Computationally efficient strand eddy current loss calculation in electric machines

Alireza Fatemi, Dan M. Ionel, Nabeel A.O. Demerdash, Dave A. Staton, Rafal Wrobel, Yew Chuan Chong

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


A fast finite element (FE) based method for the calculation of eddy current losses in the stator windings of randomly wound electric machines is presented in this paper. The method is particularly suitable for implementation in large-scale design optimization algorithms where a qualitative characterization of such losses at higher speeds is most beneficial for identification of the design solutions that exhibit the lowest overall losses including the ac losses in the stator windings. Unlike the common practice of assuming a constant slot fill factor $s-f$ for all the design variations, the maximum $s-f$ in the developed method is determined based on the individual slot structure/dimensions and strand wire specifications. Furthermore, in lieu of detailed modeling of the conductor strands in the initial FE model, which significantly adds to the complexity of the problem, an alternative rectangular coil modeling subject to a subsequent flux mapping technique for determination of the impinging flux on each individual strand is pursued. Rather than pursuing the precise estimation of ac conductor losses, the research focus of this paper is placed on the development of a computationally efficient technique for the derivation of strand eddy current losses applicable in design optimization, especially where both the electromagnetic and thermal machine behavior are accounted for. A fractional-slot concentrated winding permanent magnet synchronous machine is used for the purpose of this study due to the higher slot leakage flux and slot opening fringing flux of such machines, which are the major contributors to strand eddy current losses in the windings. The analysis is supplemented with an investigation on the influence of the electrical loading on ac winding loss effects for this machine design, a subject that has received less attention in the literature. Experimental ac loss measurements on a 12-slot 10-pole stator assembly will be discussed to verify the existing trends in the simulation results.

Original languageEnglish
Article number8662678
Pages (from-to)3479-3489
Number of pages11
JournalIEEE Transactions on Industry Applications
Issue number4
StatePublished - Jul 1 2019

Bibliographical note

Funding Information:
Manuscript received September 16, 2018; revised December 10, 2018; accepted February 11, 2019. Date of publication March 7, 2019; date of current version June 29, 2019. Paper 2018-EMC-0920.R1, presented at the 2016 IEEE Energy Conversion Congress and Exposition, Milwaukee, WI, USA, Sep. 18– 22, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Electric Machines Committee of the IEEE Industry Applications Society. This work was supported in part by the Simulation of Electrical Machines, Power Electronics and Electrical Drives Consortium and in part by the Mid-West Energy Research Consortium. (Corresponding author: Alireza Fatemi.) A. Fatemi is with the Global Research and Development Department, Warren Technical Center, General Motors Company, Warren, MI 48090 USA (e-mail:,

Publisher Copyright:
© 2019 IEEE.


  • AC copper loss
  • design optimization
  • eddy current loss
  • finite element (FE) method
  • high-speed permanent magnet (PM) machines
  • loss measurement

ASJC Scopus subject areas

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


Dive into the research topics of 'Computationally efficient strand eddy current loss calculation in electric machines'. Together they form a unique fingerprint.

Cite this