Research Article Practical Aspects of Broken Rotor Bars Detection in PWM Voltage-Source-Inverter-Fed Squirrel-Cage Induction Motors

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1 Applied Matheatics Volue 13, Article ID 18368, 11 pages Research Article Practical Aspects of Broken Rotor Bars Detection in PWM Voltage-Source-Inverter-Fed Squirrel-Cage Induction Motors Hong-yu Zhu, 1,,3,4 Jing-tao Hu, 1,,3 Lei Gao, 1,,3 and Hao Huang 1,3 1 Shenyang Institute of Autoation, Chinese Acadey of Sciences, Shenyang 1116, China University of Chinese Acadey of Sciences, Beijing 149, China 3 Key laboratory of Industrial Inforation Technology, Chinese Acadey of Sciences, Shenyang 1116, China 4 School of Electronic and Inforation Engineering, University of Science and Technology Liaoning, Anshan 11444, China Correspondence should be addressed to Hong-yu Zhu; zhuhongyu@sia.cn Received 5 June 13; Revised 18 Septeber 13; Accepted 3 October 13 Acadeic Editor: Xianxia Zhang Copyright 13 Hong-yu Zhu et al. This is an open access article distributed under the Creative Coons Attribution License, which perits unrestricted use, distribution, and reproduction in any ediu, provided the original work is properly cited. Broken rotor bars fault detection in inverter-fed squirrel cage induction otors is still as difficult as the dynaics introduced by the control syste or the dynaically changing excitation (stator) frequency. This paper introduces a novel fault diagnosis techniques using otor current signature analysis (MCSA) to solve the probles. Switching function concept and frequency odulation theory are firstly used to odel fault current signal. The copetency of the aplitude of the sideband coponents at frequencies (1 ±s)f s as indices for broken bars recognition is subsequently studied in the controlled otor via openloop constant voltage/frequency control ethod. The proposed techniques are coposed of five odules of anti-aliasing signal acquisition, optial-slip-estiation based on torque-speed characteristic curve of squirrel cage otor with different load types, fault characteristic frequency deterination, nonparaetric spectru estiation, and fault identification for achieving MCSA efficiently. Experiental and siulation results obtained on 3 kw three-phase squirrel-cage induction otors show that the odel and the proposed techniques are effective and accurate. 1. Introduction Squirrel-cage induction otors have doinated the field of electroechanical energy conversion. They consue ore than 6% of the electrical energy produced and are present in the ain industrial applications [1, ]. Although still considered proverbially robust, all coponents of induction achines are subject to increased stress, particularly when operated in a controlled ode and with repeated load cycles [3]. According to studies, broken rotor bars and cracked end-ring faults in the rotor cage are responsible for about 5 1% of all breakdowns and incipient detection of these events reains a key issue [4, 5]. The ain reason why early detection is iportant is that although broken rotor bars ay not cause iediate failure, there can be serious secondary effects associated with their presence [6, 7]. If faults are undetected, they ay lead to potentially catastrophic failures. Thus, health-onitoring techniques to prevent the induction otor failures are of great concern in the industry and are gaining an increasing attention. Motor current signature analysis (MCSA) has been successfully applied to detect broken-rotor bar faults by investigating the sideband coponents around the supplied current fundaental frequency (i.e., the line frequency) f f b = (1±s) f, (1) where f b are the sideband frequencies associated with the broken rotor bars and s is the per unit otor slip [4, 8, 9]. Soe quantitative conclusion based on the left sideband values (LSB) of the aplitude-frequency spectru plot of a otor phase current even recoends 5dB 35 db of the sideband haronics as the threshold level for generating a warning or alar [1]. In addition, MCSA has been tested in any industrial cases since the 198s with good results [11 16]. Even though nuerous successful ain-fed otor fault detection ethods are reported in the literature, bibliography relative to inverter-fed otors on this topic sees to be poor. With the increased ephasis on energy conservation and

2 Applied Matheatics lower cost, induction achines are supplied and controlled by inverters, and the use of inverter drives increases day by day. As a result, dynaic perforance is excellent due to all kinds of control ethods and the next steps in drive developent are going to be driven by attepts to increase reliability and reduce aintenance costs. By using the current sensor feedback and icroprocessing unit, the new tread for low-cost protection applications sees to be drive-integrated fault diagnosis systes without using any external hardware. Thus, it becoes ore deanding to detect faults by using MCSA in these drives. The introduction of voltage-source-inverter-fed (VSIfed) otors has produced significant changes in the field of diagnosis and control, needing further research in order to overcoe various challenges. Contrary to the otor line current taken directly fro the ain, the inverter-fed otor line current includes rearkable noise (inherent floor noise which reduces the possibility of true fault pattern recognition using line current spectru) due to the high-frequency switching devices, EMI and EMC effects, and so forth. The