Detection of Stator Short Circuits in VSI-Fed Brushless ... - IEEE Xplore

IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 1, MARCH 2006

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Detection of Stator Short Circuits in VSI-Fed Brushless DC Motors Using Wavelet Transform Mohamed A. Awadallah, Student Member, IEEE, Medhat M. Morcos, Senior Member, IEEE, Suresh Gopalakrishnan, Senior Member, IEEE, and Thomas W. Nehl, Fellow, IEEE

Abstract—The paper presents methodologies to detect and locate short-circuit faults on the stator winding of VSI-fed PM brushless dc motors. Normal performance characteristics of the motor are obtained through a discrete-time lumped-parameter network model. The model is modified to accommodate shortcircuit faults in order to simulate faulty operation. Fault signatures are extracted from the waveforms of electromagnetic torque and phase-voltage summation using wavelet transform. Three independent detection techniques are introduced. Experimental measurements agree acceptably with simulation results, and validate the proposed methods. This work sets forth the fundamentals of an automatic fault detector and locator, which can be used in a fault-tolerant drive. Index Terms—Brushless dc motor, fault detection, wavelet transform.

I. INTRODUCTION

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AULT detection in electric motors and drive systems is a topic that has recently acquired intensified attention. Correct diagnosis, precise location, and early detection of incipient faults help avoid harmful, sometimes devastative, consequences on the system under consideration. On-line condition monitoring and diagnostics could automatically set up repair plans and time frame. Also, machine downtime for unscheduled maintenance could be minimized, which reflects in less cost and enhanced reliability of the industrial process. Winding short circuits represent a very subtle fault that normally starts as insulation failure and localized excessive heat. The fault then develops into a short circuit isolating one or more turns of the winding. Several performance anomalies result due to such faults including, but not limited to, increased circulating currents and losses and lower average torque. Earlier researchers used search coils to monitor changes of the axial flux component due to inter-turn faults in three-phase motors [1]. A location algorithm was developed to identify the shorted coil during no-load operation of the motor. A single-

Manuscript received January 21, 2004; revised September 15, 2004. Paper no. TEC-00006-2004. M. A. Awadallah is with the Department of Electric Power and Machines, University of Zagazig, Zagazig 44111, Egypt (e-mail: awadallah35@ yahoo.com). M. M. Morcos is with the Department of Electrical and Computer Engineering, Kansas State University, Manhattan, KS 66506 USA (e-mail: morcos@ksu.edu). S. Gopalakrishnan and T. W. Nehl are with Delphi Research Labs, Shelby Township, MI 48315 USA (e-mail: suresh.gopalakrishnan@delphi.com; thomas.w.nehl@delphi.com). Digital Object Identifier 10.1109/TEC.2005.847964

turn detection scheme was reported for high-inductance concentrated-winding PM drives [2]. The method required no additional sensors to be used with the current-controlled drive. Monitoring the PWM current ripple, a single shorted turn could be characterized, which lead to fault-tolerant operation of the machine. Positive and negative sequence components of the stator voltage, along with negative sequence component of the current were used to detect stator short circuits of three-phase induction motors [3]. A feed-forward neural network was trained to automate the diagnostic process, and a self-organizing feature map was used to visually display the motor operating condition. The technique was extended to consider faults on inverter-fed drives with open-loop and closed-loop speed control [4]. Recent trends in the area of machine fault diagnosis have applied various digital signal-processing (DSP) tools to extract fault signatures from characteristic waveforms that could identify the fault [5]. Feature extraction performed in the frequency domain possesses high immunity to time-domain misleading phenomena such as noise and switching transients. The wavelet transform is a very efficient tool for DSP processing of nonstationary and nonperiodic signals [6]–[8]. The transform has variable time and frequency resolutions, which facilitate and localize the derivation of high and/or low frequency contents of the processed signal. The mother wavelets used to analyze the signal are capable of sensing both sharp changes and minute discontinuities. Such attributes are not associated with classical DSP algorithms, e.g., discrete Fourier transform (DFT) and its windowed version known as short-time Fourier transform (STFT). The present work introduces a wavelet-based method to detect and locate stator short-circuit faults of a VSI-fed brushless dc motor. Normal and faulty performances of the drive system are computed using a lumped-parameter network model [9], [10] implemented in MATLAB M-files. Performance anomalies under fault are reported, and feasible operational precautions are advised once the fault is detected. The waveforms of electromagnetic torque and phase-voltage summation are found to best characterize the fault. Continuous wavelet transform—performed via the MATLAB wavelet-toolbox—is used to extract low-frequency fault signature from the torque waveform. Both low and high frequency indices are derived from the voltage summation waveform. Accordingly, three independent diagnostic routines are set forth. Faulty performance is measured in the lab on a test machine in order to validate the simulation results. Findings of this research represent the foundation on which diagnosis automation and fault-tolerant operation could be built.

