Induction machine model with space harmonics for fault diagnosis based on the convolution theorem

Abstract

Fault diagnosis of induction machines (IMs) requires a fast model of the machine, for adjusting fault thresholds in data-driven diagnostic methods, for computing the residuals in model-driven diagnostic systems, or for training autonomous expert systems. Due to the interaction between time and space harmonics under faulty conditions, this model must simulate very accurately the space harmonics of the air gap magnetomotive force (MMF) generated by the machine’s windings. But the computation of the phases’ inductances, taking into account the spatial harmonics of the MMF, for every angular position of the rotor, and under non-symmetrical, faulty conditions, is a time-consuming task in IMs’ models. In this paper, a very fast method for obtaining the inductances of rotating electrical machines is proposed, based on a single discrete circular convolution. With the proposed approach, the mutual inductances of two phases, taking into account the spatial harmonics of the air gap MMF, are calculated for every relative angular position using a single equation, solved with the fast Fourier transform (FFT). Asymmetrical winding distributions, and the linear rise of the air gap MMF across skewed slots are easily modeled without increasing the computation time. The proposed method is introduced theoretically and validated with an experimental test-bed using commercial induction motors with forced broken bars faults.