Low Order PWM Inverter Harmonics Contributions to the Inverter-Fed Induction Machine Fault Diagnosis

610 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 2, FEBRUARY 2008

Low Order PWM Inverter HarmonicsContributions to the Inverter-Fed

Induction Machine Fault DiagnosisBilal Akin, Student Member, IEEE, Umut Orguner, Student Member, IEEE,

Hamid A. Toliyat, Fellow, IEEE, and Mark Rayner

Abstract—In this paper, the effects of inverter harmonics onmotor current fault signatures are studied in detail. It is theoret-ically and experimentally shown that the fault signatures causedby the inverter harmonics are similar and comparable to thosegenerated by the fundamental harmonic on the line current.Theoretically-derived extended relations including bearing fault,eccentricity, and broken rotor bar relations are found to matchexperimental results. Furthermore, it is observed and reportedthat the asymmetries on the rotor caused by broken rotor barsincrease the amplitude of even harmonics. To confirm these claims,bearing, eccentricity, and broken rotor bar faults are tested andthe line current spectrum of each faulty motor is compared withthe healthy one. The proposed additional fault data are expectedto contribute positively to the inverter-fed motor fault decision-making algorithms.

Index Terms—Bearing faults, condition monitoring, currentsignature analysis, fault diagnosis, inverter harmonics, spectralanalysis.

I. INTRODUCTION

CONDITION monitoring and incipient fault detection havebecome a mature technology in recent years to prevent

very costly shut-downs because of significant motor faults inthe industrial manufacturing facilities. Among fault diagnosismethods, current spectrum analysis of line driven motors is oneof the well-known methods that provides continuous monitor-ing in a nonintrusive way [1]–[3]. Although vibration analysiswith accelerometers and thermal analysis provide satisfactoryresults [4], [5], continuous low-cost protection without the useof extra sensors is always the most attractive method for agreater market share. Furthermore, practical issues in industrialfacilities where a lot of motors run simultaneously increasethe tendency toward line current signature analysis due to theshortcomings of other methods. Line current information ofinverter-fed motors is readily available for control and protec-tion purposes. Thus, by using the current sensor feedback and

Manuscript received April 8, 2006; revised December 12, 2006. This workwas supported by Toshiba International Corporation, Houston, TX.

B. Akin and H. A. Toliyat are with the Department of Electrical andComputer Engineering, Texas A&M University, College Station, TX 77843USA (e-mail: [email protected]).

U. Orguner is with the Department of Electrical and Electronics Engineering,Middle East Technical University, Ankara, 06531 Turkey.

M. Rayner is with Toshiba Industrial Corporation, Houston, TX 77041 USA.Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TIE.2007.911954

microprocessing unit, the new trend for low-cost protection ap-plications seems to be drive-integrated fault diagnosis systemswithout using any external hardware.

Even though numerous successful line-driven motor faultdetection methods are reported in the literature, inverter-fedmotor systems still require more attention due to remarkablenoise on the line current, transient operating conditions, andclosed-loop controller bandwidths [6]–[8]. Unlike a utility-driven motor line current, the inverter-fed motor line currentincludes EMI noise that adversely affects the fault diagnosis:inherent floor noise reduces the possibility of true fault patternrecognition using line current spectrum. Therefore, one shouldtake into consideration as many fault signatures as possible toenhance the reliability of fault diagnosis.

It is well known that adjustable speed motor drives generatesharp-edged waveforms at the output voltage, which causetime harmonics. In this paper, it is shown that the resultantlow order harmonics assist in fault diagnosis by repeating thesame physical interaction between the excitation and machinestructure consecutively similar to the fundamental harmonic.Thus, the harmonic contents, which are normally known as amajor side effect of the inverter, give rise to extra signatures andturn out to be useful in distinguishing faulty current spectrumpatterns from healthy ones.

Among motor faults, bearing faults are the most commonlyreported, with an occurrence of 40%. Because of the lowamplitude fault signatures in the current spectrum, they are alsothe most challenging to diagnose, even in line-driven motors.However, bearing fault detection of inverter-fed induction mo-tors has not been adequately investigated in the literature, andthere are limited resources on the diagnosis and side effectsof current spectrum floor noise that mask small fault-relatedsignals.

In this paper, in addition to the well-known harmonics dueto bearing failures, new bearing fault signatures excited by thelow-order inverter harmonics are investigated both theoreticallyand experimentally for inverter-driven motors to improve over-all fault diagnosis. Later sections report that eccentricity andbroken rotor bar faults introduce extra signatures on the linecurrent by the interaction of the inverter harmonics and themodified machine structure.

