Analysis of motional eddy currents in the slitted stator core of an axial-flux permanent magnet machine
Department of Electrical Engineering, Eindhoven University of Technology, the Netherlands
This paper concerns the modeling and design of a slitted stator core for single-sided axial-flux permanent-magnet machine application. The stator core is specially designed to maximize the airgap flux density in the airgap, to shield the magnetic flux density created by the permanent magnets and windings, and to minimize the eddy current losses occurring at high rotational speeds. To reduce the effort needed for computing the motional eddy current distribution in presence of nonlinear material characteristics, a novel method is proposed. It combines the harmonic balance method, which is advantageous for simulating in the frequency domain the steady-state periodic response of a nonlinear system under harmonic excitation, together with the multilevel MMF wave approximation, which introduces a set of pulsating virtual magnets, that mimics the displacement of the permanent magnet array. Following this method, time-domain distributions and losses can be reconstructed accurately with a low number of harmonics. A three-dimensional periodic model of the slotless axial-flux machine is built in the framework of isogeometric analysis and a mixed formulation is employed, which relies on high order Nédélec edge-elements. The proposed model is embedded into a gradient-based optimization problem to determine the optimal shape of the slits in the stator core of the motor. This results in a novel cost-effective solution for improving the efficiency of axial-flux permanent-magnet machines
Modal Decomposition of Three-Dimensional Quasi-Static Maxwell Equations by Cauer Ladder Network Representation
1Science Solutions International Laboratory, Inc., Japan; 2Faculty of Science and Engineering, Kindai University, Higashiosaka, Japan; 3Graduate School of Engineering, Kyoto University, Kyoto, Japan
Significant advances has been made to the Cauer ladder network method, a novel and attractive method recently proposed for the model order reduction of linear eddy current problems. However, these developments are often discussed in the context of simple two-dimensional (2D) problems with solid conductors only. The three-dimensional (3D) implementation of the method with general coil connections requires further treatment, which deserves detailed discussions. This paper reformulates the method for 3D implementation with finely stranded coil as well as solid conductors. It also considers arbitrary connection of coils and conductors.
Evaluation of Impressed Potential on Buried Pipeline near HVDC Grounding Electrode Considering Polarization Effect
Tsinghua University, China, People's Republic of
The DC current injected into the earth through the grounding electrodes of a HVDC system would aggravate the corrosion of nearby pipelines. In this paper, a numerical approach based on method of moments and circuit theory is put forwards to simulate the potential distribution in gas pipeline with insulating coating breakdown. The current-dependent electrochemical polarization between the soil and the metal tube due to the partial damage of the insulating coating is taken into account by using an iterative scheme. With the approach, the effect of the damaged insulating coating on the pipe-to-soil potential distribution along a pipeline is analyzed.
Enforcing Lumped Parameter Excitations in Edge-Element Formulations by Using a Fast Iterative Approach
1Dipartimento di Ingegneria Industriale, Università degli Studi di Padova, Italy; 2Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Italy
In order to couple external circuits to edge-element discretized electromagnetic models, with full field equations, global constraints involving voltages and currents need to be enforced. There is no canonical way to impose a voltage or a current without additional modeling information on the distribution of the field sources, that rely on topological concepts. In this work a fast solution of field sources within massive conductors in static conditions is proposed. Global basis functions, required to cope with non-trivial coil topologies, are directly generated by an iterative solver rather than pre-computing source fields e.g. from tree-cotree decomposition.
Accurate Thin Shell Finite Element Magnetic Models via an Iterative Subproblem Method
1Hanoi University of Science and Technlogy (HUST), Vietnam; 2University of Liège, Dept. of Electrical Engineering and Computer Science, ACE, B-4000 Liège, Belgium
An iterative subproblem method is herein developed for correcting the inaccuracies near edges and corners arising from thin shell models replaced volume thin regions by surfaces. Such models replace volume thin regions by surfaces but neglect border effects in the vicinity of their edges and corners. The developed surface-to-volume correction problem is defined as a step of multiple subproblems (SPs), with inductors and magnetic or conducting regions, some of them being thin region.
