Accounting for Magnetic Saturation Effects in Complex Multi-harmonic Model of Induction Machine

Computations of quasi-dynamic electromagnetic field of induction machines using the complex magnetic vector potential require the use of the so-called effective magnetization curves, i.e., such in which the magnetic permeability is proportional to the amplitudes of magnetic flux density B or magnetic field strength H , not their instantaneous values. There are several definitions of that parameter mentioned in the literature provided for the case when B or H are monoharmonic. In this paper, seven different methods of determining the effective magnetization curves are compared in relation to the use of a field-circuit multi-harmonic model of an induction machine. The accuracy of each method was assessed by computing the performance characteristics of a solid-rotor induction machine. One new definition of the effective permeability was also introduced, being a function of multiple variables dependent on amplitudes of all the harmonics considered. The analyses demonstrated that the best practical approach, even for the multi-harmonic case, is to express the effective magnetic permeability as the ratio of the amplitudes of the fundamental harmonics of the magnetic flux density and the magnetic field strength, and assuming the sinusoidal variation of the latter.