Modified Algorithm of the Vector Magnetic Hysteresis 3D Model Applied to the Spatial Integral Equations Method

Abstract

The paper proposes mathematical models of the scalar and vector magnetic hysteresis to solve the problems of calculating the three-dimensional magnetic field in electrical devices by the method of spatial integral equations. A system of spatial integral equations is presented describing processes in the electrical devices. Basic and modified algorithms of the Jiles --- Atherton scalar model implementation are considered. The model parameters were tuned using a genetic algorithm. Algorithms for constructing the Jiles --- Atherton direct and inverse vector model in the three-dimensional setting were presented in accordance with the Mayergoyz approach. Generalized model of the vector 3D hysteresis makes it possible to describe the nonlinear properties of ferromagnetic medium for the isotropic and anisotropic materials. An example of the magnetic system calculation is provided taking into account the vector magnetic hysteresis. The simulation model parameters were determined from experimental data of the limited scope. Adequacy of the computational models was checked using a test problem. Results of the numerical studies demonstrated that the models were quite accurately reproducing real hysteresis dependences for various ferromagnetic materials. Proposed models and numerical algorithms implementing them were used as the component models that specified nonlinear characteristics of the magnetic materials in a software package that implemented the spatial integral equations method

The work was prepared based on the results of research obtained in the course of fulfilling the state task for conducting scientific research within the frame-work of the project "Power Plants on Hydrogen Fuel Cells for Small Unmanned Vehicles: Modeling, Development, Research" program with the support of the Ministry of Science and Higher Education of the Russian Federation, scientific code FENN-2020-0022

Please cite this article in English as:

Podbereznaya I.B., Pavlenko A.V., Batishchev D.V., et al. Modified algorithm of the vector magnetic hysteresis 3D model applied to the spatial integral equations method. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2023, no. 3 (108), pp. 37--60 (in Russ.). DOI: https://doi.org/10.18698/1812-3368-2023-3-37-60

References

[1] Pekker I.I. Calculation of magnetic systems by the method of integration over field sources. Izvestiya vuzov. Elektromekhanika [Bulletin of Higher Educational Institutions. Electromechanics], 1964, no. 6, pp. 1047--1051 (in Russ.).

[2] Pekker I.I. On the calculation of magnetic systems by the method of integration over field sources. Izvestiya vuzov. Elektromekhanika [Bulletin of Higher Educational Institutions. Electromechanics], 1968, no. 9, pp. 940--943 (in Russ.).

[3] Pekker I.I. Calculation of magnetic systems by integration over field sources. Izvestiya vuzov. Elektromekhanika [Bulletin of Higher Educational Institutions. Electromechanics], 1969, no. 6, pp. 618--623 (in Russ.).

[4] Kurbatov P.A., Arinchin S.A. Chislennyy raschet elektromagnitnykh poley [Numerical calculation of electromagnetic fields]. Moscow, Energoatomizdat Publ., 1984.

[5] Podbereznaya I.B., Kovalev O.F., Grinchenkov V.P. Simulation of electromagnetic systems with permanent magnets by modified method of integral equations. Izvestiya vuzov. Elektromekhanika [Bulletin of Higher Educational Institutions. Electromechanics], 2004, no. 4, pp. 6--9 (in Russ.).

[6] Podbereznaya I.B. Application of the spatial integrated equations for calculation of quasistationary electromagnetic fields in electromechanical devices. Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFEDU. Engineering Sciences], 2014, no. 3, pp. 250--264 (in Russ.).

[7] Podbereznaya I.B., Ershov Yu.K., Pavlenko A.V. The method of spatial integral equations on the example of the problem of calculating the magnetic field in a rectangular prism. Izvestiya vuzov. Elektromekhanika [Bulletin of Higher Educational Institutions. Electromechanics], 2014, no. 2, pp. 3--15 (in Russ.).

[8] Podbereznaya I.B., Ershov Yu.K., Pavlenko A.V. Calculation of distribution of a magnetic field in a prism of rectangular section a method of the spatial integrated equations at various forms of an entrance signal. Izvestiya vuzov. Severo-Kavkazskiy region. Ser. Tekhnicheskie nauki [Bulletin of Higher Educational Institutions. North Caucasus Region. Technical Sciences], 2014, no. 5, pp. 15--21 (in Russ.).

[9] Podbereznaya I.B., Ershov Yu.K., Pavlenko A.V. Estimation of borders of applicability of a method of the spatial integrated equations at its numerical realization. Izvestiya vuzov. Elektromekhanika [Bulletin of Higher Educational Institutions. Electromechanics], 2015, no. 5, pp. 17--24 (in Russ.). DOI: https://doi.org/10.17213/0136-3360-2015-5-17-24

[10] Krasnoselskiy M.A., Pokrovskiy A.V. Sistemy s gisterezisom [Systems with hysteresis]. Moscow, Nauka Publ., 1983.

