基于残差U-Net和自注意力Transformer编码器的磁场预测方法

利用有限元方法对几何结构复杂的电机和变压器进行磁场分析,存在仿真时间长且无法复用的问题。因此,该文提出一种基于残差U-Net和自注意力Transformer编码器的磁场预测方法。首先建立永磁同步电机(PMSM)和非晶合金变压器(AMT)有限元模型,得到深度学习训练所需的数据集;然后将Transformer模块与U-Net模型结合,并引入短残差机制建立ResUnet-Transformer模型,通过预测图像的像素实现磁场预测;最后通过Targeted Dropout算法和动态学习率调整策略对模型进行优化,解决拟合问题并提高预测精度。计算实例证明,ResUnet-Transformer模型在PMSM和AMT数据集上测试集的平均绝对百分比误差(MAPE)均小于1%,且仅需500组样本。该文提出的磁场预测方法能减少实际工况和多工况下精细模拟和拓扑优化的时间和资源消耗,亦是虚拟传感器乃至数字孪生的关键实现方法之一。

Observation about the Classical Electromagnetic Gauge Transformation and Its Quantum Correspondence

Using the Landau and symmetric gauges for the vector potential of a constant magnetic field and the quantum problem of a charged particle moving on a flat surface, we show the classical electromagnetic gauge transformation does not correspond to a one-dimensional unitary group transformation U(1) of the wave function for the quantum case. In addition, with the re-examination of the relation between the magnetic field B and its vector potential A, we found that, in order to have a consistent formulation of the dynamics of the charged particle with both expressions, we must have that B=∇×A if and only if B≠0.

Some Properties of the Electromagnetic Radiation Emitted by the HV Transformers

One important way to control the technical condition of the high-voltage power equipment element is the monitoring and interpretation of electromagnetic radiation. Analysis of the spectra of emitted high-voltage equipment EMR provides information on which determines the intensity discharge processes occurring in insulation and other structural elements of high voltage equipment under the operating voltage without interfering with the process.

Electromagnetic and Stress Analysis of 50 kA Superconducting Transformer for ITER Conductor Test Facility

A superconducting transformer was designed for the correction coils （CC） conductor test facility in the Institute of Plasma Physics, the Chinese Academy of Sciences （ASIPP）, for validating the CC conductor of the international thermonuclear experimental reactor （ITER）. The maximum current of the superconducting transformer is 50 kA. The conductor samples could be tested at different magnetic fields and cooling conditions similar to the operational condition of ITER. During normal operation, the primary and secondary windings of the superconducting transformer will withstand the high electromagnetic （EM） stress caused by the high current. Integrated analysis of EM and structural fields can ensure these components not to encounter any over-stress problem under normal operational condition. A coupled model is proposed to combine the EM and structural analyses. A detailed finite element （FE） model and EM-structural coupled model are presented and the numerical results show that the stress of the transformer windings is within the allowable limits.

A Tool for the Assessment of the Electromagnetic Forces in Power Distribution Transformers

This paper compares the estimated electromagnetic forces due to short circuits in power transformers using two computational models. The first model is based on approximate analytical expressions of the electromagnetic lbrces as they have been compiled in earlier versions of the IEC standard 60076-5. The second model is based on a finite element model of the transformer using the software FEMM （Finite Element Method Magnetics）. The paper shows how valid the analytical model is for design purposes. Results have been obtained and compared from both models in a number of actual power distribution transformers. It is possible to conclude that the analytical formulation provides satisfactory results for the design of power transformers compared to detailed finite element models. A tool has been designed for this purpose and the main features of it will be described in the paper.

Vacuum Electromagnetic Levitation Melting and Undercooling of Peritectic Terfenol-D

For the first time, the undercooling of a magnetostrictive material a near peritectic Tb 0.27 Dy 0.73 Fe 1.90 alloy was realized by vacuum electromagnetic levitation melting and 60 K undercooling was obtained. There is one recalescence behavior during solidification of the undercooled melt,which can attribute to the priority precipitation of REFe 2 phase instead of REFe 3 phase, due to preferential nucleation and higher crystal growth rate of REFe 2 phase and the suppression of peritectic reaction. According to the crystal structural characteristics of REFe 2 and REFe 3, REFe 2 is a Laves phase intermetallics with MgCu 2 type structure, which has similar polytetrahedral structure with short range ordered structure in undercooled melt and has lower potential barrier for nucleation than that of REFe 3,which lead to the preferential nucleation of REFe 2 phase directly from the undercooled melt. Also, the similarity of structures between REFe 2 phase and undercooled melt leads to higher crystal growth rate of REFe 2 phase than that of REFe 3.