currentsignalforrotorfaultdiagnosisneedspreciseandhigh resolution inforation, which eans the diagnosis syste deands additional hardware such as a low-pass filter, highprecision AD converter, and additional software. Moreover, closed-loop control in IM drives introduces new difficulties in broken rotor bar detection, as traditional fault indicators tend to be asked by a control algorith. Therefore, the ethods developed for an open-loop operation are not able to produce adequate and reliable inforation on the extent of the fault and have to be adapted[4, 17, 18]. All these influences coplicate the utilization of frequency analysis ethods. VSI-fed otor faults have been analyzed, and the initial results are given in the literature but further investigation is still required. The classic MCSA ethod works well under constant load torque and with high-power otors, and it has ainly been designed for fixed frequency supply, such as for achines connected to the electrical grid. To obtain satisfactory test results, in [7], recoendations are given fro the author s experience. As stated in this paper, literally, the load on the otor should be sufficiently high to produce at least 35% of rated full load rotor slip for a reliable single-test broken bar analysis. and if the otor to be tested is fed fro a variable-speed converter drive, the frequency of the drive should be locked at the 5/6 Hz power supply frequency for the test. Yet, difficulties eerge when inverted-fed otors are applied to drive fans, pups, or other echaniss involving speed control for energy-saving purpose. In these cases, the excitation frequency will truly depend on the speed referenceandtheloadappliedtothesyste.therefore,unlike the utility-driven case, the stator excitation frequency will dynaically change and the position of the current haronics appearing on the stator-current spectru due to electrical faults is highly dependent on the echanical otor load and excitation frequency, which affects the slip frequency. As a consequence, the conventional MCSA ust be aended to accoodate the new scenarios. Unfortunately, to the best of our knowledge, in the published literatures there is no research work on this subject. i a i b i c i d + S ia S ib S S ua S ub S uc ic u a u b u d u c u a u b u c Z Z Z i a ib i c M Figure 1: Scheatic diagra of the PWM VSI-fed adjustable speed drive. In this context, following explicitly derivation fro a siplified fault signal odel, a new online fault diagnosis technique based on MCSA for inverter-fed squirrel-cage induction otors is present. Copared with traditional MCSA, the novelty of the proposed ethod is that broken rotor bars fault in the controlled otor via open-loop constant voltage/frequency control ethod could be identified even if the otor operates at different excitation frequencies. To do this, oversapling signal acquisition technique is used to suppress significantly noise contained in the invertedfed otor line current, and fault-indicative frequencies with variable excitation frequency are deterined by torque-speed characteristic curve of squirrel-cage otor with different load types. To obtain satisfactory results, nonparaetric spectru estiation algorith and fault identification are subsequently presented. Including this introductory section, this paper is organized into six sections. Section presents a theoretical analysis odel of stator current of inverter-fed squirrel-cage otor, which is based on switching function concept and odulation theory. A detailed description of the haronic coponents contained in current is given. Section 3 elaborates the new broken rotor bars fault diagnosis techniques. In Section 5, the proposed techniques are validated by laboratory tests; the ethod is applied to different stator currents obtained fro healthy and faulty achines. Experiental and siulation results as well as the corresponding analysis and discussion are presented in Section 4. Finally, conclusions and recoendations are presented in the last section.. Analytic Model of Stator Current Signature for Squirrel-Cage Induction Motor with Constant Volt-per-Hertz Control Technique.1. Analytic Model of Stator Current Signature for No-Fault Squirrel-Cage Induction Motor. Switching function concept is a powerful tool in understanding and optiizing the perforance of the converter [19, ]. In [], an analytical approach for characterizing the current haronics and interharonics of the VSI-fed ASD injected into the supply syste in steady is presented using the switching function concept, applicable to PWM VSI that is studied in this paper. Figure 1 shows the scheatic diagra of a typical PWM VSI-fed adjustable speed drive, where S ia, S ib,ands ic represent the rectifier converter current switching functions that correlate

