Use of a scaling power law to incorporate asymmetrical minor loops in the inverse Jiles–Atherton model

Abstract

Magnetic material characterisation and modelling are important for investigating losses and analysing the transient behaviour of electrical systems. This study attempts to contribute in modelling of magnetic materials under conditions of arbitrary flux waveforms. A simple modification of the inverse Jiles-Atherton model for accurately estimating losses in magnetic materials under asymmetrical minor loops is described. The additional losses due to minor loops are mainly due to irreversible domain wall displacements. The modelling presented in this work is based on a scaling power law, which ensures the closure of minor loops and allows better representation of the hysteresis behaviour. The proposed algorithm is verified by modelling hysteresis loops with multiple harmonics associated with pulse width modulated waveforms.

A Wavelet descriptor model of hysteresis loop phenomena

“…5, we consider a hysteresis curve with a total 501 B / H data points obtained with a frequency at 1 Hz superimposed with its third harmonic. The data is generated using a modified JA model reported in [31]. In this case, we have two asymmetric minor loops.…”

“…That is to say, most of the prior work on the JA model has not addressed the minor loops due to multiple harmonics, and if it is required to incorporate minor loops (especially for the case of PWM waveforms) then there is a need to modify the JA model formulations accordingly. For example in [31], a scaling power law was used to represent the irreversible component of magnetisation to improve the representation of minor loops associated with PWM sources. In [40], issues with symmetrical minor loops were resolved by using the knowledge of turning points, offset, and scaling factors.…”

“…Two fast Fourier transform (FFT)-based magnetostatic field evaluation schemes in micromagnetic hysteresis modelling are compared in [24]. The two most commonly used techniques by engineers to model a given hysteresis curve are the Preisach model [25][26][27] and Jiles-Atherton (JA) model [28][29][30][31][32]. Determining the parameters of the JA or Preisach model is a computationally intensive task.…”

“…This further leads to the losses, and therefore there is always a need for exact modelling and accurate hysteresis loss estimation under various operating conditions. Modelling minor loops using the classical JA model leads to nonphysical behaviour and therefore a modification is required to represent the minor loops [31]. Several modifications have been proposed in the past to the JA model that are capable of modelling hysteresis curves including minor loops [28,31,[39][40][41][42][43].…”

“…Modelling minor loops using the classical JA model leads to nonphysical behaviour and therefore a modification is required to represent the minor loops [31]. Several modifications have been proposed in the past to the JA model that are capable of modelling hysteresis curves including minor loops [28,31,[39][40][41][42][43]. While most of the work in the literature on minor loops is reported either on waveforms containing third harmonics or on waveforms containing third and fifth harmonic components, very few papers deal with the waveforms having multiple harmonics and especially PWM waveforms.…”