Conference Agenda

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Session Overview
Session
PC-M2: Mathematical Modelling and Formulations
Time:
Thursday, 18/Jul/2019:
10:50am - 12:40pm

Session Chair: Sebastian Schöps
Session Chair: Jozsef Pavo
Location: Patio 44-55

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Presentations

Study on Magnetic Properties of Magnetic Materials Using Improved Hybrid Vector Hysteresis Model

Dandan Li1, Zhenyang Qiao1, Na Yang1, Yinmao Song1, Yongjian Li2

1School of Building Environment Engineering, Zhengzhou University of Light Industry, Zhengzhou, Henan, CHINA; 2State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin, CHINA

This paper presents an improved 2-D vector hybrid hysteresis model to study the vector magnetic properties of magnetic materials under alternated and rotational magnetic field. Combining Preisach model and Stoner-Wohlfarth (S-W) model, the vector hybrid hysteresis model was established for magnetic materials in previous paper. The model is improved in this paper through adjusting the parameters to solve the question that simulation curve was not closed. The alternated and rotational hysteresis properties are calculated under different excitation frequency, respectively. It is shown that the simulation curve of improved vector model were closed and can well agree with the experimental measurement ones.



Application of Hamilton's Principle to the Electromagnetic Potential in Spacetime with Bounded Polarizable Regions

Terje Graham Vold

Continuum Technology, Inc., United States of America

The principle of stationary action is applied to the electromagnetic four-vector potential in spacetime made up of volumes, each containing a uniformly polarizable medium, separated by boundaries across which the potential, but not generally its derivative, is continuous. This leads to a simple system of equations for coefficients of an expansion in basis functions of the potential at boundary points, which may be viewed as Galerkin's method applied to the single four-vector spacetime equation expressing Maxwell's inhomogeneous scalar and three-vector equations in space and time written in terms of the scalar and vector potentials. Application to linearly polarizable media allows a boundary element method applicable to volumes with boundaries of any shape; application to nonlinear media allows a finite element method. Computational time is similar to other methods, but advantages include simpler algebra and structure, no spurious solutions, and no limits on frequency from zero to wave velocity over boundary mesh cell length, or on polarizability including complex electrical polarizability representing conductivities of good insulators, good conductors, and intermediate cases in the same problem. Theoretical details and numerical results of computational examples are given.



Computation of Eigenvalues and Eigenfunctions in the Solution of Eddy Current Problems with Modal Methods

Theodoros Theodoulidis1, Anastassios Skarlatos2

1University of Western Macedonia, Greece; 2CEA Saclay, France

For eddy current problems in bounded domains, an important aspect of the solution of the corresponding differential equation, is the accurate computation of the discrete eigenvalues and their corresponding eigenfunctions. For conductive media these eigenvalues are generally complex and in canonical geometries they are computed as roots of expressions involving trigonometric or Bessel functions. Until now, location and computation of these roots included complex plane search methods involving Newton-Raphson iterations or a Cauchy integral approach. In this paper, we follow an alternative path by treating the differential equation that describes the electromagnetic field as a general Sturm-Liouville problem. We then apply a global function method to transform the problem into a matrix eigenvalues problem. Although this approach is frequently used in high frequency studies involving wave propagation, it is applied for the first time to low frequency diffusive field configurations such as the eddy current ones.



Time-Domain Homogenization of Foil Windings in 2-D Magnetodynamic Finite-Element Models

Carlos A. Valdivieso1,2,4, Brahim Ramdane1, Gerard Meunier1, Ruth V. Sabariego2, Johan Gyselinck3, Christophe Guerin4

1Univ. Grenoble Alpes, CNRS, Grenoble INP, G2Elab, F-38000 Grenoble, France; 2KU Leuven, Dept. Electrical Engineering, EnergyVille, 3000 Leuven, Belgium; 3Université libre de Bruxelles, BEAMS department, 1050 Brussels, Belgium; 4Altair Engineering France, 38240 Meylan, France

In this paper, an approach for the time-domain homogenization of foil windings in two-dimensional (2-D) finite-element (FE) models is presented. The homogenized formulation is characterized by an axial current redistribution and a radial interturn voltage gradient. The method is successfully applied to an axisymmetric 18-turn foil-winding inductor. The local and global results agree very well with those obtained by an accurate but expensive FE model in which all turns are explicitly discretized.



