An Overview of Methods and a New Three-Dimensional FEA and Analytical Hybrid Technique for Calculating AC Winding Losses in PM Machines

Narges Taran, Dan M. Ionel, Vandana Rallabandi, Greg Heins, Dean Patterson

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


This article proposes a new hybrid analytical and numerical finite element (FE) based method for calculating ac eddy current losses in wire windings and demonstrates its applicability for axial flux permanent magnet electric machines. The method takes into account three-dimensional (3-D) field effects in order to achieve accurate results and yet greatly reduce computational efforts. The new 3-D FE-based method is advantageous as it employs minimum simplifications and considers the end turns in the eddy current path, the magnetic flux density variation along the effective length of coils, and the field fringing and leakage, which ultimately increases the accuracy of simulations. This study is one of the first ones to compare meticulous 3-D finite element analysis (FEA) models with more approximate, but faster solution methods, which can be employed in the optimization process. The accuracy of the 3-D FEA calculations has been confirmed through tests on a prototype axial flux permanent magnet machine. The proposed method is applicable for cases with majority of ac copper losses induced due to external magnetic flux sources, such as permanent magnets. Examples of such machines designs are coreless or open slot PM machines with conductors sizes smaller than skin depth.

Original languageEnglish
Article number9242250
Pages (from-to)352-362
Number of pages11
JournalIEEE Transactions on Industry Applications
Issue number1
StatePublished - Jan 1 2021

Bibliographical note

Funding Information:
Manuscript received June 13, 2020; revised August 25, 2020 and October 4, 2020; accepted October 20, 2020. Date of publication October 28, 2020; date of current version December 31, 2020. This work was supported by the National Science Foundation under Grant #1809876. Paper 2020-EMC-0843.R2, presented at the 2019 IEEE International Electric Machines and Drives Conference, San Diego, CA, USA, May 12–15, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Electric Machines Committee of the IEEE Industry Applications Society. (Corresponding author: Narges Taran.) Narges Taran was with the SPARK Laboratory, Department of Electrical and Computer Engineering, University of Kentucky, Lexington, KY 40506 USA. She is now with the BorgWarner Inc., Noblesville Technical Center, Noblesville, IN 46060 USA (e-mail:

Funding Information:
The support of National Science Foundation NSF Grant #1809876, of University of Kentucky, the L. Stanley Pigman endowment, and of ANSYS Inc. is gratefully acknowledged.

Publisher Copyright:
© 1972-2012 IEEE.


  • AC winding loss
  • PM machine
  • axial flux motor
  • eddy current loss
  • finite element (FE)
  • three-dimensional (3-D) model

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering


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