induction motor thermal aging caused by voltage distortion and imbalance.pdf

12 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 38, NO. 1, JANUARY/FEBRUARY 2002

Induction Motor Thermal Aging Caused by VoltageDistortion and Imbalance: Loss of Useful Life

and Its Estimated CostJose Policarpo G. de Abreu and Alexander Eigeles Emanuel, Fellow, IEEE

Abstract—This paper reports the effect of voltage distortion andimbalance (VDI) on the thermal aging of the insulation of low-voltage induction motors. The study is based on a detailed thermalmodeling of actual motors in the 2–200-hp range. The dollar valueof the useful life lost was estimated for different VDI conditions.Two important conclusions were reached. First, voltage subhar-monics have a dramatic effect on motor thermal aging. Second,the overall cost of motor loss of life due to harmonic pollution andvoltage imbalance, in the U.S. today, is estimated to be in the rangeof 1–2 billion dollars per year.

Index Terms—Power quality economics.

I. INTRODUCTION

T HE top two sources of squirrel-cage motor failure are: first,mechanical, with prevalence to bearing damage, and the

second is stator insulation breakdown [1]–[3].The deterioration of the stator insulation and its ultimate

breakdown is controlled by four factors that act simultaneouslyon the dielectric [4]:

• thermal aging of the insulation;• voltage surges caused by lightning, switching, or recurrent

pulses;• insulation chaffing and shearing caused by mechanical

stress due to vibrations and shearing forces;• chemical deterioration due to environmental factors such

as aggressive chemicals or hydrocarbons.Both voltage distortion and imbalance (VDI) cause signif-

icant additional power losses, thus increasing the steady-statetemperature rise of the windings. During the starting time, theheating process of rotor bars and rings is nearly adiabatic; theupper region of the bars, where the current density is larger, isreaching higher temperatures than the lower region of the bars.The significant temperature rise during the motor starting, the

Paper ICPSD 01–26, presented at the 2001 IEEE/IAS Industrial andCommercial Power Systems Technical Conference, New Orleans, LA, May13–17, and approved for publication in the IEEE TRANSACTIONS ONINDUSTRY

APPLICATIONS by the Power Systems Protection Committee of the IEEEIndustry Applications Society. Manuscript submitted for review May 15, 2001and released for publication October 10, 2001. This work was supported by theEFEI, CAPES, and Rotary Foundation.

J. P. G. de Abreu is with the Electrical and Computer Engineering Depart-ment, Worcester Polytechnic Institute, Worcester, MA 01609-2280 USA, onleave from the Escola Federal de Engenharia de Itajubá, 37500-903 Itajubá,Brazil ([email protected]).

A. E. Emanuel is with the Electrical and Computer Engineering Depart-ment, Worcester Polytechnic Institute, Worcester, MA 01609-2280 USA([email protected]).

Publisher Item Identifier S 0093-9994(02)00603-5.

differences between the expansion coefficients of the conduc-tors and silicon steel cause tremendous mechanical stresses thatlead to metal fatigue and eventual fractures. Moreover, underunbalanced or distorted voltage the electromagnetic torque de-veloped is smaller than the torque developed under ideal condi-tions; consequently, the starting time is larger, hence, the fatigueprocess is accelerated. Voltage harmonics are known to causetorque pulsations that may affect the life span of bearings, cou-plings, or gears.

The engineering literature is rich on papers that report the ef-fect of VDI on induction motors. The earlier papers were mainlyfocused on motor losses [5], [6], but more recent works have ex-panded the scope to motor derating and thermal aging [7]–[9].The advent of adjustable speed drives (ASDs) has stirred re-newed enthusiasm for this topic [10]. However, a matter thatstill remains to be examined in more detail is the loss of usefullife of motors caused by VDI and the economics of this issue.

The goal of this paper is to report the preliminary results ofa study focused on the stator thermal insulation aging in func-tion of VDI. The work is limited to integral horsepower motorssupplied directly from the power system. Voltage surges and me-chanical or chemical deterioration of the insulation are not takeninto consideration. The motors are assumed to operate at steadystate with a constant mechanical load.

II. EFFECT OFVDI ON MOTOR POWER LOSS

A. Iron Losses

The stator core losses are a function of the peak flux linkage.If the phase line-to-neutral voltage has the expression

(1)

then the flux linked by phase is

(2)

with the peak value

(3)

where is the harmonic order, and are the fundamentaland the th-order harmonic voltage, respectively (rms values),and is the angular frequency.

0093–9994/02$17.00 © 2002 IEEE

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ABREU AND EMANUEL: INDUCTION MOTOR THERMAL AGING CAUSED BY VDI 13

The rated line-to-neutral sinusoidal voltage produces apeak rated flux linkage

(4)

If the rms value of the nonsinusoidal voltage equals the ratedvoltage,

(5)

where

is the total harmonic distortion (THD) of the voltage, then from(3)–(5) results

(6)

For the typical voltage spectra, observed in 60- or 50-Hz powersystems, where the higher harmonics the ratio

. Such voltage distortions have an insignif-icant effect on the iron losses [11]. However, (6) serves as animportant warning concerning . For example, if(2.4 Hz) and , the peak flux could increase by20%, causing eventual saturation.

