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The accurate modeling of magnetic hysteresis in electrical steels is important in several electrical and electronic applications. Numerical models have long been known that can correctly reproduce some typical behaviours of these magnetic materials. Among these, the model proposed by Jiles and Atherton must certainly be mentioned. This model is intuitive and fairly easy to implement and identify with relatively few experimental data. Also, for this reason, it has been extensively studied in different formulations. The developments and numerical tests made on this hysteresis model have indicated that it is able to accurately reproduce symmetrical cycles, especially the major loop, but often it fails to reproduce non-symmetrical cycles. This paper aims to show the positive aspects and highlight the defects of the different formulations in predicting the minor loops of electrical steels excited by non-sinusoidal currents.

The different formulations are applied to different electrical steels, and the data coming from the simulations are compared with those measured experimentally. The direct and inverse Jiles–Atherton models, including the introduction of the dissipative factor approach, are presented, and their limitations are proposed and validated using the measurements of three non-grain-oriented materials. Only the measured major loop is used to identify the parameters of the Jiles–Atherton model. Furthermore, the direct and inverse Jiles–Atherton models were used to simulate the minor loops as well as the hysteresis cycles with direct component (DC) bias excitation. Finally, the simulation results are discussed and compared to measurements for each study case.

The paper indicates that both the direct and the inverse Jiles–Atherton model formulations provide a good agreement with the experimental data for the major loop representation; nevertheless, both models can not accurately predict the minor loops even when the modification approaches proposed in the literature were implemented.

The Jiles–Atherton model and its modifications are widely discussed in the literature; however, some limitations of the model and its modification in the case of the distorted current waveform are not completely highlighted. Furthermore, this paper contains an original discussion on the accuracy of the prediction of minor loops from distorted current waveforms, including DC bias.

The investigation was aimed at magnetically‐nonlinear dynamic model of a single‐phase transformer, where the effects of dynamic hysteresis losses are accounted for by a simplified model. Such a modelling could be applied when analyzing the transient operating conditions or the impact of nonlinear and unbalanced loads on the transformer operation and the big power systems modelling.

Secondly, an inverse form of the Jiles‐Atherton hysteresis model was applied for the hysteresis losses of a transformer defining. In that sense this paper compares and evaluates both hysteresis models, where the possible errors caused by simplified model application are exposed.

The Jiles‐Atherton model can be applied when more accurate hysteresis models are required, however, at the cost of increased model complexity and required computational effort. Apart from that the main drawback is impossible application of such a modelling, when some of the input parameters are unknown. On the other hand the simplified hysteresis model does not increase the required computational effort substantially.

Both methods have been modified in such a way that they can be used when the magnetizing curve of the iron‐core material is not available, whilst the magnetically‐nonlinear characteristic of the entire device can be determined experimentally. The aforementioned characteristic can be given in the form of an approximation polynomial or in the form of a look‐up table.

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.

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.

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.

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.

The purpose of this paper is to introduce a chaotic harmony search (CHS) approach based on the chaotic Zaslavskii map to parameters identification of Jiles-Atherton vector hysteresis model.

In laminated magnetic cores when the magnetic flux rotates in the lamination plane, one observes an increase in the magnetic losses. The magnetization in these regions is very complex needing a vector model to analyze and predict its behavior. The vector Jiles-Atherton hysteresis model can be employed in rotational flux modeling. The vector Jiles-Atherton model needs a set of five parameters for each space direction taken into account. In this context, a significant amount of research has already been undertaken to investigate the application of metaheuristics in solving difficult engineering optimization problems. Harmony search (HS) is a derivative-free real parameter optimization metaheuristic algorithm, and it draws inspiration from the musical improvisation process of searching for a perfect state of harmony. In this paper, a CHS approach based on the chaotic Zaslavskii map is proposed and evaluated.

The proposed CHS presents an efficient strategy to improve the search performance in preventing premature convergence to local minima when compared with the classical HS algorithm. Numerical comparisons with results using classical HS, genetic algorithms (GAs), particle swarm optimization (PSO), and evolution strategies (ES) demonstrated that the performance of the CHS is promising in parameters identification of Jiles-Atherton vector hysteresis model.

This paper presents an efficient CHS approach applied to parameters identification of Jiles-Atherton vector hysteresis model.

The high calculation effort for accurate material loss simulation prevents its observation in most magnetic devices. This paper aims at reducing this effort for time periodic applications and so for the steady state of such devices.

The vectorized Jiles-Atherton hysteresis model is chosen for the accurate material losses calculation. It is transformed in the frequency domain and coupled with a harmonic balanced finite element solver. The beneficial Jacobian matrix of the material model in the frequency domain is assembled based on Fourier transforms of the Jacobian matrix in the time domain. A three-phase transformer is simulated to verify this method and to examine the multi-harmonic coupling.

A fast method to calculate the linearization of non-trivial material models in the frequency domain is shown. The inter-harmonic coupling is moderate, and so, a separated harmonic balanced solver is favored. The additional calculation effort compared to a saturation material model without losses is low. The overall calculation time is much lower than a time-dependent simulation.

