Conference Agenda

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Session Overview
PB-M2: Material Modelling, Multi-Scale Modelling and Homogenization
Wednesday, 17/Jul/2019:
10:50am - 12:40pm

Session Chair: Laurent Daniel
Session Chair: Yongjian Li
Location: Patio 44-55

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The FEM Calculation Considering Vector Magnetic Properties of Electrical Steel Sheet under DC-Biased Field

Minxia Shi, Xuanrui Zhang, Aici Qiu, Junhao Li

State Key Laboratory of Electrical Insulation and Power Equipment, Xi'an Jiaotong University, 710049, Xi'an, China

For accurate computation of magnetic field distribution in transformer core, an improved model considering vector magnetic properties of electrical steel sheet under DC-biased field is proposed. The reliability of the improved model is verified by the comparison of measured and calculated hysteresis loop. The finite element formulation considering vector magnetic properties is derived for the magnetic field analysis of transformer core under DC-biased field. Moreover, the flux density distribution is calculated for investigating the impact of DC-biased magnetizing condition on magnetic characteristics of transformer core.

Comparison of Preisach and Congruency-Based Static Hysteresis Models Applied to Non-Oriented Steels

Reza Zeinali, Dave Krop, Elena Lomonova

Eindhoven University of Technology, The Netherlands

The Preisach model is addressed as a promising hysteresis model, broadly employed and investigated in literature. The driving force behind the extensive research on the Preisach model is to find an approach for accurate identification of the weight function. The weight function is usually determined by means of two approaches: experimental or analytic. In this study, a new methodology is proposed to obtain the weight function for the Preisach model of non-oriented laminated steels. In this methodology, first the experimental weight function is obtained from measured concentric hysteresis loops and a mathematical technique is applied to remove the existing negative values. Based on the shape of the modified weight function, a new analytic function is proposed as a weight function for the Preisach model. The proposed analytic function is more advanced than the conventional probability functions proposed in literature, so that it is able to better mimic the actual shape of the weight function. The unknown parameters of the analytic weight function are identified by minimizing the error between the Preisach model and the modified measurements. Using the proposed analytic weight function, the minimum rms-error is reduced to less than 0.5% and a decent agreement is achieved between the model and the measurement.

Simulation of post assembly magnetization of permanent magnet machine rotors

Gregor Bavendiek, Fabian Müller, Kay Hameyer

Institute of Electrical Machines, Germany

Synchronous machines with high-energy permanent magnets offer a high power density and high efficiency. The permanent

magnets have to be magnetized by a high magnetic field for retaining their magnetic energy. This study offers a nonlinear, transient,

history-dependent magnetization and demagnetization model for permanent magnets. The model is extended to cover return and

recoil loops for any inner hysteresis loop. The proposed model offers an opportunity for a better exploration of permanent magnet

material in machine rotors by improving the magnetic circuit design of post assembly rotor magnetizer and the rotor itsself by

concerning local effects during transient change of magnetization. This makes it suitable for study both variable flux and in-situ


A vector generalization of the inverse G model for magnetic vector potential FEM problems

Marcos Fernandes1, Kleyton Hoffmann1,2, João Pedro Bastos1,3, Nelson Sadowski1, Jean Vianei Leite1

1GRUCAD/EEL/CTC, Universidade Federal de Santa Catarina, Florianópolis, SC, 88040-900, Brazil; 2Universidade do Oeste de Santa Catarina, Department of Electrical Engineering, Joaçaba, SC, Brazil; 3PPGESE, Universidade Federal de Santa Catarina, Joinville, SC, Brazil

In a previous work, a hysteresis model, called G model, was proposed with the goal of representing the magnetic hysteresis by simple equations. It was the direct model using the magnetic field as the independent variable. However, with the magnetic vector potential 2D classical formulation, the magnetic induction is the independent quantity. The main contribution of this work is to present the inverse version of the G model adapted to vector potential formulation. Additionally, a Mayergoyz vector hysteresis generalization is also considered in order to couple the model with a 2D vector potential FEM formulation. The anisotropy is inserted with orientation distribution function (ODF).

