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

Abstract

This thesis aims to study different analytical methods to model a squirrel cage inductionmotor, which should have minimal simulation time than the corresponding finiteelement method (FEM) based models. The purpose of doing so is to develop a modelsuitable to simulate all major faults and be used for advanced model-dependent faultdiagnostic algorithms, such as parameters estimation and inverse problem theory. Thisthesis’s second key objective is to study various signal-processing techniques for theirpros and cons to detect fault at the embryonic stage and investigate the entire currentharmonic spectrum of induction motors both in transient and steady-state regions. Thus,the motor under healthy and broken rotor bar (BRB) conditions are simulated, andexperimental measurements are investigated for validation. The dynamic d-q model with the inclusion of non-linear magnetization inductance wasconsidered as a starting point. This model helps understand the machine's basic conceptsbecause of its comprehensiveness and ability to produce compact equations, which canbe 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 ofthe considered approximations. To address the d-q model limitations, the winding function analysis (WFA) basedmodel was prepared. In this model, the analytical equations to calculate variousinductances, resistances, currents, fluxes, torque, and speed are derived for the motorunder investigation. These equations were simulated in MATLAB, giving results near tothe practical measurements. The model is suitable for implementing some faults, suchas BRB and broken end rings. Still, the consideration of constant air gap makes it lessideal for the implementation of eccentricity and saturation-related faults. Moreover, thespatial harmonics, which are very important for fault diagnostics and sensor-less speedestimation, cannot be simulated. Those approximations can be reduced with Fouriersummation of higher-order harmonics (winding) and Taylor series to include inverse airgap 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) basedmodel was prepared to ensure that all winding functions and air gap were defined as afunction of stator and rotor individual and respective angles. The geometry of stator androtor slots is considered to calculate the leakage inductances and various resistances.The self and mutual inductances between rotor and stator are computed with a steppingrotor. The results at each rotor position are saved in offline 3D lookup tables. During theonline simulation, all pre-saved matrices are used as a rotor position function using theirindex value, and the performance parameters, such as currents, fluxes, torque, andspeed, are calculated. The FEM and hybrid FEM-analytical models of the machineunder investigation are prepared using commercial software to validate the results.The comparison of results shows an excellent agreement with a minimal simulation timeand least ill-posedness for the proposed model compared to the corresponding FEMmodel. Both analytical and hybrid FEM-analytical models are divided into online, offlineportions 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 exploitingdistributed computational resources such as cloud computation, an integral part ofindustry 4.0 standards. Towards the signal processing side, the fast Fourier transform (FFT) and wavelettransform (WT) are used extensively to study the steady-state and transient regimesignals. The infinite impulse response (IIR) based digital filters are used to improve themotor’s current spectrum’s legibility. In this way, the total harmonics are segregatedaccording to their cause of production. Moreover, the spectrum of current simulatedfrom the proposed model is compared with that simulated using the FEM model and thetest rig measurements. The comparison is made until a wide bandwidth of frequenciesfor further validation of the proposed model. Moreover, the WFA based model is also investigated during the transient regime bydoing the time-frequency analysis of the stator current. The recovered non-stationarysignal’s pattern is in good agreement with the one obtained from the practicalmeasurements. The specific fault-related pattern during the transient interval canfurther enhance the model’s effectiveness.