high-frequency signal injection-based rotor bar fault...

1624 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 4, JULY/AUGUST 2011

High-Frequency Signal Injection-Based Rotor BarFault Detection of Inverter-Fed Induction

Motors With Closed Rotor SlotsSung-Kuk Kim, Student Member, IEEE, and Jul-Ki Seok, Senior Member, IEEE

Abstract—This paper presents a nonparametric approach tofailure detection of broken rotor bars in inverter-fed inductionmotors (IMs). We lay the mathematical foundation for a diagnosticmodel of a rotor bar fault that captures the rotor bar high-frequency (HF) characteristics. The model shows that the HFequivalent motor resistance can be used as a direct indicator ofbroken rotor bars. It should be emphasized that the proposed de-tection methodology is applicable to any shape of rotor slot designby incorporating the idea of synchronous reference frame basedinjection and by taking the HF resistance as the fault detector.The proposed detection technique is also insensitive to other motorparameters and is effective under arbitrary load conditions. Thefull time-domain-based signature process provides efficient detec-tion and enhances fault isolation. The identification scheme wasimplemented and tested on an inverter-fed 1.5-kW IM.

Index Terms—Arbitrary load conditions, detection of a bro-ken rotor bar, inverter-fed induction motors (IM) with closedrotor slots, rotor bar high-frequency (HF) characteristics, time-domain-based signature analysis.

I. INTRODUCTION

INVERTER-DRIVEN adjustable speed drives of inductionmotors (IMs) are mature and well-established technologies

used in a large variety of demanding applications. Early faultdetection and diagnosis of IMs are essential for consistent andreliable operation without factory downtime. Broken rotor barsare among the most common failures that affect IMs themselvesand coupled mechanical equipment.

Broken rotor bars can be detected by monitoring any ab-normality of the spectrum amplitudes at certain frequencies inthe stator current spectrum [1]–[3]; however, these frequencycomponents are significantly affected by the operating con-ditions, such as the loading conditions and rotational speed

Manuscript received October 5, 2010; revised December 16, 2010 andJanuary 27, 2011; accepted February 7, 2011. Date of publication May 12,2011; date of current version July 20, 2011. Paper 2010-EMC-386.R2,presented at the 2010 IEEE Energy Conversion Congress and Exposition,San Jose, CA, September 12–16, and approved for publication in the IEEETRANSACTIONS ON INDUSTRY APPLICATIONS by the Electric MachinesCommittee of the IEEE Industry Applications Society. This work was sup-ported by the National Research Foundation of Korea (NRF) grant funded bythe Korea government (MEST) (2010-0029428).

S.-K. Kim is with the AE Control R&D Lab., LG Electronics Inc., Changwon641-713, Korea (e-mail: [email protected]).

J.-K. Seok is with the School of Electrical Engineering, Yeungnam Univer-sity, Kyungsan 712-749, Korea (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIA.2011.2153171

changes, because operating frequency harmonics may overlapthe harmonics caused by broken rotor bars. Thus, spectrum-based detection schemes are bound to steady-state conditions.This method may also fail in applications with closed-loopinverter-driven motors with a current regulator since the controlloop tends to attenuate the current signature resulting from thefault. Moreover, the need for high-precision motor slip or rotorfrequency information further complicates accurate diagnosis.

Since starting stresses such as high currents and mechanicalvibrations are considered as one of the major causes of rotorfailure, most of the detection researches have been the focusof line-connected IMs. However, as described in [4] and [7],frequent overloading (both thermal and electrical), as well asexcessive mechanical vibrations, fatigue parts, and environmen-tal stresses caused by contamination, may result in acceleratedfailures of squirrel-cage rotor bars. Thus, it is believed that therotor bars of inverter-fed IMs can be damaged by these reasonsother than the starting stresses. For specific failure monitoring,this paper focuses on nonstatistical detection of broken rotorbars in inverter-fed IMs.

