A novel mixedhybrid formulation for magnetostatics
Ruben Specogna
EMCLab, DPIA, Università di Udine, Italy
MixedHybrid Finite Element (MHFE) formulations for magnetostatic problems are appealing because–like the magnetic scalar potential (MSP) formulations–yield to algebraic systems that can be effectively solved by blackbox algebraic multigrid solvers. At the same time they are also algebraically equivalent to magnetic vector potential (MVP) formulations, so they provide a conservative flux and superior accuracy.
We introduce a novel MixedHybrid formulation for magnetostatic problems which combines the best features of MSP and reduced MVP formulations. First, it avoids the explicit representation in the finite element mesh of the shape of source current regions. Second, the new formulation does not require the inversion of the local mass matrices, but still provides the same solution–on tetrahedral meshes and up to linear solver tolerance–of the corresponding FE formulation. Another advantage is that it can deal with very general polyhedral meshes, where divconforming FE basis functions are not available.
3D numerical modelling of clawpole alternators with its electrical environment
Guillaume Caron^{1}, Thomas Henneron^{1}, Francis Piriou^{1}, Pierre Faverolle^{2}, JeanClaude Mipo^{2}
^{1}Univ. Lille, Arts et Metiers ParisTech, Centrale Lille, HEI, EA 2697  L2EP, F59000 Lille, France.; ^{2}Valeo Electrical Systems, 94046 Créteil Cedex, France.
This paper describes a methodology to model a sixphase clawpole alternator with its electrical environment. The movement, magnetic nonlinearities and eddy currents are taken into account. To solve magnetodynamic equations, we used the modified magnetic vector potential formulation. The complex structure of the machine requires a 3D finite element analysis. Different numerical techniques are proposed to reduce the computational time and memory consuming. To validate the approach, some results are compared with experimental ones.
Harmonics Prediction Algorithm to Solve Nonlinear Magnetostatic Problems with the Harmonic Balance Method
Emna Jaïem, Frédéric Guyomarch, Yvonnick Le Menach
Univ. Lille, Arts et Metiers Paris Tech, Centrale Lille, HEI, EA 2697  L2EP, F59000 Lille, France
The problem of harmonics selection when solving an electromagnetic problem using harmonic balance method combined with finite element method is still a challenge. In this paper, a new technique based on the time residual of the solution is proposed to handle this kind of problem. Numerical results are provided to demonstrate the efficiency of our approach for the case of 2D nonlinear magnetostatic problem.
FE EddyCurrent Characterisation of Saturable Magnetic Devices towards Model Order Reduction
Johan Gyselinck^{1}, Ruth V. Sabariego^{2}
^{1}ULB, Belgium; ^{2}KU Leuven, Belgium
This paper aims at contributing to the Model Order Reduction (MOR) of nonlinear EddyCurrent (EC) devices via their static and linearised frequencydomain (FD) FiniteElement (FE) characterisation. The linearisation is done via the differential reluctivity tensor. The sufficiently challenging case of a singleelectricalport device is considered. The MOR is readily done for the linearised case with ECs, but the final objective is to arrive at a loworder model that can be used in a circuit simulator within a certain current and frequency range, without any further recourse to highorder FE matrices and vectors.
Accuracy of homogenization techniques to model lamination stacks with interlaminar currents
Ruth Sabariego^{1}, Johan Gyselinck^{2}, Yvonnick Le Menach^{3}, Thomas Henneron^{3}
^{1}KULeuven, EnergyVille, Belgium; ^{2}Université Libre de Bruxelles, BEAMS, Belgium; ^{3}Université de Lille 1, L2EP, France
This paper studies the accuracy of homogenization techniques in laminated cores in the presence of a interlaminar currents, due to damage insulation of edge burrs. The classical magnetic vector potential formulation is adopted to model the magnetoquasistatic problem and combined with a homogenization approach based on complex reluctivity and complex conductivity tensors, accounting for net flux and net circulating current, respectively. A linear 2D application case with inplane imposed and induced current density is considered.
A New Algorithm for Tracing Flux Lines of HVDC Ionized Field Based on Bezier Curves
JinHyeok Kim^{1}, YoungSeek Chung^{2}, Gu Min Kwon^{3}, Koo Yong Shin^{3}, HyunKyo Jung^{1}
^{1}Seoul National University, Korea, Republic of (South Korea); ^{2}Kwangwoon University, Korea, Republic of (South Korea); ^{3}Korea Electric Power Research Institute (KEPRI), Korea, Republic of (South Korea)
A new method for tracing the electric flux lines in the flux tracing method (FTM) is developed by using a parametric curve. The flux lines can be traced without accumulating errors caused by numerical differentiation for the electric potential. The control points of Bezier curve are modified to minimize an error function defined by the electric field vector. Once the electric flux lines are traced, a series of flux tubes is created by bundling adjacent flux lines, and the nodal electric field and space charge distribution are iteratively updated. New flux lines are traced by the modified electric field, and the process is repeated until the effect of the space charge is fully considered.