New method to solve electromagnetic parabolic equation

This paper puts forward a new method to solve the electromagnetic parabolic equation （EMPE） by taking the vertically-layered inhomogeneous characteristics of the atmospheric refractive index into account. First, the Fourier transform and the convo- lution theorem are employed, and the second-order partial differential equation, i.e., the EMPE, in the height space is transformed into first-order constant coefficient differential equations in the frequency space. Then, by use of the lower triangular characteristics of the coefficient matrix, the numerical solutions are designed. Through constructing ana- lytical solutions to the EMPE, the feasibility of the new method is validated. Finally, the numerical solutions to the new method are compared with those of the commonly used split-step Fourier algorithm.

Electromagnetic Model and Image Reconstruction Algorithms Based on EIT System

An intuitive 2D model of circular electrical impedance tomography （EIT） sensor with small size electrodes is established based on the theory of analytic functions. The validation of the model is proved using the result from the solution of Laplace equation. Suggestions on to electrode optimization and explanation to the ill-condition property of the sensitivity matrix are provided based on the model, which takes electrode distance into account and can be generalized to the sensor with any simple connected region through a conformal transformation. Image reconstruction algorithms based on the model are implemented to show feasibility of the model using experimental data collected from the EIT system developed in Tianjin University. In the simulation with a human chestlike configuration, electrical conductivity distributions are reconstructed using equi-potential backprojection （EBP） and Tikhonov regularization （TR） based on a conformal transformation of the model. The algorithms based on the model are suitable for online image reconstruction and the reconstructed results are aood both in size and position.

Study on three dimensional electromagnetic model for permanent magnet linear synchronous motor

In this paper, with the non-salient pole permanent magnet linear synchronous motor (PMLSM)being cited, by using Fourier transform method and "slot-by-slot", "pole -by-pole" current approach, a 3D electromagnetic field model of PMLSM is established. Special attention is paid to its structure and the influence of longitudinal and transverse end effect. The distribution of electromagnetic field of PMLSM can be obtained directly and promptly by using FFT algorithm. It can also be used for the analysis of other LSM.

A three-dimensional transient electromagnetic data inversion method based on a time–frequency transformation

Herein,a three-dimensional(3D)inversion method in the frequency domain based on a time–frequency transformation was developed to improve the efficiency of the 3D inversion of transient electromagnetic(TEM)data.The Fourier transform related to the electromagnetic response in the frequency and time domains becomes a sine or cosine transform under the excitation of downward-step current.We established a transformation matrix based on the digital fi ltering calculation for the sine transform,and then the frequency domain projection of the TEM data was determined from the linear transformation system using the smoothing constrained least squares inversion method,in which only the imaginary part was used to maintain the TEM data transformation equivalence in the bidirectional projection.Thus,the time-domain TEM inversion problem was indirectly and effectively solved in the frequency domain.In the 3D inversion of the transformed frequency-domain data,the limited-memory Broyden–Fletcher–Goldfarb–Shannoquasi–Newton(L-BFGS)method was used and modifi ed with a restart strategy to adjust the regularization parameter when the algorithm tended to a local minimum.Synthetic data tests showed that our domain transformation method can stably project the TEM data into the frequency domain with very high accuracy;furthe rmore,the 3D inversion of the transformed frequency-domain data is stable,can be used to recover the real resistivity model with an acceptable effi ciency.

Invariance of the Electromagnetic Field Vectors Obtained in Course of the Lorentz Transformation Characteristic for the Relativistic Theory

The invariance of several new component electromagnetic-field vectors with respect to the Lorentz transformation has been demonstrated in the paper. The formalism of the classical relativistic mechanics has been applied in examining both the time-square variable of the field, as well as the square-values of the position coordinates of a moving particle.

WAVELET ALGORITHM FOR INTEGRAL OPERATOR EQUATION AND ITS APPLICATIONS TO ELECTROMAGNETIC PROBLEMS

A brief summary of the basic theory of wavelet is proposed. The properties of wavelet function are discussed. The possible applications of wavelet to electromagnetics are given. Examples show that the wavelet method is feasible and effective for solving electromagnetic problems.

Optimization Design of Electromagnetic Nihility Nanoparticles

Nihility material is a medium whose relative permittivity and permeability tend to zero simultaneously. In this work, comparing with the scattering properties of perfect nihility nanoparticles （made from nihility material）, we provide an optimization design of electromagnetic nihility nanoparticles, which is a coated hybrid nanosphere constituted by commutative c-negative （ENG） and μ-negative （MNG） media. Compared to a single ENG or MNG nanosphere, it is found that the total and back scattering spectra of coated hybrid nanospheres are much closer to those of perfect nihility nanospheres. Moreover, it is observed that the scattered electromagnetic field distribution of coated hybrid nanospheres is identical to that of perfect nihility nanospheres. These results indicate that the combination of commutative ENG and MNG media can constitute a composite structure which gives the closest approximation of electromagnetic scattering of perfect nihility nanospheres in a wide frequency range.

Research Progress of On-line Monitoring Technology for Electromagnetic Environment of Power Transmission and Transformation Projects

Based on the collection of relevant literature and cases,the research and application status of on-line monitoring technology for electromagnetic environment of power transmission and transformation projects at home and abroad were introduced.Moreover,the problems existing in the on-line monitoring of electromagnetic environment were expounded,and the development prospect was forecasted.