Thus, different methods have been put forward to detectthe rotor faults of inverter-fed IMs [5]–[9]. In [5], the invertercurrent harmonics have been employed to sense rotor faultsassociated with broken rotor bars. While the inverter currentis introduced as a fault indicator, it still requires spectralanalysis to detect broken bars. On the other hand, sophisticatedmultiple discriminant analysis and artificial neural networksare proposed for reliable fault detection [6]. However, thephysical basis of the training process is not clear, making ithard to understand the limitations of this method. To overcomethe difficulties that arise in the statistical approach, a time-domain-based diagnosis method is developed [7]. Althoughthis approach does not require the accurate computation ofa single frequency component and its amplitude, we need toimplement a complicated maximum covariance method foraccurate frequency tracking of the fundamental component.

More attractive approaches are described in [8] and [9],where an open-loop high-frequency (HF) voltage was injectedin the stationary reference frame. The resulting negative-sequence carrier-signal current exhibits rotor-position-dependent saliencies due to the broken bar. This idea seemslike a good choice because it produces minimal interferencewith the fundamental operation and is nearly insensitive tothe accuracy of motor parameters. However, the diagnosis isonly effective under heavy load conditions since we cannot

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KIM AND SEOK: HF SIGNAL INJECTION-BASED ROTOR BAR FAULT DETECTION OF INVERTER-FED IMS 1625

spectrally distinguish it from the harmonic caused by magneticsaturation (2fe) and the rotor-fault-related harmonic (2fr) forlow values of slip.

Both of these methods are based on the spectrum analysisof the current signature in the stationary reference frame,which requires large memories and high computational coststo achieve accurate monitoring. Neither technique is suitablefor diagnostic purposes under light loads due to load-dependentoperating restrictions. This implies that the existing algorithmsneed large rotor currents or loading for diagnosis under abroken-bar-induced pulsating torque operation. This operationcould cause secondary damage to other electrical or mechanicalcomponents as well as to the motor. Due to its injection nature,another restriction arises in diagnosing the presence of brokenbars in a machine with closed rotor slots [8].

The purpose of this paper is to detect a broken rotor bar for aninverter-fed IM using the HF model of rotor bars. The presentedHF model elaborates on the relationship between the HF rotorresistance and the rotor leakage inductance, which increasesaround faulty rotor bars. This suggests that the HF equivalentmotor resistance can be a direct indicator of broken rotor barswithout being affected by magnetic saturation. The HF motorresistance is determined by a d-axis HF voltage injection inthe synchronous coordinate. The proposed approach does notrequire the complicated computation of a frequency componentas it is a simple full time-domain-based scheme. In addition,the detection technique is insensitive to operating conditionvariations and is effective even under unloaded conditions. Thedeveloped strategy was implemented on an inverter-fed 1.5-kWIM to validate its effectiveness. The experimental evaluation ofthe proposed idea has demonstrated little sensitivity to the rotorslot design.

II. PRINCIPLES OF HF SIGNAL INJECTION-BASED

BROKEN BAR FAULT DETECTION

A. Negative-Sequence Current Detection

An HF signal injection technique was recently proposed forrotor bar fault diagnosis [8], [9]. This detection is based onopen-loop HF voltage injection, which is superimposed on thefundamental voltage, in the stationary reference frame. Theresulting negative-sequence current carries unbalanced signa-tures caused by saturation (with a frequency of 2fe) and rotorbar faults (with a frequency of 2fr), as shown in Fig. 1. Thisapproach provides some advantages over other fundamentalcurrent-based diagnostic techniques in terms of interferencewith the fundamental motor operation and the influence ofclosed-loop current control.

However, applying spectrum analysis to determine rotorfaults requires complex signal processing. At light loads, thefrequency component with 2fr spectrally approaches the com-ponent with 2fe due to a low value of slip. This restricts thedetection range.

To justify this assertion, Fig. 2 shows the frequency spectraof the resulting negative-sequence current for an IM with onebroken rotor bar at 20% and 40% loads. In this test, the motorwas operated at 10 Hz, and an HF voltage with 10 V–150 Hz

Fig. 1. Saliencies detected by the negative-sequence current.

Fig. 2. Negative-sequence current frequency spectrum in the stationary refer-ence frame (one broken rotor bar). (a) 20% load. (b) 40% load.

was injected in the stationary reference frame. It is evident thataccurate spectral quantification of faults is found to be moredifficult as the slip decreases. This results in complex thresholdfunctions and may lead to higher false alarm rates.