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Fig. 1. Schematic diagram of the integrated drive system.

II. PM BRUSHLESS DC DRIVE The drive considered in this work is a 12 V, 1000 RPM, 6 Pole PM brushless dc motor drive whose configuration is widely used for actuation applications. The system consists of the following components, as shown in Fig. 1: 1) dc supply; filter; 2) CLC 3) MOSFET-based three-phase inverter bridge; 4) three-phase machine having trapezoidal back EMF and permanent-magnet rotor with Hall rotor-position sensors. The switching logic of the inverter MOSFET’s is set by the controller following classical 120 conduction. During one electrical waveform, the inverter bridge undergoes six switching states, each of which has two different conducting MOSFET’s, and two active phases. The feedback control signals of the Hall are input to the sensors and instantaneous dc-link current controller along with a user-defined current command. The torque is controlled based on the command value by applying soft-chopping constant-frequency PWM (at 20 kHz) to the three upper switches of the inverter. III. SIMULATION RESULTS Performance characteristics of the drive system were obtained under normal and faulty operations, at constant speed, through a discrete-time lumped-parameter network model [9], [10]. The model was implemented in MATLAB M-files. Measured phase resistance and inductance were used in the model as well as measured waveforms of the machine back EMF’s. An accurate Fourier-series expression of the measured trapezoidal waveform was utilized to compute the instantaneous phase EMF’s at any rotor position. The measured values of phase , resistance, self inductance, and mutual inductance are 20 , and 5 , respectively. Therefore, the coefficient of 50 magnetic coupling between the 24-turn phase windings is 10% under normal conditions. A. Normal Operation System performance under normal operation characterizes balanced conditions where the machine voltages and currents are symmetrical and shifted in time by 120 electrical. It also means uniform torque development over all switching states. The network model of the system under such conditions is shown in Fig. 2(a). Due to the balanced condition, inductances in the network model represent the difference between self and mutual inductances of the phase windings [9], [10].

Fig. 2.

Network model of the drive system: (a) normal and (b) faulty.

B. Faulty Operation System performance during faults is obtained from a modified network model that accommodates short circuits across any number of turns on one phase winding. The shorted section of the faulty phase is represented by a series combination of resistance, inductance, and back EMF [Fig. 2(b)]. The fault current that circulates around the shorted loop adds one more state variable to the mathematical model. The fault arc resistance and mutual inductances between all four windings of the motor are taken into account since balance conditions are no longer valid. The fault deviates machine parameters and EMF constant of the faulty phase from their nominal values based on the number of shorted turns. Winding resistance, mutual inductances, and EMF constant are proportional to the number of turns, while self inductance is proportional to the square of the number of turns. 1) Fault Current and Torque Development: Simulation results show that the fault current magnitude is almost independent of the number of shorted turns. In high inductance machines, the fault current increases as the number of shorted turns decreases [2]. The reason is that the self inductance of the shorted winding, which is proportional to the square of its number of turns, dominates the faulty loop and plays a crucial rule in setting the magnitude of the fault current. All other factors that affect the current magnitude—such as EMF, resistance, and mutual inductances to other windings—are proportional to the number of turns. The machine under consideration is a low inductance machine where the resistance dominates the shorted loop especially at low and medium speed. Table I shows the ratio between resistance and self reactance of various number of turns of the phase winding at different speeds, all at the fundamental frequency of the waveform. It should be noted that the resistance is much greater than the reactance at such points. The fault current is not affected by the number of shorted turns since both the resistance and EMF are proportional to the

AWADALLAH et al.: DETECTION OF STATOR SHORT CIRCUITS IN VSI-FED BRUSHLESS DC MOTORS

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TABLE I WINDING PARAMETERS AND R/X RATIO FOR DIFFERENT NUMBER OF TURNS

Fig. 4. Electromagnetic torque waveforms at 1000 RPM and 20 A command.