The presence of the negative-sequence fundamental voltageis causing voltage imbalance. The definition of voltage im-

balance used in this paper is

(7)

where is the positive-sequence fundamental voltage. Forpractical situations where , the voltage imbalance hasbut a minute effect on the core losses. The slightly elliptical ro-tating field causes some regions of the stator core to experiencea minor increase of magnetic flux density, while in the rest ofthe core the opposite is true.

B. Stator Winding and Rotor Cage Losses

The additional power loss in the stator windings, caused byimbalance and harmonics, is

(8)

where is the dc resistance of stator winding, isthe skin-effect coefficient at harmonic of orderand at funda-mental frequency ( ), is the rms current caused by thefundamental negative-sequence voltage, andis the rms har-monic current of order .

The components of the stator current are

(9)

and and are equivalent impedances

(10)

(11)

where is the rotor slip for the th-orderharmonic rotating field, is the slip at the fundamental rotatingfield, is the rotor slip for the negative-sequence ro-tating field, is the stator reactance at fundamental frequency,

are the dc rotor resistance and inductance transferredto the stator, are the skin-effect coefficients of therotor resistance at the rotor frequency and

, respectively, and are the skin-effect co-efficients for the rotor reactance at the rotor harmonic frequen-cies and , respectively.

When computing the skin-effect coefficients for the rotor re-sistance and inductance [12], it is imperative to take into accountboth the bars and the rings. Keeping in mind that the motor op-erates at the slip, a harmonic voltage with the frequencyHz, will cause a rotor frequency

that corresponds to a rotor harmonic

with the sign for the positive-sequence harmonics andfor the negative-sequence harmonics. Since , the rotorskin-effect coefficients must be computed at the frequency.If one uses the frequency , the difference will causelarge errors at lower order harmonics, especially at subharmonicorder. The stator winding skin-effect coefficient is com-puted at harmonic order. A careful computation accounts forthe fact that the skin-effect coefficient for the end windings dif-fers from the skin-effect coefficient for the slot winding. In areliable heat-flow simulation, the end-winding losses are sepa-rated from the slot-winding losses.

The total rotor cage losses are

(12)

In the thermal model, the cage power loss is also divided intoring and bars losses.

C. Interbar (Transversal) Power Loss

When the voltage developed between adjacent bars is largeenough stray currents will flow via the rotor laminations thatbridge the adjacent bars. These additional losses due to the in-terbar currents are hard to predict, they are strongly dependenton the contact resistance between the bar and the laminations,and can be assumed to be distributed within the rotor teeth. Anapproximate expression [13] for the ratio of the interbar losses


(a) (b)

Fig. 1. Steady-state equivalent thermal circuit of an induction machine. (a) Lumped components diagram. (b) Radial heat flow through the stator.

caused by a all the harmonic voltages and the interbar losses atstandstill rated conditions with sinusoidal voltage is

(13)

where is the number of rotor teeth. For a voltage distortionusually encountered, when , the contributionof harmonics to the transversal losses is not negligible. For ex-ample, assuming , , andresults in .

D. Surface and Pulsating Losses

These are iron losses due to the high frequencies of the air-gapinduction, and are located at the surface and within the rotorteeth. The general expression [9] is

(14)

where is a constant that depends on the geometry of the ma-chine and the number of teeth and it is proportional to, (

is the velocity of the rotor in ). is the stator funda-mental current, is the no-load current and is the peakair-gap magnetic induction. Voltage harmonics, for waves with

, do not affect . In modern designs, withnearly closed rotor slots, is contained mainly in the rotorteeth.

III. T HERMAL EQUIVALENT CIRCUIT

The thermal aging of the stator insulation is a function of thestator winding temperature that can be estimated by means ofmodeling the heat flow through the motor [10]. The completethermal equivalent circuit of an induction motor for steady-stateoperation is shown in Fig. 1(a). The local losses, modeled bycurrent sources, are labeled as in Table I.

The heat is dissipated via two major paths. First is a radialpath, that leads to the external surface of the motor housing.The second path is axial, or the lateral flow where the heat isultimately dissipated through the lateral end shields or ports.Segments of these paths can be modeled by means of pi-equiv-alent cells of transmission lines. The circuit shown in Fig. 1(a)is the very basic circuit where groups of thermal resistances are


TABLE ISTATOR AND ROTOR POWER LOSSSOURCES

TABLE IISTATOR THERMAL RESISTANCES

TABLE IIIROTOR THERMAL RESISTANCES

lumped into one equivalent component. One will observe fromFig. 1(b), that the radial heat flow is divided in two parallel pathsor sectors, the tooth sector and the slot sector ( ).The main thermal resistances of the stator are labeled as inTable II.

