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The ordinary vector hysteresis stop model with constant threshold values is not able to prohibit the hysteretic property after the saturation correctly. This paper aims to develop an improved vector hysteresis stop model with threshold surfaces. This advanced anisotropic vector hysteresis stop model can represent the magnetic saturation properties and the hysteresis losses under alternating and rotating magnetizations.

By integrating anhysteretic surfaces into the elastic element of a vector hysteresis stop model, the anisotropy of the permeability of an electrical steel sheet can be represented. Instead of the commonly used constant threshold value for plastic elements of the hysteresis model, threshold surfaces are applied to the stop hysterons. The threshold surfaces can be derived directly from measured alternating major loops of the material sample. By saturated polarization, the constructed threshold surfaces are vanishing. In this way, the reversible magnetic flux density is in the same direction of the applied magnetic flux density. Thus, the saturation properties are satisfied.

Analyzing the measurements of the electrical steel sheets sample obtained from a rotational single sheet tester shows that the clockwise (CW) and counter-CW (CCW) rotational hysteresis losses decrease by saturated flux density. At this state, instead of the domain wall motion, the magnetization rotation is dominant in the material. As a result, the hysteresis losses, which are related to the domain wall motion, are vanished near the saturation. In one stop operator, the plastic element represents the hysteresis part of the model. Integrating threshold surface into the plastic element, the hysteresis part can be modified to zero near the saturation to represent the saturation properties.

The results of this work demonstrate that the presented vector hysteresis stop model allows simulation of anisotropic hysteresis effects, alternating and rotating hysteresis losses. The parameters of the hysteresis model are determined by comparing the measured and modeled minor loops in different alternating magnetization directions. With the identified parameters, the proposed model is excited with rotated excitations in CW and CCW directions. The rotated hysteresis losses, derived from the model, are then compared with those experimentally measured. The modified vector stop model can significantly improve the accuracy of representing hysteresis saturations and losses.

A major purpose of vector hysteresis models lies in the prediction of power losses under rotating magnetic fields. The well-known vector Preisach model by Mayergoyz has been shown to well predict such power losses at low amplitudes of the applied field. However, in its original form, it fails to predict the reduction of rotational power losses at high fields. In recent years, two variants of a novel vector Preisach model based on rotational operators have been published and investigated with respect to general accuracy and performance. This paper aims to examine the capabilities of the named vector Preisach models in terms of rotational hysteresis loss calculations.

In a first step, both variants of the novel rotational operator-based vector Preisach model are tested with respect to their overall capability to prescribe rotational hysteresis losses. Hereby, the direct influence of the model-specific parameters onto the computable losses is investigated. Afterward, it is researched whether there exists an optimized set of parameters for these models that allows the matching of measured rotational hysteresis losses.

The theoretical investigations on the influence of the model-specific parameters onto the computable rotational hysteresis losses showed that such losses can be predicted in general and that a variation of these parameters allows to adapt the simulated loss curves in both shape and amplitude. Furthermore, an optimized parameter set for the prediction of the named losses could be retrieved by direct matching of simulated and measured loss curves.

Even though the practical applicability and the efficiency of the novel vector Preisach model based on rotational operators has been proven in previous publications, its capabilities to predict rotational hysteresis losses has not been researched so far. This publication does not only show the general possibility to compute such losses with help of the named vector Preisach models but also in addition provides a routine to derive an optimized parameter set, which allows an accurate modeling of actually measured loss curves.

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.

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.

This paper sets out to develop analytical solution to the hysteresis, eddy current and excess losses using the T(x) model. Based on Steinmetz' postulation, the losses, represented by the area enclosed by the hysteresis loop, are individually formulated in analytical form. The model is applied to sinusoidal and triangular excitation wave forms.

The equivalent interaction fields introduced into the model represent the losses individually by applying the separation and superposition principle.

Contrary to the presently used models, this model describes the hysteresis loop with its natural sigmoid shape and describes the losses individually in simpler mathematical formulation.

Experimental verification will still be needed as to the accuracy of the model and the applicability to the various magnetic materials.

The model presented here gives a more realistic presentation of the hysteresis loop and by using simpler mathematics than other models it is more accessible to the practical user. At the same time with the easy mathematics and its visual presentation it is a great value to people engaged in theoretical research in the field of magnetics.

In contrast with present magnetic loss models, using almost exclusively MSPM with “flat power” loop or the elliptical equivalent loop approximations, these calculations based on the T(x) model of hysteresis and uses realistic shape for the hysteresis loop, resulting in a simpler mathematical formulation.

The purpose of this paper is to develop the method of taking the eddy current losses in the laminated magnetic circuits into account during implicit transient calculations. The nonlinear magnetization characteristic of iron and the hysteresis losses can also be considered in the simulations done with the developed method.

The paper presents complex equivalent magnetic permeability derived from the presumed angular frequency in a laminated magnetic circuit. On this basis, the synthesis of a magnetic permeability as a function of the Laplace variable “s” is presented. After transformation of the variable “s” to a variable “z” of the Z transformation, it is possible to conduct discrete time calculation of transient states of magnetic circuits including the eddy current losses. An iterative process is developed to take the saturation of the magnetic circuit in these calculations into account. As regards hysteresis losses, the scalar model of magnetic hysteresis by Juhani Tellinen was implemented. The new method is validated by calculations of a two-coil transformer.