Fig. 3. Fault current waveforms at 1000 RPM, 20 A command, and zero arc resistance (faults on phase C).

number of turns. However, fault current is almost proportional to the speed (like the EMF) at the same number of shorted turns. Another factor which affects the nature of the fault current waveform is the coefficient of magnetic coupling between the . It should shorted and healthy sections of the faulty phase be recalled at this point that the coefficient of magnetic coupling between different phase windings is 10% for the machine under consideration. If the shorted turns lie in a pair of stator attains a small value almost slots with no healthy turns, equal to that between any two coils on different phases under normal conditions. Therefore, the fault current is not much affected by the current chopping action in the healthy section of the phase, and the fault current waveform takes a trapezoidal becomes shape close to that of the EMF. On the other hand, higher if the faulty turns share the slots with some healthy turns. In such case, the fault current waveform depicts some chopping action like that in the healthy section. Also, the magnitude of the fault current is obviously dependent on the arc resistance value. Fig. 3 shows the fault current waveforms at 1000 RPM , and and 20 A command with one shorted turn ; both zero-arc-resistance faults four shorted turns are on phase C. The plots indicate that the fault current nearly has the same magnitude for faults across different number of turns at the same operating conditions. The short-circuit fault alters the machine torque profile significantly. The fault current flows into the shorted loop in an opposite direction to healthy phase currents. Hence, it develops a braking torque component that opposes the motoring torque

Fig. 5. Zero-torque loci at 1000 RPM, 20 A command, and zero arc resistance.

generated by the healthy windings. Curve dips are noticed in the electromagnetic torque waveform during the switching states when the faulty phase is active, Fig. 4. The braking torque due to the fault results in a less average torque than normal conditions. It may also cancel the motoring torque component leading to a zero average torque. Under worse fault conditions, the machine may develop a negative average torque (totally braking), especially at high speed and low current command. Under such conditions, the machine would not be able to operate at the user-desired torque and speed. The zero-torque loci (Fig. 5) depict the operating conditions at which the average torque is null. The area of the plot above a certain locus indicates a positive average torque (motoring), while the area under any locus signifies a negative average torque (braking). Such loci plots are essential for the determination of the current command required to produce certain average torque under different fault conditions. 2) Performance Characteristics: Deviations of the drive performance characteristics from a healthy to faulty operation

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Fig. 6.


Summation of phase voltages at 1000 RPM and 20 A command.

are a key point to fault detection. Phase currents are almost unaffected by fault since it is the controller, not the machine, that sets the waveforms. Individual phase voltages experience minor changes due to the discrepancy of motor parameters and EMF constant of the faulty phase. The deviations become clearer if the individual line-to-neutral voltages are added up together as shown in Fig. 6. Although phase voltages are equal in magnitude and shifted in time by 120 under normal operation, they do not add up to zero because of the third and multiple harmonic content of the trapezoidal EMF’s. The fault gives rise to a fundamental component of the voltage summation signal since phase EMF’s are no longer equal. Accordingly, fundamental components of phase voltages do not cancel each other under fault. The fault also results in a high frequency component of phase voltage summation during four switching states while the faulty phase is active. This is due to the asymmetry of motor parameters that leads to the fact that the resistive and inductive phase winding drops no longer cancel out. Another significant attribute of the stator short-circuit fault is the localized excessive heat loss associated with the fault current. The high loss makes it more risky to run the machine for a long time under full load, especially in case of a dead short circuit. IV. FEATURE EXTRACTION The characteristic waveforms of electromagnetic torque and phase-voltage summation were selected to develop three independent fault detection routines. Differentiation between healthy and faulty torque waveforms was based on the low-frequency component due to the braking torque associated with the fault current. Meanwhile, the voltage-based system could rely on either the low-frequency or high-frequency changes of the waveform. Although the electromagnetic torque waveform characterizes the fault fairly well, it is difficult to monitor practically. Several factors contribute to the difficulty of torque monitoring including—but not limited to—load dynamics, shaft vibrations, and rotational loss. On the other hand, voltage