On the Approach to Predict Iron Losses of Soft Magnetic Materials Based on Statistical Characteristics of IEM-formula Parameters

Pengfei Zhang1,2, Nora Leuning2, Gregor Bavendiek2, Jun Zou1, Kay Hameyer2

1State Key Laboratory of Power System, Department of Electrical Engineering, Tsinghua University, Beijing, PR China; 2Institute of Electrical Machines(IEM), RWTH Aachen University, Germany

Iron-loss predication for soft magnetic materials is crucial for various stages during the design of electrical machines. The IEM-formula [1] is used for its semi-physical approach and accuracy. However, when studying a large number of materials, fitting formula parameters by classic approach for each material can be tedious and time-consuming. In this paper, a fast approach to predict the iron losses in soft magnetic materials is proposed. Combined with measurement data of seven different grades of material, statistical characteristics of IEM-formula parameters are identified and concluded. Employing the least square method and providing initial data based on IEM-formula parameters statistics, iron losses prediction of considerable materials can be performed very time efficient. Test calculations have been done to show the strength of the approach. Simulation results show that the improvement in computational speed is more than 40% while guaranteeing the required accuracy. By the evaluation of statistical data, parameter ranges can be deduced and improve the understanding of iron losses for different material grades from their different physical properties.

A Novel Vector Hysteresis Model Based on Improved Neural Network with Parallel Strategy

Dianhai Zhang1, Lianqiang Chi1, Sen Wang2, Yanli Zhang1, Chang-Seop Koh3

1Shenyang university of technology, China, People's Republic of; 2Shenyang Institute of Engineering, China, People's Republic of; 3Chungbuk National University, Korea

A novel vector hysteresis model based on improved neural network (NN) with parallel strategy is proposed to predict the real magnetic behavior of Electrical steel sheets (ESS). To overcome the drawbacks such as low convergence rate and easy to trap into local optimum in standard Back-Propagation (BP) NN, a novel collaborative BPNN learning algorithm is introduced based on error back propagation mechanism and particle swarm optimization (PSO). A parallel strategy based on fast Fourier transformation (FFT) is applied to improve the train efficiency of BPNNs. The proposed algorithm is applied to model the vector hysteresis behavior of ESS and the comparison of measured and calculated results is discussed.

Analysis of the magneto-mechanical anisotropy of steel sheets in electrical applications

Floran Martin1, Ugur Aydin1, Abubakr Ruzibaev1, Yanling Ge2, Laurent Daniel3, Laurent Bernard4, Paavo Rasilo5, Abdelkader Benabou6, Anouar Belahcen1

1Aalto University, Department of Electrical Engineering and Automation, Finland; 2Aalto University, Department of Chemistry and Material Sciences, Finland; 3GeePs, UMR CNRS 8507, CentraleSupélec, Univ. Paris-Sud, Univ. Paris-Saclay, Sorbonne Univ., Gif-sur-Yvette, France; 4GRUCAD/EEL/CTC, Universidade Federal de Santa Catarina, Florianpolis, Brazil; 5Laboratory of Electrical Energy Engineering, Tampere University, Tampere, Finland; 6L2EP/Université Lille 1, Cité Scientifique, Villeneuve dAscq, France

We investigate the effect of magneto-mechanical and magneto-crystalline anisotropy in a test application by coupling a multiscale magneto-mechanical model with a finite element method. This test application is composed of a cylindrical conductor surrounded by a ring composed of a non oriented FeSi3% steel sheet which contains 396 representative grain orientations. In the final paper, the analysis of magneto-mechanical anisotropy due to the texture of the steel sheet will be carried out for an electrical machine.

Nonasymptotic Homogenization of Laminated Magnetic Cores

Markus Schöbinger1, Karl Hollaus1, Igor Tsukerman2

1TU Wien, Austria; 2The University of Akron, USA

We are developing a rigorous framework for homogenization of laminated magnetic cores in the non-asymptotic case, when the spatial period of the structure is not vanishingly small relative to the penetration depth. The asymptotic limit not being applicable, the effective tensor may depend on the geometry of the core. Our model is valid for a realistic cylindrical geometry typical for rotating electrical machines, and for any reasonable size and composition of the lamination lattice cell. In this paper, the model is applied in the frequency domain under the assumption of linearity, but extensions to nonlinearity and hysteresis are discussed.