Magnetic Fields Topology: a Numerical Procedure for Islands Characterization
Università degli Studi della Campania, Italy
Depending on the sources distribution, the magnetic map in 3D domains, can exhibit different characteristics, ranging from the classical regular closed lines or simple magnetic toroidal surfaces, through the more complex islands, to the fully chaotic domains. A suitable knowledge of the regions characterized by complex maps is essential to prevent instability phenomena in a number of important applications, such as controlled thermonuclear fusion machines based on the magnetic confinement. The paper proposes an effective procedure to localize and characterize the magnetic islands and a class of chaotic domains.
Modelling and FEM Computation of Dynamic Losses in Laminated Electrical Steels Excited by a Non-sinusoidal Field
1Perugia University, Italy; 2Roma Tre University, Italy; 3Ain Shams University, Egypt
A hysteresis model coupled with 2D finite element method is proposed. The hysteresis model is identified by experimental data. An experimental validation using a non-oriented electric steel M400-65A grade is done at frequencies from 5 Hz to 250 Hz. Both sinusoidal and non-sinusoidal waveforms are considered. Comparison with computed and measured results is given. A discussion about the excess losses and their prediction via analytical approach is also discussed.
Comparison of Two Different Analytical Models of Active Magnetic Bearing with Rotor Eccentricity
1Southeast University, School of Electrical Engineering, Nanjing, Jiangsu, China; 2Delft University of Technology, Department of Electrical Sustainable Energy, Delft, the Netherlands
This paper applies two different analytical methods, i.e., the perturbation method and superposition method, to calculate the magnetic flux density distribution and the magnetic force of the active magnetic bearing (AMB) with the eccentricity. The performance of these two methods is compared and discussed. The perturbation method is complex while the superposition method is intuitive. The valid range of the superposition method is larger than the perturbation method. However, the superposition method requires longer computation time. The main contribution of this paper is to compare the effectiveness of two analytical methods to predict the AMB performance with the eccentricity and to give a guideline to choose the proper analytical method to design AMB.
Parallel TP-EEC Method based on Polyphase Time-periodic Condition for Magnetic Field Analysis of Induction Motors
1Doshisha University, Japan; 2Toshiba Infrastructure Systems & Solutions Corporation, Japan; 3Hokkaido University, Japan; 4Kyoto University, Japan
This paper develops the parallel time-periodic explicit error correction (TP-EEC) method considering a polyphase time-periodic condition for magnetic field analyses of cage induction motors. In addition, the convergence behavior of the transient solution to its steady-state is improved by appropriately setting the initial values of the parallel TP-EEC method in each process by nonlinear time-harmonic analyses. Numerical results of a cage induction motor are presented to demonstrate the effectiveness of the proposed method.
CPU Time Reduction in Magnetic Field Analysis With Nonconforming Infinite Edge Element Method
Waseda University, Japan
The Infinite Edge Element Method (IEEM) is an effective method for handling open boundary problems. However, when the analysis object has a complicated shape, the number of infinite elements also increases as that of the finite elements increases, and the computational load relatively becomes large. In this paper, we propose the Nonconforming IEEM, with nonconforming connection applied to the interface boundary between finite and infinite element regions, in order to further reduce the computational burden. We analyzed the coil model which has a theoretical solution with the proposed method and showed that the calculation load can be drastically reduced while maintaining the analysis accuracy.
Unstructured–PEEC Method for Thin Electromagnetic Media
1Univ. Grenoble Alpes, CNRS, Grenoble INP, G2Elab, F-38000 Grenoble, France; 2Univ. Lyon, ECLyon, Ampère, CNRS, France; 3Altair, Meylan, France
An unstructured-PEEC method for modelling electromagnetic thin region is proposed. Two coupled circuits representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite element surface mesh. Dynamic effects across the sheet are modeled by equivalent complex conductivity and reluctivity. Non simply connected regions are treated with fundamental branch independent loop matrixes coming from the circuit representation. The formulation enables the computation of eddy current losses and can be coupled with external circuits, PEEC-1D cables or coil thanks to the circuit representation.
Cauer Ladder Network representation of Nonlinear Eddy-Current Field using First Order Approximation
Kyoto University, Japan
In this paper, an approximation approach is proposed for analyzing nonlinear quasi-static eddy-currents via Cauer Ladder Network (CLN) method. When there are nonlinear magnetic materials in the analysis domain, the electric and magnetic modes and their corresponding values for resistors and inductors in CLN may vary according to the level of saturation in the core. Considering the effect of the modes and their magnitudes on the saturation impose a heavy computational burden and might even rule out the efficiency of the CLN method. This paper will study a first-order approximation of the nonlinear CLN method to keep the nonlinearization procedure computationally effective, simple and accurate. Numerical tests will be carried out over a 2-D nonlinear inductor excited with rectangular excitations to show the accuracy of the proposed nonlinearization method.