B. HF Model of Proposed Broken Bar Detection

The current distribution in the shorted rotor bars may varysignificantly with frequency. For a rectangular rotor bar with


depth d, length l, and slot width w, the effective impedance ofthe bar can be represented as [10], [11]

Zbar =Rr(AC) + jXlr(AC)

=αdRr(DC)

[sinh 2αd + sin 2αd

cosh 2αd − cos 2αd

+jsinh 2αd − sin 2αd

cosh 2αd − cos 2αd

](1)

where α =√

πfμ◦/ρ, f represents the frequency, μ◦ indicatesthe permeability of air, ρ is the resistivity of the conducting bar,and Rr(DC) denotes the dc rotor resistance.

If the bar width is approximately equal to the slot width, thephase rotor equivalent resistance referred to the stator can besimply represented using the end-ring resistance Re [12]

Rr =2(2N1)2

N/m

[Rr(AC) + Re/

(2 sin2 ϕ

2

)](2)

where N1 is the turn number of the stator winding, N is thetotal number of rotor bars, m is the number of stator phases,and ϕ represents the electrical angular displacement betweentwo adjacent bars. If we assume that Re � Rr(AC) for all thefrequency range, then

Rr∼= 2(2N1)2

N/mRr(AC). (3)

The ac rotor bar resistance and the rotor leakage reactanceapproach equality as the frequency or bar depth increases [10],[11]. Thus, if αd > 2.5, we obtain

Rr(AC) = Xlr(AC) = αdRr(DC). (4)

By combining (3) and (4), the healthy HF rotor phase im-pedance referred to the stator can be written as

Rr_hf(0) = Xlr_hf(0) =2(2N1)2

N/mαdRr(DC). (5)

In case of n contiguous broken bars, the effective faulty HFrotor impedance becomes

Rr_hf(n) = Xlr_hf(n) =2(2N1)2

(N/m − n)αdRr(DC) (6)

which leads to an increment due to broken bars

ΔRr_hf(n) = Rr_hf(n) − Rr_hf(0) = mn

N − mnRr_hf(0).

(7)

For a three-phase machine, a plot of (7) to changes of n isshown in Fig. 3, where 3n/(N − 3n) is normalized to a perunit basis of Rr_hf(0). Note that ΔRr_hf(n) is proportional ton irrespective of the number of rotor bars (N = 28, 48, and 58),which means that the rotor leakage flux grows as the number ofbroken bars increases.

Fig. 3. Plot of ΔRr_hf(n) according to the number of broken bars.

Fig. 4. Broken rotor bar detection by HF voltage injection in the synchronousreference frame. (a) HF voltage injection to an IM with n broken bars.(b) ΔRr_hf(n)(θsl) by faulty bars.

III. PROPOSED ROTOR BAR FAULT DETECTION SCHEME

If the stator transient inductance is approximately equal tothe total leakage inductance [13] and if the injection frequencyωh is high enough, most of the HF current flows through therotor branch. Then, in the synchronous reference frame, thed-axis HF voltage equation at steady state can be written as

vedh

∼=[(Rs+Rr_hf )+p(Lls+Llr_hf )] iedh =(Req+pLeq)iedh

(8)

where Rs is the stator resistance, Lls represents the statorleakage inductance, Llr_hf is the HF rotor leakage inductancereferred to the stator, p denotes the differential operator, andiedh indicates the resulting d-axis HF current in the synchronouscoordinate. Here, we assume that the skin effect of statorparameters is negligible in the frequency range of interest(≤ 500 Hz) compared to that of the rotor parameters [14].


Fig. 5. Detectability for broken bar location of a two-pole IM. (a) Two adjacent bars. (b) Two perpendicular bars. (c) Two opposite bars.