A 2D axisymmetric Volume Integral Formulation for the calculation of transient phenomena in High Temperature Superconducting coils

Blandine Rozier1, Brahim Ramdane1, Arnaud Badel1,2, Gérard Meunier1

1Univ. Grenoble Alpes, CNRS, Grenoble INP, G2Elab, F-38000 Grenoble, France; 2High Field Laboratory for Superconducting Materials, IMR, Tohoku University, Sendai 980-8577, Japan

High Temperature Superconducting materials represent a very attractive option for high magnetic field generation as they are able to carry high current densities without dissipation. However, this promising technology is not fully exploited yet because of protection issues: the transition from a superconducting state to a dissipative one can lead to irreversible damages if not detected soon enough. In order to study transient phenomena occurring in such a coil, a 2D axisymmetric model based on a Volume Integral formulation has been developed. It has been applied to a small-scale test coil to predict the transient voltage due to complex current distribution so as to help the detection system design.

Loss separation at high frequencies in soft magnetic sheets

Olivier de la Barrière1, Carlo Ragusa2, Carlo Appino3, Fausto Fiorillo3

1Laboratoire SATIE, CNRS - ENS Cachan, F-94230 Cachan, France; 2Department of Energy, Politecnico di Torino, Torino 10129, Italy; 3Nanoscience and Materials Division, INRiM, Torino, Italy

High switching rate electronic drives, working up to hundreds of kilohertz, are becoming standard for electrical machines in embedded applications. Under these conditions, the Pulse Width Modulation (PWM) contains spectral components up to the MHz range and the hysteresis magnetic cycles are endowed with very small amplitude minor loops, lasting a few microseconds. The natural frequencies of the machine windings can also be excited by the supply voltage harmonics, because of capacitive effects between the conductors, creating common mode currents flowing through the laminations, from the conductors to the machine chassis, and ensuing electromagnetic disturbances. In order to minimize adverse effects, the machine designers must rely on reliable modeling of the magnetic core, namely of the response of the magnetic laminations up to hundreds of kHz. To such modeling and the comprehensive characterization up to 300 kHz of 0.20 mm thick non-oriented Fe-Si sheets is devoted this work. Attention is focused, in particular, on the broadband modeling of magnetic losses, developed under the general framework of the loss decomposition theory and enhanced to achieve predictive formulations in the presence of deep skin effect. It is shown that, in spite of the frequency-evolving skin depth profile, reliable prediction of the concurrently evolving loss components can be made.

Accurate Minor Loops Calculation with A Modified Energetic Hysteresis Model

Ren Liu, Lin Li

North China Electric Power University, China, People's Republic of

The parameters of original energetic hysteresis model except for the loss coefficient are assumed to be independent of the maximum (peak) magnetic induction Bp, and can be directly extracted from the measured saturation hysteresis loop. In this paper, we firstly demonstrate that the parameters vary with Bp rapidly for soft magnetic materials. Subsequently, the characteristics of each parameter’s variation with Bp are identified. In addition, the effects of model parameters’ variation on the shape of the modeled hysteresis loops are also presented. Thus, some useful suggestions regarding to the energetic model parameters’ correct selection are obtained, and a technique is consequently proposed to simulate the hysteresis behaviors of magnetic materials using energetic model when Bp is rapidly changing.

Hysteresis Model Implementation into a FEM-code formulated for voltage driven coil problems

Werner Renhart1, Oszkar Biro1, Christian Magele1, Kurt Preis1, Alexander Rabel2

1Graz University of Technology; 2TransformersWeiz, Austria

To handle the magnetic history of iron parts of electromagnetic devices necessitates a hysteresis model. In this paper the analytical hysteresis model in use will be described briefly. Hereafter, the implementation of the hysteresis model into a finite element code for simulating the transient answer while switching will be described. Thereby, a focus has been drawn to model the excitation with voltage driven coils. The aspects, how to deal with convex and concave B-H characteristics while applying a secant method for the nonlinear iteration procedure will be described. Subsequently a way is shown, how to treat contrarily signed B-H pairs causing negative permeability values. Finally, the code will be applied to compute an inductor device. Numerical results will be compared with an equivalent network solution.

A Novel Deperming Protocols to Reduce a Demagnetizing Time of a Warship

Sang Hyeon Im, Ho Yeong Lee, Gwan Soo Park

Pusan National University, Korea, Republic of (South Korea)

In order to prevent a damage caused by the magnetic mine detecting the residual magnetic field of the ship, many attempt based on the deperming protocol have been carried out. Several researches have shown that the performance of Deperm-ME that decreasing nonlinearly is better than Anhysteretic that decreasing linearly. However, Deperm-ME has difficulty in control due to exponential variation and there is a limit to use in warship that should operate in real time. In order to develop a protocol with easy control and excellent performance, the protocol composed of two Anhysteretics was proposed by using Preisach model. In the first step, it works in the low density region, and in the second step, the high density region was delicately demagnetized. Simulations were performed using the Preisach model and verified through experiments using SPCC specimen.