A Method for the Definition of Hysteresis Operator in Three Dimensional Case

Dandan Li1, Zhenyang Qiao1, Na Yang1, Yinmao Song1, Yongjian Li2

1School of Building Environment Engineering, Zhengzhou University of Light Industry, Zhengzhou, Henan, CHINA; 2State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin, CHINA

This paper presents a method for the definition of hysteresis operator in 3-D case based on the definition method of 2-D hysteresis operator. According to the principle of minimum energy of magnetized steady state, the 3-D hysteresis operator is established for anisotropic and isotropic materials in spherical coordinate system. The magnetization process of the hysteresis operator is studied when alternated and rotational magnetic field are applied. The properties of the hysteresis operator defined in this paper are analyzed from different perspectives. The definition of hysteresis operator lays a foundation for the establishment of 3-D hybrid vector hysteresis model.



Matrix Based Rational Interpolation for New Coupling Scheme Between MHD and Eddy Current Numerical Models

Matteo Bonotto1,2, Fabio Villone3, Yueqiang Liu4, Paolo Bettini1,5

1Consorzio RFX, 35127 Padova, Italy; 2University of Padova, Centro Ricerche Fusione, 35131 Padova, Italy; 3Consorzio CREATE, DIETI, University of Naples Federico II, Napoli, Italy; 4General Atomics, San Diego, California, United States; 5Department of Industrial Engineering, University of Padova, 35131 Padova, Italy

In this paper, we present a new self-consistent coupling scheme between linear MHD model and eddy current equations, numerically

solved with a 3D integral formulation. The new strategy, based on matrix-valued rational interpolation, is able to model frequency

dependent plasma response, and takes into account plasma inertia: therefore it is valid for model both Resistive Wall Modes (RWMs)

and ideal kinks. Moreover, also toroidal flow and kinetic damping physic can be modelled.



Characteristics of 3D Magnetic Field of Square and Double-D Coils Geometry for Wireless Power Transmission System

Lili Wang1,2, Xian Zhang3, Hui Xia1, Zhaohui Wang3, Guoqiang Liu1

1Institute of Electrical Engineering,Chinese Academy of Sciences, China, People's Republic of; 2University of Chinese Academy of Science, Beijing, China; 3Tianjin Polytechnic University, Tianjin, China

Magnetic field coupling is the key to the wireless power transmission. In this paper, we study the spatial magnetic field distribution of the two coils geometry- Square Coils and Double-D coils, which are the most commonly used in wireless charging systems. In the simulation calculation, the mathematical expression of the magnetic flux density of the Square Coils and Double-D Coils is derived instead of using finite element simulation software. In the experiment, we built a three-dimensional magnetic field measurement platform of the wireless energy transmission system to obtain the magnetic field distribution. By comparing the magnetic flux density between square coils and Double-D coils in stimulation and experiment, we find the Double-D coils analytical results are in good agreement with the experimental results, Moreover, the range of uniform magnetic field is generated by Double-D coils is twice that of the Single-D coupling coils. The theoretical values of Single-D differ from the actual measured value by nearly 1/3. It shows that the Double-D coils geometry can help strength the ability of the coupling between the coils and reduces the attenuation of the magnetic induction density during transmission. Through the study of the spatial magnetic field distribution between the two coupling mechanisms, it provides a basis for the optimization of the coupling geometry of the wireless charging system.



Magnetic Forces Behind Hyperelastic Behavior of Magnetorheological Elastomers

Ondrej Sodomka, Vojtech Skrivan, Frantisek Mach

University of West Bohemia, Faculty of Electrical Engineering, Czech Republic

A magnetic and nonlinear structural mechanic coupled problem is discussed concerning behavior of an magnetorheological elastomer. Material properties and hyperelastic character of the material were found by measurements. Based on the measurements and computations, a coupled mathematical model is proposed involving the Yeoh hyperelastic model.



