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One way to deal with non‐linearity in the case of time harmonic excitation of the electric and magnetic fields in ferromagnetic media is to introduce an effective material to model the ferromagnetic region. This fictitious material is constant throughout a period but inhomogeneous and it takes into account the non‐linear relationship between the field quantities. Several methods to create an effective magnetization curve are presented and different finite element formulations are applied to these. Some of these methods are known from the literature for 1D and 2D problems but not for 3D ones and they have only be used for a magnetic vector potential formulation so far. In the present paper they are extended for general vector and scalar potential formulations. Further possible ways to introduce such an effective material to take into account saturation effects are shown. All these different methods are investigated on a non‐linear 3D time harmonic eddy current problem using complex formalism.

This paper presents various available and new techniques for prediction of the hysteresis loop, no‐load current curve and hysteresis losses. It is shown that linearization is a convenient method to be employed for quick estimation of the hysteresis loop with acceptable accuracy. Although the third and fifth order functions for saturation curve prediction lead to more accurate results, it requires more data and also more complicated equations resulting in longer computation time. Use of various third and fifth order functions for saturation curve are the noticeable advantages of the techniques. The three proposed techniques could predict the hysteresis loop of transformers using simple experiments and iterative computer computations.

The purpose of this paper is to define a time‐efficient numerical procedure for the extraction of load‐dependent equivalent circuit (EC) parameters of induction machines. The parameters are determined for every operating point, thus their variation due to skin effect and material saturation under arbitrary load condition is taken into consideration.

Two methods are presented and compared. The first one is based on the numerical simulation of the standard measurement process, yielding an EC with constant parameters. A time‐harmonic finite element analysis is applied in the second method to calculate the load‐dependent EC parameters. Material linearization and the superposition principle for the magnetic flux are employed to define the leakage inductances.

A distinct load dependence of all EC parameters has been proven as well as the clear disparity between stator and rotor leakage inductances. These effects can only be taken accurately into account by the EC obtained by the second numerical procedure proposed.

The presented method successfully overcomes typical problems of the measurement process and of the standard numerical procedure for EC parameter estimation, thus the obtained EC parameters are load‐dependent while the physical interpretation of the variables and parameters remains straightforward. Hence, the paper of the internal machine variables is enabled.

The paper sets out to formulate the intermolecular forces leading to Barkhausen instability. In the approach the known concept of effective field is used within the framework of the T(x) model. The aim is to provide a mathematical tool to theoreticians and applied scientists in magnetism that is easier to use than those of other models. At the same time to demonstrate the easy applicability of the T(x) model to hysteretic phenomena.

With the combination of the effective and the external field the model is applied to hysteresis loops as well as to the anhysteretic state showing in both cases the local development of unstable conditions at beyond a critical point, leading to local hysteresis loops.

The paper formulates the critical conditions for the hysteretic and the anhysteretic process and calculates the susceptibility as the functions of magnetisation and the applied field.

Experimental verification will be required to prove the applicability to the various magnetic materials and to the accuracy of the model.

The paper provides an easy mathematical and visual method to show the conditions before and after the Barkhausen instability sets in during the magnetisation process.

The paper provides an easy mathematical tool for theoreticians and experimental scientists with a visual presentation of processes leading to Barkhausen instability and magnetic behaviour beyond that by using the T(x) model.

The purpose of this paper is to focus on the frequency-dependent non-linear magnetization behaviour of the soft magnetic material, which influences both the energy loss and the performance of the electrical machine. The applied approach is based on measured material characteristics for various frequencies and magnetic flux densities. These are varied during the simulation according to the operational conditions of the rotating electrical machine. Therewith, the fault being committed neglecting the frequency-dependent magnetization behaviour of the magnetic material is examined in detail.

The influence of non-linear frequency-dependent material properties is studied by variation of the frequency-dependent magnetization characteristics. Two different non-oriented electrical steel grades having the same nominal losses at 1.5 T and 50 Hz, but different thickness, classified as M330-35A and M330-50A are studied in detail. Both have slightly different magnetization and loss behaviour.

This analysis corroborates that it is important to consider the frequency-dependency and saturation behaviour of the ferromagnetic material as well as its magnetic utilization when simulating electrical machines, i.e., its performance. The necessity to change the magnetization curve according to the applied frequency for the calculation of operating points depends on the applied material and the frequency range. Using materials, whose magnetization behaviour is marginally affected by frequency, causes a deviation in the flux-linkage and the electromagnetic torque in a small frequency range. However, analysing larger frequency ranges, the frequency behaviour of the material cannot be neglected. For instance, a poorer magnetizability requires a higher quadrature current to keep the same torque leading to increased copper losses. In addition, the applied iron-loss model plays a central role, since changes in magnetization behaviour with frequency lead to changes in the iron losses. In order to study the impact, the iron-loss model has to be capable to incorporate the harmonic content, because particularly the field harmonics are influenced by the shape of the magnetization curve.

This paper gives a close insight on the way the frequency-dependent non-linear magnetization behaviour affects the energy loss and the performance of electrical machines. Therewith measures to tackle this could be derived.