Therefore, the aim of this paper is to develop a theoreticalapproach, supported by experimental verifications, for bearingfaults, eccentricity, and asymmetry faults including low-order

0278-0046/$25.00 © 2008 IEEE

AKIN et al.: PWM INVERTER HARMONICS CONTRIBUTIONS TO INDUCTION MACHINE FAULT DIAGNOSIS 611

Fig. 1. Typical bearing geometry.

inverter harmonics, and their positive effects for diagnosticpurposes. In addition, generalized theoretical fault relationshipsthat are supported by experimental results for each fault will bepresented. Finally, it is claimed and experimentally confirmedthat rotor asymmetry gives rise to even harmonics of the linecurrent spectrum that can be used as new fault signatures.

II. BEARING FAULT ANALYSIS OF INVERTER FED MOTORS

Bearing faults can be classified as outer race, inner race, balldefect, or cage defect, which are the main sources of machinevibration. These mechanical vibrations in the air-gap can beconsidered as slight rotor displacements which result in instanteccentricities. Therefore, the basic fault signature frequencyequation of line current due to bearing defects is adopted fromeccentricity literature [2].

A. Mechanical Vibration Frequencies Characteristics

Each fault has specific vibration frequency components thatare characteristic of each defect type which is a function of boththe rotor speed [9] and bearing geometry as shown in Fig. 1.The middle point between the outer and inner raceways isassumed as the reference point to develop mechanical vibrationcharacteristic frequency expressions. That is, the middle pointvelocity, wx, is the mean of the inner and outer race linearvelocities as given by

wx =Vx

rx=

winrin + woutrout

2rx(1)

where rx is the radius of the cage, win and wout are the angularvelocity of the inner and outer raceways, rin and rout arethe radius of the inner and outer raceways, respectively. Therespective rotational frequencies are fx, fout and fin, therefore

fx =finrin + foutrout

2rx. (2)

The outer raceway defect frequency ford is associated withthe rate at which the balls pass a defect point on the outer race.Obviously, the frequency increases linearly with the number ofballs, therefore the outer race defect frequency is calculated

by multiplying the number of balls with the difference of thereference point and the outer race frequencies as given by

ford =n|fx − fout|

=n

∣∣∣∣finrin + foutrout

2rx− fout

∣∣∣∣=

n

2

∣∣∣∣(fin − fout)(

1 − BD cos β

PD

)∣∣∣∣ (3)

where n is the number of balls, β is the contact angle, BD andPD are the ball and pitch diameters, respectively. Since the outerrace is stationary and the inner race rotates at the same speedas the rotor shaft, the characteristic outer race defect vibrationfrequency is rewritten as

ford =n

2frmech

(1 − BD

PDcos β

)(4)

following the same method for inner race, the characteristicinner race defect vibration frequency fird can be found as

fird =n

2frmech

(1 +

BDPD

cos β

)(5)

where frmech is the mechanical rotor speed.The mechanical oscillations due to bearing faults change the

air-gap symmetry and machine inductances like eccentricityfaults. The machine inductance variations are reflected to thestator current in terms of current harmonics, which are the indi-cators of bearing fault associated with mechanical oscillationsin the air-gap. Therefore, the bearing fault current harmonicfrequencies are given in (6) employing the previously foundmechanical characteristic frequencies

fcf = |f1 ± mfv| (6)

where f1 is the fundamental stator (carrier) frequency, fv is thecharacteristic mechanical vibration (modulation) frequency dueto bearing fault and m is an integer.

B. Accelerometer Outputs and Signatures Due toFundamental Harmonic

Detection of bearing fault using accelerometer output is moreexpensive but relatively easier than stator current data analy-sis. In Fig. 2, accelerometer results of bearing type RU6206outer race defect are given for two different fault levels. It isobvious that the outer race defect signals are located exactly atthe multiples of fundamental mechanical vibration frequency,ford = 107.9 Hz. The amplitude of the fault signal increasesdepending on the severity of mechanical fault; therefore, onecan easily monitor the condition of the bearing and classify thefault level by analyzing the vibration spectra. In addition to thecharacteristic vibration frequencies, the mean and rms of the vi-bration signal boost up according to the severity of the fault.The mean of the accelerometer output increases from −38 to−32 dB due to the introduced severe fault as shown in Fig. 2(a)and (b), respectively.