A moderate working point is chosen, so highly saturated materials may lead to a worse coupling. A single material model is evaluated. Researchers are encouraged to evaluate the suggested method on different material models. Frequency domain approaches should be in favor for all kinds of periodic steady-state applications.

Because of the reduced calculation effort, the simulation of accurate material losses becomes reasonable. This leads to a more accurate development of magnetic devices.

This paper proposes a new efficient method to calculate complex material models like the Jiles-Atherton hysteresis and their Jacobian matrices in the frequency domain.

This paper presents the development of a procedure for the determination of the local magnetic loss distribution in transformer cores. An efficient identification method of the parameters of the Jiles‐Atherton model is first described. This method uses nonlinear optimization techniques and several experimental loops with different magnitudes, or measurements obtained with a low frequency supply signal, for a precise determination of the hysteresis model parameters. It is validated by the identification of two different kinds of magnetic materials: a standard laminated material made of 1008 steel and a soft magnetic composite Atomet‐EM1. The implementation of the hysteresis Jiles‐Atherton model in a 2D field calculation tool is detailed. The field calculation procedure is illustrated by two application examples involving single phase tranformers with cores made of the soft magnetic composite Atomet‐EM1.

Non-oriented electrical steel presents anisotropic behaviour. Modelling such anisotropic behaviour has become a necessity for accurate design of electrical machines. The main aim of this study is to model the magnetic anisotropy in the non-oriented electrical steel sheet of grade M400-50A using a phenomenological hysteresis model.

The well-known phenomenological vector Jiles–Atherton hysteresis model is modified to correctly model the typical anisotropic behaviour of the non-oriented electrical steel sheet, which is not described correctly by the original vector Jiles–Atherton model. The modification to the vector model is implemented through the anhysteretic magnetization. Instead of the commonly used classical Langevin function, the authors introduced 2D bi-cubic spline to represent the anhysteretic magnetization for modelling the magnetic anisotropy.

The proposed model is found to yield good agreement with the measurement data. Comparisons are done between the original vector model and the proposed model. Another comparison is also made between the results obtained considering two different modifications to the anhysteretic magnetization.

The paper presents an original method to model the anhysteretic magnetization based on projections of the anhysteretic magnetization in the principal axis, and apply such modification to the vector Jiles–Atherton model to account for the magnetic anisotropy. The replacement of the classical Langevin function with the spline resulted in better fitting. The proposed model could be used in the numerical analysis of magnetic field in an electrical application.

This paper deals with the incorporation of a vector hysteresis model in 2D finite‐element (FE) magnetic field calculations. A previously proposed vector extension of the well‐known scalar Jiles‐Atherton model is considered. The vectorised hysteresis model is shown to have the same advantages as the scalar one: a limited number of parameters (which have the same value in both models) and ease of implementation. The classical magnetic vector potential FE formulation is adopted. Particular attention is paid to the resolution of the nonlinear equations by means of the Newton‐Raphson method. It is shown that the application of the latter method naturally leads to the use of the differential reluctivity tensor, i.e. the derivative of the magnetic field vector with respect to the magnetic induction vector. This second rank tensor can be straightforwardly calculated for the considered hysteresis model. By way of example, the vector Jiles‐Atherton is applied to two simple 2D FE models exhibiting rotational flux. The excellent convergence of the Newton‐Raphson method is demonstrated.

This paper deals with the magnetic vector and scalar potential formulation for two‐dimensional (2D) finite element (FE) calculations including a vector hysteresis model, namely a vectorized Jiles‐Atherton model. The particular case of a current‐free FE model with imposed fluxes and magnetomotive forces is studied. The non‐linear equations are solved by means of the Newton‐Raphson method, which leads to the use of the differential reluctivity and permeability tensor. The proposed method is applied to a simple 2D model exhibiting rotational flux, viz the T‐joint of a three‐phase transformer.

The purpose of this paper is to implement a simple, fast and accurate heuristic method for parameter determination of Jiles‐Atherton (JA) hysteresis model for representing magnetization in electrical steel sheets. The performance of the method is validated using measured data and comparison with previous methods.

JA model requires five parameters to represent the hysteretic behavior of ferromagnetic materials. In order to determine these parameters, measured hysteresis loop is used here to calculate a fitness function which is defined by comparing the measured and simulated magnetization loops. This fitness function is minimized by optimization algorithms.

In total, four different measured hysteresis loops are studied in this paper. Each optimization algorithm is executed 50 times to investigate the convergence, speed, and accuracy of six methods. All methods begin with the same randomly generated initial parameters. Physical boundaries are used for parameters to avoid unaccepted results. Thorough examination of results shows that the proposed method is more appropriate than previously implemented methods for the parameter determination of Jiles‐Atherton model in all studied cases. The required parameters for each optimization method are also presented.

Shuffled frog leaping algorithm (SFLA) is implemented for the first time for JA model parameter determination. The results show that SFLA is faster and more accurate in comparison with other methods. Furthermore, this algorithm is easy to implement and tune.