Homogenized 3D FEM Model Intended for Quench Simulation of Large HTS Coils
Szabolcs Gyimóthy, Anett Kenderes, Sándor Bilicz, József Pávó
Budapest University of Technology and Economics, Hungary
The spiral coil made of thin coated conducting tape is substituted by a homogenized bulk medium for the finite element simulation of its electromagnetic and thermal behavior. The homogenized medium is represented by an anisotropic conductivity tensor utilizing the underlying spiral structure. The targeted application of the proposed method is the simulation of quench phenomena in large hightemperature superconducting coils. In addition to the significant reduction of the computation efforts, the method notably makes voltage constraint on the coil terminals available. In this paperprior to a real applicationthe feasibility study of the method and its sensitivity analysis on the mesh parameters are carried out using a linear test problem.
Eddy current analysis on uniform induction heating of a hemispherical surface
Yiyang Zhu^{1}, Weimin Guan^{1}, Di Zhang^{1}, Yao Luo^{1}, Yanhui Gao^{2}, Kazuhiro Muramatsu^{2}
^{1}School of Electrical Engineering, Wuhan University, Wuhan 430072, P.R.China; ^{2}Department of Electrical and Electronic Engineering, Saga University, Saga 8408502, Japan
The induction heating has advantages of quick and high temperature heating compared with other heating methods such as lamp heating and resistance heating but it is difficult to achieve uniform heating because excitation current control is required for different zones of coils. To achieve uniform heating of a hemispherical conductive surface without excitation current control, a fractal coil conFig.uration is proposed and the effectiveness of the proposed magnetic topology is investigated by using the threedimensional eddy current analysis. And the factors such as the frequency and the magnitude of excitation currents in the coils, and the fractal characteristics, which influence the uniformity of eddy currents are investigated. Induction heating experiments are also conducted to observe the distribution of temperature during heating of the ordinary spiral coil and proposed coil topologies. The experimental results validate the uniformity of temperature distribution on the hemispherical surface.
On the Modeling of Magnetic Pickups for Electric Musical Instruments
Isoharu Nishiguchi^{1}, Hiroyuki Kaimori^{2}, Akihisa Kameari^{2}, Eiichi Takebuchi^{1}, Yuta Nojima^{1}
^{1}Kanagawa Institute of Technology, Japan; ^{2}Science Solutions International Laboratory, Inc.
In this paper, modeling of the magnetic pickup of electric musical instruments, such as an electric guitar, an electric bass and an electromechanical keyboard instrument, is investigated. Focus is placed on the Rhodes electric piano, which gained popularity in 1960s and is still highly valued among jazz, soul and popular musicians. In most existing studies, the induced electromotive force (EMF) in the pickup is calculated using simplified methods in which a permanent magnet is modeled as a pair of magnetically charged plates. In this study, a detailed finite element analysis is performed to calculation the EMF in the pickup system as well as the estimation of the effect of the eddy current in the system. The method for sound synthesis based on the pickup model is also discussed.
Study about the surface charge accumulation and dissipation of insulators under corona condition
Fan Yi, Zhiye Du, Qi Jin, Jiaxin Yuan, Jiangjun Ruan
Wuhan University, China, People's Republic of
In HVDC transmission, the insulator surface charge accumulation problem is an important factor affecting the electric field on insulator surface. In order to obtain insulator surface charge accumulation and dissipation regularity under DC high voltage, the electrostatic probe method is used to measure the surface potential and complete surface potential of different insulator under the corona condition. The surface potential measurement is used to study the variation trend of the insulator surface potential with time. Based on the measured potential, Surface charge density is inversed to obtain the accumulation and dissipation regularity of insulator surface charge in the corona condition. Hanging two layers of insulators under the corona sphere electrode, surface potential of upper and lower two layers insulators is measured to study the difference of potential distribution and charge accumulation . In this paper, a charge density inversion method for curved surface is proposed. Potential measurement points are selected reasonably and intensively, and then curved surface is divided into triangular meshes according to the selected measurement points.The study shows that the insulator which’s surface is covered with PRTV coating is easy to accumulate charge, and the charge accumulation of insulator surface can be saturated.When hanging two layers of insulators, the upper insulator surface is more likely to accumulate charge, and the upper insulator surface charge’s dissipation is slower than the lower insulator.
Model Order Reduction based on Augmented Dynamic Mode Decomposition applied to magnetodynamic problems
Guillaume Caron, Thomas Henneron
Univ. Lille, Arts et Metiers ParisTech, Centrale Lille, HEI, EA 2697  L2EP, F59000 Lille, France.
The Dynamic Mode Decomposition (DMD) is a recent equationfree method based on a datadriven computational technique in order to approximate of the Finite Element solution. This method is known to be able to catch the periodic, quasiperiodic or nonlinear behaviour of many physical systems. However, the DMD fails when the dynamic of the solution is described with a low number of harmonic. Then, to improve the robustness, the augmented DMD has been introduced. In this communication, we propose to investigate the augmented DMD (aDMD) in order to solve magnetodynamic problems.