A Broadband Thermodynamic Hysteresis Model Based on the Fractional Order Derivation

Xiwei Zhang, Lin Li, Yan Zhang, Jian Pang, Xuebao Li

State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, P. R. China

This paper constructed a lumped circuit model to extend the static hysteresis model to high frequency condition. A thermodynamic hysteresis model based on the energy conservation, which is essentially a vector hysteresis model, is adopted to express the static hysteresis losses. In this paper, a novel method considering the hysteresis phenomenon’s physical progress, which behaves as the motion of magnetic domains, is presented to calculate dynamic magnetic losses with the aid of fractional order derivation, in which only two parameters are needed identified and only one group of measured BH hysteresis loops at a certain frequency is enough to acquire parameters. Compared with finite element method (FEM), the proposed method reduced the calculation time greatly and guaranteed the accuracy. By making investigation on the relation of parameters varied with different temperature, the magnetic characteristics of material coupling with thermal condition can be deduced. At last, the accuracy of proposed model has been verified by measurements.

Inclusion of Dynamic Losses in a Scalar Magneto-elastic hysteresis Model Derived Using Multi-scale and Jiles-Atherton Approaches

Sai Ram Boggavarapu1, Ajay Pal Singh Baghel1,2, Shrikrishna V. Kulkarni1, Laurent Daniel2

1Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, 400076, India; 2Group of Electrical Engineering - Paris (GeePs), UMR CNRS 8507, CentraleSupélec, Univ. Paris-Sud, Université Paris-Saclay, Sorbonne Université, 3 & 11 rue Joliot-Curie, Plateau de Moulon 91192 Gif-sur-Yvette Cedex, France

Soft magnetic materials generally exhibit non-linear, hysteretic, and dynamic magnetic behavior which can be measured in terms of dynamic or frequency-dependent hysteresis loops. The performance of these materials is also significantly affected by mechanical stresses in terms of coupled magneto-elastic behavior. The coupled behavior can be described in terms of modifications in the domain configurations of materials under the application of mechanical stresses, which in turn affects the static and dynamic or frequency-dependent magnetic behavior. An adequate dynamic magneto-elastic model is required to consider the dynamic behavior of materials. In this work, a static magneto-elastic scalar hysteresis model is proposed which combines multi-scale approach and the Jiles-Atherton model, and it is extended to include dynamic losses using the field separation approach. The effect of stress on dynamic loss components, particularly on the excess loss, is approximated using an exponential function. The proposed model still preserves its simplicity in terms of differential equation and inverse form representation which makes it quite amenable to numerical implementations. The proposed model is validated with measured dynamic hysteresis loops over a frequency range upto 1 kHz and uni-axial mechanical loadings up to 50 MPa.

Transient Magnetic Model of Silicon Steel Sheets and Transformer Remanence Calculation by the Finite Element Method

Weiying Yuan, Jiansheng Yuan, Jun Zou

Tsinghua University, Beijing, China

In the remanence calculation of the iron core, clusters of hysteresis loops and the transient magnetic properties should be applied. The transient properties of the ferromagnetic materials are characterized by different clusters of hysteresis loops at different frequencies. However, in the calculation of the transient magnetic field, there is no concept of frequency, so these hysteresis loops defined by frequencies cannot be applied directly. The Preisach model commonly used considers the historical working process of the ferromagnetic material, but it does not consider the transient properties. This paper introduces a description model of magnetic materials that only considers the transient property but not the history. This model is suitable for remanence calculation of the core of transformers or other equipment, since the remanence calculation is a monotonic attenuation transient process after the equipment exits from the sinusoidal steady working state, so that the historical influence is not obvious. The establishment of the proposed transient magnetic model utilizes clusters of hysteresis loops under excitations of different frequencies and amplitudes. In the measurement of hysteresis loops, the slope of the excitation current at each point (H, B) is recorded. Then a number of points are set or chosen on the B-H plane, and for each point (H, B), all the hysteresis loops passing through it and the corresponding slopes of the excitation current are extracted and recorded as the description of the model. In the calculation of the transient magnetic field with the proposed model, at each time step, the slope of the excitation current is determined firstly. Then for each point of the iron core or each element of the finite element method, on basis of the (H, B) values and the current slope, the hysteresis loop which has the closest current slope is taken out from the model as the material property for the solution.

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