jorge Garcia, 2020. "Modeling of Magnetic Elements Including Losses—Application to Variable Inductor," Energies, MDPI, vol. 13(8), pages 1-19, April.
    2. Roman Gozdur & Piotr Gębara & Krzysztof Chwastek, 2020. "A Study of Temperature-Dependent Hysteresis Curves for a Magnetocaloric Composite Based on La(Fe, Mn, Si) 13 -H Type Alloys," Energies, MDPI, vol. 13(6), pages 1-15, March.
    3. Xishan Wen & Jingzhuo Zhang & Hailiang Lu, 2017. "Automatic J–A Model Parameter Tuning Algorithm for High Accuracy Inrush Current Simulation," Energies, MDPI, vol. 10(4), pages 1-15, April.
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    Cited by:

    1. Gustav Mörée & Mats Leijon, 2023. "Review of Hysteresis Models for Magnetic Materials," Energies, MDPI, vol. 16(9), pages 1-66, May.
    2. Fabio Corti & Alberto Reatti & Gabriele Maria Lozito & Ermanno Cardelli & Antonino Laudani, 2021. "Influence of Non-Linearity in Losses Estimation of Magnetic Components for DC-DC Converters," Energies, MDPI, vol. 14(20), pages 1-16, October.
    3. Krzysztof Roman Chwastek & Paweł Jabłoński & Dariusz Kusiak & Tomasz Szczegielniak & Václav Kotlan & Pavel Karban, 2023. "The Effective Field in the T(x) Hysteresis Model," Energies, MDPI, vol. 16(5), pages 1-18, February.

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