Short Circuit Fault Detection in PMSM by means of Empirical Mode Decomposition (EMD) and Wigner Ville Distribution (WVD)

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1 Short Circuit Fault Detection in PMSM by means of Empirical Mode Decomposition (EMD) and Wigner Ville Distribution (WVD) J. Rosero 1, L. Romeral 1, J. A. Ortega 1, E. Rosero 2 1 Motion Control and Industrial Applications Group, Technical University of Catalonia, C/ Colon 1 Tr Terrassa. Catalonia. Spain, romeral@eel.upc.edu 2 Research Group of Industrial Control (GICI), University of Valle, Calle 13 N 1-, Cali Colombia, emilros@univalle.edu.co Abstract This paper presents and analyzes short circuit failures for Permanent Magnet Synchronous Motor (PMSM). The study includes stable condition and speed transients in simulation and realistic experimental conditions. The stator current is analyzed by the empirical mode decomposition (EMD) method, which will generate a collection of intrinsic mode functions (IMF). Finally, the Hilbert Huang transform (HHT) is used to compute the instantaneous frequencies resulting from the IMFs obtained from the stator currents. Moreover, the IMF 1 and IMF 2 have been analyzed by means of Wigner Ville distribution (WVD). Experimental laboratory results validate the analysis and demonstrate that this kind of time-frequency analysis can be applied to detect and identify short circuit failures in synchronous machines. Index Terms PMSM drive, motor fault, short circuit, Hilbert Huang Transform, HHT, empirical mode decomposition, EMD, intrinsic mode functions, IMF, Wigner Ville, WVD. I. INTRODUCTION In many applications the failure of a drive has a serious impact on the operation of a system. In some cases the failure results in lost production, whilst in others it may jeopardize human safety. In such applications it is advantageous to use a continuous operation in the presence of any single point failure. Such a drive is termed fault tolerant and the development of a fault tolerant drive is the aim of the research presented here [1, 2]. Stator or Armature faults are usually related to insulation failure. In common parlance, they are generally known as phase-to-ground or phase-to-phase faults. It is believed that these faults start as undetected turn-to-turn faults that finally grow and culminate into major ones [3, 4]. Short circuit between turns is the most critical fault in the machine, and is quite difficult to detect and almost impossible to remove. Stator winding faults might have a destructive effect on the stator coils [5]. There are many techniques to detect turn-to-turn faults, the majority of them based on the analysis of stator voltages and currents, axial flux and d-q current and voltage component. Toliyat [6, 7] and Penman [8] have described the operation of induction motor drives under the conditions of loss of one phase, broken bars and shorted stator turns using winding functions. However, they considered models that did not include either saturation or control interactions. From years ago, the failure detection in a motor is studied by analyzing the stator current harmonic by means of FFT [9]. Hovewer FFT cannot be applied in no-stationary signals [1, 11]. Fortunately, signal processing theories provide several algorithms for applications with no-stationary signals [12]. Joint time-frequency analysis is a novel approach in the motor diagnosis applications. Successful use of these techniques requires understanding of their respective properties and limitations. The selection of a suitable temporal window size is required when computing the Short- Time Fourier Transform (STFT) to match with the specific frequency content of the signal, which is generally not known a priori [13]. A very appealing feature of the continuous wavelet analysis (CWT) is that it provides a predetermined resolution for each scale [14]. Moreover, an important limitation of the wavelet analysis is its non-adaptive nature. Once the basic wavelet is selected, one will have to use it to analyze all the data [15]. The Wigner-Ville distribution (WVD) is a time-frequency representation, which is part of the Cohen class of distribution [16]. The drawback of this transform is the presence of cross terms as indicated by the existence of negative power for some frequency ranges. In addition, the WVD of discrete time signals suffers from the aliasing problem, which may be overcame by employing various approaches [15]. The Hilbert Huang transform (HHT) is based on the instantaneous frequencies resulting from the intrinsic mode functions (IMF) of the signal being analyzed; thus, it is not constrained by the uncertainty limitations with respect to the time and frequency resolutions to which other time-frequency techniques are subject [13]. The result is a three-dimensional energy-frequency-time spectrum designated as Hilbert spectrum that provides an effective way to get the local information which is vital to the non-stationary signals. In recent years, HHT has been used to characterize the time evolution of non-stationary power system oscillations following large perturbations [17]. Xu [18] has applied the EMD method to multiscale decomposition and raw textile defect detection over synthetic and actual texture images. In this work, the HHT is applied to stator currents for analysis of PMSM under failures [19]. This paper shows that /8/$ IEEE 98