monitoring is feasible and inexpensive; however, the proposed method requires three sensors. Each diagnostic routine detects some changes of the characteristic waveform during the switching states associated with the faulty phase. The magnitude of these changes could assess the fault severity (number of shorted turns), and the switching states of the changes could identify the faulty phase (locate the fault). The characteristic waveforms are cyclically identical when equally severe faults occur across different phases. Therefore, a zero time-resolution DSP tool, such as DFT, would not be able to detect and locate the fault with one transform process since it blocks all time information while in the frequency domain. Wavelet transform possesses variable time and frequency resolutions making it possible to evaluate and localize the fault signatures of the characteristic waveforms. Continuous wavelet transform—as implemented in MATLAB wavelet-toolbox—was utilized to extract low frequency indices from the electromagnetic torque waveform. It was also used to derive both low and high frequency indices from the waveform of phase-voltage summation. Figs. 7 and 8 show continuous wavelet coefficients of the torque waveform under normal operation and four shorted turns on phase C, respectively. The second Daubechies (db2) mother wavelet was used to derive the coefficients between scales of 1000 and 1064. The plots show higher coefficients for faulty condition than under normal operation during states 3 and 6 (where the faulty phase is inactive). The time axis of the plot was divided into six intervals corresponding to the six switching states of the inverter bridge; each was further divided into three equal windows. One noticeable attribute of the plots is a beam of high coefficients at the transitions between consecutive switching states. The high coefficients are associated with the sharp changes of the time-domain waveform at the designated points. Three diagnostic indices were extracted by averaging the coefficients across the middle third of the first three states at the mother wavelet scale of 1042. Coefficients of the two outer thirds were discarded to avoid possible effects of the high beams of coefficients illustrated above. The same mother wavelet (db2) was used to extract low and high frequency indices from the voltage waveform. Figs. 9 and 10 show wavelet coefficients, between 1st and 64th scales of the mother wavelet, of the voltage waveforms, under normal operation and four shorted turns on phase A, respectively. The three diagnostic indices were derived by averaging the coefficients across the middle third of the first three states at the 20th scale of the mother wavelet. Low frequency content of the voltage waveforms at normal operation and four shorted turns of phase C are shown in Figs. 11 and 12, respectively. Coefficients’ averages over the middle thirds of states 1, 2, and 3—between scales 1200 and 1230 of the mother wavelet—are used as the diagnostic indices in this case. Table II shows diagnostic indices under normal operation and fault conditions of one to four shorted turns derived by the routines illustrated above. The nonlinear pattern of indices’ change versus fault condition makes evident the possibility of detecting the number of faulty turns following any of the proposed methods. For instance, the operating condition is normal if the three torque-de-


Fig. 7. Wavelet coefficients of simulated torque waveform at 1000 RPM, 20 A command, and normal operation.

Fig. 8. Wavelet coefficients of simulated torque waveform at 1000 RPM, 20 A command, and four shorted turns on phase C.

rived indices are almost equal. When indices 1 and 2 are nearly equal, and both are less than index 3, a short circuit on phase C is detected. The number of shorted turns is proportional to the difference in magnitude between index 3 and both indices 1 and 2. The distinction between same faults across different phases is also possible since two indices would switch positions if the fault moves from a phase to another. The reason is that signals of two switching states would swap in the time-domain if the faulty phase changes. For example, phase C is faulty if torque-derived index 3 is higher than indices 1 and 2, while phase A is faulty if index 2 is higher, and so on. Similar patterns could be recognized for the voltage-derived indices. Therefore, any of the suggested routines could identify, locate, and assess the fault severity with one wavelet transform process only. V. EXPERIMENTATION Faulty performance characteristics were measured experimentally and compared to the computed waveforms in order

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Fig. 9. Wavelet coefficients of simulated voltage waveform at 1000 RPM, 20 A command, and normal operation (high-frequency content).