In spite of using expensive external sensors like an ac-celerometer, the stator current analysis can be realized with


Fig. 2. Mechanical vibration spectrum of the motor with outer race defectivebearing. Top to bottom: (a) tolerable fault, (b) severe fault.

readily available current sensors integrated into inverters. Themain disadvantage of current spectrum analysis is the noise thatcauses uncertainty while separating the healthy bearing patternfrom the defective. Although the inverter-fed motor stator androtor faults have been analyzed and the initial results are givenin the literature [10]–[12], they still require further investigationespecially for bearing fault. When focusing on the bearingfaults during this project, it was noticed that the floor noiselevel is comparable with bearing fault signature amplitude,hence making it very hard to diagnose incipient bearing defectsat early stages. When compared to the line-driven motor testresults, the test results of V/f control obtained from the sametest setup under the same conditions still look promising despitethe higher inverter current spectrum noise floor. Further ex-perimental analysis showed that, unlike open loop V/f control,closed loop field-oriented control (FOC) current regulators andhigh stator current spectrum floor noise mask the small bearingfault signatures. Therefore, to observe the bearing fault of themotor driven by a field-oriented controlled ac drive, sensingeither voltage or current is not enough without certain changeson the FOC structure.

C. Theoretical Approach to Determine BearingFault Signatures

The main difference between the dynamic eccentricity andbearing fault is the characteristic of the mechanical oscilla-tions. Regardless of rotor positions; an eccentric rotor causes anonuniform sinusoidal air-gap. However, bearing raceway andball defects cause an instantaneous mechanical impulse in theair-gap. For instance, in case of outer race defect, a rollingelement pass over the defect and generate a force vector period-ically. What is measured with the accelerometer is the responseof the motor to this radial force. Assuming the outer race isstationary, the mechanical impulse train can be represented by

x(t) = a∞∑

z=−∞δ(t − Tz) (7)

where δ(t) is continuous time impulse, T is the period ofimpulse train, and a is the amplitude of periodic impulse train.These mechanical vibrations directly affect the permeance of

the air-gap and give rise to current harmonics associated withvibration frequency. If the permeance oscillates at frequencyfosc and the excitation frequency is f1, then the current will bemodulated with harmonics at frequency f1 ± fosc. References[13] and [14] physically show the current harmonic frequenciesdue to the permeance variations for a small level of rotoreccentricity describing the air-gap length as

g(ϕ) = g0 − ρ · g0 · cos(ϕ). (8)

Fourier series expansion of permeance variation due to staticeccentricity is

Pg ≈ P0 +∑

n

Pn cos(nϕ + φn) ≈ P0 + P ′ cos(ϕ). (9)

The air-gap in case of dynamic eccentricity is given by

g(ϕ, θr) = g0 − ρ · g0 · cos(ϕ − θr) (10)

where ρ is the degree of eccentricity, ρ ∈ (0, 1), θr is the angu-lar position of the rotor with respect to the stator reference andg0 is the radial air-gap length in the case of a uniform air-gap,and ϕ is the particular angular position along the stator innersurface. The Fourier series expansion of permeance variationdue to dynamic eccentricity is represented by

Pg ≈P0 +∑

n

Pn cos (n(ϕ − θr) + φn)

≈P0 + P ′′ cos(ϕ − θr) (11)

where P0 is the average air-gap permeance and φ is the phasedelay. However, in the case of bearing fault, an exact eccen-tricity does not occur. Instead of a continuously rotating off-centered rotor, instant mechanical replacements of the rotoroccur when the balls pass over the defect points. This situationcan be generalized as vibrations causing permeance variationthat is a complex sum of an infinite number of rotating eccen-tricities [5].

Thus, the air-gap should be rewritten taking these instanteccentricities into consideration

g(ϕ,wbf , t) ≈ g0 −∑

k

ρ · g0 · cos(ϕ − wbfkt) (12)

and the Fourier series expansion of permeance variation due tobearing fault vibration is given by

Pg(ϕ, θ) ≈P0 +∑

k

∑n

Pn,k cos(nϕ − wbfkt − φn,k)

≈P0 +∑

k

Pk cos(ϕ − wbfkt) (13)

where wbfk is the frequency of the kth vibration due to bearingdefect. MMFs due to stator current can be shown by

F1 = A cos(pmϕ ± wt) (14)

where pm = mp; m is the number of harmonic, w is theexcitation frequency. The stator air-gap field, the interaction


TABLE ICURRENT SPECTRUM FAULT SIGNATURE FREQUENCIES DUE TO

INVERTER HARMONIC CONTENT (FOR F1 = 60 Hz)

of the bearing fault with stator MMFs with respect to thestator, can be expressed by (15), shown at the bottom of thepage. When the frequency of the kth mechanical vibration andinverter harmonics are taken into consideration, (15) can berewritten as (16), shown at the bottom of the page, where irepresents the ith inverter harmonic. It is clear from (16) that thebearing fault vibrations interact with the inverter harmonics andgenerate stator current sidebands at frequencies correspondingto (wbfk ± wi).

