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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.

The purpose of this paper is to combine the Jiles-Atherton (J-A) hysteresis model with the field separation approach to realize the accurate simulation of dynamic magnetostrictive characteristics of silicon steel sheet.

First, the energy loss of silicon steel sheet is divided into hysteresis loss Why, classical eddy current loss Wed and anomalous loss Wan according to the statistical theory of losses. The Why is calculated by static J-A hysteresis model, Wed and Wan are calculated by the analytical formulae. Then, based on the field separation approach, the dynamic magnetic field is derived. Finally, a new dynamic magnetostrictive model is proposed by means of the quadratic domain rotation model.

Comparison of simulation and experimental results verifies that the proposed model has high accuracy and strong universality.

The proposed method improves the existing method’s problem of relying on too much experimental data, and the method ensures the calculation accuracy, parameter identification accuracy and engineering practicability. Consequently, the presented work greatly facilitates further explorations and studies on simulation of dynamic magnetostrictive characteristics of silicon steel sheet.

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.

In this communication, the Preisach and Jiles‐Atherton models are studied to take hysteresis phenomenon into account in finite element analysis. First, the models and their identification procedure are briefly developed. Then, their implementation in the finite element code is presented. Finally, their performances are compared with an electromagnetic system made of soft magnetic composite. Current and iron losses are calculated and compared with the experimental results.

To analyze the Jiles and Atherton hysteresis model used for hysteresis losses estimation in soft magnetic composite (SMC) material.

The Jiles and Atherton hysteresis model parameters are optimized with genetic algorithms (GAs) according to measured symmetric hysteresis loop of soft magnetic composite material. To overcome the uncertainty, finding the best‐optimized parameters in a wide predefined searching area is done with the proposed new approach. These parameters are then used to calculate the hysteresis losses for the modeled hysteresis. The asymmetric hysteresis loops are also investigated.

The classical GAs are good optimization methods when a pre‐defined possible set of solutions is known. If no assumption on solutions is present and a wide searching area range for parameter estimation is selected then the use of the new approach with nested GAs gives good results for symmetric hysteresis loops and further for the estimation of hysteresis losses.

The use of the Jiles and Atherton hysteresis model for asymmetric hysteresis must be explored further. Only one set of optimized Jiles and Atherton hysteresis model parameters used for estimation of hysteresis losses gives good results for only symmetric hysteresis loops. These parameters have limitations for asymmetric hysteresis loops.

Nested GAs are a useful method for optimization when a wide searching area is used.

The originality of the paper is in the establishment of nested GAs and their application in Jiles and Atherton hysteresis model parameters optimization. Also, original is the use of the Jiles and Atherton hysteresis model for hysteresis loop description of soft‐magnetic composite material.

Although the original Jiles‐Atherton (J‐A) hysteresis model is able to represent a wide range of major hysteresis loops, in particular those of soft magnetic materials, it can produces non‐physical minor loops with its classical equations. The purpose of this paper is to show a modification in the J‐A hysteresis model in order to improve the minor and inner loops representation. The proposed technique allows the J‐A model representing non‐centred minor loops with accuracy as well as improving the symmetric inner loops representation.

Only the irreversible magnetization component is slightly modified keeping unchanged the other model equations and the model simplicity. The high‐variation rate of the irreversible magnetization, which causes the non‐physical behaviour of minor loops, is limited by introducing a new physical parameter linked to the losses. Contrarily to other modifications of the original model found in the literature, the previously knowledge of the magnetic field waveform is not needed in this case.

The modified hysteresis model is validated by comparison with experimental results. A good agreement is observed between calculations and measurements. The modified model retains the low‐computational effort and numerical simplicity of the original one.

This paper shows that a classical scalar hysteresis model can be suitably used to take into account the minor loops behaviour and be included in a finite element code. The methodology is useful for the design and analysis of electromagnetic devices under distorted flux patterns.

Improperly fitted parameters for the Jiles–Atherton (JA) hysteresis model can lead to non-physical hysteresis loops when ferromagnetic materials are simulated. This can be remedied by including a proper physical constraint in the parameter-fitting optimization algorithm. This paper aims to implement the constraint in the meta-heuristic simulated annealing (SA) optimization and Nelder–Mead simplex (NMS) algorithms to find JA model parameters that yield a physical hysteresis loop. The quasi-static B(H)-characteristics of a non-oriented (NO) silicon steel sheet are simulated, using existing measurements from a single sheet tester. Hysteresis loops received from the JA model under modified logistic function and piecewise cubic spline fitted to the average M(H) curve are compared against the measured minor and major hysteresis loops.

A physical constraint takes into account the anhysteretic susceptibility at the origin. This helps in the optimization decision-making, whether to accept or reject randomly generated parameters at a given iteration step. A combination of global and local heuristic optimization methods is used to determine the parameters of the JA hysteresis model. First, the SA method is applied and after that the NMS method is used in the process.

The implementation of a physical constraint improves the robustness of the parameter fitting and leads to more physical hysteresis loops. Modeling the anhysteretic magnetization by a spline fitted to the average of a measured major hysteresis loop provides a significantly better fit with the data than using analytical functions for the purpose. The results show that a modified logistic function can be considered a suitable anhysteretic (analytical) function for the NO silicon steel used in this paper. At high magnitude excitations, the average M(H) curve yields the proper fitting with the measured hysteresis loop. However, the parameters valid for the major hysteresis loop do not produce proper fitting for minor hysteresis loops.

The physical constraint is added in the SA and NMS optimization algorithms. The optimization algorithms are taken from the GNU Scientific Library, which is available from the GNU project. The methods described in this paper can be applied to estimate the physical parameters of the JA hysteresis model, particularly for the unidirectional alternating B(H) characteristics of NO silicon steel.

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.