Conference Agenda

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Session Overview
PB-M3: Mathematical Modelling and Formulations
Wednesday, 17/Jul/2019:
10:50am - 12:40pm

Session Chair: François Henrotte
Session Chair: Zuqi Tang
Location: Patio 44-55

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Semi-Analytical Nonlinear Model of Slotless Electrical Machines

Loïc Quéval1, Bastien Roucaries2, Jiling Guo3, Lionel Vido2, Frederic Trillaud4, Christophe Berriaud5

1GeePs, UMR CNRS 8507, CentraleSupelec, Univ. Paris-Sud, Univ. Paris-Saclay, Sorbonne Univ., 91192 Gif-sur-Yvette CEDEX, France; 2SATIE, CNRS UMR 8029, Univ. of Cergy Pontoise, 95000 Cergy-Pontoise, France; 3School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031,China; 4Instituto de Ingeniería, Universidad Nacional Autónoma de M\'exico, 04510, CDMX, Mexico; 5DRF/IRFU/DACM, CEA Saclay, Univ. Paris-Saclay, 91191 Gif-sur-Yvette, France

An incremental improvement of the classical current sheet model of slotless wound rotor electrical machines is proposed. It allows considering the rotation of the rotor field winding and the time-dependent stator armature windings currents, at the same time. Additionally, an iterative scheme is introduced into the model to take into account the magnetization of the rotor and stator iron cores. The results of this semi-analytical model are compared with those of a 2-D nonlinear finite element model.

Subproblem finite-element refinement of transformers from 1D ideal flux tube to 2D modeling via surface sources

Bruno S. Alves1, Patrick Kuo-Peng2, Patrick Dular3

1Polytechnique Montreal, Canada; 2Federal University of Santa Catarina, Brazil; 3University of Liège, Belgium

Progressive transformer modeling is performed via the subproblem (SP) technique applied to the finite element method (FEM). The general 2D FEM problem of a single-phase transformer is split into small and simplified subproblems starting from the ideal flux tube model in 1D. Its solution is refined via surface sources allowing to include 2D effects on the initial FEM simulation model. The sum of the reaction and the source fields in 2D provides the inclusion of the core corners and the leakage magnetic flux effects on the transformer model. This approach simplifies both meshing and solving procedures enabling systematic studies and improving the solution accuracy. The efficiency of the SP technique in FEM is then demonstrated by comparing its results with classical 2D FEM simulations in terms of local fields distribution.

Magnetostriction Model of Grain-Oriented Sheet Steels Based on J-A Theory

Yang Li1, Jianguo Zhu1,2, Lihua Zhu3, Gang Lei2

1Hebei University of Technology, China, People's Republic of; 2University of Sydney, Australia; 3Tianjin Polytechnic University, Tianjin, China

Grain-oriented (GO) electrical sheet steels are widely used as the core material in large size power transformers. The strong magnetostriction in GO sheet steels, however, causes undesired vibrations and acoustic noises, and is difficult to estimate in the design optimization of power transformers. This paper proposes a new magnetostriction model of GO sheet steels by combining the Becker–Döring crystal magnetization model and the dynamic Jiles-Atherton (J-A) hysteresis model. The proposed model when incorporated in the finite element analysis can correctly simulate the butterfly loops of magnetostriction in GO sheet steels. The effectiveness and accuracy of proposed model are verified by the experimental measurements of a single sheet sample in free state with no external stress.

Introduction and validation of the APEC code for the simulation of plasma equilibrium and evolution in presence of 3D passive structures

Pietro Testoni, Alfredo Portone

F4E, Spain

Recently a novel code for the simulation of the plasma equilibrium and its evolution has been developed and fully implemented in ANSYS. It is based on the solution of the Grad-Shafranov equation, and exploits the finite element method using the magnetic potential vector formulation. In this paper we present a further development we have introduced on the coupling of the axisymmetric plasma equilibrium equations, describing the plasma behavior, with the full 3D eddy currents equations, describing the surrounding three-dimensional structures. One test case, related to the ITER tokamak, has been fully analyzed showing the validity of the proposed approach.

H-Φ Field Formulation with Lumped Sources and Unbounded Domains

Daniele Casati1, Jasmin Smajic2, Ralf Hiptmair1

1Seminar for Applied Mathematics, ETH Zurich, Switzerland; 2Institute for Energy Technology, Hochschule für Technik Rapperswil, Switzerland

We consider a H-Φ field formulation to solve 3D frequency-domain eddy current problems. This formulation uses vector and scalar tetrahedral finite elements within, respectively, the conductive and non-conductive domain. It is able to solve multiply connected regions and eliminates the need to compute the source current density and the source magnetic field before the actual simulations.