Fig. 10. Wavelet coefficients of simulated voltage waveform at 1000 RPM, 20 A command, and four shorted turns on phase C (high-frequency content).

to validate the simulation results. An 18-slot, 6-pole, 24-turns per phase, machine was prepared for this purpose. Each phase winding was made up of six series connected coils, each of four turns. Tapings were taken at each turn of one coil in phase C; the terminals of another coil in the same phase were also accessible. The arrangement made it possible to artificially create external short circuits across any number of turns in phase-C, between one and eight. Fault current and phase voltages waveforms were recorded, and the average load torque was measured. Simulated and measured fault current waveforms at 1000 RPM, 20 A command, and two shorted turns on phase C are shown in Fig. 13. Plots are given at an arc reand a high coefficient of magnetic coupling sistance of 1.5 —between shorted and healthy sections of the faulty phase—of 50%. Fault current waveforms at 2000 RPM, 10 A , command, 8 shorted turns on phase C, arc resistance of 14 of 10% are depicted in Fig. 14. The figures and a normal illustrate the change in based on the location of the shorted

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TABLE II DIAGNOSTIC INDICES AT 1000 RPM AND 20 A COMMAND BASED ON SIMULATED WAVEFORMS

Fig. 11. Wavelet coefficients of simulated voltage waveform at 1000 RPM, 20 A, and normal operation (low-frequency content).

Fig. 12. Wavelet coefficients of simulated voltage waveform at 1000 RPM, 20 A command, and four shorted turns on phase C (low-frequency content).

turns. The two shorted turns of Fig. 13 share the same slots with healthy turns of the phase winding. Meanwhile, the eight turns of Fig. 14 do not share the slots with healthy turns based on the topology of the test machine windings as explained earlier. The high coefficient of magnetic coupling allows chopping transients to appear in the fault current waveform (Fig. 13), while the fault current has almost a trapezoidal waveform with normal (low) coefficient of coupling, as shown in Fig. 14. Phase voltages were also recorded under different operating conditions. Fig. 15 shows the summation of phase voltage

Fig. 13. Fault current at 1000 RPM, 20 A command, two shorted turns with arc resistance of 1.5 m : (a) simulated and (b) measured.

Fig. 14. Fault current at 2000 RPM, 10 A command, eight shorted turns with arc resistance of 14 m : (a) simulated and (b) measured.

waveforms at 1000 RPM, 20 A command, and two shorted turns arc resistance. Simulated and measured wavewith 1.5 forms agree on the high frequency content of the switching states when the faulty phase is active. They also agree on the low frequency component reflected in the asymmetry between positive and negative peaks of the waveforms. The two aspects represent the core of the voltage-based diagnostic process. All measured waveforms show low-magnitude, high-frequency components where the simulated waveforms show smooth


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TABLE III SIMULATED AND MEASURED AVERAGE TORQUE UNDER DIFFERENT OPERATING CONDITIONS

Fig. 15. Summation of phase voltages at 1000 RPM, 20 A command, and two shorted turns with arc resistance of 1.5 m : (a) simulated and (b) measured.

