Non Linear Magnetic Hysteresis Modelling by Finite Volume Method for Jiles-Atherton Model Optimizing by a Genetic Algorithm

Seddik Azzaoui, Kamel Srairi, Mohamed El Hachemi Benbouzid

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DOI: 10.4236/jemaa.2011.36032                

Abstract

This paper describes a generalization methodology for nonlinear magnetic field calculation applied on two-dimensional (2-D) finite Volume geometry by incorporating a Jiles-Atherton scalar hysteresis model. The scheme is based upon the definition of modified governing equation derived from Maxwell’s equations considered the magnetization M. This paper shows how to extract optimal parameters for the Jiles-Atherton model of hysteresis by a real coded genetic algorithm approach. The parameters identification is performed by minimizing the mean squared error between experimental and simulated magnetic field curves. The calculated results are validated by experiences performed in an SST’s frame.

Keywords

Magnetic Hysteresis, Jiles-Atherton Model, Genetic Algorithm Optimization, Parameters Identification, Finite Volume Method (FVM)

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	H. L. Toms, R. G. Colclaser and M. P. Krefta, “Tow Dimensional Finite Element Magnetic Modeling for Scalar Hysteresis Effects,” IEEE Transaction on Magnetics, Vol. 37, 2001, pp 982-988.
[2]	N. Sadowski, N. J. Batistela, J. P. A. Bastos and M. Lajoie-Mazenc, “An Inverse Jiles-Atherton Model to Take into Account Hysteresis in Time-Stepping Finite-Element Calculations,” IEEE Transaction on Magnetics, Vol. 38, 2002, pp. 797-800.
[3]	D. C. Jiles and D. L. Atherton, “Theory of Ferromagnetic Hysteresis,” Journal of Magnetism and Magnetic Materials, Vol. 61, 1986, pp. 48-60. doi:10.1016/0304-8853(86)90066-1
[4]	K. Chwastek, “Description of Henkel Plots by the Magnetization-Dependent Jiles-Atherton Model,” Journal of Magnetism and Magnetic Materials, Vol. 322, No. 2, 2010, pp. 214-217.
[5]	K. Chwastek and J. Szczyg?owski, “An Alternative Method to Estimate the Parameters of Jiles-Atherton Model,” Journal of Magnetism and Magnetic Materials, Vol. 314, No. 1, 2007, pp. 47-51. doi:10.1016/j.jmmm.2007.02.157
[6]	J. V. Leite, S. L.Avila, and others, “Real Coded Genetic Algorithm for Jiles-Atherton Model Parameters Identification,” IEEE Transaction on Magnetics, Vol. 34, 2004, pp 888-891.
[7]	J. A. Vasconcelos, J. A. Ramirez, R. H. C. Takahashi, and R. R. Saldanha, “Improvements in Genetic Algorithms,” IEEE Transaction on Magnetics, Vol. 37, 2001, pp 3414-3417.
[8]	P. R. Wilson, N. Ross, and A. D. Brown, “Optimizing the Jiles-Atherton Model of hysteresis by a Genetic Algorithm,” IEEE Transaction on Magnetics, Vol. 37, 2001, pp. 989-993.
[9]	B. Gallardo, D. A. Lowther, “Some Aspects of Niching Genetic Algorithms Applied to Electromagnetic Device Optimization,” IEEE Transaction on Magnetics, Vol. 36, 2000, pp1076-1079.
[10]	K. Chwastek and J. Szczyglowski, “Identification of a Hysteresis Model Parameters with genetic Algorithms,” Journal of Mathematics and Computers in Simulation, Vol. 71, 2006, pp. 206-211. doi:10.1016/j.matcom.2006.01.002
[11]	L. A. L. Almeida, G. S. Deep, A. M. N. Lima and H. Neff, “Modeling a Magnetostrictive Transducer Using Genetic Algorithm,” Journal of Magnetism and Magnetic Materials, Vol. 266-230, 2001, pp. 1262-1264.
[12]	S. V. Patankar, “Numerical Heat Transfer and Fluid Flow,” Series in computational methods in mechanics and thermal sciences, Taylor & Francis, 1980.
[13]	T. L. Mthombeni, “Improved Lamination Core Loss Measurements and Calculations”, Doctorate Thesis, Clarkson University, 2006.