2 is possible to identify short circuits in the windings of the PMSM, even in an early stage, by means of empirical mode decomposition (EMD) and Wigner Ville Distribution (WVD). Healthy and faulty PMSM motors were simulated and experimentally tested. Faulty conditions were generated with a short circuit in fourth, eight or twelfth stator winding turns. PMSM motors were operated at nominal torque and with different speeds between 15 rpm and 6 rpm. Simulation and experimental results obtained from healthy and faulty machines were compared, and finally conclusions are also presented. II. HILBERT HUANG TRANSFORM (HHT) The traditional time frequency analysis techniques have their own limitations [2, 21]. The consequence is the misleading energy-frequency distribution for nonlinear and non-stationary data analysis. The Hilbert Huang transform (HHT) represents the characteristic oscillations of the original signal from time scales contained in the IMF functions. The local energy and the instantaneous frequency derived from the intrinsic mode function (IMF) through the Hilbert transform can give us a full frequency-time energy distribution of the signal. IMF is the decomposition of signal at different frequency ranges. A) Empirical Mode Decomposition (EMD) The EMD method was motivated by computation of instantaneous frequency defined in terms of Hilbert transform. As is well known, for a real-valued signal x(; the Hilbert transform is defined by the principal value (PV) integral. + 1 x( t') y( = P t' (1) π t t' Where P indicates the Cauchy principal value (constan. This leads to the definition of an analytic signal, z(. jθ ( t ) z( = x( + j. y( = a( e (2) 2 2 1/ 2 [ x ( + y ( ], arctan( y( / x( ) a ( = θ = Where a( is amplitude and θ( is phase. The instantaneous frequency is then defined by ω(=dθ(/dt. In the above equation, both the amplitude and instantaneous frequency are function of time. One would therefore hope to construct a time frequency representation based on Hilbert transform. An intrinsic mode function (IMF) is a function that satisfies two conditions: First, in the whole signal set, the number of extremes and the number of zero crossings must be either equal or differ at most by one; and second, at any point, the mean value of the envelope defined by the local maxima and the envelope defined by the local minima has to be zero [21]. The EMD extracts the IMFs by the following iterating process [2], as can been seen in Fig. 1. Considering r (= x(: 1. Find the upper envelope of r n ( as the cubic spline interpolate of its local maxima, and the lower envelope. Fig. 1. Empirical mode decomposition (EMD) algorithm 1 IMF Time(s) Fig. 2. IMF of stator current in PMSM with 12 short circuit turns running at 6 rpm. Simulation results IMF 2 IMF 3 IMF 4 IMF 5 As the cubic spline interpolate of its local minima. 2. Compute the mean envelope m n, k ( as the average of the upper and lower envelopes. 3. Compute hn, k ( = hn, k 1( mn, k (. Considering h n, (=r n-1 (. 4. If h n,,k ( fulfill the condition expressed in equation (3), IMF was obtained and then stop. Otherwise, treat h n,k ( as the signal and iterate to h n, k ( through Steps 1 4. The stopping condition is: 2 [ hn, k 1( hn, k ( ] < SD (3) 2 t = hn, k 1( where h n,k ( is the sifting result in the kth iteration for calculus of IMF n, and SD is standard deviation, typically set between.2 and The EMD extracts the next IMF (see Fig. 2) by applying the above procedure to the residue: rn ( = rn 1( Cn( (4) Where C n ( denotes the IMF n. This process is repeated until the last residue r n ( has at most one local extremum. III. WIGNER VILLE DISTRIBUTION The best way to analyze the content frequency of non stationary stator current is by means of a joint time-frequency analysis as the Wigner Ville distribution (WVD). Furthermore, it possesses a great number of good 99

3 properties and it has wide interest for non stationary signal analysis [22]. WVD is a time frequency energy density computed by correlating f( with a time and frequency translation of itself. This avoids any loss of time frequency resolution. The discrete Wigner-Ville distribution is possible for a discrete signal f(n) defined over n<n, the integral is replaced by discrete sum: WVD( n, k) = N 1 p= N [, p] R n e * p 2 j 2πkp N p R [ n, p] = f n + f n (5) 2 where R[n,p] is the instantaneous correlation, f[n] is the discrete signal, p is an integer. This calculation requires knowing the value of f at half integers. These values are computed by interpolating f, with an addition of zeros to its Fourier transform. If the analyzed signal contains more than one frequency components, the WVD method suffers from cross term interference. Assigning different weights to R[n,p] suppresses the less important parts and enhances the fundamental parts of the signal. Two traditional methods: the Pseudo Wigner Ville Distribution (SPWVD) or Zao-Atlas-Marks distribution (ZAM) are usually applied as the weighting function to the instantaneous correlation. The