Using a Jiles‐Atherton vector hysteresis model for isotropic magnetic materials with the finite element method, Newton‐Raphson method, and relaxation procedure
Finite element method; magnetic hysteresis; Newton‐Raphson method; relaxation factor; three‐limb transformer
Abstract :
[en] This paper deals with the use of a Jiles‐Ather ton vector hysteresis model included in 2D finite element modeling. The hysteresis model is only valid for isotropic materials. It is implemented with the vector potential formulation in 2D along with electric circuit equations to account for a possible external circuit. The Newton‐Raphson algorithm is used with a relaxation procedure, whereby at each iteration, th e relaxation coefficient is sought so as to minimize the Euclidean norm of the residual of the finite element nonlinear system of equations. We have simulated several numerical examples with the proposed approach. First, simulation s on a square domain were conducted so as to validate the model. We have further simulated a T‐shaped magnetic circuit (exhibiting rotating flux) and a 3‐phase 3‐limb transformer model. For these 2 cases, the eddy current losses in the laminations are taken into account by a low‐frequency model. We have finally performed simulations on the TEAM workshop problem 32, which consists of a 3‐limb transformer with 2 windings, for which current and local magnetic flux density measurements are available. We obtained a good agreement between computed and measured results.
Disciplines :
Electrical & electronics engineering
Author, co-author :
Guérin, Christophe; CEDRAT France
Jacques, Kevin ; Université de Liège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)
Vazquez Sabariego, Ruth; KU Leuven > Department of Electrical Engineering (ESAT)
Dular, Patrick ; Université de Liège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)
Geuzaine, Christophe ; Université de Liège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)
Gyselinck, Johan; Université Libre de Bruxelles - ULB > BEAMS Department
Language :
English
Title :
Using a Jiles‐Atherton vector hysteresis model for isotropic magnetic materials with the finite element method, Newton‐Raphson method, and relaxation procedure
Mayergoyz ID. Mathematical Models of Hysteresis and Their Applications. Elsevier: New-York; 2003.
Jiles D, Atherton P. Theory of Ferromagnetic hysteresis, J Magnetism Magnetic Mater, 61, issue 1-2, 48-60, 1986.
Gyselinck J, De Wulf M, Vandevelde L, Melkebeek J. Incorporation of vector hysteresis and eddy current losses in 2D FE magnetodynamics, in Proc. Electrimacs'99, Lisbon, Portugal, Sept., 14-16. 1999;3:37–44.
Mayergoyz ID. Mathematical models of hysteresis. IEEE Trans Magnetism. 1986;22(5):603–608.
Dlala E. Efficient algorithms for the inclusion of the Preisach hysteresis model in nonlinear finite-element methods. IEEE Trans Magnetism. 2011;47(2):395–408.
Sadowski N, Batistela NJ, Bastos JPA, Lajoie-Mazenc M. An inverse Jiles-Atherton model to take into account hysteresis in time-stepping finite-element calculations. IEEE Trans Magnetism. 2002;32(5):797–800.
Bergqvist A. A simple vector generalisation of the Jiles-Atherton model of hysteresis. IEEE Trans Magnetism. 1996;32(5):4213–4215.
Leite JV, Sadowski N, Kuo-Peng P, Batistela NJ, Bastos JPA, de Espíndola AA. Inverse Jiles-Atherton vector hysteresis model. IEEE Trans Magnetism. 2004;40(4):1769–1775.
Leite JV, Benabou A, Sadowski N. Transformer inrush currents taking into account vector hysteresis. IEEE Trans Magnetism. 2010;46(8):3237–3240.
Leite JV, Benabou A, Sadowski N, Clenet S, Bastos JPA, Piriou F. Implementation of an anisotropic vector hysteresis model. IEEE Trans Magnetism. 2008;44(6):918–921.
