Numerical determination of Jiles‐Atherton model parameters

Abstract

Purpose

The purpose of this paper is to propose a robust method to estimate the parameters of Jiles‐Atherton model of ferromagnetic hysteresis by fitting the model to symmetrical hysteresis loops. The performance of the method is evaluated by both theoretical and experimental data.

Design/methodology/approach

Jiles‐Atherton model with five parameters describes the hysteretic behaviour of ferromagnetic materials. To calculate the model parameters, the most common data displaying the hysteresis features are the hysteresis loops stimulated by symmetrical steady state excitations, e.g. sinusoidal sources. Using the characteristic equations at specific points on these hysteresis loops, the Jiles‐Atherton model parameters can be determined by curve fitting and numerical optimized iteration.

Findings

Practicality and robustness were not well considered by the conventional parameter estimation method: the initial curve starting from demagnetization is not always available and a direct iterative algorithm to solve the characteristic equations is sensitive to the initial values of the iteration and the evaluation order of the equations because of two main reasons. The first one is that the basic equation group has non‐unique solutions, which is caused by the nonlinearity of the characteristic equations and the fact that there are more unknown quantities (i.e. five model parameters) than the equations available; the second reason is the multimodal feature of the problem, which means that there are many local minima for the iteration algorithm to be trapped in. So curve fitting around the loop tips is proposed before numerical iteration. The goal is to make the initial values, particularly saturation magnetization M_s, not far away from the desired solution to increase the possibility of converging to a physical result. The optimized iterative method with the enhanced ability to avoid local minima and find global roots is then applied to obtain the model parameters.

Originality/value

The proposed method overcomes the difficulties of the other techniques which assume zero remanence. It is also robust as it is guaranteed to converge to physical solutions. The method can facilitate further development and it formed the preliminary basis of our earlier work, where the variation of the Jiles‐Atherton model parameters with different magnetic field strengths was investigated and applied to the simulation of transformer inrush current.

Citation

Wang, X., Thomas, D.W.P., Sumner, M., Paul, J. and Cabral, S.H.L. (2009), "Numerical determination of Jiles‐Atherton model parameters", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 28 No. 2, pp. 493-503. https://doi.org/10.1108/03321640910929344