Preisach’s Model Extended With Dynamic Fractional Derivation Contribution

Accurate and simple magnetic material behavior law is necessary to correctly model complete electromagnetic systems. In this paper, a new formulation based on the scalar quasi-static hysteresis Preisach model extended to dynamic behavior using fractional derivation dynamic contribution is proposed. The fractional contribution is solved using convolution which highly reduces the numerical issues. The order of the fractional derivation provides a new degree of freedom and allows to correctly obtain simulation results on a very large frequency bandwidth. By using such formulation, space discretization techniques (finite differences, finite elements) are avoided which are highly space and time consuming while keeping the global simulation results precise. The numerical implementation of the problem and some experimental validations are shown in this paper.

[1]  Grzegorz Litak,et al.  Fractional model of magnetic field penetration into a toroidal soft ferromagnetic sample , 2018 .

[2]  E. Cardelli.  A General Hysteresis Operator for the Modeling of Vector Fields , 2011, IEEE Transactions on Magnetics.

[3]  D. Guyomar,et al.  Dynamical hysteresis model of ferroelectric ceramics under electric field using fractional derivatives , 2007 .

[4]  G. Biorci,et al.  Analytical theory of the behaviour of ferromagnetic materials , 1958 .

[5]  Krzysztof Chwastek,et al.  An alternative method to estimate the parameters of Jiles–Atherton model , 2007 .

[6]  Grzegorz Litak,et al.  Dynamics of magnetic field penetration into soft ferromagnets , 2015 .

[7]  M. Soula,et al.  TRANSIENT RESPONSES OF POLYMERS AND ELASTOMERS DEDUCED FROM HARMONIC RESPONSES , 1997 .

[8]  F. Preisach.  Über die magnetische Nachwirkung , 1935 .

[9]  Mayergoyz,et al.  Mathematical models of hysteresis. , 1986, Physical review letters.

[10]  Daniel Guyomar,et al.  The use of fractional derivation in modeling ferroelectric dynamic hysteresis behavior over large frequency bandwidth , 2010 .

[11]  T. Meydan,et al.  Use of novel adaptive digital feedback for magnetic measurements under controlled magnetizing conditions , 2005, IEEE Transactions on Magnetics.

[12]  D. Jiles,et al.  Theory of ferromagnetic hysteresis , 1986 .

[13]  G. Bertotti.  General properties of power losses in soft ferromagnetic materials , 1988 .

[14]  S. V. Kulkarni,et al.  Hysteresis modelling of GO laminations for arbitrary in-plane directions taking into account the dynamics of orthogonal domain walls , 2016 .

[15]  J. Liouville.  Mémoire sur l'usage que l'on peut faire de la formule de Fourier, dans le calcul des différentielles à indices quelconques. , 1835 .

[16]  G. Bayada,et al.  The magnetic field diffusion equation including dynamic hysteresis: a linear formulation of the problem , 2004, IEEE Transactions on Magnetics.

[17]  E. Torre,et al.  Parameter identification of the complete-moving-hysteresis model using major loop data , 1994 .