3 Applied Matheatics 3 the three-phase AC source currents i a, i b,andi c and the inverter input DC current i d, S ua, S ub,ands uc represent the inverter voltage switching functions that correlate inverter dc input voltage and output phase voltages u a, u b and u c, Z is the ipedance operator seen fro the inverter output terinals corresponding to the neutral point of induction otor. In order to calculate and analyse the haronic currents generatedbythevsi-fedasd,ananalyticalodelbased on the odulation theory and switching function concept is proposed and expressed by () (6). After obtaining the phase currents of PWM VSI-fed otor, the haronic coponents of the current ight be extracted by the use of a certain spectru analysis ethod as follows: (i a,i b,i c )=i d (S ia,s ib,s ic ), () i d =(i a,i b,i c )(S ua,s ub,s uc ), (3) u d = (u a,u b,u c )(S ia,s ib,s ic ), (4) (u a,u b,u c )=u d (S ua,s ub,s uc ), (5) (i a,i b,i c ) = (u a,u b,u c ). (6) Z As shown in Figure 1, for the two-level natural sapled PWM with a triangular wave of carrier signal, the three-phase voltage switching functions S ua, S ub and S uc canbeexpressed as the following double Fourier series, as follows: S ua (t) = M sin (ω st) + π sin ( π ) sin (ω ct) + π n=±1 sin (ω c t+nω s t), S ub (t) = M sin (ω st π 3 )+ π sin ( π ) sin (ω ct) + π n=±1 J ( Mπ ) sin [ (+n) π ] J ( Mπ ) sin [ sin [ω c t+n(ω s t π 3 )], S uc (t) = M sin (ω st+ π 3 )+ π sin ( π ) sin (ω ct) (+n) π ] J ( Mπ ) + π n=±1 sin [ (+n) π ] sin [ω c t+n(ω s t+ π 3 )]. (7) For a hypothetical ideal otor supplied fro a balanced three-phase source of sinusoidal voltages and driving a constantload,thefollowingwaveforofselectedphase-a stator current ay be assued by substituting (7) into(5) and (6), where the coutation effect is ignored and proper origin of coordination selected for convenience of analysis is as follows: ME i a = d Z(ω cos [ω s t φ(z(ω s ))] s) + E d π Z(Nω s) cos [Nω s t φ(z(nω s ))] + E d π Z((N + n) ω s). sin [ J ( Mπ ) sin ( π ) ± n=±1 (+n) π ] cos [ (N + n) ω s t φ (Z ((N + n) ω s ))] =I 1 cos (ω s t φ 1 )+I J ( Mπ ) sin ( π ) cos (Nω s t φ ) ± n=±1 +I 3 cos [(N + n) ω s t φ 3 ], sin [ (+n) π ] where M is aplitude odulation index, M=U s /U c 1;ω s is frequency of the odulation wavefor (reference) (rad/s), ω s = πf s ; ω c is frequency of the carrier signal (rad/s); N ratio of the carrier frequency to the odulation frequency, N = ω c /ω s 1;andJ,J n are Bessel functions of the first kind with order and order n,respectively... Analytic Model of Stator Current Signature for Faulty Squirrel-Cage Induction Motor. When broken rotor bar or cracked end-ring faults develop in the rotor cage, the current, torque, and speed of the otor are affected, typically, in a periodic anner. In the case of periodic disturbances, all threelinecurrentsi a, i b,andi c are siultaneously odulated with the fundaental frequency f o of the fault-induced oscillation of otor variables. If only aplitude odulation and fundaental frequency f o are considered, current in phase-a of the supply line ay now be expressed as (8) i f =i a [1 + a cos (ω o t)], (9)

4 4 Applied Matheatics where a denotes the odulation depth (odulation index) and ω o =πf o =sω s =4πsf s.thevalueoftheodulation index depends on the severity of the abnorality and otor loads. Substituting (8)in(9)yields i f =I 1 cos (πf s t φ 1 )+I J ( Mπ ) sin ( π ) cos (πnf s t φ ) ± n=±1 +I 3 cos [π (N + n) f s t φ 3 ] sin [ +ai 1 {cos [π (1+s) f s t φ 1 ] + cos [π (1 s) f s t φ 1 ]} +ai J ( Mπ ) sin ( π ) {cos [π (N + s) f s t φ ] + cos [π (N s) f s t φ 3 ]} +ai 3 ± n=±1 sin [ {cos [π (N+n+s) f s t φ 3 ] (+n) π ] + cos [π (N+n s) f s t φ 3 ]}, (+n) π ] (1) indicating that the spectru of stator current for inverter-fed healthy squirrel-cage otor contains, apart fro the fundaental f s equal to the inverter excitation (stator) frequency, Nf s haronics at the carrier frequency and ultiples of the carrier frequency and (M+n)f s haronics in the sidebands around each ultiple of the carrier frequency. When a bar breaks,arotorasyetryoccurs.theresultisthatitinduces in the stator current additional frequency at f b =(1±s)f s, f b1 = (N ± s)f s,andf b = (N + n ± s)f s around haronics frequency depicted above. The aplitude of faultindicative frequencies f b =(1±s)f s, f b1 = (N±s)f s, and f b =(N+n±s)f s depends on faulty severity, loads and excitation (stator) frequency, and the distance between f b, f b1,andf b and corresponding haronics frequency f s, Nfs, (M + n)f s is equal to sf s.theaplitudeoff b1 and f b canbeconsiderednegligiblecoparedtothatoff b ; as a result, f b = (1 ± s)f s are adopted as fault-indicative frequencies. In practice, the current is odulated with respect to not only the aplitude but also the phase, and the odulation process is ore coplex than that described by (9), but the derived equation (1) provides an adequate basis for qualitative assessent of diagnostic edia. 3. Diagnosis Techniques of Broken Rotor Bars for Squirrel-Cage Induction Motor with Constant Voltage/Frequency Control Method 3.1. Principles of Diagnosis. Aotordiagnosistechnique, which contains the five processing odules illustrated in Figure,ispresented,basedonodelofsquirrel-cageinduction otor stator current signature depicted in Section. The current flowing in single phase of the induction otor is sensed by anti-aliasing signal acquisition odule and sent to spectru estiation odule, where the obtained tie-doain signal can be decoposed into coponents of different frequency using Welch s periodogra ethod. In optial-slip-estiation odule, based on the real speed, the inverter excitation frequency, and torque-speed characteristic curve of squirrel-cage otor with different load types, the otor slip is calculated and the consequent optial slip estiation value is transitted to fault characteristic frequency deterination odule, where characteristic frequencies of broken rotor bars are calculated. Depending on whether the characteristic frequencies of f b =(1±s)f s could be found in power spectru obtained in spectru estiation odule, the conclusion of failure or not could be drawn, this work is done in fault identification odule. 