Computation of Eddy Losses in a 36 Pulse Rectifier Transformers
Sheppard Salon
RPI, United States of America
Rectifier transformers are growing in size and complexity due to the increased prevalence of large motor drives. In order to reduce the line harmonics, rectifiers with high pulse numbers are now being used. In this paper a 3 phase 36 pulse rectifier transformer is studied to find the extra winding losses produced by high radial flux concentrations between the phase breaks. Nonphase shifting transformers produce mostly axial flux in the window except near the ends of the winding. The size and orientation of the copper strands reduce the eddy current losses. In a rectifier transformer the field distribution is much more complex. A finite element analysis of a 3 phase transformer with a single core design using a delta primary and 18 extended delta secondaries was conducted to identify the losses and their distribution. We also identify the very large variations in eddy current losses which are necessary to determine the hot spot of the winding. A discussion of the effects of the harmonics in the waveform is also included.
Generalized finite element based study on the impact of permanent magnets' imperfections on performance measures of electric machines
Gerd Bramerdorfer
Johannes Kepler University Linz, Austria
This work is about analyzing the impact of permanent magnets’ tolerances on electric machine performance. A generalized model is presented allowing for the analysis of single mmfharmonics of the permanent excitation or a combination of selected harmonics. The approach can be used both for the standard symmetric case as well as if tolerances are present. It is based on finite element simulations of the machine’s cross section utilizing a thin current layer in the air gap. Results reveal that these investigations can provide general insight in how the harmonics take effect on torque and linked fluxes of the stator coils. Thus, this study can be the basis for evaluating different machine configurations concerning their sensitivity to toleranceaffected permanent magnets.
An H2LU preconditioner for MQS model based on Integral formulation
Salvatore Ventre^{1}, Bruno Carpentieri^{3}, Gaspare Giovinco^{1}, Antonello Tamburrino^{1}, Guglielmo Rubinacci^{2}, Fabio Villone^{2}
^{1}University of Cassino and Southern Lazio, Italy; ^{2}University of Naples “Federico II”,; ^{3}University of Bolzano, Bolzano
In this paper, an effective numerical technique has been developed for solving MQS problems based on integral formulation. In the past, the authors proposed a compression technique in parallel enviroment, in order to tackle largescale fully 3D problems. In this paper, the proposed technique is optimized by means of a preconditioner based on LU decomposition of a H2matrix structure using ad hoc factorization. The results demonstrates that the proposed methodology performs much better than the existing one.
The Working Principle of Flux Switching Machines
Gerd Bramerdorfer^{1}, Wolfgang Gruber^{1}, Andrea Cavagnino^{2}, Silvio Vaschetto^{2}
^{1}Johannes Kepler University Linz, Austria; ^{2}Politecnico di Torino, Italy
This work is about clearly illustrating the working principle of flux switching machines. In the past, different topologies regarding stator/rotor configurations were presented and evaluated. Moreover, optimization of the operational characteristics was considered. The focus was on optimizing the shape of utilized components. However, the principle of torque generation is not clear at first sight, as typically the number of poles of the magnetic field due to the permanent magnets and due to the winding arrangement are not of same number. The reason for generating a net torque considering an entire period is the flux modulation due to the rotor teeth. A thorough explanation is presented featuring both, theoretical aspects as well as numerical studies utilizing finite element simulations. Results can help to derive general understanding of the working principle and will facilitate the development of new configurations.
On the use of nonlinear complex polyharmonic finite element models of induction motors
Tomasz Garbiec, Mariusz Jagiela, Marcin Kulik
Opole University of Technology, Poland
The application of a nonlinear complex De Gersem  type polyharmonic finite element model in the steadystate analysis of threephase solidrotor induction motors is discussed. The effective magnetic permeability dependent on the fundamental timeharmonic of the magnetic field is used for representation of nonlinear effects. A new coupling scheme for the airgap mesh nodes is proposed in order to make the model even more competitive to the timestepping model. By means of comparative analysis of computed electromagnetic torque and harmonic losses it is shown that for relatively fine airgap meshes omitting some nodes at the interface boundary results in reduction of the execution time by the factor of 100 with only slight loss of accuracy.
Prediction of Magnetic Loss inside Silicon Steel Laminations under ACDC Hybrid Excitation
Xiaojun Zhao^{1}, Jiawen Wang^{1}, Lanrong Liu^{2}, Junwei Lu^{3}, Zhiguang Cheng^{2}, Xiaona Liu^{1}, Danhui Hou^{1}, Yutong Du^{1}
^{1}North China Electric Power University, China, People's Republic of; ^{2}Institute of Power Transmission and Transformation Technology, Baoding, China; ^{3}Griffith University, Australia
Based on the engineeringoriented model TEAM P21CM1, an experimental platform is established to obtain the magnetic properties and strayfield loss of the grainoriented silicon steel under practical working conditions. In order to calculate the strayfield loss of magnetic materials under ACDC hybrid excitation, an improved loss model is presented to investigate the strayfield loss of silicon steel laminations. This model is also used to calculate the magnetic loss of silicon steel laminations excited by 3D multiharmonic magnetic field. The strayfield loss of magnetic shielding is separated from the total load loss under ACDC hybrid excitation and AC excitation, and the conclusion can be drawn that the DC magnetic field increases the magnetic shielding strayfield loss. The proposed modeling method is validated by comparing the calculated results of magnetic field and strayfield loss with the experimental results.
