Electric machinery parameters and torques by current and energy perturbations from field computations - Part I: Theory and formulation

In this first of a two-part companion papers the well-established energy/cu rrent (E/C) perturbation method of computation of machine winding inductanc es is reviewed. The method's efficacy in machine performance calculations i s delineated and verified in a companion paper by comparison to experimenta l results. The critical role that winding inductance parameters have in mod eling and simulation of the nonsinusoidal steady state time-domain (forced response) performance of electric machinery is demonstrated using state mod els in both the winding flux linkage and current-based frames of reference. The computed machine performance characteristics include profiles of windi ng inductances, induced terminal voltage waveforms, and instantaneous torqu e profiles that contain all the ripples due to the significant space harmon ics 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 fiel d solutions involving substantial degrees of saturation and complexity of c onstruction. The machines analyzed in the comparison paper include a 15-hp permanent magnet brushless de motor, a 1.2-hp three-phase induction motor, and a 14.3 kVA three-phase modified Lundell alternator possessing very comp lex magnetic circuit geometries. The well-posedness of the method held true for all these cases, as well as many other case-studies briefly reviewed h ere.