3.. Method of Antialiasing Signal Acquisition. When carrying out diagnostic analysis one of the key eleents to obtain good results is to properly choose acquisition paraeters: the sapling frequency and the nuber of saples. There are two different constraints: analysis signal bandwidth and frequency resolution for the spectru analysis. It ust be considered, when capturing the stator current signal, that the sapling frequency f saple plays an iportant role. Generally, statistical bands of fault-indicative frequencies can be ascertained fro theory analysis and any MCSA experients [, 8, 1 3]. Table 1 suarizes the range of sideband frequencies in ters of faulty types. We see in Table 1 that the spectral analysis of stator currents ight be done in low frequency range (typically between and khz) to focus on the significant phenoena [4], and in the case of broken rotor bars fault, the fault-indicative frequencies are under 4 Hz. Thus, taking into account the Nyquist criterion, a very high sapling frequency value is not andatory in case that the otors are supplied by the ac grid. Sapling frequencies of k or 5k saples/s (standard in data acquisition devices) enable good resolution analysis. Incontrast,fortheinverter-fedotors,saplingprocedure is ore deanding. As it is known, stator current contains high-order frequency haronics, in this case, due to switching frequencies in odern inverter, typically above 1 khz. Thus, aliasing ay occur due to wrong sapling. Antialiasing techniques have to be used in order to have a correct current spectru and prevent a false failure alert. For decreasing alias to an acceptable level, it is coon to design a sharp-cutoff low-pass anti-aliasing filter and saple the signal at a frequency lower than the doinant frequency coponents such as the fundaental and the switching

5 Applied Matheatics 5 3 phase AC supply Reference frequency Signal acquisition Down-sapling A/D over-sapling Anti-aliasing filter Speed n M f s Optial slip estiation s constant =s e /(f 1 /f s ); s fans /pup /(1 s fans /pup ) = [s e /(1 s e ) ]/(f s /f 1 ) Spectru estiation K 1 1 (f, P(f)) = (f, P k (f)) K K= Fault identification f=f b : faulty ; f f b : healthy Characteristic frequency deterination f b = (1 ± s)f s Figure : Scheatic diagra of fault diagnosis. Table 1: Range of sideband frequencies in ters of faulty types. Fault types Theoretical forula Range Frequencies Air-gap eccentricity f ecc =f s [1 ± ( 1 s )] p Low, high 9 Hz Broken rotor bars f b =f s [k ( 1 s )±s] Low 4 Hz p Bearing failure f i,o = n b f r [1 ± b d cos β] High Hz p d Interturn short circuit f stl =f s [ p (1 s) ±k], f sth =f s [1 ± Z ( 1 s )] Low, high 1 Hz p frequencies [5]. However, such sharp-cutoff analog filters are difficult and expensive to ipleent, and if the syste is to operate with a variable sapling rate, adjustable filters would be required. Furtherore, sharp-cutoff analog filters generally have a highly nonlinear phase response, particularly at the pass-band edge. In our proposed ethod, oversapling as an alternative technique is used. The principle of oversapling is briefly reviewed as follows (see [6] for details). A very siple anti-aliasing filter that has a gradual cutoff with significant attenuation is firstly applied to prefilter the otor stator phase-a current. Next, ipleent the A/D conversion at a higher sapling rate. After that, downsapling the obtained signal with a lower sapling frequency is ipleentedusingadigitallow-passfilter. As for the inverter supply, several haronics could be ixedupincasethatlowresolutionofthebandsidewas chosen. In general, one can take the following steps to select data acquisition paraeters in order to achieve the correct resolution needed. (1) Definition of sapling frequency. For anti-aliasing purpose, f saple has liitation as f saple f c,where f c is the highest fault-indicative frequency. () Selection of required frequency resolution Δf. (3) Specification of the nuber of saples N = f saple /Δf. (4) Deterination of sapling tie T = N/f saple = NT s Calculation of Slip and Fault-Indicative Frequencies with Variable Excitation Frequency. Fro Section,brokenrotor bars can be detected by onitoring the stator current spectral coponents f b =(1±s)f s, where haronic frequenciesf b are a function of slip s and excitation frequency f s. In case of broken rotor bars fault, excitation frequency f s and the corresponding slip s ust be firstly deterined in order to find haronic frequenciesf b.theresultofa otor diagnosis using MCSA is incorrect if the detected slip has an error [8, 7]. One of the ost popular ways to obtain the inforation of the slip frequency is to use speed sensor. In our proposed ethod, slip s is calculated in optial-slip-estiation odule, based on the real easured speed and torque-speed characteristic curve of squirrel-cage otor. The torque-speed characteristic curve of different load types is shown in Figure 3.Curves(1),()and(3)areinherent characteristic curves of squirrel-cage otor corresponding to different excitation frequency f s. For ease of analysis, it is assued that torque characteristic curves (1), () and (3) intersect echanical characteristic curvef 1 at noinal operating point A and only excitation frequency f s <f 1 is considered (if f s >f 1, otor operates at pointa 3 of curve (3)). In Figure 3, thevalueofslips corresponding to point A is s e =(n 1 n e )/n 1. The no-load speedes corresponding to different excitation frequency can be expressed as n 1 = 6f 1 /p and n = 6f s /p, wherep denotes the nuber of pole-pairs.

