3D harmonic modeling of eddy currents in segmented conducting structures

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Purpose: The purpose of this paper is to describe a semi-analytical modeling technique to predict eddy currents in three-dimensional (3D) conducting structures with finite dimensions. Using the developed method, power losses and parasitic forces that result from eddy current distributions can be computed. Design/methodology/approach: In conducting regions, the Fourier-based solutions are developed to include a spatially dependent conductivity in the expressions of electromagnetic quantities. To validate the method, it is applied to an electromagnetic configuration and the results are compared to finite element results. Findings: The method shows good agreement with the finite element method for a large range of frequencies. The convergence of the presented model is analyzed. Research limitations/implications: Because of the Fourier series basis of the solution, the results depend on the considered number of harmonics. When conducting structures are small with respect to the spatial period, the number of harmonics has to be relatively large. Practical implications: Because of the general form of the solutions, the technique can be applied to a wide range of electromagnetic configurations to predict, e.g. eddy current losses in magnets or wireless energy transfer systems. By adaptation of the conductivity function in conducting regions, eddy current distributions in structures containing holes or slit patterns can be obtained. Originality/value: With the presented technique, eddy currents in conducting structures of finite dimensions can be modeled. The semi-analytical model is for a relatively low number of harmonics computationally faster than 3D finite element methods. The method has been validated and shown to be computationally accurate.

Original languageEnglish
Pages (from-to)2-23
Number of pages22
JournalCOMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
Issue number1
Publication statusPublished - 7 Jan 2019


  • Eddy currents
  • Fourier
  • Magnetic fields
  • Modelling
  • Semi-analytical


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