[11] Mayergoyz I.D. Hysteresis models from the mathematical and control theory points of view. J. Appl. Phys., 1985, vol. 57, iss. 8, pp. 3803--3805. DOI: https://doi.org/10.1063/1.334925

[12] Brown W.F., Jr. Micromagnetics, domains, and resonance. J. Appl. Phys., 1959, vol. 30, iss. 4, pp. 62--69. DOI: https://doi.org/10.1063/1.2185970

[13] Aharoni A. Some recent developments in micromagnetics at the Weizmann Institute of Science. J. Appl. Phys., 1959, vol. 30, iss. 4, pp. 70--78.DOI: https://doi.org/10.1063/1.2185971

[14] Aharoni A. Introduction to the theory of ferromagnetism. Oxford Univ. Press, 2000.

[15] Jiles D.C. A self consistent generalized model for the calculation of minor loop excursions in the theory of hysteresis. IEEE Trans. Magn., 1992, vol. 28, iss. 5, pp. 2602--2604. DOI: https://doi.org/10.1109/20.179570

[16] Jiles D.C. Modelling the effects of eddy current losses on frequency dependent hysteresis in electrically conducting media. IEEE Trans. Magn., 1994, vol. 30, iss. 6, pp. 4326--4328. DOI: https://doi.org/10.1109/20.334076

[17] Jiles D.C., Ramesh A., Shi Y., et al. Application of the anisotropic extension of the theory of hysteresis to the magnetization curves of crystalline and textured magnetic materials. IEEE Trans. Magn., 1997, vol. 33, iss. 5, pp. 3961--3963. DOI: https://doi.org/10.1109/20.619629

[18] Jiles D.C., Atherton D.L. Theory of ferromagnetic hysteresis. J. Magn. Magn. Mater., 1986, vol. 61, iss. 1-2, pp. 48--60. DOI: https://doi.org/10.1016/0304-8853(86)90066-1

[19] Jiles D.C., Thoelke J.B. Theory of ferromagnetic hysteresis: determination of model parameters from experimental hysteresis loops. IEEE Trans. Magn., 1989, vol. 25, iss. 5, pp. 3928--3930. DOI: https://doi.org/10.1109/20.42480

[20] Jiles D.C., Atherton D.L. Ferromagnetic hysteresis. IEEE Trans. Magn., 1983, vol. 19, iss. 5, pp. 2183--2185. DOI: https://doi.org/10.1109/TMAG.1983.1062594

[21] Chan J.H., Vladirimescu A., Gao X.-C., et al. Nonlinear transformer model for circuit simulation. IEEE Trans. Comput.-Aided Design Integr. Circuits Syst., 1991, vol. 10, iss. 4, pp. 476--482. DOI: https://doi.org/10.1109/43.75630

[22] Leite J.V., Sadowski N., Kuo-Peng P., et al. Inverse Jiles --- Atherton vector hysteresis model. IEEE Trans. Magn., 2004, vol. 40, iss. 4, pp. 1769--1775. DOI: https://doi.org/10.1109/TMAG.2004.830998

[23] Leite J.V., Benabou A., Sadowski N. Transformer inrush currents taking into account vector hysteresis. IEEE Trans. Magn., 2010, vol. 46, iss. 8, pp. 3237--3240. DOI: https://doi.org/10.1109/TMAG.2010.2046401

[24] Leite J.V., Benabou A., Sadowski N., et al. Implementation of an anisotropic vector hysteresis model in a 3-D finite-element code. IEEE Trans. Magn., 2008, vol. 44, iss. 6, pp. 918--921. DOI: https://doi.org/10.1109/TMAG.2007.915810

[25] Lin D., Zhou P., Fu W.N., et al. A dynamic core loss model for soft ferromagnetic and power ferrite materials in transient finite element analysis. IEEE Trans. Magn., 2004, vol. 40, iss. 2, pp. 1318--1321. DOI: https://doi.org/10.1109/TMAG.2004.825025

[26] Podbereznaya I.B., Pavlenko A.V. To calculation of dynamic characteristics of high-speed electromagnets of traction automatic switches. Izvestiya vuzov. Elektromekhanika [Bulletin of Higher Educational Institutions. Electromechanics], 2019, no. 2, pp. 21--28 (in Russ.). DOI: https://doi.org/10.17213/0136-3360-2019-2-21-28

[27] Wilson P.R., Neil Ross J., Brown A.D. Optimizing the Jiles --- Atherton model of hysteresis by a genetic algorithm. IEEE Trans. Magn., 2001, vol. 37, iss. 2, pp. 989--993. DOI: https://doi.org/10.1109/20.917182

[28] Salvini A., Fulginei R.F. Soft computing for the identification of the Jiles --- Atherton model parameters. IEEE Trans. Magn., 2005, vol. 41, iss. 3, pp. 1100--1108. DOI: https://doi.org/10.1109/TMAG.2004.843345

