# Mathematical Modelling of Three Phase Squirrel Cage Induction Motor and Related Signal Processing for Fault Diagnostics

Tutkimustuotos: Doctoral ThesisCollection of Articles

## Abstrakti

This thesis aims to study different analytical methods to model a squirrel cage induction motor, which should have minimal simulation time than the corresponding finite element method (FEM) based models. The purpose of doing so is to develop a model suitable to simulate all major faults and be used for advanced model-dependent fault diagnostic algorithms, such as parameters estimation and inverse problem theory. This thesis’s second key objective is to study various signal-processing techniques for their pros and cons to detect fault at the embryonic stage and investigate the entire current harmonic spectrum of induction motors both in transient and steady-state regions. Thus, the motor under healthy and broken rotor bar (BRB) conditions are simulated, and experimental measurements are investigated for validation. The dynamic d-q model with the inclusion of non-linear magnetization inductance was considered as a starting point. This model helps understand the machine's basic concepts because of its comprehensiveness and ability to produce compact equations, which can be used for drives as general and in observers and state estimators as particular. However, this model was found to be less suitable to simulate machine faults because of the considered approximations. To address the d-q model limitations, the winding function analysis (WFA) based model was prepared. In this model, the analytical equations to calculate various inductances, resistances, currents, fluxes, torque, and speed are derived for the motor under investigation. These equations were simulated in MATLAB, giving results near to the practical measurements. The model is suitable for implementing some faults, such as BRB and broken end rings. Still, the consideration of constant air gap makes it less ideal for the implementation of eccentricity and saturation-related faults. Moreover, the spatial harmonics, which are very important for fault diagnostics and sensor-less speed estimation, cannot be simulated. Those approximations can be reduced with Fourier summation of higher-order harmonics (winding) and Taylor series to include inverse air gap functions but at the cost of the self-defined number and amplitude of harmonics. To get more realistic results, the modified winding function analysis (MWFA) based model was prepared to ensure that all winding functions and air gap were defined as a function of stator and rotor individual and respective angles. The geometry of stator and rotor slots is considered to calculate the leakage inductances and various resistances. The self and mutual inductances between rotor and stator are computed with a stepping rotor. The results at each rotor position are saved in offline 3D lookup tables. During the online simulation, all pre-saved matrices are used as a rotor position function using the irindex value, and the performance parameters, such as currents, fluxes, torque, and speed, are calculated. The FEM and hybrid FEM-analytical models of the machine under investigation are prepared using commercial software to validate the results. The comparison of results shows an excellent agreement with a minimal simulation time and least ill-posedness for the proposed model compared to the corresponding FEM model. Both analytical and hybrid FEM-analytical models are divided into online, offline portions and compatible for the solution on cluster computation. Their division in the online and offline portions reduces the complexity and gives the model the freedom to simulate faults in the online portion without doing unnecessary offline calculations again. Moreover, the compatibility with cluster computation is excellent for exploiting distributed computational resources such as cloud computation, an integral part of industry 4.0 standards. Towards the signal processing side, the fast Fourier transform (FFT) and wavelet transform (WT) are used extensively to study the steady-state and transient regime signals. The infinite impulse response (IIR) based digital filters are used to improve the motor’s current spectrum’s legibility. In this way, the total harmonics are segregated according to their cause of production. Moreover, the spectrum of current simulated from the proposed model is compared with that simulated using the FEM model and the test rig measurements. The comparison is made until a wide bandwidth of frequencies for further validation of the proposed model. Moreover, the WFA based model is also investigated during the transient regime by doing the time-frequency analysis of the stator current. The recovered non-stationary signal’s pattern is in good agreement with the one obtained from the practical measurements. The specific fault-related pattern during the transient interval can further enhance the model’s effectiveness.
Julkaisun otsikon käännös Mathematical Modelling of Three Phase Squirrel Cage Induction Motor and Related Signal Processing for Fault Diagnostics Englanti Tohtorintutkinto Aalto-yliopisto Vaimann, Toomas, VastuuprofessoriBelahcen, Anouar, VastuuprofessoriKallaste, Ants, VastuuprofessoriKallaste, Ants, Ohjaaja Aalto University 978-952-64-0427-1, 978-9949-83-726-7 978-952-64-0428-8, 978-9949-83-727-4 Julkaistu - 2021 G5 Tohtorinväitöskirja (artikkeli)

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