Further experimental studies to confirm (16) and the expla-nations given above proved that the frequencies of these currentfault signatures can be expressed as the extension of the generalbearing fault in (6) given by

fcf = |hf1 ± mfv| (17)

where k is an integer. The associated frequencies where extrafault signatures are expected due to inverter harmonics are givenin Table I.

Besides the given mathematical explanations, the physicalphenomenon reflected in the line current due to the inverter-driven motor with a bearing fault can be briefly summed upusing the well-known stationary reference frame equationsgiven by (18) and (19)

vsqs = rsi

sqs +

d

dtλs

qs

vsds = rsi

sds +

d

dtλs

ds. (18)

If the voltage drops on the stator resistor are neglected, itcan be clearly seen from the above equations that the fluxlinkages oscillate at the frequency of fundamental componentand harmonics of the inverter. The stator flux linkages canbe expressed in terms of self and mutual inductances of themachine as

λsqs =Lsi

sqs + Lmisqr

λsds =Lsi

sds + Lmisdr (19)

wherevsdqs dq-axis stator voltages in stationary reference

frame;isdqs dq-axis stator currents in stationary reference

frame;isdqr dq-axis rotor currents in stationary reference

frame;λs

dqs dq-axis stator flux linkages in stationary referenceframe;

Ls, Lm stator self inductance and magnetizing inductance.Because the machine inductances are functions of the flux,

the fault harmonics produced in the air-gap by the bearing de-fects are reflected as fault harmonics in the self and the mutualinductance of the machine. Since the flux linkages oscillate atthe frequency of the fundamental component and harmonics ofthe inverter, it is clear from the above equations that any faultharmonics in the inductances at the bearing fault characteristicfrequencies result in current harmonics at the sidebands of thefundamental and each inverter harmonic frequency as explainedpreviously.

D. Experimental Verifications of Fault Signatures Due toInverter Harmonics

As explained in the previous section, the consecutive per-meance variations in the air-gap due to mechanical vibrationscaused by raceway defect reflect their effects on the line currentunder the excitation of each of the inverter harmonics similar tothe fundamental harmonic. The experimental results in Fig. 3show the new fault signatures at some of the frequencies givenin Table I. Some of these signatures that are produced byinverter harmonics are comparable with the previously definedbearing fault signatures as shown in Fig. 4 and are given by(6). Thus, one can use these extra fault indicators reliably toreinforce the fault claim. The source of the inverter harmonicsand associated signatures are roughly given below.

The well-known inverter harmonics, 6k ± 1 (i.e., 5, 7, 11,13, . . .) odd harmonic pairs, are the most common low orderharmonics on the voltage spectrum. These odd harmonics gen-erate new fault signatures in the current spectrum at frequenciessuch as f = 12 Hz, 192 Hz, 228 Hz, etc. A similar resultis mentioned in [10] where motors are driven with a six-stepconverter and 6k ± 1 harmonics reported to be dominant whencompared to others.

Besides the odd harmonic pairs, some of the remarkablesignatures other than the fundamental are observed due tomultiples of third and sixth harmonics commonly expected

Bs(ϕ, t) =AP0 cos(pmϕ ± wt)+∑

k

APk

2[cos ((pm + 1)ϕ − (wbfk ± w)t) + cos ((pm − 1)ϕ + (wbfk ± w)t)] (15)

Bs(ϕ, t) =∑

i

AP0 cos(pmϕ ± wit)+∑

k

∑i

APk

2[cos ((pm + 1)ϕ − (wbfk ± wi)t) + cos ((pm − 1)ϕ + (wbfk ± wi)t)]

(16)


Fig. 3. Current spectrum of the inverter fed induction motor with healthy and outer race defective bearing (for f1 = 60 Hz).

according to Table I such as f = 288 Hz where (h = 3, m = 1;h = 6, m = 6; h = 12, m = 4), f = 504 Hz where (h = 3,m = 3; h = 6, m = 7; h = 12, m = 2), etc. Although the thirdharmonic is not expected to exist in a Y-connected system,during the experiments a remarkable third harmonic is noticedas a result of nonideal machine conditions and imperfectionseven for a healthy machine. The sources of the third harmonicand multiples are the dc bus voltage utilization maximizationstrategy of space vector pulsewidth modulation (SVPWM),saturation of iron core, and winding harmonic effects. On theother hand, it is known that the dead-time effect, nonidealitiesand PWM zero state space phasor also give rise to multiples of

sixth harmonics [15]. In two-level three-phase PWM strategies,six nonzero and two zero voltage vectors are used. Generally,the zero voltage vector varies six times over a constant timeperiod. Hence, the ratio of “on” and “off” states will varysix times in one period, generating sixth harmonics and theirmultiples of which cause new fault signatures at frequenciessuch as f = 144 Hz, 468 Hz, 504 Hz, etc., as shown in Fig. 3.

