Improved Winding Losses Calculation based on Bessel Functions

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In this article, an approach combining semi-empirical equations and the method of images is proposed for round conductor layer windings with un-gapped core. The new equation for proximity effect can convert the constant field strength from the magneto-motive force (MMF) across the core window into a frequency-dependent uniform background magnetic field strength, which can take partly the interaction between conductors into account. Geometric factors are introduced by fitting the finite element method (FEM) results to improve the accuracy. The method of images is used to calculate the field strength in order to counteract the impact of the 2-D edge effect. The new method is compared with the 2-D FEM, analytical methods, and is also validated by measurements with EE core transformers. The proposed method shows good accuracy (< 10% error) compared with 2-D FEM for both high and low porosity factor windings. Therefore, it can handle more winding configurations than other 1-D analytical methods.

Original languageEnglish
Article number6300410
Number of pages10
JournalIEEE Transactions on Magnetics
Issue number6
Publication statusPublished - 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Conductors
  • Eddy current
  • Finite element analysis
  • losses
  • Magnetic cores
  • Magnetic fields
  • Mathematical models
  • Proximity effects
  • skin effect
  • transformer winding
  • Windings

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