A Schwarz–Christoffel-Based Analytical Method for Electric Machine Field Analysis

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.