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The Cauer ladder network (CLN) model order reduction (MOR) method is applied to an industrial inductor. This paper aims to to anaylse the influence of different meshes on the CLN method and their parameters.

The industrial inductor is simulated with the CLN method for different meshes. Meshes considering skin effect are compared with equidistant meshes. The inductor is also simulated with the eddy current finite element method (ECFEM) for frequencies 1 kHz to 1 MHz. The solution of the CLN method is compared with the ECFEM solutions for the current density in the conductor and the total impedance.

The increase of resistance resulting from the skin effect can be modelled with the CLN method, using a uniform mesh with elements much larger than the skin depth. Meshes taking account of the skin depth are only needed if the electromagnetic fields have to be reconstructed. Additionally, the convergence of the impedance is used to define a stopping criterion without the need for a benchmark solution.

The work shows that the CLN method can generate a network, which is capable of mimicking the increase of resistance usually accompanied by the skin effect without using a mesh that takes the skin depth into account. In addition, the proposed stopping criterion makes it possible to use the CLN method as an a priori MOR technique.

The convergence of the transfinite‐element (TFE) method for high frequency methods is analyzed in this paper. Two different potential formulations will be compared in the frequency and time domain.

The A*‐and A,v‐formulation for time domain and frequency domain transfinite elements are described. The convergence properties of the methods are investigated and demonstrated on a simple test problem.

It is shown that the convergence of the frequency domain method depends also on the discretization of areas where the field values do not change very much. A numerical example shows that for the calculation of the whole frequency range, the time domain approach is much more faster than the frequency domain method.

Further, work should also cover additional formulations like, e.g. the T,Φ‐formulation.

Pros and cons of different formulations and methods for solving high frequency problems for printed circuit boards or microwave structures are investigated.

The originality of the paper is the comparison, the discussion and the explanations of the convergence of the TFE method for wave propagation.

The purpose of this paper is to introduce a new method to model a stranded wire efficiently in 3D finite element simulations.

In this method, the stranded wires are numerically approximated with the Cauer ladder network (CLN) model order reduction method in 2D. This approximates the eddy current effect such as the skin and proximity effect for the whole wire. This is then projected to a mesh which does not include each strand. The 3D fields are efficiently calculated with the CLN method and are projected in the 3D geometry to be used in simulations of electrical components with a current vector potential and a homogenized conductivity at each time step.

In applications where the stranded wire geometry is known and does not change, this homogenization approach is an efficient and accurate method, which can be used with any stranded wire configuration, homogenized stranded wire mesh and any input signal dependent on time steps or frequencies.

In comparison to other methods, this method has no direct frequency dependency, which makes the method usable in the time domain for an arbitrary input signal. The CLN can also be used to interconnected stranded cables arbitrarily in electrical components.

The purpose of this paper is to describe a method for solving eddy current problems. Discontinuous basis functions are applied to conducting regions in eddy‐current problems. This results in a block‐diagonal mass matrix allowing explicit time stepping without having to solve large algebraic systems.

The effect of the basis functions in the conducting region is limited to the respective finite element. This yields to a block‐diagonal mass matrix, whereas each block in this matrix belongs to one finite element. In the nonconducting region, traditional finite elements are used which leads to well‐conditioned system matrices. For the two regions, different time steps are used.

To avoid instability, a term which penalizes the tangential jump of the magnetic vector potential A has to be added. A value for weighting this term is suggested and tested on a simple two dimensional example.

The proposed method leads to a potentially fast method for solving eddy‐current problems.

Different solution methods, using finite element method in continuous and discrete frequency domain, are compared with each other in order to find the most appropriate method for the estimation of steady state vibrations in linear structural and mechanical problems. The purpose of this paper is to describe the procedures.

The continuous and some relevant discrete frequency domain solution methods are compared by an analytical investigation as well as by the numerical examination of a simple model. Finally, results for a more relevant example using finite elements are presented.

It is shown that the steady state computation using the continuous frequency domain system description delivers the exact solution for a given system.

Based on the presented results, the use of continuous frequency domain system description is recommendable in most cases.

