Analytical derivation of induction motors inductances under eccentricity conditions

Abstract

Geometrical modeling of induction machines under eccentricity conditions involves a signi-cant number of self and mutual inductances. These inductances are functions of rotor angular position, and calculating them at each time step requires solving computationally-intensive de-nite integrals. Conventional techniques use numerical look-up tables, or employ approximated analytical expressions such as limited-term Fourier series expression of turn functions. The former approach needs large memory volume given the size of inductance matrix. Moreover, numerical interpolations are needed upon model execution, which signi-cantly slows down the simulation. The later technique is computationally tasking for a large set of Fourier series terms, or lacks su±cient accuracy if only a few terms are used. Alternatively, computationally e±cient closed-form solutions for self- and mutual- inductance expressions are presented here. The step variations of turn functions are considered which streamlines the model formulation. The experimental results validate the proposed model. In particular, the frequency spectrum of the stator current illustrates the ability of proposed technique to detect eccentricity.