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Article
Publication date: 2 December 2021

Xiao Xiao, Fabian Müller, Martin Marco Nell and Kay Hameyer

This paper aims to use a history-dependent vector stop hysteresis model incorporated into a two dimensional finite elements (FE) simulation environment to solve the magnetic field…

Abstract

Purpose

This paper aims to use a history-dependent vector stop hysteresis model incorporated into a two dimensional finite elements (FE) simulation environment to solve the magnetic field problems in electrical machines. The vector stop hysteresis model is valid for representing the anisotropic magnetization characteristics of electrical steel sheets. Comparisons of the simulated results with measurements show that the model is well appropriate for the simulation of electrical machines with alternating, rotating and harmonic magnetic flux densities.

Design/methodology/approach

The anisotropy of the permeability of an electrical steel sheet can be represented by integrating anhysteretic surfaces into the elastic element of a vector hysteresis stop model. The parameters of the vector stop hysteresis model were identified by minimizing the errors between the simulated results and measurements. In this paper, a damped Newton method is applied to solve the nonlinear problem, which ensures a robust convergence of the finite elements simulation with vector stop hysteresis model.

Findings

Analyzing the measurements of the electrical steel sheets sample obtained from a rotational single sheet tester shows the importance to consider the anisotropic and saturation behavior of the material. Comparing the calculated and measured data corroborates the hypothesis that the presented energy-based vector stop hysteresis model is able to represent these magnetic properties appropriately. To ensure a unique way of hysteresis loops during finite elements simulation, the memory of the vector stop hysteresis model from last time step is kept unchanged during the Newton iterations.

Originality/value

The results of this work demonstrates that the presented vector hysteresis stop model allows simulation of vector hysteresis effects of electrical steel sheets in electrical machines with a limited amount of measurements. The essential properties of the electrical steel sheets, such as phase shifts, the anisotropy of magnetizations and the magnetization characteristics by alternating, rotating, harmonic magnetization types, can be accurately represented.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 41 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 February 2022

Michael Nierla, Manfred Kaltenbacher and Stefan Johann Rupitsch

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…

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Originality/value

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.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 41 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 27 March 2023

Xiao Xiao, Fabian Müller, Martin Marco Nell and Kay Hameyer

The goal of this research is to investigate the convergence behavior of the Newton iteration, when solving the nonlinear problem with consideration of hysteresis effects…

Abstract

Purpose

The goal of this research is to investigate the convergence behavior of the Newton iteration, when solving the nonlinear problem with consideration of hysteresis effects. Incorporating the vector hysteresis model in the magnetic vector potential formulation has encountered difficulties. One of the reasons is that the Newton method is very sensitive regarding the starting point and states distinct requirements for the nonlinear function in terms of monotony and smoothness. The other reason is that the differential reluctivity tensor of the material model is discontinuous due to the properties of the stop operators. In this work, line search methods to overcome these difficulties are discussed.

Design/methodology/approach

To stabilize the Newton iteration, line search methods are studied. The first method computes an error-oriented search direction. The second method is based on the Wolfe-Powell rule using the Armijo condition and curvature condition.

Findings

In this paper, the differentiation of the vector stop model, used to evaluate the Jacobian matrix, is studied. Different methods are applied for this nonlinear problem to ensure reliable and stable finite element simulations with consideration of vector hysteresis effects.

