## Mathematical Field Computation as an Analytical Tool for Electric Machines

**Tim O’Connell with adviser Philip T. Krein**

We have continued to investigate alternative mathematical field computation methods for electric machines diverging from the well-known finite element method. In particular, Schwarz-Christoffel (SC) mapping theory has been implemented using the SC Toolbox for Matlab® to conduct electric machine simulation studies. The long-term goal of this project is to develop mathematical tools that will allow machine designers to quickly and accurately synthesize and analyze new machine designs without prematurely resorting to overly burdensome numerical methods.

Most recently, a new method for simulating induction machine rotor currents has been developed that combines SC mapping theory with electromagnetic field reconstruction techniques. Detailed static field solutions calculated using the SC Toolbox at several rotor positions are superposed in a finite difference time-domain simulation to calculate the steady-state rotor currents. Using the proposed method, one can also simulate numerous machine geometries and stator excitations, winding and slot harmonics, and torque ripple at various slips. This is the first example that we know of that uses SC mapping to simulate induced rotor currents in an induction machine. Figure 5 shows a calculated induced rotor current along with the three-phase stator source currents in a wound rotor induction machine at a slip of 0.2. The slot and winding harmonics, evident in the ripple on the waveform, can be examined in post-processing of the data.