We couple finite elements with the Multiple Multipole Program (MMP) to solve the H-Φ variational form on an unbounded domain. MMP is a method that uses exact solutions of the homogeneous equations of the considered problem as basis functions (the so-called multipoles). Interface conditions with the FEM domain allow to solve the coupled FEM–MMP problem. The desired behavior at infinity is given by the chosen multipoles, which eliminates the need of artificially truncating the computational domain.

Dynamic Energetic Hysteresis Model Based on Fractional Derivatives for Broadband Loss Calculation of Magnetic Materials

Ren Liu1,2, Lin Li1, Carlo Ragusa2, Olivier de la Barrière3, Yang Zhang2

1State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China; 2Energy Department “Galileo Ferraris”, Politecnico di Torino, Torino 10129, Italy; 3Laboratoire SATIE, CNRS-ENS Cachan, F-94230 Cachan, France

The computation of loss in electrical steels over a large frequency bandwidth is of great significance for the design and optimization of magnetic components. It is also known that the simplest application of loss separation methods can be limited to low frequency regime because of the assumption of negligible skin effect in the lamination. In this paper a novel broadband dynamic energetic model based on fractional derivatives is proposed to overcome this limitation. Since the order of fractional derivatives provides an alternative new degree of freedom, it can widely increase the applicable bandwidth of the energetic model. In addition, a reduction in computation resources is obtained by application of convolution methods to solve fractional derivatives. Using such dynamic hysteresis model, the conventional solution of the coupled nonlinear diffusion problem is avoided and a practical formula for the magnetic loss is eventually provided. The simulation and experimental results confirm the accuracy and efficiency of the proposed method.

Calculation of Recoil Curves in Isotropic and Anisotropic Stoner-Wohlfarth Materials

Marcos Flavio de Campos, Jose Adilson de Castro

Federal Fluminense University, Brazil

Concerning hard magnetic materials, the recoil curves of hysteresis are relevant for motor designers. It is discussed how to calculate recoil curves of isotropic and anisotropic Stoner-Wohlfarth hysteresis, with different distributions as Gaussian and cos^n(alpha). The Gaussian distribution is the most commonly used for representing texture in hard magnetic materials as NdFeB or ferrites. The Gaussian and cosn(alpha) distributions are compared and analytical functions are given. The analytical functions can reduce the time of calculation and also increase the accuracy of the results.

Characteristics Investigation of the Electrodynamic Wheel Suspension Device with two DOF Motions

Jiaheng Duan1,2, Kunlun Zhang1,2, Song Xiao1,2, Jan Sykulski3

1Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, P.R.C; 2School of Electrical Engineering, Southwest Jiaotong University, Chengdu, China; 3Electronics and Computer Science, University of Southampton, Southampton, UK

The three-dimensional (3-D) derivation of an analytical model for an electrodynamic wheel suspension (EDWS) device is proposed in this paper. The equations of source field generated by the magnetic wheel are derived by the superposition principle of magnetic charge sheets. The eddy current field and 3-D forces of semi-circular pipe track are modeled using the second-order potential (SOVP) method. The analytical models describing fields and forces are validated by finite element simulations and experimental results. In addition, the characteristics of the EDWS device with two degree-of-freedom (DOF) motions are studied based on the proposed equations.

Equality of Kelvin Force Density and Korteweg–Helmholtz Force Density in Dielectric Material

Byung Su Park, Il Han Park

SungKyunKwan University, Korea, Republic of (South Korea)

Various expressions are used to calculate the electric forces acting on a dielectric object. The Kelvin force and the Korteweg–Helmholtz force are the most commonly known electric body forces. Both these forces are derived from the Lorentz force, and they have same resulting net force; however, their distributions in a dielectric are different. This is because the expressions for both the forces lose their physical manifestation in the process of derivation. This article primarily aims to show the common mistake in derivation of volumetric force density. Then, concept of source-field duality and concept of infinitesimal particle are introduced. Using these concepts, electric force density in dielectric is uniquely determined regardless of what force expression is used on an arbitrary situation.

Force computation between ferromagnetic beads in a source magnetic field

Stephane Dufour, Gerard Vinsard

Ensem-Université de Lorraine, France

The force computation of ferromagnetic beads when

submitted to an external magnetic field, is considered, and the

saturation is taken into account. The force exerted in the beads

depends on the direction of the field and its intensity. Several

methods are investigated to quantify accurately this force.