first is in the time domain and known as the Pseudo Wigner-Ville distribution (SPWVD), it can be computed by [23]: WVD( n, k) = N 1 p= N w [ p] R[ n, p] e j 2πkp N where w(p) is a regular windows The use of weighted functions allow to eliminate cross term interference [24]. Comparing both transforms, ZAM transforms shows relatively small cross terms, the behavior regarding rise time are similar and, in certain cases, has better transition ripple properties than SPWVD. Fig. 3 shows SPWVD for IMF 1 and 2 during speed change from 15 rpm to 1 rpm in healthy PMSM. The speed falling ramp stars at.2 s and ends at.3 s. (6) IV. WORKBENCH OF SIMULATIONS AND EXPERIMENTS Some experiments and experiments have been carried out for different motors with 4, 8 and 12 shorted turns of stator phase winding. The motors are PMSM of 6 rpm of nominal speed, 2.3 Nm of nominal torque, and 3 poles pair [11]. The motors were driven at nominal, medium (3 rpm) and low (15 and 6 rpm) speed. Both simulations and experiments were carried out under stationary and not stationary conditions. The short circuits implemented are a few turns ones, in relation of whole winding (144 turns of stator phase winding). Fig. 4 shows the circuit scheme for short circuit simulation. Experimental workbench to emulate real operation of the motor was built-up at the laboratory g p g Fig. 3. SPWVD of IMF 1 & 2 in healthy PMSM. Speed change from 15 to 1 rpm Fig. 4. Circuit scheme for short circuit simulation A special winding manufactured equal to the original but with external connections to optional short circuit of fourth, eight or twelfth turns of the winding has been used. Closing a switch to provoke a short circuit, and after waiting to stabilize the currents, a linear speed variation, programmed in the drive controller, was performed. Finite element analysis (FEA) is usually proposed for the simulation of electrical machines with short circuit fault. FEA analysis reveals itself like an accurate an easy method to determine the interaction between non-linear effects. Coupling between the non-linear magnetic effects and nonlinear electric circuits should be taken into account in order to determine the behavior of the electrical motor under fault conditions [25], this can be achieved by means of FEA. In this work, PMSM in a healthy state and with short circuit turns are simulated at different working points using a two-dimensional (2-D) finite-element analysis software (FLUX 2D) [26]. The empirical mode decomposition algorithm (EMD) and Hilbert-Huang transform (HHT) were implemented by means of Hilbert-Huang Transform Data Processing System (HHT- DPS) software [27] of NASA. The Rice University Time Frequency analysis toolbox [28] from Matlab is used to compute the Fast Fourier transforms, Wigner Ville distributions and spectrums

4 V. SIMULATION AND EXPERIMENTAL RESULTS The analysis of the current is carried out mainly for low speeds, that is to say, for the cases where the classic methods of fault detection have lower performance. The short circuit is analyzed under different speed conditions. Five IMF are obtained from the stator current by means of EMD and afterwards HHT is calculated. The results of machine with short circuit are compared with those obtained from a healthy machine. A. Steady State (constant speed and torque) IMF 3 contains the stator main current harmonic and IMF 1 and IMF2 together contain the failure harmonic. By this way, the empirical mode decomposition (EMD) allow to obtain the intrinsic mode functions (IMF) that contain the short circuit fault harmonic and thus concentrate our analyses on them, obtaining better resolution and accuracy in the fault detection. The IMF 1 and 2 together contain the failure frequency and by means of the Fast Fourier transform (FFT) could be clearly detected the short circuit. In relation to standard MCSA, EMD allows filtering fault frequencies and removing the other frequencies. By this way, we can achieve the best resolution. Fig. 5 show the Fourier transform of IMF 1 and 2 for 15 rpm. Now, the biggest harmonic of FFT is the 9 th harmonic (9 Hz in this case). The main harmonic corresponding to power supply, that is always higher to the other ones when it is analyzed with standard MCSA [29], has been eliminated. Amplitude (db) w=15 rpm Short Circuit -5 M Healthy -6 M 4 Short turns M 8 Short turns M 12 Short turns Fig. 5. FFT of IMF 1 & 2 in PMSM with 12 short circuit turns, Speed at 15 rpm Failure harmonic Fig. 6. SPWVD of IMF 1 & 2 in PMSM with 12 short circuit turns. Speed at 6 rpm. Simulation results Failure harmonic Fig. 7. SPWVD of IMF 1 & 2 in PMSM with 12 short circuit turns. Speed at 6 rpm. Experimental results On the other hand, IMF 1 and IMF2 can be used for analysis with WVD transforms. In this case, the spectrum for healthy machine results clean or empty; On the contrary, for short circuit fault we could located the fault frequency in a more easy and evident way. To analyse time frequency of IMF 1 and 2 we can use the SPWVD. The results of distribution are compared to find the best technique regarding failure detection. Fig. 6 shows SPWVD of IMF 1 and 2 for PMSM running at 6 rpm with 12 short circuit turns. SPWVD