6 6 Applied Matheatics α=: constant torch load n α=1: load proportional to speed n 3 A 3 α=: fans/pup load n 3 n 1 A n e n (3) f A s >f 1 n (1) f n 1 1 A 1 () f s <f 1 T T e T L Figure 3: Torque-speed characteristic curve of squirrel-cage otor with different load types. If otor works with constant torque load, the operate point shifts fro A to A 1,theslips corresponding to A 1 is equal to s constant =(n n 1 )/n. Considering the congruent relationship between Δn 1 n e A and Δn n 1 A 1,wecandeduce the specific slip forula as follows: s constant =s e /(f 1 /f s ). If otor works with fans/pup load, the operating point shifts fro A to A and the slip s corresponding to A is equal to s fans/pup =(n n )/n. Considering the siilarity of Δn 1 n e A to Δn n 1 A 1 and relationship of T/T e = (n /n e ) between speed and torque of fans/pup, we can deduce the specific slip forula as follows: s fans/pup /(1 s fans/pup ) = [s e /(1 s e ) ]/(f s /f 1 ) Nonparaetric Spectru Estiation Algoriths. MCSA techniques include paraetric and nonparaetric spectru analysis of the otor current in general [8]. Aong the nonparaetric algoriths, we use Welch s periodogra algoriths based on DFT to copute the power spectru of the phase-a otor current data. Let i N [n] = {i[],i[1],...,i[n 1]} be a discrete tie signal, which is obtained by sapling the phase-a otor current signal i(t) for a duration of sapling tie T. To reduce the variance of power spectru estiate, the Npoint data sequence, i N [n] = {i[], i[1],..., i[n 1]}, is first partitioned into K overlapping segents. The length of each segent consistsof Lsaples and these segents can be overlapping on each other with (L S) overlapping saples, where S is the nuber of points to shift between segents. Thereafter, the periodogra of each segent is calculated andtheobtainedperiodograsarethenaveragedtogivethe power spectru estiate. The length of segent L is dependent on the required resolution. In order to increase the quality of power spectru estiates, the signal segents can be windowed before calculatingfft.theproposedethodsperitreducethevariance of the estiate at the expense of a decreased frequency resolution. However, it is difficult to trade off between the frequency resolution and the estiate variance. It has been noted that the use of 5% overlapping percentage aong the partitioned segents leads to efficient ipleentation of the fast Fourier transfor (FFT) algorith and in this case the relationship between K and L of segent as follows K = (N L/)/(L/). Algorith 1. Step 1. Subdividing N-point sapled data sequence, i N [n] = {i[],i[1],...i[n 1]}, into K overlapping segents; the kth segent data x[n + ks], n L 1and k K 1,is as follows: Segent 1: x[],x[1],...,x[l 1]; Segent 1: x[s], x[s + 1],..., x[l + S 1];. Segent K: x[n L],x[N L+1],...,x[N 1]. Step. Weighting kth segent, d[n] denote rectangular window function: x k [n] = d[n] x [n+ks], n L 1, k K 1. (11) Step 3. Calculating power spectru of the kth segent data: P k (f) = 1 ULT X (f)[x(f)] = 1 ULT X (f), (1) where X(f) = T L 1 n= x(k) [n]e jπfnt denote DFT of the kth segent data and U = T L 1 n= d [n] denote noralization factor. Step 4. Averaging all segents power spectru: P(f)= 1 K 4. Experient Setup and Signal Acquisition Methods K 1 P k (f). (13) k= 4.1. Experient Setup. Scheatic diagra of the experient setup is shown in Figure 4.Thissystecanbeusedtosaple line current i a and line voltage u ab (if necessary, it can be arranged to saple the other line currents i b and i c and line voltages u bc and u ca, too), and speed signals. The ain coponents of the experient setup are as follows. (1) Three-phase 3 kw SCIM (see Table for details). () Digital stroboscope coupled with the shaft of the SCIM as angular-speed sensor to easure and record the tie variation of the speed. (3) DC generator coupled with the SCIM to provide its adjustable load. (4) Mechanical coupling between SCIM and dc generator. (5) Variable resistor bank as a variable load of the generator: the load of the generator and, consequently, the induction otor can be adjusted by varying this