curves. The phenomenon is believed to be due to noise pickups caused by MOSFET switching since the frequency is so close to the chopping frequency. However, it should not affect the diagnostic routine, as wavelet transform would still be able to differentiate between healthy and faulty performances using the proposed techniques. Simulated and measured voltage waveforms of Fig. 15 are processed using continuous wavelet transform in order to extract and compare diagnostic indices. The high-frequency indices derived from simulated waveform are 0.7765, 0.7755, and 0.0083; indices derived from measured waveform are 0.7985, 0.6955, and 0.0117. Low-frequency indices based on simulation are 13.3748, 3.7656, and 8.7837; while measured waveform yields the indices as 13.4013, 3.6842, and 7.4312. High and low frequency indices, computed through simulated and measured waveforms, are compared also under normal operation at 1000 RPM and 20 A current command. High-frequency indices derived from simulated waveform are all equal to 5.64e-12, while those of measured waveform are 1.02e-6, 3.11e-6, and 9.85e-5, respectively. It should be noted that the low values of the indices indicate the absence of high-frequency content. On the other hand, low-frequency indices based on simulation are 8.43, 7.81, and 36.67, respectively. Indices derived from measured waveform are 6.92, 8.07, and 30.56, respectively. The good matching between diagnostic indices derived from simulated and measured waveforms show the ability of wavelets to diagnose and locate the fault even when measured signals are used. Unfortunately, a similar comparison based on the electromagnetic-torque profile is impossible, since torque pulsations were not possible to measure in the lab. Readings of the average torque measurements were recorded under different operating conditions. Simulated and measured values are given under different fault cases in Table III. The net effect of the short circuit fault is a reduction of the average torque value due to the braking component associated with the fault current. All torque values in Table III are compared to the normal operation case at the same speed and current command

in order to evaluate the overall reduction due to the fault. Results show acceptable consistency of the percentage torque reduction between simulated and measured values. Absolute values of the simulated torque are greater than those of the measured torque, since the simulated entries represent the electromagnetic developed torque, while measurements indicate the output load torque of the machine. At 3 A command and 8 shorted turns, the machine could not operate at a speed higher than 550 rpm, even if commanded; this supports the zero-torque loci concept introduced in Fig. 5. In general, the good agreement between simulation and measured results is sufficient to verify the computed performance, and hence the proposed diagnostic methodology. VI. CONCLUSIONS The paper introduces various routines to detect and locate short-circuit faults on the stator winding of VSI-fed PM brushless dc motors. Healthy and faulty performance characteristics are obtained through a classical lumped-parameter network model. Fault current magnitude of the low-inductance machine considered in this work is almost independent of the number of shorted turns. The short-circuit current produces a braking torque component during the switching states when the faulty phase is active. The braking component tends to reduce the average torque of the machine such that it would be possible to have zero torque especially at high-speed, low-torque operation. Under normal conditions, the instantaneous sum of phase voltages is a sinusoid at triple the fundamental frequency. The fault causes discrepancies in the machine parameters and EMF constants, which affects the phase voltage summation. The fault gives rise to a high-frequency component due to the asymmetry of phase parameters, and a low-frequency component due to asymmetry of phase EMF magnitudes. Continuous wavelet transform is used to process both waveforms of electromagnetic torque and phase voltage summation. Plots of wavelet coefficients show qualitative distinction between healthy and faulty operations. Three different routines are

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set forth to extract diagnostic indices based on low frequency content of the torque, and both low and high frequency components of the voltage summation. Once the fault is detected, temporary precautions could be taken to keep the machine running in fault-tolerant mode. The present work paves the road toward a comprehensive and automatic agent for detecting short-circuit faults. An intelligent paradigm, such as neural networks or adaptive fuzzy systems, could be trained based on diagnostic indices derived at various operating conditions. The overall system could be implemented on a fixed-point processor to perform the on-line condition-monitoring mission.

Medhat M. Morcos (M’78–SM’86) received the Ph.D. degree in electrical engineering from the University of Waterloo, Waterloo, ON, Canada, in 1984. Currently, he is Professor of electrical and computer engineering and Distinguished Teaching Scholar at Kansas State University, Manhattan, where he has been since 1986. He was an Associate Professor of electrical engineering at the Egyptian Air Force Academy, Belbeis, Egypt, from 1985 to 1986. His current research includes power electronics, electrical machines, power quality, power systems protection, and gaseous insulation. Dr. Morcos is a member of the America Society for Engineering Education, Eta Kappa Nu, Sigma Xi, Tau Beti Pi, and Phi Kappa Phi.