On a Study of Magnetic Force Evaluation by Double-Layer Approach
1POLOPT Technologies, Switzerland; 2Berlin Scientific, Germany; 3Pavia University, Italy
The double-layer approach (DLA) can easily and correctly treat the edges and corners of magnetic bodies. In this paper we introduce two kinds of double-layers: one is on the surface of magnetic body and the other is on the cut-surface within the exciting current loop. From the double-layer on the cut-surface, we derive a novel, unified exciting potential (UEP), which facilitates the treatment of the multiply connected problems. Furthermore, utilizing the similarity between the surface currents and the double-layer, we derive the improved approach for the analysis of the forces acting on the magnetic bodies. This new DLA is an originally nonlinear approach and enables improved analysis of the real-world devices, which will be analyzed in details in the final paper.
Semi-Analytical modeling of eddy current inspection of multilayered, anisotropic and homogeneous media
1CEA, France; 2IREENA, Université de Nantes, France
This paper deals with the development of a Semi-Analytical model for the fast computation of a quasi-static field induced by a 3D eddy current probe in a flawless composite material. Each ply of the composite is assumed to be homogeneous and anisotropic. Therefore, the specimen is characterized by a constant biaxial conductivity tensor according to the main orientation of the fibers. The adopted modeling approach is based on a modal decomposition of the Electromagnetic (EM) field in the Fourier domain. A recursive scattering matrix algorithm (S-matrix) has been implemented to address multilayered media. For numerical validations, simulated data obtained by the SA model at CEA LIST are compared to data provided by a home FE code developed at IREENA.
Analysis of Ion Flow Field Considering Dielectric Film Under HVDC Overhead Transmission Lines
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources,North China Electric Power University, China, People's Republic of
Dielectric film is widely used in the agricultural greenhouse. When the HVDC transmission lines cross over the greenhouse, the space charges generated by the corona discharge of the lines will accumulate on the surface of dielectric film. The surface charges will distort the ground-level electric field seriously. In this paper, the ion flow field under the HVDC line is computed by Upstream Finite Element Method (Upstream FEM). A charge accumulation algorithm is presented to deal with the effect of dielectric film on electric field and space charges. Therefore, the ion flow field near the film can be predicted without relying on measurement. In order to verify the computation, an experimental platform is set up in the laboratory, and the measured electric field on the ground is consistent with the computational results. Finally, the distributing characteristics of electric field considering the influence of dielectric film are analyzed, which is helpful to design the HVDC overhead lines crossing over greenhouses.
MoM Computation of Losses of an Array of Parallel Magnetic and Conductive Wires in a Transverse Magneto-quasi-static Field
1Politecnico di Milano, Italy; 2Prysmian S.p.A., Italy
A fast 2D method is proposed for the computation of hysteresis and eddy current losses in an array of parallel magnetic and conductive wires placed in a transversal time-harmonic magneto-quasi-static field. The method is applied to the computation of losses in the armature of a submarine high-voltage cable. Its accuracy is verified by comparing the results with a reference finite-element solution.
Applicability of the Time Periodic FEM approach with commercial simulation codes
1Università di Padova, Italy; 2COMSOL S.r.l., Italy
This paper examines the feasibility of implementing the Time Periodic Finite Element Method within the framework of modern commercial codes. In particular it considers cases without and with motion and focuses on the ease of implementation, accuracy and
required computational resources.
An Inverse Integral Formulation for Steel Shell Magnetization Identification
1G2elab, France; 2Naval Group
An algorithm for the reconstruction of unknown magnetization in an iron sheet is proposed. The magnetization distribution is reconstructed from magnetic measurements made on sensors placed in the surrounded air region. The problem is solved thanks to the inversion of an integral formulation, based on the face interpolation of the flux density in the sheet and leading to a linear matrix system. The final system is solved with a balanced singular value decomposition in order to stabilize the solution. The efficiency of the method is demonstrated with both numerical and experimental test cases.