To recognize the faulty bearing pattern using the currentspectrum, various methods are proposed in the literature suchas: time and frequency domain techniques, high order spectralanalysis, neural network, model-based techniques, and sta-tistical analysis [16]–[20]. The accuracy of these algorithms


Fig. 4. Current spectrum of the inverter fed healthy and eccentric induction motor (for f1 = 60 Hz).

depends on the clarity and quantity of data provided. Therefore,the additional fault signatures correlated with the characteristicmechanical vibration and excitation frequencies are expected tocontribute positively to bearing fault analysis.

III. ECCENTRICITY DIAGNOSIS OF

INVERTER-FED MOTORS

Today, eccentricity is a quite well-known problem and an-alytical results supported by experiments have already beenreported. In the literature, there are several successful worksthat report diagnosis of eccentricity based on line current mea-surement [3], [4] where a few of which analyzed the inverter-fed motor case [21]. Unlike bearing faults, it is easier todiagnose eccentricity even for inverter driven cases due to theirhigh amplitude of fault signatures with respect to the noise floorin the current spectrum.

Because both static and dynamic eccentricities tend to co-exist in practice, only mixed eccentricity is considered in thispaper to show the effects of inverter harmonics. Magnetic fieldin the air gap of an eccentric motor is always nonuniform.Since the flux linkages in the air gap oscillate with synchronousfrequency, any additional harmonics oscillating at the rotorspeed due to nonuniform structure are expected to take placeat rotating frequency sidebands of the synchronous frequency.Monitoring mixed eccentricity using single-phase line currentcan be computed using (9), (11), and (14) by Nandi et al. [3] as

Bs(ϕ, t) = AP0 cos(pmϕ ± wt)

+AP1

2[cos ((pm + 1)ϕ ± wt)

+ cos ((pm − 1)ϕ ± wt)]

+AP2

2[cos ((pm + 1)ϕ − (wr ± w)t)

+ cos ((pm − 1)ϕ + (wr ± w)t)] . (20)

The sidebands of the excitation frequency are given as

feccentricity = f1

[1 ± m

(1 − s

p/2

)]

= f1 ± m.fr m = 1, 2, 3, . . . . (21)

where m is an integer, s is the per unit slip, f1 is the fundamen-tal excitation frequency, fr is the mechanical rotation frequency,and p is the number of the poles. When the inverter harmonicsare taken into consideration and substituted with the excitationfrequency in (14), then (20) can be rewritten as

Bs(ϕ, t) =∑

i

AP0 cos(pmϕ ± wit)

+∑

i

AP1

2[cos ((pm + 1)ϕ ± wit)

+ cos ((pm − 1)ϕ ± wit)]

+∑

i

AP2

2[cos ((pm + 1)ϕ − (wr ± wi)t)

+ cos ((pm − 1)ϕ + (wr ± wi)t)]

(22)

where i represents the ith inverter harmonic. It is clear from(22) that the eccentric air-gap excited by the inverter harmonicsresults in stator current sidebands at frequencies correspondingto (wr ± wi). When the effects of the inverter harmonics aretaken into consideration, (21) above can be rewritten as

feccentricity = k · f1 ± m · fr (23)


Fig. 5. Increase in second, fourth, and sixth harmonics due to rotorasymmetry.

where k is an integer representing inverter harmonics and fr isthe rotating frequency. These fault signatures due to the inverterharmonics given by (23) are observed during the experiments asshown in Fig. 4. Although not all the introduced signatures bythe inverter are as noticeable as the sidebands of the fundamen-tal, they can be used as extra fault information to support thefault decision-making algorithms.

IV. ROTOR ASYMMETRY

The electric and magnetic asymmetry in induction machinerotors boosts up the left-hand side sideband of the excitationfrequency [22]. A broken rotor bar can be considered as rotorasymmetry [22], [23] that causes unbalanced currents, torquepulsation, and decreased average torque. One of the significantchallenges in the rotor broken bar detection is to distinguish thenearby sidebands especially under low slip operation. In thissection a new signature is proposed to support the cage faultinformation provided by sidebands to enhance the reliability ofthe fault decision.

It is obvious that even number harmonics can be detected bya lack of symmetry about the x-axis. If the top and bottom halfof the waveforms do not look like mirror images of each other,the even harmonics are present. Therefore, even harmonic coef-ficients in the Fourier series expansion of symmetrical systemsare always zero. A typical induction motor stator and rotor aredesigned to be mechanically and electrically symmetric withthe exception of tolerable manufacturing imperfections. There-fore, only inherent even harmonics due to stator and rotor canbe observed on the current spectrum of an inverter-fed healthymachine. When the inverter harmonic content is considered,the quarter-wave symmetry assumption guarantees that the evenharmonics will be zero. If the quarter-wave symmetry constraintis relaxed to a half-wave symmetry constraint, then the evenharmonics are still zero [24]. When a rotor bar is broken, theMMF waveform cannot stay symmetric with respect to thex-axis due to the asymmetric bar current distribution. Eventu-ally, this phenomenon reacts to the terminal quantities of thestator.