7 Applied Matheatics 7 Squirrel cage otor Inverter Conditioning circurt DC generator 3-phase source PC Data acquisition card Excitation circurt Resistor bank Figure 4: Scheatic diagra of the experient. resistance and/or regulating the excitation current of thegeneratorbyrelevantvariableresistor.theresistance of this variable-resistor bank can be selected step by step by a selector on the bank. In the operating otor, a suitable position of the selector is selected and consequently the induction otor is loaded. By regulating the output voltage of the generator inserted in the excitation current path, the load level is regulated precisely. (6) Induction-otor drive syste type Siens44 with rating values in accordance with that of the SCIM: this drive has been ainly designed and built for openloop scalar controller in constant voltage/frequency (CV/f)ethod. (7) Three-phase change-over switch to exchange the otor connections fro the ains for the drive output. (8) Signal conditioning circuits: since the used DAQ card accepts only voltage signals with axiu aplitudes of ±1V,thetypeandaplitudeofthesignals arepreparedbeforeconnectiontothecard.atthefirst stage, TBC3LTP Hall-effect current transforer is used to prepare the current signal and isolate it fro the power circuit. Secondary side current is then converted to proportional voltage signals by current shunts. Then, all signals are transitted to the DAQ card using a special shielded cable. (9) PC equipped with a self-ade data acquisition card for sapling the electrical data at a certain adjustable frequency and storing the in the eory. Experient setup to collect otor data and broken rotor used in the tests are illustrated in Figure Signal Acquisition Requireents. The experients involved collecting the phase-a stator current and speed data of the induction otor for different load conditions and different excitation frequencies of Hz, 3Hz, 4Hz and 5Hz, with three broken-rotor-bar fault and without any fault. The load conditions of the otor are 5%, 5%, 75%, and 94% full load, respectively. These load Table : Induction otor technical data. Paraeter Value Unit Noinal power 3. kw Noinal voltage 38 V Noinal current 6.8 A Noinal frequency 5 Hz Connection Δ Nuber of poles 4 Rotor slots nuber 8 condition percentages are deterined according to the otor naeplate inforation given in Table. Signal over-sapling ethod has been chosen in order to avoid aliasing. The stator current of otor was sapled with a frequency of khz for ain-fed and 4 khz for inverter-fed case. In the inverter-fed case, software filters have been ipleented in order to avoid aliasing. More specifically, an 8-order anti-aliasing digital butter-worth filter was ipleented and resapling of the signal has been done at khz. In our case, thirty seconds long data is acquired fro all two otors for each load condition at each frequency entioned above. Thus, the analyzed frequencies vary fro to 1 khz with a resolution of.3 Hz. For the feature extraction and discriinant analysis, starting with the first saple, the acquired data is processed with a sliding window size of 3, saples at a slide aount of 1,, resulting in 6 different data sets all together. Figure 6 illustrates the intercept parts of 5 Hz stator current signal fro the (a) ain-fed and (b) inverterfed healthy squirrel-cage otors. An expert inspection of these wavefors reveals that the inverter-fed otor current wavefor is heavily containated by the noise-like additive wavefor due to PWM switching of the voltage source inverter. If we were to use this otor current wavefor data to extract necessary features for fault detection and classification, we need to preprocess the data. 5. Experiental Results 5.1. Experient 1. A noinally healthy squirrel-cage otor was firstly tested and the power spectru of the stator current centered on the fundaental coponent supplied by (a) ain and (b) inverter is shown in Figure 7. Theresults confir that the otor rotor is healthy since the sidebands f b are not present. Coparisons of Figures 7(a) and 7(b) shows that a large aount of haronic coponents is included in Figure 7(b) and the inverter supply does affect the spectruidentifiability. Figure 8 indicates power spectru of the stator current around the fundaental coponent for (a) ainfedand(b)inverter-fedfaultsquirrel-cageotorswiththree broken bars and full load. The annotations appearing in the figure denote the ain sideband coponents around the supply frequency and corresponding aplitudes. Coparison of Figures 7 and 8 indicates that sideband coponents appear, which deonstrates the broken bars occurred. Although ore frequency inforation appears, one could still identify

8 8 Applied Matheatics (a) (b) Figure 5: Experient setup to collect otor data and broken rotor used in the tests. 1 1 Aplitude Aplitude Saples Saples (a) (b) Figure 6: 5 Hz stator current signal fro the (a) ain-fed and (b) inverter-fed healthy squirrel-cage otor. Aplitude (db) 4 6 Healthy n = 145 r/in; f=5hz (a) Aplitude (db) (b) Healthy; n = 145 r/in; f s =5Hz Figure 7: Power spectru of the stator current around the fundaental coponent for (a) ain-fed and (b) inverter-fed healthy squirrel-cage otor. Aplitude (db) Hz, 34 db n = 145 r/in; f=5hz (a) Aplitude (db) Hz, 34 db n = 145 r/in; f s =5Hz 55 Hz, 4 db (b) Figure 8: Power spectru of the stator current around the fundaental coponent for (a) ain-fed and (b) inverter-fed fault squirrel-cage otor.