Research on Magnetostrictive Model for Electrical Steel Based on Improved Jiles-Atherton Model

Zhu Lihua1, Li Jingjing1, Qingxin Yang1, Jianguo Zhu2, Chang-Seop Koh3

1Tianjin Polytechnic University, Tianjin,China; 2The University of Sydney, Sydney, Australia; 3TChungbuk National University, Cheongju, Chungbuk 28644, Korea

The magnetostriction of electrical steel is the main cause of the electromagnetic vibration of transformers and reactors. In order to analysis the feature of hysteresis in magnetostriction for silicon steel, a model is established based on the improved Jiles-Atherton model by introducing the parameter k1, which considers the domain moment rotation. To verify the feasible of the model, it is applied to oriented and non-oriented electrical steel. The parameters in the proposed model are extracted by particle swarm optimization algorithm. By comparing the measured data to calculated data obtained from model, excellent agreement in the result is shown. All these demonstrate the proposed model in the paper is accurate for electrical steel. It provides a good description of magnetostriction under magnetic field with different amplitudes.

Dynamic Coupled Model of Vibration System with Galfenol Damper Considering Eddy Currents and Hysteresis

Shuying Cao1,2, Xiufeng Yue1,2, Jiaju Zheng1,2, Chengcheng Liu1,2, Jun Zhao1,2, Yongjian Li1,2

1State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin; 2Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province, Hebei University of Technology, Tianjin

Based on the effective magnetic field expression, the constitutive equations with eddy currents and variable coefficients, the Armstrong hysteresis model and the structural dynamic theory, a dynamic mechanical-magnetic-electro bidirectional coupled (MMEBC) model of the vibration system with Galfenol damper is established, and the system’s transmissibility and key frequency-dependent stiffness are derived. Comparisons between the calculated and measured results show that the proposed model can accurately describe the static major-loop and dynamic minor-loop curves of Galfenol rod, thus can provide reasonable data trends of the frequency-dependent Young’s modulus, permeability, piezomagnetic coefficients, and can predict the changing laws of the resonant frequency and the resonant peak with bias point and shunt resistance. It is found that the damper without coil or shunt can provide the peak attenuation rate 79.58% while the damper with shunt resistance can provide the peak attenuation rate 87.91%.

Modelling of Road–Embedded Transmitting Coils for Wireless Power Transfer

Vincenzo Cirimele1, Riccardo Torchio2, Fabio Freschi1, Piergiorgio Alotto2

1Politecnico di Torino, Italy; 2University of Padova, Italy

The present work stems from practical experiences in the implementation of a wireless power transfer charging lane based on transmitter coils directly embedded under the road surface. After the embedment, unexpected phenomena appeared which strongly modified the behaviour of the coil thus compromising the effectiveness of the system. This paper proposes the development of a dedicated model based on a PEEC formulation that is used to identify the physical causes of these effects. The accuracy of the model is verified by comparison with measurements. Furthermore, by means of a sensitivity analysis, it allows to investigate the main geometrical and electromagnetic parameters that influence the behaviour of the coil.

Residual-based error estimator with guaranteed error bounds for mixed-hybrid geometric formulations for electrostatics

Paolo Bettini1,2, Antonio De Lorenzi2, Nicolò Marconato1,2, Tommaso Patton1,2, Nicola Pilan2, Ruben Specogna3

1Dipartimento di Ingegneria Industriale, Università di Padova, 35131 Padova, Italy; 2Dipartimento Politecnico di Ingegneria e Architettura, Università di Udine, 33100 Udine, Italy; 3Consorzio RFX, 35127 Padova, Italy

In the last decades, a lot of research has been conducted on the insulation of high voltage in vacuum. Recently, an innovative

numerical tool, reffered to as Voltage Holding Predictive Model (VHPM), has been developed to asses the voltage holding capability

of multi–electrode multi–voltage systems in vacuum. In this paper, a residual-based error estimator with guaranteed error bounds

for mixed-hybrid geometric formulations for electrostatics is presented, and a novel algorithm for automatic mesh refinement is

proposed, enabling a feature very important in many electrostatic applications and mandatory in the VHPM tool.

Implementations of an Energy-Based Ferromagnetic Hysteresis Model for 3D Finite Element Simulations

Kevin Jacques1,2, Francois Henrotte3, Johan Gyselinck2, Christophe Geuzaine1

1Department of Electrical Engineering and Computer Science, Montefiore Institute, University of Liege; 2Department of Bio- Electro- And Mechanical Systems (BEAMS), Universite Libre de Bruxelles; 3Department of Applied Mechanics and Mathematics (MEMA), Universite catholique de Louvain

Because the computation of the magnetic hysteresis is time-consuming, most electrical finite-element (FE) models that explicitly take hysteresis into account are 1D or 2D. The energy-based (EB) hysteresis model however is intrinsically 3D and it is worth having at disposal a validated 3D implementation for those applications where the explicit modeling of hysteresis is important and the 2D geometry too crude an approximation. The EB hysteresis model has two practical formulations: the variational one (var) is trivially generalized to 3D whereas the more efficient differential one (diff) requires some geometrical work, presented in this paper.

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