A Schwarz-Christoffel-based analytical method for electric machine field analysis

Tim C. O'Connell, Philip T. Krein

Research output: Contribution to journalArticlepeer-review


With the recent increase in the availability and widespread use of inverters, exotic rare earth permanent-magnet materials, and low-cost, precision manufacturing, new design tools are needed to aid engineers in designing state-of-the-art electromechanical systems. For this purpose, recent software advances allow a reexamination of previously intractable analytical solutions to the boundary value problems governing these systems. This paper presents an analytical field analysis method for electric machines utilizing the Schwarz-Christoffel transformation and implemented with the SC Toolbox software package. With the method, general 2-D electric machine cross sections with linear magnetic materials are analyzed. The method is then extended using superposition to analyze wound-rotor induction machines in the time domain. With this extension, numerous machine geometries, stator excitations, winding and slot harmonics, and torque ripple can be examined.

Original languageEnglish (US)
Pages (from-to)565-577
Number of pages13
JournalIEEE Transactions on Energy Conversion
Issue number3
StatePublished - 2009


  • Analytical model
  • Conformal mapping
  • Electric machines
  • Field reconstruction (FR)
  • Induction machines (IMs)
  • SCToolbox
  • Schwarz-Christoffel (S-C) mapping
  • Slotted structure

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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