Electric machinery parameters and torques by current and energy perturbations from field computations. I. Theory and formulation

In this first of a two-part article, the well-established energy/current (E/C) perturbation method of computation of machine winding inductances is reviewed. The method's efficacy in machine performance calculations is delineated and verified in a companion paper by comparison to experimental results. The critical role that winding inductance parameters have in modeling and simulation of the nonsinusoidal steady state time-domain (forced response) performance of electric machinery is demonstrated using state models in both the winding flux linkage and current-based frames of reference. The computed machine performance characteristics include profiles of winding inductances, induced terminal voltage waveforms, and instantaneous torque profiles that contain all the ripples due to the significant space harmonics in a machine. The method and associated formulations and techniques are shown to be very effective in both 2D-FE and 3D-FE electric machinery field solutions involving substantial degrees of saturation and complexity of construction. The machines analyzed in the comparison paper include a 15-HP permanent magnet brushless DC motor, a 1.2-HP three-phase induction motor, and a 14.3 kVA three-phase modified Lundell alternator possessing very complex magnetic circuit geometries. The well-posedness of the method held true for all these cases, as well as many other case-studies briefly reviewed here.