During the experiments, it was recorded that the inherenteven harmonics boost up remarkably as shown in Fig. 5 when

the healthy rotor is replaced with the broken bar rotor. Sincesymmetric SVPWM references are characterized by modulatedpulses which are centered with respect to each PWM period, theobserved even harmonics are introduced by asymmetry formedon the rotor. In both healthy and broken rotor bar cases, thesame stator used and the rest of the system ran under exactlythe same conditions to make a precise comparison. Hence, theamplified even harmonics are additional signatures for the rotorasymmetry which are easily noticeable fault signature compo-nents supporting broken bar fault detection technique. Evenharmonics can also be used to support model and parameterestimation-based broken rotor bar diagnosis to distinguish pa-rameter variations either because of fault or evenly distributedtemperature increase.

Furthermore, other widely used approaches for diagnosis ofbroken rotor bars in induction machines are based on the mon-itoring of the stator current sidebands around the fundamentalharmonic in the line current [22] and air-gap torque, and speedprofile of induction machines [25]. It is well known that anyelectrical or magnetic asymmetry in the rotor increases the left-hand side and speed oscillation boosts up the right-hand sidesideband of the excitation frequency. Indeed, [25] shows thatbroken bars actually give rise to a sequence of such sidebandsgiven by

fb = (1 ± 2ks)f1, k = 1, 2, 3, . . . (24)

where f1 is the fundamental frequency. During regular oper-ations, a symmetrical stator winding excited at frequency f1

induces rotor bar currents at sf1 frequencies. When an asym-metry is introduced in the rotor structure, the backward rotatingnegative sequence −sf1 components start the chain of electricaland mechanical interactions between the rotor and stator of themotor. Initially, stator EMF at frequency (1 − 2s)f1 is inducedthat causes torque and speed ripples. Afterwards, torque andspeed ripples are reflected to the stator as line current oscil-lations at frequency (1 + 2s)f1. Next, (1 + 2s)f1 componentinduces rotor currents at ±3sf1 and this chain reaction goeson until completely being filtered by the rotor inertia. Whenthe motor is driven by the PWM inverter, the rotor currents areinduced at frequency

frotor,current = (6k ± 1)|s|f1, k = 0, 1, 2, . . . . (25)

The same chain effect mentioned above is repeated for allodd harmonic pairs due to induced rotor currents given by (25).In addition, each of the mechanical and electrical oscillationsintroduced by inverter harmonics will mutually interact witheach other and the harmonic content of the line current isenriched by the combination of these oscillations. On the otherhand, the very first impact of the fundamental harmonic on eachof the supply harmonics is given by [1]

fb =((

k

p

)(1 − s) ± s

)f1,

k

p= 1, 5, 7, . . . (26)

where k is the harmonic index and p is the number of polepairs. However, (24) does not cover effects of low order inverter


harmonics, and (26) covers asymmetrical signatures only dueto the impacts of the fundamental harmonic around each of theinverter harmonics neglecting chain reactions. Therefore, (24)is extended to cover odd harmonic pairs as given by

fb =(m ± 2nks)f1

k=1, 2, 3, . . .

m=1, 5, 7, . . . (stator current odd harmonic pairs)

n=1, 5, 7, . . . (induced rotor current odd harmonic pairs)

(27)

where m represents the odd inverter harmonic pairs inducingrotor bar currents and n represents the induced rotor currentharmonics. Indeed, in the second term, k alone represents theeffect of consecutive asymmetry signatures due to fundamen-tal harmonic around other odd harmonic pairs. The nk termrepresents the odd pair multiples of the fundamental harmonicincluding combinations of the mutual interaction between theinduced backward rotating rotor currents and their consecu-tive reflections on the stator side around the odd harmonicpairs.

Referring to the same argument mentioned above, whichexplains the physical facts because of asymmetry on the rotorstructure, (26) is extended using the original index terms as

fb =((

k

p

)(1 − s) ± lhs

)f1,

k

p=1, 5, 7, . . .

l=1, 3, 5, . . .

h=1, 5, 7, . . . (induced rotor current odd harmonic pairs)

(28)

where the first term transfers the induced asymmetry signaturesto the stator reference frames, and the second term representsthe frequency of induced rotor currents due to rotor asymmetrycovering all harmonics and chain reactions. Actually, both (27)and (28) give the same asymmetry signature clusters tracingthe different chain paths due to different relationship configu-rations and indexing. The extended (27) and (28) were justifiedexperimentally using a 3 hp induction motor with broken rotorbars driven by an inverter. The motor is driven under full loadat rated speed with s = 0.05. The consecutive impacts of therotor asymmetry around the fundamental, fifth, and seventhinverter harmonics due to the induced backward rotating ro-tor currents can be explicitly observed in Fig. 6(a) and (b),respectively.

