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.
Highlights
Wireless Power Transfer (WPT) by means of an inductive coupling is widely applied in applications where physical electrical contact is problematic or undesirable, for example in aerospace, biomedical, and robotics applications [1]
As a result of the Finite Element Method (FEM) solution having the highest number of d.o.f. being the reference, the FEM was able to converge to zero; whereas, the Spectral Element Method (SEM) converged to a relative error with respect to the reference, approaching zero, while reducing the required number of d.o.f. and computation time by 76.5% and 75.1%, respectively
The SEM has been applied for the modeling of eddy currents in conductive materials in the vicinity of a high-frequency transformer
Summary
Wireless Power Transfer (WPT) by means of an inductive coupling is widely applied in applications where physical electrical contact is problematic or undesirable, for example in aerospace, biomedical, and robotics applications [1]. In various research areas, such as computational seismology, nanodevice applications, and waveguide analysis, the SEM has been successfully implemented and applied to three-dimensional problems [12,20,21]. It is demonstrated that by applying the SEM to a benchmark system, a higher accuracy per degree of freedom (d.o.f.) is obtained, which results in a significant reduction of the computational effort as compared to the FEM. These features prove to be useful for efficient and accurate solving of eddy current loss problems with high ratios between the object dimensions and skin-depth. The formulation of the method, as well as the implementation of the specific transformer model are discussed and analyzed
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