It is important to take into account the losses in sheet metal directly in the implicit transient calculations. This possibility is provided by the presented method based on the synthesis of the equivalent magnetic permeability μ^(s). The presented method was proved to be correct and efficient. The calculated sheet metal losses were compared with the results presented in literature. Good conformance of results was attained.

The method enables calculation of eddy current and hysteresis losses in laminated magnetic circuits during calculations of transient states. It does not need, unlike the previous methods, previously provided information (“a priori”) about the content of higher harmonics in waveforms. The method takes into account mutual dependence of transient waveforms of currents in the analysed system and losses of laminated magnetic circuit, expressed by eddy currents and hysteresis losses. Its implementation comes down to using in calculations a filter of the IIR type and corresponds to its calculation complexity. The author plans to use the presented method in the finite elements method transient calculations.

A new approach is a synthesis of the equivalent magnetic permeability in Laplace domain, which creates an equivalent RC circuit for permeability. Analytic equations for parameters of this equivalent circuit are original. A method for considering nonlinear magnetization characteristic and hysteresis losses was presented. In calculations of transient states of systems with magnetic circuits, one can use the developed equivalent circuit of magnetic permeability in a form of the IIR filter. Operator magnetic permeability includes fractional derivative of Laplace’s variable “vs”. Therefore, the equivalent IIR filter includes “history” of the processes that take place in the laminated magnetic circuit to the current, calculated time moment. This “history” in terms of its content is limited only by the degree of the applied IIR filter. It enables to calculate “step by step”, without previous (“a priori”) knowledge about harmonic components of the whole waveforms. It was necessary in the previously used methods, when determining parameters of magnetic permeability. The method proposed in the paper allows for calculations with taking into account direct dependence of an electric part of the system on its magnetic part.

The electrical machines connected to modern electric power grids are non-sinusoidal excited, and their augmented losses, including iron losses, limit their working characteristics. This paper aims to propose a prediction method for iron losses in non-oriented grains (NO) FeSi sheets under non-sinusoidal voltage, involving an inverse classical Preisach hysteresis model and the time-integration of each loss component.

The magnetic history management in inverse Preisach model is optimized and a numerical Everett function is identified from measured symmetrical hysteresis cycles. The experimental data for sinusoidal waveforms obtained by a single sheet tester were also used to identify the parameters involved in Bertotti’ losses separation method. The non-sinusoidal magnetic induction waveform, corresponding to a measured voltage in an industrial electrical grid, was the input for Preisach model, the output magnetic field being accurately computed. The hysteresis, classical and excess losses are calculated by time-integration and the total losses are compared with those obtained for sinusoidal excitation.

The proposed method allows to estimate the iron losses for non-sinusoidal magnetic induction, using carefully identified parameters of FeSi NO sheets, using experimental data from sinusoidal regimes.

The method accuracy is assured by using a numerical Everett function, a variable Preisach grid step (adapted for the high non-linearity of FeSi sheets) and high-order fitting polynomials for the microscopic parameters involved in the excess loss estimation. The procedure allows a better design of magnetic cores and an improved estimation of the electric machine derating for non-sinusoidal voltages.

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.

To study the magnetic shielding and the losses of non‐linear, hysteretic multilayered shields by using fast to evaluate analytical expressions.

In order to evaluate the shield in the frequency domain, the non‐linear shield is divided into a sufficient number of piecewise linear sublayers. Each sublayer has a permeability that is constant (space independent) and complex (to model hysteresis). This expression for the permeability is found from the Preisach model by a Fourier transform. Once H is known in the entire shield, analytical expressions calculate the eddy current losses and hysteresis losses in the material. The validity of the analytical expressions is verified by numerical experiments.

In the Rayleigh region, the shielding factor of perfectly linear material is better than the one of non‐linear metal sheets, but also the eddy current losses are higher. The results of the optimization show that steel is only a useful shielding material at low frequencies.

The analytical method is valid for infinitely long shields and for weak imposed fields in the Rayleigh region.

As the analytical expressions can be evaluated very fast (in comparison with slow finite elements models), many magnetic shields can be compared in parametric studies.

Analytical expressions exist for the shielding factor and the losses of linear materials. In this paper, the method is extended for non‐linear hysteretic materials. The effects of several parameters (material parameters, incident fields parameters) on the shielding and the losses are shown.

The thermally extended Tellinen model (Kühn et al., to appear) is here investigated and equipped with a hysteresis loss model, while preserving its simple structure.

As in the original model, these approaches are based upon phenomenal observations and measured saturation curves. The authors start with the original model and step-by-step add their extensions, such that in the end they can apply the extended model in a finite element method (FEM) simulation. During the process, care is taken to ensure that the applicability in a FEM simulation is not impaired, in terms of memory requirements and computing power.

In comparison to the original model, this extended model needs some further requirements and so is a little bit more limited in its application. It is in itself coherent and well defined. The authors provide an on-the-fly algorithm computation of hysteresis losses. First numerical results for a coupled field/thermal system show expected behavior.

The original model (Tellinen, 1998) does not take temperature into account. It includes a model for calculating hysteresis losses, but it differs largely from the approach presented here. The thermal extension is now also equipped with an on-the-fly method for hysteresis losses. Furthermore, the authors provide some analysis of simple, stable loops.