has less interference frequencies linking to the fault. The harmonics 6 th, 9 th, and 12 th only can be seen in this spectrum. Experimental results have been carried out and they verified the fault detection by means of the EMD decomposition and analysis of SPWVD transform of IMF 1 and 2. Fig. 7 shows the importance of the 9 th harmonic in case of short circuit in experimental results. Although, the 5 th and 7 th can also be seen lightly. But, the amplitude difference is significant with regards to the whole stator currents. That is to say, the 9 th harmonic is the biggest value we can see in the SPWVD. B. Speed Change (constant torque) In a second step, a no-stationary working conditions of the PMSM motor were considered. Specifically, the speed operation of the motor changes along the experiment, while the load torque remains constant. This is obtained by simulation with a linear speed change from 6 rpm to 55 rpm, starting at.2 s and ending at.29 s. The stator currents decomposition by means of EMD allows to obtain 5 IMF and each one contains its own characteristic frequency range. Fig. 8 shows SPWVD of IMF 1 and 2 of the stator currents of a PMSM with 12 short circuit turns. This is obtained from simulation with a speed change from 15 rpm to 1 rpm. Fig. 9 shows SPWVD of IMF 1 and 2 of PMSM stator current with 8 and 12 short circuit turns. These are obtained by simulation with a speed change from 6 rpm to 55 rpm. Some experimental results are showed in Fig. 1 and Fig. 11. These figures represent SPWVD transform of IMF 1 and IMF 2 PMSM stator currents with a 12 turns short circuited. These are the results for low speed where the fault detection is more critical. The results for the whole speed range are also very satisfactory

5 Fig. 8. SPWVD of IMF 1 & 2 in PMSM with 12 short circuit turns. Speed change from 15 to 1 rpm g p g Fig. 9. SPWVD of IMF 1 & 2 in PMSM with 12 short circuit turns. Speed change from 6 to 55 rpm Fig. 1. SPWVD of IMF 1 & 2 in PMSM with 8 short circuit turns. Speed change from 15 to 1 rpm, Experimental results The method allows remarking the analysis in the characteristic failure and decreasing the computational burden; besides, it maximizes the failure relative value. The quick filter by means of EMD allows eliminating the undesired frequencies for the fault detection and the system can be more accurate. VI. CONCLUSIONS This paper presents the short circuit analysis with stator currents of PMSM by means of empirical mode decomposition (EMD) and intrinsic mode functions (IMF). Next, Wigner Ville distribution (WVD) has been applied to IMF 1 and 2. This method allows to completely eliminate the noise or to lessen it to no significant values. The IMF considered contains the 9 th rotor speed harmonic but not the main harmonic of the motor power supply. This fact maximizes the performance of the fault detection in PMSM. The empirical mode decomposition (EMD) analysis and smoothed Pseudo Wigner Ville distribution (SPWVD) show the ability to quantify different types of no-stationary fault currents for the full motor operation speed range. By means of variable speed drive, experimental results were obtained. They show the ability of smoothed pseudo Wigner Ville distribution to identify the fault within a short time of calculation. These transforms do not need many samples, and they can work independently of the speed variations. The featured signature allows differentiating between healthy and faulty conditions, as well as between different degrees of fault. The results can be used for fault detection and diagnosis of such internal faults at low speed and dynamic conditions. This method is suitable to be implemented in embedded on-line applications. VII. ACKNOWLEDGMENT The authors would like to acknowledge the economic support received from the Spanish Ministry of Science and Technology for realizing this work under the DPI C2-1 Research Project. Also, the work was supported by the Programme Alban, the European Union Programme of High Level Scholarships for Latin America, scholarship No.E4D27632CO, Mr. J. A. Rosero Fig. 11. SPWVD of IMF 1 & 2 in PMSM with 12 short circuit turns. Speed change from 15 to 1 rpm, Experimental results VIII. REFERENCES [1] J. A. Haylock, B. C. Mecrow, A. G. Jack, and D. J. Atkinson, "Operation of a fault tolerant PM drive for an aerospace fuel pump application," in Eighth International Conference on Electrical Machines and Drives (Conf. Publ. No. 444), 1997, pp [2] N. Ertugrul, W. L. Soong, S. Valtenbergs, and H. Chye, "Investigation of a fault tolerant and high performance motor drive for critical applications," in TENCON. Proceedings of IEEE Region 1 International Conference on Electrical and Electronic Technology, 21, pp vol.2. [3] J. A. Haylock, B. C. Mecrow, A. G. Jack, and D. J. Atkinson, "Operation of fault tolerant machines with winding failures," IEEE Transactions on Energy Conversion, vol. 14, issue 4, p. 149, [4] J. A. Haylock, B. C. Mecrow, A. G. Jack, and D. J. Atkinson, "Operation of a fault tolerant PM drive for an aerospace fuel pump application," IEE Proceedings Electric Power Applications, vol. 145, issue 5, p. 441,

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