Determination of hot spots and temperature distributions in transformer tank walls with different surrounding media
Daniel CahueDiaz^{1}, Serguei Maximov^{1,2}, JuanCarlos OlivaresGalvan^{2}, Rafael EscarelaPerez^{2}
^{1}Instituto Tecnologico de Morelia, Mexico; ^{2}Universidad Autonoma Metropolitana, Azcapotzalco, Mexico
One of the great challenges in the field of transformer design is the calculation of temperature distribution in transformer tanks and estimation of hot spots, taking into account different types of surrounding media. The presence of skineffect results in high density of power losses in boundary layers, which demands thin meshes within finite element (FE) analysis. Moreover, the result of FEM calculations is very sensitive to variation of the mesh density in boundary layers. Therefore, alternative methods for analysis of temperature distributions in those regions are required. Analytical methods are an excellent choice when geometry and boundary conditions are properly established. In this research, a new rigorous analytical method for calculating temperature profiles in bushing regions of transformer tank walls is developed by solving the heat equation. The heat source is calculated both analytically, from a previously published investigation, and a FEM analysis. The efficiency of the developed method is proved using several study cases.
Stray losses in transformer tank walls considering harmonics
Sohail Khan^{1}, Serguei Maximov^{2}, Rafael EscarelaPerez^{3}, Juan C. OlivaresGalvan^{3}, Enrique Melgoza Vazquez^{2}
^{1}Universidad Nacional Autonoma de Mexico, Mexico; ^{2}Instituto Tecnologico de Morelia, Morelia; ^{3}Universidad Autonoma MetropolitanaAzcapotzalco
The presence of harmonics in the load current might considerably increase stray losses in electric transformers. In this research paper, a new model for computing the electromagnetic field and Foucault current losses in tank walls of transformers is derived considering harmonics. Maxwell’s equations are solved with their corresponding boundary conditions. The differential equation thus obtained in the tank wall is solved using the method of separation of variables. The losses are calculated for different harmonics. The results are in good agreement with simulations carried out using commercial finite element (FE) software.
Airgap Magnetic Field Analysis of an Axial Flux Permanent Magnet Vernier Machine considering Dimensional Constraints
Encheng Tao, Fei Zhao
Harbin Institute of Technology(Shenzhen), Shenzhen, China, People's Republic of
This paper presents an improved analytical model of the magnetic field in an axial flux permanent magnet vernier machine (AFPMVM), considering strict inner and outer dimensional constraints for special application. Due to the unbalanced radial lengths of stator and rotor, the conventional analytical method is not suitable for this kind of AFPMVM. Therefore, the presented analytical model utilizes an effective radial dependent analysis method to estimate the airgap magnetic field distribution more accurately. Furthermore, machine performance evaluation by the analytical method is proposed, considering the magnetic field variation of airgap in radial direction. The magnetic field distribution and performance results using the proposed method are compared with those from the threedimensional finite element method (3D FEM).
Fast Characteristics Calculation of Large Transformers with StepLap Joints by Dividing Regions of Finite Element Analysis
Katsumi Yamazaki, Shunpei Yoshioka, Ryouma Utsunomiya
Chiba Institute of Technology, Japan
This paper describes fast characteristics calculation of large transformers with step lap joints by dividing regions of finite element analysis (FEA). The flux in of the core in each divided region is given by fixing the magnetic vector potential at the divided surface due to Stoke’s theorem. The exiting current of the coil is calculated from the magnetic field with Ampere’s law. The validity and advantage of the proposed method is confirmed by comparing the calculated iron loss and exciting current with the FEA of whole region. The usefulness of the proposed method is clarified by the application of the characteristics improvement of the transformers.
Demagnetization Correction Method by Using Inverse Analysis Considering Demagnetizing Field Distribution
Jun Fujisaki^{1}, Atsushi Furuya^{1}, Hideyuki Shitara^{1}, Yuji Uehara^{2}, Kurima Kobayashi^{3}
^{1}Fujitsu Limited, Japan; ^{2}Magnetic Device Laboratory Limited, Japan; ^{3}Shizuoka Institute of Science and Technology, Japan
A new demagnetization correction method is explained in this paper. Since a magnetic curve in an open magnetic circuit is considerably affected by the demagnetizing field which depends on the shape of the magnetic material, the demagnetization correction is significantly important to evaluate the magnetic properties of magnetic materials. In the new demagnetization correction method, a proper closed magnetic circuit curve is obtained in a way that a curve defined as a mathematical function is repeatedly modified in a computer feedback loop. In the method, the distribution of the demagnetizing field inside the magnetic material is taken into account by using finite element method in the computer calculation. Some calculation results are shown about NdFeB sintered magnets, and it is revealed that the new demagnetization correction method is able to reproduce the measured curves in the closed magnetic circuit with much higher accuracy than that of the classical demagnetization correction method.
