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The magnetic modeling of materials has been focused on computing magnetization and forces in devices. With increasing efforts to make energy efficient devices, attention must now be paid to hysteresis losses in magnetizing processes. The purpose of this paper is to discuss the pertinent parameters that determine these losses and a method of identifying them.

A vector model was used that is designed to compute losses correctly, to focus on hysteresis losses in models that compute the same magnetization, but have different losses.

The model computes the same cyclic losses as expected.

The analysis of this paper is limited to isotropic media, but it can be generalized to anisotropic media. The accuracy of the Della Torre, Pinzaglia and Cardelli (DPC) model is also limited.

Once the model has been validated, the designer can minimize the instantaneous as well as the average dissipation. This will permit the design of more reliable devices.

The DPC model used in this work has not been fully explored previously.

The use of gradient-based methods in finite element schemes can be prevented by undefined derivatives, which are encountered when modeling hysteresis in constitutive material laws. This paper aims to present a method to deal with this problem.

Non-smooth Newton methods provide a generalized framework for the treatment of minimization problems with undefined derivatives. Within this paper, a magnetostatic finite element formulation that includes hysteresis is presented. The non-linear equations are solved using a non-smooth Newton method.

The non-smooth Newton method shows promising convergence behavior when applied to a model problem. The numbers of iterations for magnetization curves with and without hysteresis are within the same range.

Mathematical tools like Clarke's generalized Jacobian are applied to magnetostatic field problems with hysteresis. The relation between the non-smooth Newton method and other methods for solving non-linear systems with hysteresis like the M(B)-iteration is established.

This paper aims to discuss the problems associated with using a new vector hysteresis model.

The implementation of this new model is independent of the coordinate system used, thus is more tractable mathematically. It is simpler to use than other models. It has the correct energy properties.

The model requires fewer variables to describe anisotropic media.

The simplicity of the coordinated vector hysteresis model is only valid for ellipsoidally magnetizable media.

The design of vector hysteresis devices will be far more accurate using this model.

The elaboration of this model has not been presented before.

This paper aims to present a novel stageless evaluation scheme for a vector Preisach model that exploits rotational operators for the description of vector hysteresis. It is meant to resolve the discretizational errors that arise during the application of the standard matrix-based implementation of Preisach-based models.

The newly developed evaluation uses a nested-list data structure. Together with an adapted form of the Everett function, it allows to represent both the additional rotational operator and the switching operator of the standard scalar Preisach model in a stageless fashion, i.e. without introducing discretization errors. Additionally, presented updating and simplification rules ensure the computational efficiency of the scheme.

A comparison between the stageless evaluation scheme and the commonly used matrix approach reveals not only an improvement in accuracy up to machine precision but, furthermore, a reduction of computational resources.

The presented evaluation scheme is especially designed for a vector Preisach model, which is based on an additional rotational operator. A direct application to other vector Preisach models that do not rely on rotational operators is not intended. Nevertheless, the presented methodology allows an easy adaption to similar vector Preisach schemes that use modified setting rules for the rotational operator and/or the switching operator.

Prior to this contribution, the vector Preisach model based on rotational operators could only be evaluated using a matrix-based approach that works with discretized forms of rotational and switching operator. The presented evaluation scheme offers reduced computational cost at much higher accuracy. Therefore, it is of great interest for all users of the mentioned or similar vector Preisach models.

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 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.

In this paper are summarized our research activities dealing with the theoretical and experimental analysis of high voltage direct current (HVDC) ionizers. We present here the basic principle of a hybrid charge simulation‐finite difference method, that has been used to simulate the electric behaviour of these devices, by computing the electric field strength and the ionic current density distribution, therefore the efficiency of emission. We have realized an experimental ion counter and we have used it to verify the values predicted by means of this numerical technique.

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.

Using appropriate solution techniques for transformer inrush current transient study is of great prominence owing to the inevitable inclusion of differential equations leading to complicated analysis procedures. This study aims to propose an analytical-numerical method to accurately analyze the three-phase three-limb core-type transformer inrush current in different cases considering the nonlinear behavior of the iron core.

The proposed method focuses on acquiring equations for inrush current and also the magnetic core flux by the application of a simulation-based iterative approach. In this regard, multiple integral equations are solved taking the time intervals into account. Then several derivations and integrations of matrix terms are substituted into the obtained results so as to simplify the solution process.

The method provides notable enhancements in computation time and also excellent qualities of accuracy compared with conventional numerical methods.

The proposed method is simulated for two three-phase transformers via MATLAB software. The obtained simulation results have been also compared with experimental tests.

Actually, the analytical-numerical method is capable of computing higher number of iterations in a shorter time efficiently, while making use of the conventional numerical procedures may not result in expected convergences. The simulation results of the proposed analytical-numerical technique illustrate a close agreement with the experimental test, and hence, verify the method preciousness.

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.