Fig. 6(a) shows the sidebands of the healthy motor due to theinherent asymmetry and asymmetric motor as well. Generally,the first left sideband is considered to monitor the broken rotorbar which can most easily be distinguished from healthy motorsidebands [22]. This phenomenon again repeats itself for theodd harmonic pairs. The amplitude of the first left sidebandsaround the odd harmonic pairs are reported to be approximately5 dB higher than healthy motor sidebands and can be used tomonitor the broken bar as an additional signature.

Fig. 6. Rotor asymmetry signatures in inverter-fed motor line currentspectrum (a) around fundamental, (b) around fifth and seventh harmonics.

Fig. 7. Experimental setup.

V. EXPERIMENTAL SETUP

A number of identical induction motors are artificially mod-ified to test broken rotor bar, eccentricity, and bearing faults.A conventional test bed has been used to validate the pro-posed analytical expressions of the stator current fault signaturecomponents for the three-phase induction machine. The 3 hpinduction motor is loaded by a dc generator and is drivenby a custom-designed Semikron inverter as shown in Fig. 7,respectively. The inverter is controlled by a 32-bit fixed-point,150 MHz digital signal processor TMS320F2812. A signalconditioning board including voltage and current sensors isdesigned and connected to the data acquisition board throughvoltage amplifiers to scale the magnitude and low-pass filtersto set the frequency bandwidth to a correct range. To obtainraw current–voltage data, a 1.25 MS/s, 12-bit resolution dataacquisition card is used. A 16 bit A/D at 256 kHz SR760 fastFourier transform spectrum analyzer is used to monitor the realtime current and voltage spectrums.


VI. CONCLUSION

The additional signatures excited by the inverter harmonicson the stator current spectrum have been theoretically andexperimentally analyzed in detail. It is proved that analyticallyobtained extended relations for bearing faults, eccentricity,and broken rotor bars match the experimental stator currentharmonics spectrum.

After explaining the challenges often encountered in faultdiagnosis of adjustable-speed drive systems, the analytical per-meance and the field density oscillations under bearing andeccentricity faults are derived. These relationships are used todetermine fault signatures for inverter-fed machines. The newsignatures are modeled in terms of extended fault equationswhich account for the impact of inverter harmonics and thecorresponding increase in fault signature data.

The developed equations will also be tested on field-orientedcontrolled systems with certain changes on control algorithmsto decrease fault signature suppression. The precise positiveeffects of the proposed signatures will also be examined usingvarious pattern-recognition algorithms.

ACKNOWLEDGMENT

The authors wish to acknowledge the support of ToshibaInternational Corporation, Houston, TX and in particular thehelp of Mark Rayner.

REFERENCES

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[2] R. Schoen, T. Habetler, F. Kamran, and R. Bartfield, “Motor bearing dam-age detection using stator current monitoring,” IEEE Trans. Ind. Appl.,vol. 31, no. 6, pp. 1274–1279, Nov./Dec. 1995.

[3] S. Nandi, M. Bharadwaj, and H. A. Toliyat, “Performance analysis of athree-phase induction motor under mixed eccentricity condition,” IEEETrans. Energy Convers., vol. 17, no. 3, pp. 392–399, Sep. 2002.

[4] D. G. Dorrell, W. T. Thomson, and S. Roach, “Analysis of airgap flux,current, and vibration signals as a function of the combination of static anddynamic air gap eccentricity in 3-phase induction motors,” IEEE Trans.Ind. Appl., vol. 33, no. 1, pp. 24–34, Jan./Feb. 1997.

[5] C. Riley, K. Lin, T. Habetler, and G. B. Kliman, “Stator current harmon-ics and their causal vibrations: A preliminary investigation of sensorlessvibration monitoring applications,” IEEE Trans. Ind. Appl., vol. 35, no. 1,pp. 94–99, Jan./Feb. 1999.

[6] F. Briz, M. W. Degner, A. B. Diez, and J. M. Guerrero, “Online diagnosticsin inverter-fed induction machines using high-frequency signal injection,”IEEE Trans. Ind. Appl., vol. 40, no. 4, pp. 1153–1161, Jul./Aug. 2004.