VECTOR WAVE FUNCTION EXPANSION FOR SOLVING ELECTROMAGNETIC SCATTERING BY BURIED OBJECTS

An analysis of solving the electromagnetic scattering by buried objects using vectorwave function expansion is presented.For expanding the boundary conditions both on the planarair-earth interface and on the spherical surface,the conversion relations between the cylindricaland spherical vector wave functions are derived.Hence the vector wave function expansion isconveniently applied to solve this complex boundary-value problem.For the excitation of the in-cident plane wave and the dipole above the earth,the scatterlng patterns of the buried conductingand dielectric spheres are presented and discussed.

Fast SSED-MoM /FEM Analysis for Electromagnetic Scattering of Large-Scale Periodic Dielectric Structures

A hybrid method combining simplified sub-entire domain basis function method of moment with finite element method( SSED-MoM /FEM) is accelerated for electromagnetic( EM) scattering analysis of large-scale periodic structures.The unknowns are reduced sharply with non-uniform mesh in FEM. The computational complexity of the hybrid method is dramatically declined by applying conjugate gradient-fast Fourier transform( CG-FFT) to the integral equations of both electric field and magnetic field. The efficiency is further improved by using OpenMP technique. Numerical results demonstrate that the SSED-MoM /FEM method can be accelerated for more than three thousand times with large-scale periodic structures.

The Stability of Some Viable Stars and Electromagnetic Field

We examine the impact of electromagnetic field on the stability of compact stars corresponding to embedded class one metric using the concept of cracking. For this purpose, we develop the generalized hydrostatic equi- librium equation for charged perfect fluid distribution of compact stars and perturb it by means of local density perturbation scheme to check the stability of inner matter configuration. We investigate the cracking of Her X-I, PSR 1937＋21, PSR J 1614-2230, PSR J 0348＋0432 and B.X J 1856-37. We conclude that PSR J 0348＋0432 and RX J 1856-37 exhibit cracking when charge is introduced on these astrophysical objects.

Extensions to the Finite Element Technique for the Magneto-Thermal Analysis of Aged Oil Cooled-Insulated Power Transformers

It is well known that the hot spot temperature represents the most critical parameter identifying the power rating of a transformer. This paper investigates the effect of the degradation of core magnetic properties on temperature variation of aged oil-cooled transformers. Within this work, 2D accurate assessment of time average flux density distribution in an oil insulated-cooled 25 MVA transformer has been computed using finite-element analysis taking into account ageing and stress-induced non-uniform core permeability values. Knowing the core material specific loss and winding details, local core and winding losses are converted into heat. Based upon the ambient temperature outside the transformer tank and thermal heat transfer related factors, the detailed thermal modeling and analysis have then been carried out to determine temperature distribution everywhere. Analytical details and simulation results demonstrating effects of core magnetic properties degradation on hot spot temperatures of the transformer’s components are given in the paper.

Some issues on 2.5-D transient electromagnetic forward

Numerical calculation for two integral transforms in 2.5-D transient electromagnetic forward is a difficult and key task, namely, the inverse Fourier transform and the inverse Laplace transform. Some effective algorithms for them were described. Based on the known algorithms in DC resistivity on wave-number distribution and selection, we proposed a principle on how to choose the least wave-number concerning the central-loop transient electromagnetic method. First, observe the behavior of transformation function curve with regard to wave-number in Fourier domain. In the light of its asymptote, ascertain the coverage scope of wave-number. Compared with analytic solution, the least wave-number in Fourier domain can be derived. Furthermore, the Laplace numerical inversion algorithm which needs only a few Laplace variables in pure real domain was also introduced here. The procedure was applied to forward modeling on transient electromagnetic field of a vertical magnetic dipole over uniform half-space to demonstrate them effectiveness and general applicability.

Finite Element CAD Experiments on the Effect of Magnetic Loss in Power Transformers with Laminated Cores

The paper describes a simulated experiment that focuses on the numeric computation of magnetic loss in the laminated core of a single-phase power transformer. The students’ laboratory work is part of the library of experiments of the Electrical Machines virtual laboratory and makes use of the two-dimensional open-access electromagnetic field analysis software Finite Element Method Magnetics. The idea of the simulated exercise is to demonstrate how the magnetic loss caused by time-varying excitations affects the magnetic permeability, μ, of the laminated core and the terminal quantities of the energizing winding. A parametric analysis employing different values for the electrical conductivity and maximum hysteresis-induced angle of the laminated material yields five different field problems with increasing magnetic loss. Electric circuits characterized by the (I-V) operating point and reflected impedance of the energizing winding provide the information required to compute the changes in real power ΔP, reactive power ΔQ and magnetically stored energy ΔWm between successive problems characterized by increasing magnetic loss. The concept of reflected impedance helps to explain the physical meaning of the changes in power dissipation and energy storage in the laminated core.