Hoffmann K, Bastos JPA, Sadowski N, Leite JV. Convergence Procedures Applied for Solving 3D Vector Hysteresis Modeling Coupled with FEM, CEFC'2014. France: Annecy; 2014.
Bastos JPA, Sadowski N, Leite JV, et al. A differential permeability 3-D formulation for anisotropic vector hysteresis analysis. IEEE Trans Magnetism. 2014;50(2). doi: 10.1109/TMAG.2013.2282697
Gyselinck J, Vandevelde L, Melkebeek J, Dular P. Complementary two-dimensional finite element formulations with inclusion of a vectorized Jiles-Atherton model. COMPEL. 2004;23(4):959–967.
Gyselinck J, Dular P, Sadowski N, Leite J, Bastos JPA. Incorporation of a Jiles-Atherton vector hysteresis model in 2D FE magnetic field computations—application of the Newton-Raphson method. COMPEL. 2004;23(3):685–693.
Chiampi M, Chiarabaglio D, Repetto M. A Jiles-Atherton and fixed-point combined technique for time periodic magnetic field problems with hysteresis. IEEE Trans Magnetism. 1995;31(6):4306–4311.
Leite JV, Sadowski N, Kuo-Peng P and Benabou A. Minor loops calculation with a modified Jiles-Atherton hysteresis model. J Microw, Optoelectronics Electromagnetic Appl. June 2009; 8(1): 49-55.
Nourdine A, Meunier G, Kedous-Lebouc A. Numerical computation of a vectorial hysteresis H(B) magnetization law. IEEE Trans Magnetism. 2014;50(2):1393–1396.
Jacques K, Sabariego RV, Geuzaine C, Gyselinck J. Inclusion of a direct and inverse energy-consistent hysteresis model in dual magnetostatic finite element formulations. IEEE Trans Magnetism. 2015. doi: 10.1109/TMAG.2015.2490578
Bergqvist A. Magnetic vector hysteresis model with dry friction-like pinning. Physica B. 1997;233(4):342–347.
Lin D, Zhou P, Bergqvist A. Improved vector play model and parameter identification for magnetic hysteresis materials. IEEE Trans Magnetism. 2003;39(3). doi: 10.1109/TMAG.2013.2281567
Chwastek K. The applications of fixed-point theorem in optimisation problems. Arch Electr Eng. 2012;61(2):189–198.
Zaman MA, Matin MA. Optimization of Jiles-Atherton hysteresis model parameters using Taguchi's method. IEEE Trans Magnetism. 2015;51(5):
Zaman MA, Sikder U. Bouc-Wen hysteresis model identification using modified firefly algorithm. J Magnetism Magnetic Mater. 2015;395:229–233.
Fujiwara K, Nakata T, Okamoto N, Muramatsu K. Method for determining relaxation factor for modified Newton-Raphson method. IEEE Trans Magnetism. 1993;29(2):1962–1965.
Meunier G. The finite element method for electromagnetic modeling. Chapter 7. Coupling with circuit equations. London: ISTE; 2008;277–320.
Dular P, Geuzaine C, Henrotte F, Legros W. A general environment for the treatment of discrete problems and its application to the finite element method. IEEE Trans Magnetism. 1998;34(5):3395–3398.
Flux software, www.cedrat.com.
Meunier G. The Finite Element Method for Electromagnetic Modeling, Chapter 5, Behaviour Laws of Materials. London: ISTE; 2008;177–244.
Fujiwara K, Okamoto Y, Kameari A, Ahagon A. The Newton-Raphson method accelerated by using a line search—comparison between energy functional and residual minimization. IEEE Trans Magnetism. 2005;41(5):1724–1727.
Bottauscio O, Chiampi M, Ragusa C, Rege L and Repetto M. Description of TEAM problem: 32 A—test case for validation of magnetic field analysis with vector hysteresis, 2010, [online] Available: http://www.compumag.org/jsite/images/stories/TEAM/problem32.pdf and http://www.cadema.polito.it/team32