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[11] G. R. Bossio et al., “Effects of rotor bar and end-ring faults over thesignals of a position estimation strategy for induction motors,” IEEETrans. Ind. Appl., vol. 41, no. 4, pp. 1005–1012, Jul./Aug. 2005.

[12] J. Yang, S. B. Lee, J. Yoo, S. Lee, Y. Oh, and C. Choi, “A stator wind-ing insulation condition monitoring technique for inverter-fed machines,”IEEE Trans. Power Electron., vol. 22, no. 5, pp. 2026–2033, Sep. 2007.

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[14] B. Heller and V. Hamata, Harmonic Field Effects in Induction Machines.New York: Elsevier, 1977.

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[25] F. Filippetti, G. Franceschini, C. Tassoni, and P. Vas, “AI techniques ininduction machines diagnosis including the speed ripple effect,” IEEETrans. Ind. Appl., vol. 34, no. 1, pp. 98–108, Jan./Feb. 1998.

Bilal Akin (S’03) received the B.S. and M.S. degreesin electrical engineering from Middle East TechnicalUniversity, Ankara, Turkey, in 2000 and 2003, re-spectively. He is currently working toward the Ph.D.degree at Texas A&M University, College Station.

From 1999 to 2000, he was an R&D Engineer inTUBITAK BILTEN, Ankara, Turkey. He was withTYCO Electronics, Mesquite, TX, in 2004. Since2005, he has been an R&D Engineer in ToshibaIndustrial Division, Houston, TX. His research inter-ests are advanced control methods in motor drives,

fault diagnosis of electric machinery, machine design and DSP based industrialapplications.

Umut Orguner (S’99) received the B.S. and M.S.degrees in electrical engineering from Middle EastTechnical University, Ankara, Turkey, in 1999 and2002, respectively.

He is currently a Teaching Assistant and aPh.D. candidate in the Department of Electricaland Electronics Engineering of the same univer-sity. His research interests include estimation theory,multiple-model estimation, target tracking and infor-mation fusion.


Hamid A. Toliyat (S’87–M’91–SM’96–F’08) re-ceived the B.S. degree in electrical engineering fromSharif University of Technology, Tehran, Iran, in1982, the M.S. degree in electrical engineering fromWest Virginia University, Morgantown, in 1986,and the Ph.D. degree in electrical engineering fromthe University of Wisconsin—Madison, Madison,in 1991.

Following receipt of the Ph.D. degree, he joinedthe faculty of Ferdowsi University of Mashhad,Mashhad, Iran, as an Assistant Professor of electrical

engineering. In March 1994, he joined the Department of Electrical and Com-puter Engineering, Texas A&M University, College Station. He has supervisedmore than 35 graduate students, published over 265 technical papers, raisedover $3.4 M in research funding, and presented more than 45 invited lecturesall over the world. He has ten issued and pending U.S. patents in these fields.He is the author of DSP-Based Electromechanical Motion Control (CRC Press,2003) and the coeditor of Handbook of Electric Motors-2nd Edition (MarcelDekker, 2004). His main research interests and experience include analysis anddesign of electrical machines, variable speed drives for traction and propulsionapplications, fault diagnosis of electric machinery, and sensorless variablespeed drives.

Dr. Toliyat is a member of Sigma Xi and a Senior Member of the PowerEngineering, Industrial Applications, Industrial Electronics, Power ElectronicsSocieties of the IEEE. He is an Editor of IEEE TRANSACTIONS ON ENERGY

CONVERSION and was an Associate Editor of IEEE TRANSACTIONS ON

POWER ELECTRONICS. He is also Vice Chair-Papers, IEEE-IAS IndustrialPower Conversion Systems Department of IEEE-IAS Electric Machines Com-mittee. He was the General Chair of the 2005 IEEE International ElectricMachines and Drives Conference in San Antonio, TX. He was the recipientof the 1996 IEEE Power Engineering Society Prize Paper Award for his paperon the Analysis of Concentrated Winding Induction Machines for AdjustableSpeed Drive Applications-Experimental Results, the Space Act Award fromNASA in 1999, the Texas A&M Select Young Investigator Award in 1999from Texas A&M University, the Schlumberger Foundation Technical Awardsin 2000 and 2001, the Eugene Webb Faculty Fellow Award in 2000, theE.D. Brockett Professorship Award in 2002, the Distinguished Teaching Awardin 2003, the TEES Fellow Award in 2004, the prestigious Cyrill Veinott Awardin Electromechanical Energy Conversion from the IEEE Power EngineeringSociety in 2004, and the Outstanding Professor Award in 2005 from TexasA&M University.

Mark Rayner, photograph and biography not available at the time ofpublication.

Low Order PWM Inverter Harmonics Contributions to the Inverter-Fed Induction Machine Fault Diagnosis

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