Modelling of StepLap Joints using the Harmonic Balance Method
Florian Toth, Dominik Mayrhofer, Klaus Roppert, Manfred Kaltenbacher
TU Wien, Austria
The harmonic balance method is applied to efficiently compute the steady state dynamics of nonlinear magnetic systems. As an example problem we use a periodic section of a three phase transformer, where the steplap joints are modelled in detail. A measurementbased material model is used to incorporate the nonlinear, anisotropic behaviour of grain oriented electrical steel. Nonconforming grids are used to efficiently connect dissimilar meshes in air and steel domains.
Application of nfold Rotational Symmetries to Eddy Currents Integral Model in the Time Domain
Guglielmo Rubinacci^{2}, Antonello Tamburrino^{1}, Salvatore Ventre^{1}, Fabio villone^{2}
^{1}University of Cassino and Southern Lazio, Italy; ^{2}University of Naples “Federico II”, Napoli
Group Theory is a powerful “tool” which has been extensively exploited to reduce the computational cost in numerical analysis of several physical problems, including computational electromagnetics.. This paper proposes the extension of the application of group theory to an integral formulation of the eddy current problems in the presence of nfold rotational symmetries. The proposed approach is applied to the eddy currents computation in toroidal fusion devices, where rotational symmetries play a key role.
A New Application of Sensitivity Analysis Method to Interpret the Variation of the MutualInductance Effect on FRA Response
Shuhong Wang, Song Wang, Shuang Wang, Hao Qiu
State Key Laboratory of Electrical Insulation and Power Equipment, Xi'an Jiaotong University, Xi'an, China, People's Republic of
Frequency response analysis (FRA) method has been globally accepted as a feasible and reliable technique to detect the inner faults of the transformer winding. As a graphic method, all the important information that reflects the deformation of the winding is hidden in the FRA signatures. Therefore, identifying and interpreting these valuable messages existing in the signatures as much as possible is always our target. This paper tries to provide a quantitative interpretation of the variation of mutualinductances of a twowinding transformer winding equivalent circuit model effect on FRA response through the sensitivity analysis method. In this paper, firstly, the sensitivities of FRA response to mutualinductances will be elaborately deducted by Tellegen theorem. Then, the variation laws of the sensitivities of FRA response to the mutualinductances, including mutual inductances between high voltage (HV) discs, mutual inductances between low voltage (LV) discs and mutual inductances between HV and LV discs, will be investigated. Besides, it is believed that the contributions of this paper will help technicians have a new idea of the mutualinductances effect on FRA results and enhance their abilities of FRA interpretations.
Combining Domain Decomposition and Model Order Reduction in 2D Simulations of Wireless Power Transfer
Antero Marjamäki, Paavo Rasilo
Unit of Electrical Engineering, Tampere University, Finland
In this paper domain decomposition and model order reduction techniques are combined to efficiently model wireless power transfer setups in which the sending and receiving coils move relative to each other. Domain decomposition is used to decouple the problem into two subdomains which contain the coils and a master domain which contains the medium and the relative placement. The subdomains are dictated by the coil design and only the master domain must be modified to vary the relative placement of the coils. Model reduction is used to reduce the amount of degrees of freedom of the subdomain problems. This approach greatly reduces the overall complexity of the computations.
Fast and Accurate Solution of Integral Formulations of Large MQS Problems Based on Hybrid MPI/OpenMP Parallelization
Francesca Cau^{1}, Andrea Chiariello^{2}, Gaspare Giovinco^{3}, Antonio Maffucci^{3}, Guglielmo Rubinacci^{4}, Pietro Testoni^{1}, Salvatore Ventre^{3}, Fabio Villone^{4}
^{1}Fusion For Energy (F4E), Barcelona; ^{2}University of Campania “Luigi Vanvitelli”, Aversa; ^{3}University of Cassino and Southern Lazio, Italy; ^{4}University of Naples “Federico II”, Napoli
This paper presents an optimized strategy to parallelize the numerical solution of an integral model, based on the combined use of the MPI and OpenMP paradigms. The casestudy analysed in this paper is a large 3D magnetoquasistatic problem associated to a real life device, such as the fusion reactor ITER, whose complexity implies a high computational burden, only affordable with parallel computing strategies. The hybrid approach MPI/OpenMP is applied to parallelized clusters of nodes: the job is shared at the node level by using the OpenMP paradigm, whereas the process level between nodes is implemented by using the MPI approach. This hybrid parallelization reduces both the allocated memory and the communication between nodes, thus lowering the demand of the system resources.