The paper aims to take a critical view of the Wholfarth's assumption and the Henkel plots as the measure of molecular mean‐field interaction in magnetic materials. At the same time it seeks to formulate the effect of the molecular field interaction on the anhysteretic remanence.

Based on the recently verified Bosorth's original definition of anhysteretic state, the paper verifies Wohlfarth's conjecture. By including the molecular field interaction into the effective field expression it formulates the hysteretic and anhysteretic remanent behavior of the magnetic material.

The hysteretic and anhysteretic character of the material can be formulated up to and beyond the Barkhausen jump. The paper also points out that, the now verified, Wholfarth's conjecture is applicable to not only major hysteresis loops but also to symmetrical minor loops as well, within the same set. By doing so it removes the uncertainty surrounding its mathematical formulation.

In the light of these findings the conjecture's relation to multi‐phase magnetic materials has to be investigated in the future.

The formulation of the hyteretic and anhysteretic remanent character can provide a graphical interpretation of the materials behavior. The paper demonstrate how the Henkel plots, based on the Wholfarth's conjecture, used as an indicator of the magnitude of the molecular interaction, can be simplified to the benefit of the theoretical and practical users.

The aim of the paper is to provide a simple and reliable hysteresis model for prediction of magnetization curves of a resistance spot welding transformer (RSWT) core, operating in a wide range of flux densities and excitation frequencies.

The hysteresis model considered in the paper is the T(x) description advanced by J. Takács. Three options to extend the model to the dynamic magnetization conditions are considered. The excitation conditions differ from those prescribed by international standards.

The quasi‐static Takács model combined with a fractional viscosity equation similar to that proposed by S.E. Zirka outperforms other considered options. The effect of eddy currents may be considered as a disturbance factor to the frequency‐independent quasi‐static hysteresis loop.

The combined approach yields in most cases a satisfactory agreement between theory and experiment. For highest frequency considered in the paper (1 kHz) excessive “heels” were observed in the modelled loops. This artifact may be reduced by the introduction of a more complicated relationship for the viscous term. Future work shall be devoted to this issue.

The combined Takács‐Zirka model is a useful tool for prediction of magnetization curves of a RSWT core in a wide range of flux densities and excitation frequencies.

The usefulness of the Takács description has been verified in a practical application. The model is able to predict magnetization curves under non‐standard excitation conditions.

This paper aims to compare different static history-independent hysteresis models (mathematical-, behavioural- and physical-based ones) and a history-dependent hysteresis model in terms of parameter identification effort and accuracy.

The discussed models were tested for distorted-excitation waveforms to explore their predictions of complex magnetization curves. Static hysteresis models were evaluated by comparing the calculated and measured major and minor static hysteresis loops.

The analysis shows that the resulting accuracy of the different hysteresis models is strongly dependent on the excitation waveform, i.e. smooth excitations, distorted flux waveforms, transients or steady-state regimes. Obtained results show significant differences between predictions of discussed static hysteresis models.

The general aim was to identify the models on a very basic and limited set of measured data, i.e. if possible using only the measured major static loop of the material. The quasi-static major hysteresis loop was measured at B_max = 1.5 T.

The presented analysis allows selection of the most-suited hysteresis model for the sought-for application and appraisal of the individual limitations.

The presented analysis shows differences in intrinsic mechanisms to predict magnetization curves of the majority of the well-known static hysteresis models. The results are essential when selecting the most-suited hysteresis model for a specific application.

Owing to the excellent performance, giant magnetostrictive materials (GMMs) are widely used in many engineering fields. The dynamic Jiles–Atherton (J-A) model, derived from physical mechanism, is often used to describe the hysteresis characteristics of GMM. However, this model, despite cited by many different literature studies, seems not to possess unique expressions, which may cause great trouble to the subsequent application. This paper aims to provide the rational expressions of the dynamic J-A model and propose a numerical computation scheme to obtain the model results with high accuracy and fast speed.

This paper analyzes different published papers and provides a reasonable form of the dynamic J-A model based on functional properties and physical explanations. Then, a numerical computation scheme, combining the Newton method and the explicit Adams method, is designed to solve the modified model. In addition, the error source and transmission path of the numerical solution are investigated, and the influence of model parameters on the calculation error is explored. Finally, some attempts are made to study the influence of numerical scheme parameters on the accuracy and time of the computation process. Subsequently, an optimization procedure is proposed.

A rational form of the dynamic J-A model is concluded in this paper. Using the proposed numerical calculation scheme, the maximum calculation error, while computing the modified model, can remain below 2 A/m under different model parameter combinations, and the computation time is always less than 0.5 s. After optimization, the calculation speed can be enhanced with the computation accuracy guaranteed.

To the best of the authors’ knowledge, this paper is the first one trying to provide a rational form of the dynamic J-A model among different citations. No other research studies focus on designing a detailed computation scheme targeting the fast and accurate calculation of this model as well. And the performance of the proposed calculation method is validated in different conditions.

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.