The purpose of this paper is to approximate the convective heat transfer using a few non-dimensional parameters in the design process of large synchronous machines. The computed convective wall heat transfer coefficient can be used in circuit models or can be defined in numerical heat conduction (HC) models to compute the thermal field in the solid domains without the time consuming computation of the fluid domain.

Computational fluid dynamics (CFD) has been used to include a wide range of different designs, operating conditions and cooling schemes to ensure accurate results for a wide range of possible machines. Neural networks are used to correlate the computed heat transfer coefficients to various design parameters. The data set needed to define the weights and bias layers in the network has been obtained by several CFD simulations. A comparison of the evaluated solid temperatures with those obtained using the conjugate heat transfer (CHT) method has been carried out. The results have also been validated with calorimetric measurements.

The validation of the HC model has shown that this model is capable of yielding accurate results in a few minutes, in contrast to the several hours needed by the CHT solution. The workflow to determine the convective heat transfer in a specific part of an electrical machine has been also been established. The approximation of the convective wall heat transfer coefficient is shown to be obtainable in sufficient detail by using a neural network.

The paper describes a method to approximate the convective heat transfer accurately in a few seconds, which is very useful in the design process. The heat convection can then be characterized in a HC model including the solid domains only. The losses can be defined as sources in the solid domains, e.g. copper and iron, obtained by electromagnetic calculations and the thermal field can hence be easily computed in these parts. This HC model has the main advantage that the time consuming computation of the fluid domain is avoided.

The novelty in this work is the approximation of the convective heat transfer by using a neural network with an accuracy of less than 5 percent as well as the development of a HC model to compute the temperature in the solid domains. The investigations presented pinpoint relevant issues influencing the thermal behavior of electrical machines.

The aim of the present work is to find an efficient solution concerning the computational effort of quasi‐static electric field (QSEF) problems involving anisotropic conductivity and permittivity in the frequency domain.

Numerical simulations are carried out with tetrahedral nodal finite elements of first‐ and second‐order and with Withney elements. The solution of the boundary value problem with the aid of the electric scalar potential approximated by nodal finite elements is compared with those by the electric current vector potential represented by edge finite elements.

The simulation with an electric current vector potential approximated by the edge elements of first‐order prevail over that by the electric scalar potential approximated by nodal elements of second‐order concerning the memory requirements and the computation time at comparable accuracy.

The application of edge finite elements to solve QSEF problems considering an anisotropic complex conductivity in 3D.

This paper presents a summary of results for the TEAM workshop problem 14. Thirteen results are given and seven computer codes applied.

A transformer model is used as a benchmark for testing various methods to solve 3D nonlinear periodic eddy current problems. This paper aims to set up a nonlinear magnetic circuit problem to assess the solving procedure of the nonlinear equation system for determining the influence of various special techniques on the convergence of nonlinear iterations and hence the computational time.

Using the T,ϕ-ϕ formulation and the harmonic balance fixed-point approach, two techniques are investigated: the so-called “separate method” and the “combined method” for solving the equation system. When using the finite element method (FEM), the elapsed time for solving a problem is dominated by the conjugate gradient (CG) iteration process. The motivation for treating the equations of the voltage excitations separately from the rest of the equation system is to achieve a better-conditioned matrix system to determine the field quantities and hence a faster convergence of the CG process.

In fact, both methods are suitable for nonlinear computation, and for comparing the final results, the methods are equally good. Applying the combined method, the number of iterations to be executed to achieve a meaningful result is considerably less than using the separated method.

To facilitate a quick analysis, a simplified magnetic circuit model of the 3D problem was generated to assess how the different ways of solutions will affect the full 3D solving process. This investigation of a simple magnetic circuit problem to evaluate the benefits of computational methods provides the basis for considering this formulation in a 3D-FEM code for further investigation.

To circumvent the high computational costs of modelling each lamination to compute the eddy current distribution in three dimensions in conducting laminations, a simple method has been developed. The laminar nature of the eddy currents due to the magnetic leakage field has been considered by applying an anisotropic conductivity with zero or very low value in the direction normal to the laminations. This yields an overall field distribution serving as basis. In a second step, the much smaller eddy current loops caused by the main magnetic flux parallel to the laminations have been taken into consideration by a one‐dimensional analytical model. Nonlinearity is neglected.