Finite Element Modeling of Thin Conductors in Frequency-Domain

Jonathan Velasco1, François Henrotte1,2, Christophe Geuzaine1

1Université de Liège, Belgium; 2Université Catholique de Louvain

This paper describes the development of an impedance condition for the modeling of thin round wires in a finite-element framework. This approach exploits the use of the H(curl}; \Omega) function space, in addition to cylindrical symmetry, enabling the treatment of edges in a finite element mesh to be modeled as thin conductors. The procedure proposed solves the full-wave Maxwell problem under sinusoidal excitation (i.e. time-harmonic) using the magnetic vector potential (a-v) formulation.



Time Domain Analysis of Homogenized Finite Element Method for Eddy Current Analysis with Reduced Unknown Variables

Shingo Hiruma, Hajime Igarashi

Hokkaido university, Japan

This paper presents a new time domain analysis of a homogenized finite element (FE) equation. In the proposed method, the complex permeability is expressed by the continued fraction for the time-domain analysis. The unknowns relevant to the circuit equation are eliminated using the finite difference method. The resultant homogenized FE equation for reduced unknows can be effectively solved.



Using a Magnetic Charge Fourier Series to Studying the Force Density of Magnetic Lead Screws

Jonathan Bird, Mojtaba Bahrami Kouhshahi

Portland State University, United States of America

A 3-D magnetic charge analytic based field analysis approach is presented that models an array of magnets by using a magnetic vector Fourier series representation. Using a Fourier series function enables the magnets relative permeability to be accounted for and also reduces the computational burden. The accuracy of the presented modelling approach is validated by studying the fields and forces created by a magnetic lead screw. The presented analytic based approach enables fundamental force density sizing relationships to be

determined.



Fast iterative schemes for the solution of eddy current problems featuring multiple conductors by integral formulations

Mauro Passarotto1, Ruben Specogna1, Christophe Geuzaine2

1Polytechnic Department of Engineering and Architecture, University of Udine, Italy; 2Institut Montefiore, Université de Liège, Belgium

In recent years there has been a revival in the use of integral formulations for the numerical solution of electromagnetic problems. These formulations lead to full matrices whose computation and storage represent their bottleneck, thus, for this reason, efficient low-rank approximation techniques have been introduced to alleviate the issue. To tackle the same problem, in this paper, we propose a novel and efficient way to iteratively solve an eddy current problem using a boundary integral formulation by taking advantage of the domain splitting into disjoint conductors. Once the domain is subdivided into smaller subdomains, Krylov subspace techniques are applied to reduce the iteration time and improve the convergence performance.



Study on the Offline Inter-turn Fault Diagnosis Performance According to the Parameter of Interior Permanent Magnet Synchronous Machine

Hyunwoo Kim1, Seung-Taek Oh1, Hyung-Woo Lee2, Jongsuk Lim1, Yeji Park1, Ju Lee1, Seung-Heon Lee1

1Hanyang University, Korea, Republic of (South Korea); 2Korea National University of Transportation, Korea, Republic of (South Korea)

This paper analyze the performance of an inter-turn fault diagnosis according the parameter of interior permanent magnet synchronous motor (IPMSM). If the inter-turn fault occurs in IPMSM, the d-axis current is different from the d-axis current in the healthy condition. Through the difference between the d-axis current in the healthy and faulty condition, the inter-turn fault can be detected. Consequently, the magnitude of the d-axis current determines the performance of the inter-turn fault diagnosis. The offline diagnosis is performed by injecting a high-frequency voltage into the IPMSM. The performance of the offline diagnosis depends on the parameter of the IPMSM. Thus, the performance of the offline diagnosis is analyzed according parameter of the IPMSM that is fault resistance, winding resistance and saliency ratio. In addition, to verify analytical method, inter-turn fault diagnosis is performed by co-analysis that is the link between the finite element analysis (FEA) and the control simulation tool.



 
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