Modelling dynamic hysteresis loops in steel sheets

Krzysztof Chwastek (Faculty of Electrical Engineering, Częstochowa University of Technology, Częstochowa, Poland)
Jan Szczygłowski (Faculty of Electrical Engineering, Częstochowa University of Technology, Częstochowa, Poland)
Wiesław Wilczyński (Institute of Electrical Engineering, Warsaw, Poland)



The aim of the paper is to present a simple approach to modelling minor hysteresis loops in grain‐oriented steel sheets under quasi‐static and dynamic conditions. The hysteresis phenomenon is described with a recently developed hybrid model, which combines ideas inherent in the product Preisach model and the Jiles‐Atherton description. The dynamic effects due to eddy currents are taken into account in the description using a lagged response with respect to the input.


It is assumed that some model parameters might be dependent on the level of relative magnetization within the material. Their dependencies could be given as power laws. The values of scaling coefficients in power laws are determined.


A satisfactory agreement of experimental and modelled quasi‐static and dynamic hysteresis loops is obtained.

Research limitations/implications

The present study provides a starting point for further verification of the approach for other classes of soft magnetic materials, which could be described with the developed model. At present, the approach to model minor loops by the update of model parameters is verified for the B‐sine excitation case.

Practical implications

The “branch‐and‐bound” optimization algorithm is a useful tool for recovery of the values of both model parameters and scaling coefficients as well.


The recently developed hybrid description of hysteresis phenomenon can be successfully extended to take into account symmetric minor loops. The developed approach could be a framework to develop a comprehensive description of magnetization phenomena in the future.



Chwastek, K., Szczygłowski, J. and Wilczyński, W. (2009), "Modelling dynamic hysteresis loops in steel sheets", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 28 No. 3, pp. 603-612.

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