Optimizing the Jiles-Atherton model of hysteresis by a genetic algorithm

Modeling magnetic components for simulation in electric circuits requires an accurate model of the hysteresis loop of the core material used. It is important that the parameters extracted for the hysteresis model be optimized across the range of operating conditions that may occur in circuit simulation. This paper shows how to extract optimal parameters for the Jiles-Atherton model of hysteresis by the genetic algorithm approach. It compares performance with the well-known simulated annealing method and demonstrates that improved results may be obtained with the genetic algorithm. It also shows that a combination of the genetic algorithm and the simulated annealing method can provide an even more accurate solution than either method on its own. A statistical analysis shows that the optimization obtained by the genetic algorithm is better on average, not just on a one-off test basis. The paper introduces and applies the concept of simultaneous optimization for major and minor hysteresis loops to ensure accurate model optimization over a wide variety of operating conditions. It proposes a modification to the Jiles-Atherton model to allow improved accuracy in the modeling of the major loop.

I. Introduction

Transformers and inductors are essential components in a wide variety of power and communications applications, and the accurate modeling of these devices for use in circuit simulation is essential to predict design performance. It is required to accurately represent the hysteresis behavior of the magnetic core material used in these components in the simulation model. One model that has been used quite widely is that of Jiles and Atherton [1], [2]. Jiles et al. [7] show how the parameters for the model may be extracted from a set of measured data for a major hysteresis loop but do not consider arbitrary loop sizes, and Prozygy [8] has established the effects of parameter variations on the major loop. Optimization methods applied to fit the Jiles—Atherton hysteresis loops to measured data have been investigated by Schmidt and Guldner [9], and Lederer et al. [10] using the well-known simulated annealing approach. Genetic algorithms provide an alternative approach to optimization which may have some advantages, especially when considering the more complex problem of fitting several loops simultaneously.