REFERENCES [1] J. Penman, H. G. Sedding, B. A. Lloyd, and W. T. Fink, “Detection and location of interturn short circuits in the stator windings of operating motors,” IEEE Trans. Energy Convers., vol. 9, no. 4, pp. 652–658, Dec. 1994. [2] J. A. Haylock, B. C. Mecrow, A. G. Jack, and D. J. Atkinson, “Operation of fault tolerant machines with winding failure,” IEEE Trans. Energy Convers., vol. 14, no. 4, pp. 1490–1495, Dec. 1999. [3] R. M. Tallam, T. G. Habetler, R. G. Harley, D. J. Gritter, and B. H. Burton, “Neural network based on-line stator winding turn fault detection for induction motors,” in Proc. IEEE-IAS Conf., 2000, pp. 375–380. [4] R. M. Tallam, T. G. Habetler, and R. G. Harley, “Stator winding turnfault detection for closed-loop induction motor drives,” IEEE Trans. Ind. Appl., vol. 39, no. 3, pp. 720–724, May/Jun. 2003. [5] M. E. H. Benbouzid and G. B. Kliman, “What stator current processingbased technique to use for induction motor rotor faults diagnosis?,” IEEE Trans. Energy Convers., vol. 18, no. 2, pp. 238–244, Jun. 2003. [6] M. Misiti, Y. Misiti, G. Oppenheim, and J.-M. Poggi, Wavelet Toolbox for Use With MATLAB. Natick, MA: The Mathworks, Inc., 2000. [7] C. K. Chui, An Introduction to Wavelets. New York: Academic, 1992. [8] G. Strang and T. Nguyen, Wavelets and Filter Banks. Cambridge, MA: Wellesley-Cambridge Press, 1996. [9] N. A. Demerdash and T. W. Nehl, “Dynamic modeling of brushless DC motors for aerospace actuation,” IEEE Trans. Aerosp. Electron. Syst., vol. 16, no. 6, pp. 811–821, Nov. 1980. [10] T. W. Nehl, F. A. Fouad, N. A. Demerdash, and E. A. Maslowski, “Dynamic simulation of radially oriented permanent magnet-type electronically operated synchronous machines with parameters obtained from finite element field solution,” IEEE Trans. Ind. Appl., vol. IA-18, no. 2, pp. 172–182, Mar./Apr. 1982.

Mohamed A. Awadallah (S’00) received the B.S. (Hons.) and M.S. degrees in electrical engineering from the University of Zagazig, Zagazig, Egypt, in 1993 and 1997, respectively, and the Ph.D. degree in electrical engineering from Kansas State University, Manhattan, in 2004. He was a Teaching and Research Assistant in the Department of Electrical Power and Machines Engineering, University of Zagazig, from 1994 to 1999. His research interests include condition monitoring of electrical machines and drives, artificial intelligence applications to drive systems, and power electronics. Dr. Awadallah is a member of Eta Kappa Nu, Tau Beta Pi, and Phi Kappa Phi.

Suresh Gopalakrishnan (S’95–M’00–SM’03) received the B.E. degree in electrical engineering from Annamalai University, Annamalai, Nagan, India, the M.S. degree in electrical engineering from the Indian Institute of Technology, Chennai, India, in 1989 and 1992, respectively, and the Ph.D. degree in electrical engineering from Texas A&M University, College Station, in 2000. From 1992 to 1995, he was with the R&D Department of Kirloskar Electric Company, Bangalore, India. In 2000, he joined the Mechatronics group of Delphi Corporation, Shelby Township, MI. His research interests include power electronics, control of variable-speed motor drives, and digital-signal-processor (DSP) applications in automotive actuators.

Thomas W. Nehl (S’76–M’77–SM’86–F’94) received the B.S., M.S., and Ph.D. degrees in electrical engineering from Virginia Polytechnic Institute and State University (Virginia Tech), Blacksburg, in 1974, 1976, and 1980, respectively. From 1980 to 1983, he was an Assistant Professor of electrical engineering at Virginia Tech. In 1983, he joined the General Motors Research Labs, Warren, MI, where he became Senior Staff Research Engineer in the Electrical and Electronics Department in 1996. In 1999, this department became the nucleus of the newly formed Delphi Research Labs (DRL), Shelby Township, MI, where he is currently Manager of the Mechatronics Group and its Chief Scientist for the Delphi Saginaw Division.