Enhanced Field Reconstruction Method Considering End Effect for a Linear Tubular Permanent Magnet Motor
KiHoon Kim^{1}, ByungHwan Jeong^{2}, DongKyun Woo^{1}
^{1}Dept. of Electrical Eng., Yeungnam University, Gyeongbuk 38541, Korea; ^{2}Power and Industrial System Research and Development Center, Hyosung, Seoul 14080, Korea
This paper considers a linear tubular permanent magnet motor (LTPMM) for an active suspension system. The LTPMM has an end effect due to its structure. This can be an important factor for analysis and design of the LTPMM. The field reconstruction method (FRM) was developed for an efficient evaluation of the magnetic field in the electric machine. It can reduce the computational time through the basis function which constructs an airgap magnetic flux distribution. In this paper, the FRM, which has been used in the rotating machine, was applied to the LTPMM. However, the conventional FRM did not take into account an end effect in the LTPMM. This limits its application to a tool for a rotating machine. To deal with this problem, we proposed an enhanced FRM that considers the endeffect in the LTPMM. This approach is based on new basis function. The accuracy of this proposed method is verified by comparing between finite element analysis, experiment result, conventional and enhanced FRM.
Modeling Approach for Transformer with Different Saturation Levels
Yingying Wang^{1}, Weiying Yuan^{2}, Qiwei Lu^{1}
^{1}China University of Mining and Technology, Beijing, China; ^{2}Tsinghua University, Beijing, China
This paper presented a modeling approach for transformer with different saturation degrees. First, the magnetic field distributions at different saturation degrees in the transformer are analyzed by using numerical simulations. Then, the characteristics of the leakage magnetic flux are analyzed, and the magnetic circuits with varying leakage reluctance topologies are modeled. Finally, based on the mature duality relationship between electric and magnetic circuits, the equivalent electric circuit models are obtained. These kinds of models embody the effect of different saturation degrees on the connection points of the leakage flux branches, and it can fully reflect the various working states of the transformer. The accuracy of the models is verified by comparing the circuit simulation results with those of FEM transient simulations.
Improved Analytical Model for Predicting Vibration due to Magnetostriction in Axial Flux Permanent Magnet Synchronous Machines
Shengnan Wu, Wenming Tong, Wenjie Li, Shenbo Yu, Renyuan Tang
Shenyang University of Technology, China, People's Republic of
This paper presents an improved analytical model for predicting the vibration due to magnetostriction in axial flux permanent magnet synchronous machines (AFPMSMs). Firstly, an improved analytical model of stator core vibration is set up based on piezomagnetic equations and Newton's second law. The radial component, circumferential component and axial component of the stator core stress are taken into account. Then, the analytical model was implemented on a 24pole and 36slot, 7kW AFPMSM. The distribution characteristics of the vibration displacement and stress in the stator core are calculated. Finally, a 7kW AFPMSM prototype has been manufactured and the vibration of the prototype is tested.
Improvement of Torque and Power Factor Characteristics of a Vernier Motor through Series Compensation
Abdur Rehman, Byungtaek Kim
Kunsan National University, Korea, Republic of (South Korea)
In this paper, the power factor of a vernier motor is improved through series compensation, resulting in improved torque performance in the flux weakening region as well as reducing input voltage. Series compensation is performed by supplying the desired reactive power to the motor from an additional inverter with a floating capacitor through the openended winding motor. First, the problems caused by the low power factor of a PM vernier motor are described which are the poor torque performance in the flux weakening region and excessive input voltage, and then the operation principle of series compensation is explained. For a given prototype vernier motor, we determine the reactive power to be supplied through the proposed method of series compensation, and verify the improved power factor, torque and input voltage performances through finite element analysis.
Analytical Calculation of Airgap Magnetic Field in Linear and Rotary Magnetic Transmission Using Subdomain Method and Equivalent Model
Xinghe Fu, Yaqian Hu, Qiang Li, Yixiang Tu
Southeast University, China, People's Republic of
It is difficulty to analytically compute the magnetic field of linear and rotary magnetic transmission based on the original model owing to the existence of two coordinate systems (rectangular coordinate and cylindrical coordinate). This paper presents a novel equivalent solved model to describe the linear and rotary magnetic transmission in rectangular coordinate for magnetic field computation. Then, an analytical method based on subdomain method is proposed to calculate the magnetic field distribution in transmission. The results based subdomain method and equivalent model are consistent with the FEM.