Then, Req and Xeq can be estimated using a low-pass filter(LPF) as

R̂eq =LPF (ve

dh · iedh)LPF (ie2dh)

(9a)

X̂eq =

√LPF

{(ve

dh − R̂eq · iedh

)2}

√LPF (ie2dh)

. (9b)

Broken rotor bars produce a nonuniform leakage flux rise inthe airgap because there is no current flow in the broken bar. Thenonuniform leakage flux variation provides an opportunity toidentify broken bar faults that can be represented by an increaseof the HF rotor leakage reactance. Equations (5) and (6) clearlystate that R̂eq or X̂eq can be fault indicators; however, X̂eq isfound to be less adequate in this application with respect to R̂eq

since the stator leakage inductance changes due to magneticsaturation by the fundamental load current. Thus, in this paper,we take R̂eq as a diagnostic metric since it is nearly independentof the operating conditions.

Fig. 4(a) shows a general squirrel-cage IM with n brokenbars when operated with a nonzero slip of ωsl. If an HF voltageis added on the synchronous de-axis, it can be viewed asrotating or scanning the rotor with a ωsl velocity in the rotorreference frame (dr-axis). Thus, the resulting HF current iedh

will contain the rotor saliency effect (as shown in Fig. 1) dueto the nonuniform rotor leakage flux. This imbalance gives riseto a sinusoidal component with a double slip frequency (2ωsl)in R̂eq. Note that, from (8), the fault detector R̂eq contains theunknown stator resistance, which is a function of temperature.Because of relatively large thermal inertia, the stator resistanceitself and the temperature variations from motor resistances canbe treated as a dc offset in R̂eq. We can obtain an offset-freecomponent of R̂eq using a high-pass filter (HPF) as

ΔR̂r_hf(n)(θsl) = HPF (R̂eq). (10)

Then, the magnitude of the high-pass filtered R̂eq corre-sponds to ΔR̂r_hf(n) in (7), as shown in Fig. 4(b). In other

words, the magnitude of ΔR̂r_hf(n)(θsl) is proportional to thenumber of broken bars, and the frequency is proportional to anexisting load or a slip.

The sinusoidal signal with a double slip frequency does notappear at zero slip even when a bar fault is present. However,in real world, there is no such zero load condition because ofthe load from internal friction. This implies that the proposeddetection process is not affected by external load conditions.

Thus, it is worth mentioning that the fault detection problemis converted into one that identifies whether ΔR̂r_hf(n)(θsl) isan ac or dc signal. The ac signal represents the occurrence ofa fault, and the dc signal represents a no fault condition. Thisalleviates the need for designing threshold values or functionsfor failure detection. This simple decision rule allows theproposed approach to be a nonstatistical scheme and greatlyimproves the signal-to-noise ratio compared with other existingtechniques. These benefits are explained by the suitably chosenfault detector based on the rotor leakage flux variations, whichis more directly correlated with the nature of the rotor bar faultsthan with the current spectrum signature.

Although the proposed detection method is promising, moreresearch is required to extend its application to all types of IMswith various physical rotor disturbances, such as interbar cur-rents, skewing, and structural rotor unbalances. The existenceof the significant interbar currents may affect detection accu-racy because it creates axial rotor fluxes which flow through therotor shaft [15]. Skewing, which results in the variation of theinterbar currents, and structural rotor unbalances also give riseto rotor leakage flux variations.

The location of the broken rotor bars gives a direct impact onthe proposed rotor fault detectability. For two broken bars dis-placed by 0◦ and 180◦ electrical degrees [as shown Fig. 5(a) and(c)], the rotor saliency due to the magnetic unbalances almostdoubles the magnitude of ΔR̂r_hf(n)(θsl) compared to a singlebroken bar. However, symmetric breakages separated by a halfpole pitch [90◦ electrical degree; as shown Fig. 5(b)] may result


Fig. 6. Proposed HF voltage-injection-based bar fault detection strategy.

TABLE IRATINGS AND KNOWN PARAMETERS OF IM UNDER TEST

Fig. 7. Photograph of the tested motor. (a) Stator and three rotors tested.(b) Drilled rotor with closed slots.

in the masking of the proposed fault metric ΔR̂r_hf(n)(θsl)and may lead to a possible misdiagnosis. This fault scenariomasks the fault index of any other existing methods using

Fig. 8. Injection frequency effect of closed rotor slots for the negative-sequence current-based method and for the proposed method.

electric and magnetic signatures [16]. Even though the fault isnot diagnosed during its early stages, it gets worse, propagatingtoward the adjacent bars, and some symptoms enabling its easydiagnosis appear.