Entropy Snapshot Filtering for QRbased Model Reduction of Transient Nonlinear ElectroQuasistatic Simulations
Fotios Kasolis, Markus Clemens
University of Wuppertal, Germany
Approximations of the entropy of a transient nonlinear electroquasistatic field system induce an ordering of highfidelity snapshots, in terms of their information content. The resulting ordering enables a direct reduction of the snapshot matrix and hence, a QRbased / SVDfree model reduction framework. Numerical experiments for a threedimensional surge arrester verify the benefits of the proposed method, both in terms of accuracy and computational effort.
Comparison of Two ElectroQuasistatic Field Formulations for the Computation of Electric Field and Space Charges in HVDC Cable Systems
Christoph Jörgens, Markus Clemens
University of Wuppertal, Germany
Electroquasistatic (EQS) field simulations are used to calculate electric field and space charge distributions in high voltage direct
current (HVDC) cable systems. The constant voltage results in the accumulation of space charges and a time varying electric field. To
simulate the electric field different EQS formulations are introduced in literature. In a first formulation, the electric field and the space
charge density are updated consecutively via the continuity equation and the electrostatic Poisson equation. In the second EQS
formulation, the continuity formulation is reformulated using the electric scalar potential and only the electric field is updated per time
step. To compare both EQS formulations, the electric fields are simulated in different HVDC cable systems. Simulation results of the
electric field in a cable insulation result in relative errors of less than 2 % between the numerical computation the analytic solution.
Simulation results of a cable joint show instabilities for the fieldspace charge update EQS formulation, whereas the scalar potential EQS
formulation yield the results.
Effectiveness Evaluation of Dynamic Mode Decomposition for Model Order Reduction of QuasiMagnetostatic Problems
Sarbajit Paul, JungHwan Chang
DongA University, Korea, Republic of (South Korea)
Model order reduction (MOR) is considered as a good alternative to reduce the computational scale for quasimagnetostatic problems. The aim of this work is to introduce the use of dynamic mode decomposition (DMD) as an promising tool for MOR to
analyze its effectiveness in solving quasimagnetostatic problems. Using a singualr value decomposition (SVD) based DMD, TEAM problem 21a0 is analyzed and compared with the full model to ensure the effectiveness of DMD.
EquivalentCircuit Model for Axisymmetric HighTemperature Superconducting Film: Application to Contactless jC Measurement System and Pellet Injection System
Takazumi Yamaguchi^{1,2}, Teruou Takayama^{1}, Hiroaki Ohtani^{2,3}, Atsushi Kamitani^{2}
^{1}The Graduate University for Advance Studies SOKENDAI; ^{2}Yamagata University, Japan; ^{3}National Institute for Fusion Science
An equivalentcircuit model (ECM) is proposed for analyzing the shielding current density in an axisymmetric hightemperature superconducting (HTS) film. It is applied to not only the simulation of two contactless measurement systems of the critical current density but also that of a pellet injection system. As a result, it is found that the ECM is an effective tool for analysis of the shielding current density in axisymmetric HTS devices.
Modelling Nonlinear Steady State Induction Heating Processes
Klaus Roppert, Florian Toth, Manfred Kaltenbacher
Institute of Mechanics and Mechatronics, TU Wien, Vienna, Austria
In this work, an efficient simulation strategy for a fully coupled nonlinear magnetic thermal problem is presented. The solution dependent magnetic subproblem is solved with a harmonic balancing scheme, with the main focus on the correct choice of the material model (magnetization curve). Exploiting scale separation between magnetic and thermal time scales, the nonlinear thermal problem can be considered in transient as well as steady state case. To further increase computational efficiency, a nonconforming interface approach is used, based on jump operators and penalty terms. Furthermore, different types of excitations are investigated, including eddy currents in inductors, based on a power balance approach.
Cauer Ladder Network Representation of MultiTurn Coil Considering Skin and Proximity Effect
Kengo Sugahara^{1}, Hassan Ebrahimi^{2}, Akihisa Kameari^{2}, Tetsuji Matsuo^{3}, Tadashi Tokumasu^{4}, Yuji Shindo^{5}
^{1}Kindai University, Japan; ^{2}Science Solutions International Laboratory; ^{3}Kyoto University; ^{4}Toshiba Infrastructure Systems & Solutions Corporation; ^{5}Kawasaki Heavy Industries, Ltd.
This paper proposes Cauer Ladder Network (CLN) representation of multiturn coil considering skin and proximity effect. When native finiteelement method is applied on the analysis of multiturn coils, each wire has to be subdivided into sufficiently fine elements and requires long computation time. Therefore, semianalytical approach for multiturn coil combined with homogenization method has been proposed to reduce the computational resources. Aside from the semianalytical approach, a novel and effective model order reduction method, called CLN method, has also been proposed in which linear quasistatic electromagnetic fields are expressed by a linear combination of a sequence of static electric and magnetic field modes. In this paper, we combine the semianalytical approach and the CLN method to analyze multiturn coils with highorder coupling between each wire.