[29] Shuying C., Boweng W., Rongge Y., et al. Optimization of hysteresis parameters for the Jiles --- Atherton model using a genetic algorithm. IEEE Trans. Appl. Supercond., 2004, vol. 14, iss. 2, pp. 1157--1160. DOI: https://doi.org/10.1109/TASC.2004.830462

[30] Salvini A., Fulginei F. R. Genetic algorithms and neural networks generalizing the Jiles --- Atherton model of static hysteresis for dynamic loops. IEEE Trans. Magn., 2002, vol. 38, iss. 2, pp. 873--876. DOI: https://doi.org/10.1109/20.996225

[31] Grimaldi D., Michaeli L., Palumbo A. Automatic and accurate evaluation of the parameters of a magnetic hysteresis model. IEEE Trans. Instrum. Meas., 2000, vol. 49, iss. 1, pp. 154--160. DOI: https://doi.org/10.1109/19.836327

[32] Mordjaoui M., Chabane M., Boudjema B., et al. Qualitative ferromagnetic hysteresis modeling. J. Comput. Sci., 2007, vol. 3, no. 6, pp. 399--405. DOI: https://doi.org/10.3844/JCSSP.2007.399.405

[33] Marion R., Siauve N., Raulet M.-A., et al. A comparison of identification techniques for the Jiles --- Atherton model of hysteresis. XX Symp. EPNC, 2008. Available at: https://hal.science/hal-00359384 (accessed: 15.12.2022).

[34] Chwastek K., Szczyglowski J., Najgebauer M. A direct search algorithm for estimation of Jiles --- Atherton hysteresis model parameters. Mater. Sci. Eng. B, 2006, vol. 131, iss. 1-3, pp. 22--26. DOI: https://doi.org/10.1016/j.mseb.2005.11.030

[35] Amelin S.A., Novikov A.A. To calculate the dynamic characteristics of fast acting electromagnets for traction circuit breakers. Elektrichestvo, 1995, no. 9, pp. 46--51 (in Russ.).

[36] Amelin S.A., Novikov A.A., Stroev K.N., et al. Modification of the Jiles --- Atherton model to take into account the frequency properties of ferromagnets. Elektrichestvo, 1995, no. 11, pp. 60--63 (in Russ.).

[37] Bergqvist A.J. A simple vector generalization of the Jiles --- Atherton model of hysteresis. IEEE Trans. Magn., 1996, vol. 32, iss. 5, pp. 4213--4215. DOI: https://doi.org/10.1109/20.539337

[38] Podbereznaya I.B., Medvedev V.V., Pavlenko A.V., et al. Selection of optimal parameters for the Jiles --- Atherton magnetic hysteresis model. Russ. Electr. Engin., 2019, vol. 90, no. 1, pp. 80--85. DOI: https://doi.org/10.3103/S1068371219010115

[39] Podbereznaya I.B., Pavlenko A.V. Accounting for dynamic losses in the Jiles --- Atherton model of magnetic hysteresis. J. Magn. Magn. Mater., 2020, vol. 513, art. 167070. DOI: https://doi.org/10.1016/j.jmmm.2020.167070

[40] Mayergoyz I.D. Mathematical models of hysteresis. Phys. Rev. Lett., 1986, vol. 56, iss. 15, pp. 1518--1521. DOI: https://doi.org/10.1103/physrevlett.56.1518

[41] Mayergoyz I.D. Mathematical models of hysteresis. IEEE Trans. Magn., 1986, vol. 22, iss. 5, pp. 603--608. DOI: https://doi.org/10.1109/TMAG.1986.1064347

[42] Bastos J.P., Sadowski N., Leite J.V., et al. A differential permeability 3-D formulation for anisotropic vector hysteresis analysis. IEEE Trans. Magn., 2014, vol. 50, iss. 2, art. 7008304. DOI: https://doi.org/10.1109/TMAG.2013.2282697

[43] Podbereznaya I.B., Tkachev A.N. Simulation of transient and steady-state periodic processes in nonlinear inductive element of electric circuit taking into account magnetic hysteresis. Izvestiya vuzov. Elektromekhanika [Bulletin of Higher Educational Institutions. Electromechanics], 2022, vol. 65, no. 1, pp. 3--12 (in Russ.). DOI: https://doi.org/10.17213/0136-3360-2022-1-3-12

[44] Podbereznaya I.B., Tkachev A.N. Simulation of ferroresonance modes in nonlinear electrical circuits taking into account magnetic hysteresis. Izvestiya vuzov. Elektromekhanika [Bulletin of Higher Educational Institutions. Electromechanics], 2022, vol. 65, no. 1, pp. 13--24 (in Russ.). DOI: https://doi.org/10.17213/0136-3360-2022-1-13-24