| This work reports on a new method of multi-phase machine modeling, one that separates the effects of the machine's magnetic structure from that of the winding configuration. A generic winding configuration is defined and the process by which one may transform to and from the generic configuration and the actual winding configuration is described. By this method, the transformations and the machine model for the generic machine may be easily derived and readily extended to a machine with any number of phases. In this thesis, the completely generalized n phase Symmetrical Component, Clarke and Park transformations are developed along with the complete harmonic model of an n phase wound-field salient synchronous machine. The full harmonic machine model yields some important results, the most notable of which are: (a) Non-negligible winding function harmonics result in magnetizing inductance in the harmonic dq reference frames. This larger inductance value can make it easier to control the low-order harmonic currents that have been so widely reported in conjunction with high phase order machines. (b) Current in the harmonic reference frames could be used to produce useful torque, provided that a matching harmonic exists in the rotor field. And (c) if saliency exists, it can result in a dynamic coupling term between adjacent harmonic dq reference frames. As a means to verify the model, a nine-phase interior permanent magnet (IPM) synchronous machine with single-slot per-pole per-phase overlapped stator windings (high spatial harmonic content) was constructed and driven by a nine-phase PWM converter. It is shown that by the proper application of the true n phase Park transformation, together with the implementation of multiple harmonic synchronous reference frame controllers, the prevalent low order harmonic currents can be successfully controlled. |