Largescale numerical human body analysis using parallel geometric multigrid method
Masamune Nomura^{1}, Hiroo Tarao^{2}, Amane Takei^{1}
^{1}University of Miyazaki, Japan; ^{2}National Institute of Technology, Kagawa College, Japan
This paper describes the effectiveness of geometric multigrid (GMG) methods on current density analysis using a numerical human body model. The scalar potential finite difference (SPFD) method is used as a method for analyzing current density inside a human body in the lowfrequency domain, and research on a method to solve more quickly largescale simultaneous equations made by the SPFD method has been conducted. In the previous research, the block incomplete Cholesky conjugate gradient (ICCG) method is proposed as an effective method to solve the simultaneous equations more quickly. However, even though the block ICCG method is used, many iterations are still needed. Therefore, in this research, we focus on geometric multigrid (GMG) methods as a method to solve the problem. We develop GMG methods and evaluate their performance compared with the block ICCG method in terms of computation time and the number of iterations. The results show that the number of iterations needed for GMG methods is much smaller than that for block ICCG. In addition, computation times are much shorter, depending on the number of threads and the number of coarse grids. Also, by using multicolor ordering, the parallelism of GMG methods can be greatly improved.
Harmonic Balance Finite Element Method Applied to Electrical Machines with rotor movement : Comparison of Two Potential Formulations
Emna Jaïem^{1}, Frédéric Guyomarch^{1}, Yvonnick Le Menach^{1}, Karim Beddek^{2}
^{1}Univ. Lille, Arts et Metiers Paris Tech, Centrale Lille, HEI, EA 2697  L2EP, F59000 Lille, France; ^{2}EDF, R&D Lab Saclay, 7 boulevard Gaspard Monge, F91120 Palaiseau, France
In the field of computational electromagnetics, taking into account the motion of the rotor in electrical machines requires special attention. In this work, we propose to compare the solutions obtained by the Harmonic Balance Finite Element Method (HBFEM) coupled, on the one hand, with the A formulation and, on the other hand, with Omega formulation with those obtained by the reference method namely, the Time Stepping Finite Element Method (TSFEM). This comparison is carried out in the case of electrical machines while considering the movement of the rotor. To this issue, a permanent magnet machine is considered.
Current Density Reconstruction of High Current Vacuum Arcs in a Vacuum Circuit Breaker from its Magnetic Field
Yun Geng^{1}, Jinlong Dong^{1,2}, Yingsan Geng^{1}, Jianhua Wang^{1}
^{1}Xi'an Jiaotong University, China, People's Republic of; ^{2}Politecnico di Milano, Italy
This paper investigates the magnetic inverse problem of the current density reconstruction for high current vacuum arcs in a high voltage vacuum circuit breaker. Using Whitney face elements, it enables us to incorporate the zerodivergence condition and the boundary conditions of the current density into the formulation of the inverse problem. The treecotree gauging technique for the current density is applied in order to reconstruct a divergence free current density. Tikhonov regularization complemented by the generalized cross validation method is applied to address the illposedness of the inverse problem.
Mathematical Optimization of Coils Used in Electromagnetic Forming
Marcus Stiemer, Michael Hagel, Marco Rozgic
Helmut Schmidt University, Germany
Tool coils applied in electromagnetic forming provide pulsed magnetic fields to induce Lorentz forces in a nearby work piece. Based on the magnetoquasistatic model, a mathematical framework is developed here that allows for identification of optimum shape parameters to achieve a desired force distribution in the work piece. The shape of the coil is parametrized via a mathematical function. According to each choice of parameters, a mesh is constructed to solve the eddy current equation with edge elements in a 3D transient context yielding the Lorentz force density in the work piece, which is compared with a desired force density. Identification of optimum parameters is carried out by different versions of gradient based mathematical optimization methods that are compared to each other. Techniques to determine gradient information are developed, particularly to consider geometry variations during the optimization process in an efficient way.
Accuracy and Quality Analysis for the Numerical Calculation of Electromagnetic Fields
Georg Wilhelm Wimmer^{1}, Sebastian Lange^{2}
^{1}University of Applied Sciences WürzburgSchweinfurt, Germany; ^{2}Bundeswehr Research Institute for Protective Technologies and CBRN Protection, Germany
The analysis of errors when solving electromagnetic field problems is important in order to
assure the quality of code and accuracy of the numerical solution which is calculated
from a mesh based method as the finite element method.
The solution accuracy is subject to the mesh qualitiy, discretization error,
order of basis functions and the accuracy of the linear system that is finally solved.
These errors are investigated using 2D finite element basis functions on triangular
meshes. An efficient implementation is using 2D related functions following
the idea of discrete differential forms.
