# Spectral element method modeling of eddy current losses in high-frequency transformers

### Uittreksel

This paper concerns the modeling of eddy current losses in conductive materials in the vicinity of a high-frequency transformer; more specifically, in two-dimensional problems where a high ratio between the object dimensions and the skin-depth exists. The analysis is performed using the Spectral Element Method (SEM), where high order Legendre–Gauss–Lobatto polynomials are applied to increase the accuracy of the results with respect to the Finite Element Method (FEM). A convergence analysis is performed on a two-dimensional benchmark system, for both the SEM and FEM. The benchmark system consists of a high-frequency transformer confined by a conductive cylinder and is free of complex geometrical shapes. Two different objectives are investigated. First, the discretizations at which the relative error with respect to a reference solution is minimized are compared. Second, the discretizations at which the trade-off between computational effort and accuracy is optimized are compared. The results indicated that by applying the SEM to the two-dimensional benchmark system, a higher accuracy per degree of freedom and significantly lower computation time are obtained with respect to the FEM. Therefore, the SEM is proven to be particularly useful for this type of problem.
Originele taal-2 Engels 28 13 Mathematical and Computational Applications 24 1 https://doi.org/10.3390/mca24010028 Gepubliceerd - 21 feb 2019

### Vingerafdruk

High frequency transformers
Spectral Element Method
Eddy Currents
Transformer
Eddy currents
Finite element method
Finite Element Method
Benchmark
Modeling
Conductive materials
Discretization
Skin
Relative Error
Convergence Analysis
Polynomials
High Accuracy
Degree of freedom
Higher Order
Polynomial

### Citeer dit

@article{5fd815af181149fbb68331f0d378371f,
title = "Spectral element method modeling of eddy current losses in high-frequency transformers",
abstract = "This paper concerns the modeling of eddy current losses in conductive materials in the vicinity of a high-frequency transformer; more specifically, in two-dimensional problems where a high ratio between the object dimensions and the skin-depth exists. The analysis is performed using the Spectral Element Method (SEM), where high order Legendre–Gauss–Lobatto polynomials are applied to increase the accuracy of the results with respect to the Finite Element Method (FEM). A convergence analysis is performed on a two-dimensional benchmark system, for both the SEM and FEM. The benchmark system consists of a high-frequency transformer confined by a conductive cylinder and is free of complex geometrical shapes. Two different objectives are investigated. First, the discretizations at which the relative error with respect to a reference solution is minimized are compared. Second, the discretizations at which the trade-off between computational effort and accuracy is optimized are compared. The results indicated that by applying the SEM to the two-dimensional benchmark system, a higher accuracy per degree of freedom and significantly lower computation time are obtained with respect to the FEM. Therefore, the SEM is proven to be particularly useful for this type of problem.",
keywords = "Pareto analysis, eddy currents, finite element analysis, inductive power transmission, numerical models, spectral element method",
author = "Koen Bastiaens and Mitrofan Curti and Dave Krop and Sultan Jumayev and Elena Lomonova",
year = "2019",
month = "2",
day = "21",
doi = "10.3390/mca24010028",
language = "English",
volume = "24",
journal = "Mathematical and Computational Applications",
issn = "1300-686X",
publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",
number = "1",

}

In: Mathematical and Computational Applications, Vol. 24, Nr. 1, 28, 21.02.2019.

TY - JOUR

T1 - Spectral element method modeling of eddy current losses in high-frequency transformers

AU - Bastiaens, Koen

AU - Curti, Mitrofan

AU - Krop, Dave

AU - Jumayev, Sultan

AU - Lomonova, Elena

PY - 2019/2/21

Y1 - 2019/2/21

N2 - This paper concerns the modeling of eddy current losses in conductive materials in the vicinity of a high-frequency transformer; more specifically, in two-dimensional problems where a high ratio between the object dimensions and the skin-depth exists. The analysis is performed using the Spectral Element Method (SEM), where high order Legendre–Gauss–Lobatto polynomials are applied to increase the accuracy of the results with respect to the Finite Element Method (FEM). A convergence analysis is performed on a two-dimensional benchmark system, for both the SEM and FEM. The benchmark system consists of a high-frequency transformer confined by a conductive cylinder and is free of complex geometrical shapes. Two different objectives are investigated. First, the discretizations at which the relative error with respect to a reference solution is minimized are compared. Second, the discretizations at which the trade-off between computational effort and accuracy is optimized are compared. The results indicated that by applying the SEM to the two-dimensional benchmark system, a higher accuracy per degree of freedom and significantly lower computation time are obtained with respect to the FEM. Therefore, the SEM is proven to be particularly useful for this type of problem.

AB - This paper concerns the modeling of eddy current losses in conductive materials in the vicinity of a high-frequency transformer; more specifically, in two-dimensional problems where a high ratio between the object dimensions and the skin-depth exists. The analysis is performed using the Spectral Element Method (SEM), where high order Legendre–Gauss–Lobatto polynomials are applied to increase the accuracy of the results with respect to the Finite Element Method (FEM). A convergence analysis is performed on a two-dimensional benchmark system, for both the SEM and FEM. The benchmark system consists of a high-frequency transformer confined by a conductive cylinder and is free of complex geometrical shapes. Two different objectives are investigated. First, the discretizations at which the relative error with respect to a reference solution is minimized are compared. Second, the discretizations at which the trade-off between computational effort and accuracy is optimized are compared. The results indicated that by applying the SEM to the two-dimensional benchmark system, a higher accuracy per degree of freedom and significantly lower computation time are obtained with respect to the FEM. Therefore, the SEM is proven to be particularly useful for this type of problem.

KW - Pareto analysis

KW - eddy currents

KW - finite element analysis

KW - inductive power transmission

KW - numerical models

KW - spectral element method

U2 - 10.3390/mca24010028

DO - 10.3390/mca24010028

M3 - Article

VL - 24

JO - Mathematical and Computational Applications

JF - Mathematical and Computational Applications

SN - 1300-686X

IS - 1

M1 - 28

ER -