9 Applied Matheatics 9 Aplitude (db) 4 6 n = 19 r/in; f s =45Hz 41 Hz, 38 db 49 Hz, 39 db Aplitude (db) Hz, 37.5 db n = 115 r/in; f s =4Hz 43.4 Hz, 38 db Aplitude (db) Hz, 4 db (a) n=91r/in; f s =3Hz 34.6 Hz, 4 db (c) Aplitude (db) (b) n=576r/in; f s =Hz 18 Hz, 4 db Hz, 4 db (d) Figure 9: Power spectru of the stator current around different excitation frequency of (a) 45 Hz, (b) 4 Hz, (c) 3 Hz, and (d) Hz. Aplitude (db) Hz, 43 db n=947r/in; f s =3Hz 3.9 Hz, 45 db Aplitude (db) Hz, 41 db n=935r/in; f s =3Hz 33.7 Hz, 43 db Aplitude (db) Hz, 44 db (a) n = 148 r/in; f s =5Hz 51.3 Hz, 44 db (c) Aplitude (db) Hz, 4 db (b) n=146r/in; f s =5Hz 5.7 Hz, 4 db (d) Figure 1: Power spectru of the stator current around (left) 5% and (right) 5% full loads. Top row: 3 Hz and botto row: 5 Hz reference frequency. in Figure 8(b) broken rotor bars haronics at 45 Hz and 55 Hz using our proposed ethod. Coparison of Figures 8(a) and 8(b) also indicates that, for the sae level of daage atthesaeload,thespectrusidebandshavethesae aplitude for different supply. 5.. Experient. The second experient involved fault squirrel-cage otor operating at different excitation frequency of inverter with three broken basr and full load. Figure 9 gives the power spectru of the stator current around the excitation frequencies of 45 Hz, 4 Hz, 3 Hz, and Hz. As expected, the sideband coponents f b =(1±s)f s, depending on excitation frequency and load are present. Coparison of Figures 9(a), 9(b), 9(c),and 9(d) indicates that the left sideband haronic coponent (1 s)f s varies fro (41 Hz, 36 db) to (18 Hz, 4 db) and right haronic (1 + s)f s fro (49 Hz, 39 db) to( Hz, 4 db), when excitation frequencyvariesfro45hztohz.anexpertinspectionof

10 1 Applied Matheatics these spectrus reveals that f b =(1±s)f s are always located around the excitation frequency and the distance fro the excitation frequency is sf s.italsocanbeseenfrofigure 9 that the aplitude of left sideband haronic coponent (1 s)f s decreases with the excitation frequency, which is the result that when excitation frequency decreases the output voltage becoes lower and uch saller current is drawn by otor Experient 3. In Experient 3, additional experients were perfored with the faulty otor at different excitation frequencies (3 Hz, 5 Hz) under two different loads (5%, 5%) to assess the perforance of the proposed ethod over the full range of otor loads. Using the proposed diagnosis ethod, the collected phase current data of the fault otor with three broken bars were analyzed. Figures 1(a) and 1(b) show the results with 3 Hz excitation frequency at different loadsanditcanbeseenthatthefaultcharacteristicfrequency of broken rotor bars is exposed clearly. With the increase of load, the coponents of characteristic frequency becoe ore and ore significant, such as in Figure 1(a) of 5% load and Figure 1(b) of 5% load. The siilar results could be received for fault otor with 5 Hz excitation frequency at different loads; see Figure 1(c) of 5% load and Figure 1(d) of 5% load. 6. Conclusion Open-loop voltage-source-inverter-fed squirrel-cage otors with constant voltage/frequency control ethod are widely used to drive fans, pups, or other echaniss involving speed control for energy-saving purpose. In these cases, the otor operates steadily with different excitation frequencies. Unlike the utility-driven case, the position of the current haronics appearing on the stator-current spectru due to broken rotor bar faults is highly dependent on the echanical otor load and excitation frequency, which affects the slip frequency. As a consequence, the reliable identification and isolation of faults reains an open issue. In this paper, a siplified fault current signal odel is firstly established using switching function concept and frequency odulation theory. It is deonstrated that the inverter-fed otor current is heavily containated due to PWM switching of the voltage source inverter. However, the broken rotor bars fault characteristic frequency f b = (1 ± s)f s, depending on faulty severity, loads, and excitation frequency, is always located around the excitation frequency and the distance fro the excitation frequency is sf s.novel broken rotor bar fault diagnosis techniques using otor current signature analysis (MCSA) for open-loop voltagesource-inverter-fed squirrel-cage induction otors with constant voltage/frequency control ethod are subsequently proposed. Experiental results obtained on self-ade 3 kw three-phasesquirrel-cageinductionotorsarediscussed. It is shown that experiental and siulation results are consistent with those of the odel revealed and the proposed techniques are effective and accurate. The ethod described works well under constant load torque, but soe difficulties appear with regard to closedloop control-operated achines, when f s and s vary alost siultaneously and it is ipossible to eploy the proposed ethod to diagnose broken rotor bar fault. At the oent, further research is carried out for the features, advantages, liitations, and iproveents of the proposed techniques. Acknowledgent This work was supported by the Chinese acadey of Sciences Key Deployent Project under Grant no. KGZD-EW-3. References [1] M. E. H. Benbouzid and G. B. Klian, What stator current processing-based technique to use for induction otor rotor faults