IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v13y2020i24p6500-d459270.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/13/24/6500/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/1996-1073/13/24/6500/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bingbing Dong & Yu Gu & Changsheng Gao & Zhu Zhang & Tao Wen & Kejie Li, 2021. "Three-Dimensional Electro-Thermal Analysis of a New Type Current Transformer Design for Power Distribution Networks," Energies, MDPI, vol. 14(6), pages 1-13, March.
    2. Łukasz Ciepliński & Michał Gwóźdź & Rafał M. Wojciechowski, 2022. "Application of a Tuned Inductor in a DC Power Supply with an Active Compensation Function," Energies, MDPI, vol. 15(17), pages 1-15, August.
    3. Miklós Kuczmann & Tamás Orosz, 2023. "Temperature-Dependent Ferromagnetic Loss Approximation of an Induction Machine Stator Core Material Based on Laboratory Test Measurements," Energies, MDPI, vol. 16(3), pages 1-17, January.
    4. Guangming Xue & Hongbai Bai & Tuo Li & Zhiying Ren & Xingxing Liu & Chunhong Lu, 2022. "Numerical Solving Method for Jiles-Atherton Model and Influence Analysis of the Initial Magnetic Field on Hysteresis," Mathematics, MDPI, vol. 10(23), pages 1-16, November.
    5. Krzysztof Górecki & Kalina Detka, 2023. "SPICE-Aided Models of Magnetic Elements—A Critical Review," Energies, MDPI, vol. 16(18), pages 1-27, September.
    6. Daniele Scirè & Gianpaolo Vitale & Marco Ventimiglia & Giuseppe Lullo, 2021. "Non-Linear Inductors Characterization in Real Operating Conditions for Power Density Optimization in SMPS," Energies, MDPI, vol. 14(13), pages 1-19, June.
    7. Wieslaw Lyskawinski & Wojciech Szelag & Cezary Jedryczka & Tomasz Tolinski, 2021. "Finite Element Analysis of Magnetic Field Exciter for Direct Testing of Magnetocaloric Materials’ Properties," Energies, MDPI, vol. 14(10), pages 1-17, May.
    8. P. Sathishkumar & T. N. V. Krishna & Himanshu & Muhammad Adil Khan & Kamran Zeb & Hee-Je Kim, 2018. "Digital Soft Start Implementation for Minimizing Start Up Transients in High Power DAB-IBDC Converter," Energies, MDPI, vol. 11(4), pages 1-18, April.
    9. Anna Przybył & Piotr Gębara & Roman Gozdur & Krzysztof Chwastek, 2022. "Modeling of Magnetic Properties of Rare-Earth Hard Magnets," Energies, MDPI, vol. 15(21), pages 1-18, October.
    10. 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.
    11. Michał Gwóźdź, 2022. "The Application of Tuned Inductors in Electric Power Systems," Energies, MDPI, vol. 15(22), pages 1-13, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jeners:v:13:y:2020:i:24:p:6500-:d:459270. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.