Computation of Losses in Metallic Cooling Tubes of Electric Machines with Direct Coil Cooling
Mohamed Nabil Fathy Ibrahim^{1,2,3}, Peter Sergeant^{1,2}
^{1}Department of Electrical Energy, Metals, Mechanical Constructions and Systems, Ghent University, Ghent 9052, Belgium; ^{2}Core lab EEDTMP, Flanders Make, the strategic research centre for the manufacturing industry, Gaston Geenslaan 8, 3001 Leuven, Belgium; ^{3}Electrical Engineering Department, Kafrelshiekh University, Kafrelshiekh 33511, Egypt
The direct coil cooling method is one of the existing cooling techniques for electric machines of concentrated windings, in which cooling tubes of conductive material are inserted between the windings. Eddy current losses are induced in those cooling tubes because of the time variant magnetic field. This paper proposes a simple and an accurate semianalytical based finite element method to calculate the losses of electric machines having cooling tubes. The 2D magnostatic solution of the magnetic field is obtained using e.g. the free package “FEMM”. Then, the eddy current losses in the tubes are computed based on simple analytical equations. Besides, the iron core loss could be obtained as well. A 6 teeth stator of electric machines is employed as a case study, in which 6 cooling tubes are used. The results obtained using the proposed method correspond very well with those computed from the commercial 2D transient Ansys Maxwell. Moreover, the proposed method is validated by experimental measurements. The proposed method is simple and fast to be constructed and it is almost free of cost.
An Improved MsFEM for Multiscale Modeling of Ribbon Magnetic Cores with Arbitrary Geometries
Hailin Li^{1}, Zuqi Tang^{2}, Shuhong Wang^{1}, Jianguo Zhu^{3}
^{1}Xi'an Jiaotong University, China, People's Republic of; ^{2}University of Lille, France; ^{3}University of Sydney, Australia
An improved multiscale finite element method (iMsFEM) is proposed for calculating eddy current of ribbon magnetic cores with complex corner structure. Our proposed iMsFEM is based on shell element technique, as well as multiscale finite element method (MsFEM). The shell element is used to represent the coating on each sheet which can reduce the number of fine grids for each coarse element, therefore, the computation cost can be further alleviated. Results calculated by conventional finite element method (CFEM) and iMsFEM are compared to verify the accuracy and the computation cost are also analyzed. According to the results, iMsFEM can effectively save the hard device, less than 1/3 of the maximum random access memory (RAM) of the CFEM consumes, and the CPU time can either be reduced as long as the number of coarse elements, and the number of fine grids in coarse elements thoroughly arranged.
Effects of Manufacturing Imperfection of Magnets on PMSM with Parallel Winding Connections
DeokJae Kwon, JunHyuck Im, SeungTae Lee, Jin Hur
Incheon National University, Korea, Korea, Republic of (South Korea)
Previous papers are assumed that the permanent magnet (PM) is ideal in order to study the circulating current by the winding method and tolerances. This study is researched for prove that the effect of circulating current due to the tolerance of the PM should be considered in the strategy proposed in the above papers for the reduction of the circulating current by the manufacturing tolerance. The nonuniform magnetic characteristics and circulating current by the PM manufacturing tolerance have been researched in order to expand the field of analysis of the influence of the circulating current according to manufacturing tolerances.
Electromagnetic Field Analysis of Distributed Winding Permanent Magnet Synchronous Motor Taking Into Account Axial End Leakage Flux by TwoDimensional Finite Element Analysis
DongKyun Ahn^{1}, ByeongHwa Lee^{2}, MyungSeop Lim^{3}, JungPyo Hong^{1}, JaeWoo Jung^{4}
^{1}Hanyang University, Republic of (South Korea); ^{2}Korea Automotive Technology Institute, Republic of (South Korea); ^{3}Yeungnam University, Republic of Korea; ^{4}Hyundai Mobis, Korea, Republic of (South Korea)
This paper proposes a method for electromagnetic field analysis of permanent magnet synchronous motor considering axial end leakage flux. In order to take into account the axial end leakage flux using the 2dimensional finite element analysis (FEA), the permeance of axial end leakage path is added into slot region by increasing permeability of elements in the slot region. The increased permeability is calculated from the permeance relationship of the main magnetic path and the axial end leakage path, which are calculated through the equivalent magnetic circuit method. The effect of the proposed method is verified by comparing with the 3 dimensional FEA results and experimental results.
An Analytical and Numerical Hybrid Model of Interior Permanent Magnet Synchronous Machine with Slotless Concentrated Windings
Ping Jin, Yujing Guo
College of Energy and Electrical Engineering, Hohai University, Nanjing, P. R. China
This paper presents an analytical and numerical hybrid model of an interior permanent magnet synchronous motor (IPMSM) with slotless concentrated windings. The magnetic field is decomposed into a PM magnetic field and a winding current magnetic field. The distribution of the former is fitting by discrete Fourier transform (DFT) of flux density calculated by a finite element model (FEM), and that of the latter is equivalent by a surfaced PM magnetic field with virtually variable residual magnetization vector, governed by the Laplacian equation and Possion equation with the magnetic scalar potential. The results of the coupled model are verified by 2D finite element.