Originality/value

In this paper, two different line search Newton methods are applied to solve the magnetic field problems with consideration of vector hysteresis effects and ensure a stable convergence successfully. A comparison of these two methods in terms of robustness and efficiency is presented.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 42 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 September 2004

J. Gyselinck, P. Dular, N. Sadowski, J. Leite and J.P.A. Bastos

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…

Abstract

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.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 23 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 September 1999

Carlo Ragusa and Maurizio Repetto

The implementation of a vector Preisach model for the modelling of anisotropic hysteretic soft magnetic materials is outlined. Some comparisons with measurements on alternate and…

Abstract

The implementation of a vector Preisach model for the modelling of anisotropic hysteretic soft magnetic materials is outlined. Some comparisons with measurements on alternate and rotational magnetic field excitations are shown. The hysteresis model is inserted inside a two‐dimensional finite element solver formulated in terms of magnetic vector potential and nonlinear solution is handled by means of the fixed point method with H‐scheme. Results obtained on a two‐dimensional geometry are described and discussed.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 18 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 4 September 2017

Michael Nierla, Alexander Sutor, Stefan Johann Rupitsch and Manfred Kaltenbacher

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…

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Research limitations/implications

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.

Originality/value

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.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 25 July 2019

Stephan Willerich and Hans-Georg Herzog

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…

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Originality/value

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.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 38 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 8 August 2019

Michael Nierla, Michael Loeffler, Manfred Kaltenbacher and Stefan Johann Rupitsch

The numerical computation of magnetization processes in moving and rotating assemblies requires the usage of vector hysteresis models. A commonly used model is the so-called…

Abstract

Purpose

The numerical computation of magnetization processes in moving and rotating assemblies requires the usage of vector hysteresis models. A commonly used model is the so-called Mayergoyz vector Preisach model, which applies the scalar Preisach model into multiple angles of the halfspace. The usage of several scalar models, which are optionally weighted differently, enables the description of isotropic as well as anisotropic materials. The flexibility is achieved, however, at the cost of multiple scalar model evaluations. For solely isotropic materials, two vector Preisach models, based on an extra rotational operator, might offer a lightweight alternative in terms of evaluation cost. The study aims at comparing the three mentioned models with respect to computational efficiency and practical applicability.

Design/methodology/approach

The three mentioned vector Preisach models are compared with respect to their computational costs and their representation of magnetic polarization curves measured by a vector vibrating sample magnetometer.

Findings

The results prove the applicability of all three models to practical scenarios and show the higher efficiency of the vector models based on rotational operators in terms of computational time.

Originality/value

Although the two vector Preisach models, based on an extra rotational operator, have been proposed in 2012 and 2015, their practical application and inversion has not been tested yet. This paper not only shows the usability of these particular vector Preisach models but also proves the efficiency of a special stageless evaluation approach that was proposed in a former contribution.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 38 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 16 November 2010

E. Della Torre, E. Cardelli and L.H. Bennett

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…

217

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

The model computes the same cyclic losses as expected.

Research limitations/implications

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.

Practical implications

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.

Originality/value

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

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 29 no. 6
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 28 October 2014

Miklós Kuczmann

The purpose of this paper is to develop a viscous-type frequency dependent scalar Preisach hysteresis model and to identify the model using measured data and nonlinear numerical…

Abstract

Purpose

The purpose of this paper is to develop a viscous-type frequency dependent scalar Preisach hysteresis model and to identify the model using measured data and nonlinear numerical field analysis. The hysteresis model must be fast and well applicable in electromagnetic field simulations.

Design/methodology/approach

Iron parts of electrical machines are made of non-oriented isotropic ferromagnetic materials. The finite element method (FEM) is usually applied in the numerical field analysis and design of this equipment. The scalar Preisach hysteresis model has been implemented for the simulation of static and dynamic magnetic effects inside the ferromagnetic parts of different electrical equipment.

Findings

The comparison between measured and simulated data using a toroidal core shows a good agreement. A modified nonlinear version of TEAM Problem No. 30.a is also shown to test the hysteresis model in the FEM procedure.

Originality/value

The dynamic model is an extension of the static one; an extra magnetic field intensity term is added to the output of the static inverse model. This is a viscosity-type dynamic model. The fixed-point method with stable scheme has been realized to take frequency dependent anomalous losses into account in FEM. This scheme can be used efficiently in the frame of any potential formulations of Maxwell's equations.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 33 no. 6
Type: Research Article
ISSN: 0332-1649

Keywords

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