diagnosis? IEEE Transactions on Energy Conversion,vol. 18, no., pp , 3. [] J. Cusido, L. Roeral, J. A. Ortega, J. A. Rosero, and A. G. Espinosa, Fault detection in induction achines using power spectral density in wavelet decoposition, IEEE Transactions on Industrial Electronics, vol. 55, no., pp , 8. [3] T. M. Wolbank, P. Nussbauer, H. Chen, and P. E. Macheiner, Monitoring of rotor-bar defects in inverter-fed induction achines at zero load and speed, IEEE Transactions on Industrial Electronics,vol.58,no.5,pp ,11. [4] A. Bellini, F. Filippetti, C. Tassoni, and G. A. Capolino, Advances in diagnostic techniques for induction achines, IEEE Transactions on Industrial Electronics, vol. 55, no. 1, pp , 8. [5] A. H. Bonnett and C. Yung, Increased efficiency versus increased reliability, IEEE Industry Applications Magazine,vol. 14,no.1,pp.9 36,8. [6]J.Cusido,L.Roeral,J.A.Ortega,A.Garcia,andJ.R.Riba, Wavelet and PDD as fault detection techniques, Electric Power Systes Research,vol.8,no.8,pp ,1. [7] I. Culbert and W. Rhodes, Using current signature analysis technology to reliably detect cage winding defects in squirrel cage induction otors, in Proceedings of the 5nd Annual Petroleu and Cheical Industry Conference, pp.95 11, Septeber 5. [8]J.H.Jung,J.J.Lee,andB.H.Kwon, Onlinediagnosisof induction otors using MCSA, IEEE Transactions on Industrial Electronics,vol.53,no.6,pp ,6. [9] S. H. Kia, H. Henao, and G. A. Capolino, A high-resolution frequency estiation ethod for three-phase induction achine fault detection, IEEE Transactions on Industrial Electronics,vol. 54,no.4,pp ,7. [1] D. Matic, F. Kulić, M. Pineda-Sánchez, and I. Kaenko, Support vector achine classifier for diagnosis in electrical achines: application to broken bar, Expert Systes with Applications,vol.39,no.1,pp ,1. [11] M. E. H. Benbouzid, A review of induction otors signature analysis as a ediu for faults detection, IEEE Transactions on Industrial Electronics,vol.47,no.5,pp ,. 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11 Applied Matheatics 11 [13]R.A.Gupta,A.K.Wadhwani,andS.R.Kapoor, Earlyestiation of faults in induction otors using sybolic dynaicbased analysis of stator current saples, IEEE Transactions on Energy Conversion,vol.6,no.1,pp.1 114,11. [14] W. T. Thoson and M. Fenger, Case histories of current signature analysis to detect faults in induction otor drives, in Proceedings of the IEEE International Electric Machines and Drives Conference (IEMDC 3),3. [15] S. Choi, B. Akin, M. M. Rahiian, and H. A. Toliyat, Ipleentation of a fault-diagnosis algorith for induction achines based on advanced digital-signal-processing techniques, IEEE Transactions on Industrial Electronics,vol.58,no. 3, pp , 11. [16]B.Akin,S.B.Ozturk,H.A.Toliyat,andM.Rayner, DSPbased sensorless electric otor fault diagnosis tools for electric and hybrid electric vehicle powertrain applications, IEEE Transactions on Vehicular Technology, vol.58,no.5,pp , 9. [17] A. Bellini, Closed-loop control ipact on the diagnosis of induction otors faults, IEEE Transactions on Industry Applications,vol.36,no.5,pp ,. [18] S. M. A. Cruz and A. J. M. Cardoso, Diagnosis of rotor faults in closed-loop induction otor drives, in Proceedings of the IEEE 41st IAS Annual Meeting on Industry Applications, pp , October 6. [19] B. K. Lee and M. Ehsani, A siplified functional siulation odel for three-phase voltage-source inverter using switching function concept, IEEE Transactions on Industrial Electronics, vol.48,no.,pp.39 31,1. [] G. W. Chang and S. K. Chen, An analytical approach for characterizing haronic and interharonic currents generated by VSI-fed adjustable speed drives, IEEE Transactions on Power Delivery,vol.,no.4,pp ,5. [1] S. Nandi, H. A. Toliyat, and X. D. Li, Condition onitoring and fault diagnosis of electrical otors a review, IEEE Transactions on Energy Conversion, vol., no. 4, pp , 5. [] M. Eltabach and A. Charara, Coparative investigation of electric signal analyses ethods for echanical fault detection in induction otors, Electric Power Coponents and Systes, vol.35,no.1,pp ,7. [3] M. Eltabach, J. Antoni, and M. Najjar, Quantitative analysis of noninvasive diagnostic procedures for induction otor drives, Mechanical Systes and Signal Processing, vol.1,no.7,pp , 7. [4] A. Yazidi, H. Henao, G. A. Capolino, M. Artioli, and F. Filippetti, Iproveent of frequency resolution for threephase induction achine fault diagnosis, in Proceedings of the IEEE 4th IAS Annual Meeting on Industry Applications, vol.1, pp. 5,October5. [5] I. P. Georgakopoulos, E. D. Mitronikas, and A. N. Safacas, Detection of induction otor faults in inverter drives using inverter input current analysis, IEEE Transactions on Industrial Electronics,vol.58,no.9,pp ,11. [6] A. V. Oppenhei, R. W. Schafer, and J. R. Buck, Discrete-Tie Signal Processing, Tsinghua University Press, Beijing, China, nd edition, 5. [7] J. Faiz and B. M. Ebrahii, A new pattern for detecting broken rotor bars in induction otors during start-up, IEEE Transactions on Magnetics,vol.44,no.1,pp ,8. [8] B. Ayhan, M. Y. Chow, and M. H. Song, Multiple discriinant analysis and neural-network-based onolith and partition fault-detection schees for broken rotor bar in induction otors, IEEE Transactions on Industrial Electronics,vol.53, no. 4, pp , 6.

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