Fig. 6 shows the block diagram of the proposed HF voltage-injection-based rotor bar fault detection strategy. In this pa-per, we advocate an intermittent injection scenario to reduceadditional losses and acoustic noise. The resulting HF currentwill not affect the fundamental current regulation performancebecause a band-stop filter removes the HF current from thecurrent feedback to the current controller. Here, the HPF wasemployed to decouple the dc offset component resulting fromthe temperature effect. Phase current measurement for controland protection purposes is a standard feature of inverter-fed IMdrives. In addition, most drives typically have A/D convertersfor the current measurement with 10–12 b. This implies that noadditional sensors, cabling, and A/D converters are thereforeneeded to implement the proposed method. Since the proposedscheme is based on a two-phase current measurement system,it is suitable in retrofitting IM drives where two current sensorsare commonly used.


Fig. 9. Frequency spectrum of the measured negative-sequence current in case of different injection frequencies with closed rotor slots (one broken bar;40% load). (a) 150 Hz. (b) 500 Hz.

IV. EXPERIMENTAL RESULTS

The proposed algorithm was implemented on a 1.5-kW IMwith 28 rotor bars, as described in Table I. Two-phase currentswere sampled at 100 μs, and the nominal deadtime was setto 3.5 μs. A 4096-pulses-per-revolution encoder is mounted toone end of the IM to measure the rotor speed. The other endof the shaft was coupled to a 1.5-kW dc generator to controlexternal loads. In the experiments shown in this paper, Hall-effect current sensors and 12-b A/D converters captured thestator currents.

The injection condition was fixed at 5 V–500 Hz in the d-axissynchronous reference frame. The monitoring period of motorfault diagnosis depends on the motor output capacity and itsworking environments or applications. It is desirable that theinjection interval, which is a code to be stored in the inverter, isdecided by a field personnel who has some degree of expertiseon the system.

In the test, the cutoff frequency of the first-order discrete-time HPF is 0.05 Hz. The proposed algorithm is imple-mented through a signal processing method using second-orderdiscrete-time bandpass/stop filters, two first-order discrete-timeLPFs for (9a), and a first-order discrete-time HPF for (10). Eachfilter just requires a couple of multiplications and additions forreal-time implementation.

Fig. 7(a) shows the stator and three identical rotors used fortesting. The rotor with closed slots was intentionally drilled toemulate the actual rotor fault, as shown in Fig. 7(b).

A. Sensitivity Evaluation of the Rotor Slot Design

The method in [8] and [9] injects an HF voltage in thestationary reference frame. Based on the resulting negative-sequence HF current, spectral separation is required betweenthe components at the saturation-induced frequency (2fe) andat the rotor bar fault-related frequency (2fr). For rotors withclosed slots, however, the magnitude of the rotor bar fault-related component at 2fr is reduced as the injection frequencyincreases in the range of 150–750 Hz, as shown in Fig. 8. Itcan be observed from the figure that it is nearly impossible todistinguish a faulty rotor from a healthy rotor over 400 Hz.The corresponding results are shown in Fig. 9, where the

Fig. 10. Estimated HF resistance of two broken rotor bars in load change test.

frequency spectra are investigated at the injection frequency of150 and 500 Hz, respectively. As discussed in [8], the use ofthe negative-sequence current-based method in the stationaryreference frame for closed rotor slots has been limited over awide range of high frequencies.

In contrast, the voltage injection of the proposed methodis synchronized with the synchronous reference frame or thesaturation-induced frequency. This allows the proposed detec-tion to have a reduced sensitivity to saturation-induced har-monic variations. In addition, as shown in Fig. 8, the magnitudeof ΔR̂r_hf(n)(θsl) (marked with �) tends to increase withinjection frequency due to the skin effect. This feature providesa better signal-to-noise ratio at higher frequencies. From theseobservations, it can be concluded that the proposed detectiontechnique is applicable to IMs with closed rotor slots as well asto open rotor slots.

B. Rotor Fault Detection

One test was performed on a rotor with two broken bars,while the external load was stepwise increased from 0% to 15%of the rated torque. The external load, the d-axis synchronousstator voltage command ve∗

ds , R̂eq, and ΔR̂r_hf(n)(θsl) are


Fig. 11. Experimental results of the proposed bar fault detection method.(a) External load torque. (b) ΔR̂r_hf(n)(θsl) of two broken rotor bars (n=2).(c) ΔR̂r_hf(n)(θsl) of one broken rotor bar (n = 1). (d) ΔR̂r_hf(n)(θsl)of a healthy rotor bar.

Fig. 12. Experimentally measured amplitude of ΔR̂r_hf(n)(θsl).

shown in Fig. 10. At the instant of HF voltage injection, acsignals can be observed in ΔR̂r_hf(n)(θsl). The waveform of

ΔR̂r_hf(n)(θsl) shows that the HPF decouples the dc offset

resulting from the stator resistance in R̂eq, and the proposedrotor bar fault detection responds well to light loads.

The performance of the proposed detection method wasinvestigated through experiments at 300 r/min. The externalload increased from zero to the rated load, as shown in Fig. 11.In the absence of a fault, the high-pass filtered ΔR̂r_hf(n)(θsl)of Fig. 11(d) gives a clear dc signal irrespective of the externalload. In contrast, as shown in Fig. 11(b) and (c) for rotorfaults, ac signals are observed under arbitrary load conditions,including a zero external load. The designed HPF could result ina certain amount of distortions in terms of amplitude and phaseof ΔR̂r_hf(n)(θsl) at light loads, but this does not significantlyaffect the diagnostic decision. In a fault condition, the ampli-tude of ΔR̂r_hf(n)(θsl) slightly decreases as the load increasesdue to the magnetic saturation of the rotor leakage inductance.The experimentally measured amplitude of ΔR̂r_hf(n)(θsl) isshown in Fig. 12.

The test results show that the proposed scheme achievesreliable tracking of the rotor bar fault even in an unloadedcondition where the low slip frequency mainly results from thefriction load.

V. CONCLUSION

This paper has developed a method of detecting a broken ro-tor bar fault in an inverter-fed IM based on an HF model of rotorbars. The proposed detection scheme uses rotor leakage fluxas a fault-interpreting quantity, which directly indicates brokenbars, while existing approaches rely on external symptoms,such as rotor asymmetries or torque oscillation, that mostlyappear in sideband current components. As a result, the faulttracking accuracy of the available approaches is significantlydisturbed by external operating conditions. The proposed ap-proach does not require rotor speed information or the com-plicated computation of a frequency component. In addition,the detection technique is insensitive to operating conditionvariations and is effective in unloaded conditions. The devel-oped strategy was implemented in an inverter-fed 1.5-kW IM tovalidate its effectiveness. By incorporating the idea of the syn-chronous reference frame based injection and by taking the HFresistance as the fault detector, the proposed detection becomeseffective to a machine with closed rotor slots.

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Sung-Kuk Kim (S’10) received the B.S. and M.S.degrees in electrical engineering from the Schoolof Electrical Engineering, Yeungnam University,Kyungsan, Korea, in 2009 and 2011, respectively.

He is currently with the AE Control R&D Lab.,LG Electronics Inc., Changwon, Korea. His specificresearch interests are high-performance electricalmachine drives and ac motor fault diagnosis.

Jul-Ki Seok (S’94–M’98–SM’09) received the B.S.,M.S., and Ph.D. degrees in electrical engineeringfrom Seoul National University, Seoul, Korea, in1992, 1994, and 1998, respectively.

From 1998 to 2001, he was a Senior Engineer withthe Production Engineering Center, Samsung Elec-tronics, Suwon, Korea. Since 2001, he has been amember of the faculty of the School of Electrical En-gineering, Yeungnam University, Kyungsan, Korea,where he is currently an Associate Professor. FromFebruary 2008 to February 2009, he was a Visiting

Researcher with the Electrical and Computer Engineering Department, Uni-versity of Wisconsin, Madison. His specific research interests are in high-performance electrical machine drives, sensorless control of ac machines, andnonlinear system identification related to the power electronics field.

Dr. Seok is currently a member of the Editorial Board of the Institution ofEngineering and Technology Electric Power Applications.

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