The equalizing thermal resistors help make thethermal model more accurate. All the lateral heat flows throughthe thermal resistance [Fig. 1(a)] computed from [14]. Inthe rotor, we have the thermal resistances listed in Table III

Totally enclosed fan-cooled (TEFC) motors transfer65%–85% of the heat through the stator cover surface and theremainder through the end shields. The drip proof (DP) motorsdissipate 60%–80% of the heat via the end-shield ports and therest through the outer surface of the stator. The stator hottestspot is found at the points or (Fig. 2). For TEFC motors,

is the hottest spot, and 5%–15% of the total heat flowsfrom . For the DP design, is the critical spot and4%–11% of the total heat flows from .

This work is based on the experimental motor aging curvesdetailed by Brancato [15] and the IEEE Std. 117. According to[15], the life of a class F insulation motor can be estimated withthe expression

(years) (15)

Fig. 2. Hot spotsM; N and the critical spotC.

where is the hot-spot temperature of the statorinsulation, is the ambient temperature, and is the tem-perature rise determined from the heat transfer model. For

C and C results an expected useful lifeof years. If additional losses cause an additional tem-perature rise , the hot-spot temperature will reach

and the corresponding percent loss of life is

(16)

The halving interval, i.e., the temperature that yields, is , (for class F insulation C), and

(16) can be approximated with

(17)

For small temperature excursions, the thermal equivalent cir-cuit is linear and the temperature rise at any location (node) forthe steady-state operating motor is expressed by a linear equa-tion

(18)

where is the power loss dissipated at node(W), andare equivalent thermal resistances (C/W).

From (18), it results that

or

(19)

that is the incremental change in temperature at nodecausedby the incremental change in power loss .

One of the most critical spots where insulation failure occursis the point (Fig. 2). At this particular location, the insulationaging is affected by a multitude of factors: the basic thermalaging, the edge effect that causes electric field stress amplifica-tions, and high mechanical stresses due to time-varying shearingforces. The incremental temperature change at the criticalspot can be estimated from the expression

(20)


where

(21)

are the incremental temperature rises at the pointsand ,respectively. The total VDI-caused stator winding power loss

is the sum of the VDI power loss in the end windingsand in the slots

(22)

Based on the fact that

where and are the lengths of the stator package andlength of the end turn, respectively, the substitution of (19) in(20) gives

indicating that the incremental temperature rise at the crit-ical point is proportional with the incremental increase in powerloss in the stator winding . This proportionality constant isan equivalent thermal resistance

Choosing a base value for the thermal resistance, where is the motor rated apparent power and

a reference temperature rise, one will obtain the normalizedthermal resistance

(pu) (23)

From (23), it results that

(24)

and substitution of (24) and (8) in (17) gives the approximation

(25)

where is the normalized harmonic voltage

(26)

and

are the normalized stator resistance and equivalent impedancesto a base impedance .

Equation (25) shows that the loss of life due to thermal agingis a quadratic function of the unbalance and harmonic voltage.

It is learned from (26) that the ratio is an indi-cator of the motor susceptibility to VDI-caused thermal aging.This important conclusion is reflected in the following section.

Fig. 3. Equivalent thermal resistances for low-voltage motors.

TABLE IVCOEFFICIENTSa FORPOSITIVE-SEQUENCEHARMONICS AND SUBHARMONICS)

TABLE VCOEFFICIENTSa FORNEGATIVE-SEQUENCEHARMONICS AND SUBHARMONICS)

IV. RESULTS

The data obtained for this study is based on the thermal mod-eling of five modern squirrel-cage motors, 460 V, 60 Hz, fourpoles, class F insulation, rated 2, 10, 30, 100, and 200 hp. Allmotors were assumed to have a useful life years whenoperating continuously at 75% rated load with a 30C am-bient temperature. In Fig. 3 is presented the graph of theversus the rated mechanical power of the studied motors. Thenormalized thermal resistance of the DP motor is smaller thanthe TEFC motor’s, hence, for the same electrical parameters andVDI, the DP motor will suffer smaller loss of useful life than theTEFC motor.

The percent values of thecoefficients for TEFC motors arepresented in Tables IV and V. One will readily observe that forall the subharmonics and all the motors, the positive-sequencecoefficients are larger than the negative-sequencecoefficients.The explanation is found in the expression of the transferredrotor resistance , more precisely the expression ofthe rotor slip , with the sign for the positivesequence.


Fig. 4. Percent loss of life versus percent voltage imbalance (TEFC motors,sinusoidal voltage).

Fig. 5. Percent loss of life versus percent voltage harmonics, or imbalance,(100-hp motor).

For positive sequence and , , thus yielding asmaller motor equivalent impedance (10). For the nega-tive-sequence is larger than the positive-sequenceand thetrend is reversed, i.e., for equal harmonic orders the motors aremore susceptible to the negative-sequence harmonic.

In Figs. 4–8 are presented the graphs that summarize the re-sults of this study. The effect of voltage imbalance on TEFCmotors is shown in Fig. 4. The loss of life was calculated from(16). The quadratic expression (25) holds true in the range

%. For imbalance larger than 3%, the error caused bythe approximation (17) becomes noticeable. In Fig. 5 is shownthe effect of voltage distortion on the 100-hp motor for 0.1,0.5, 1, 3, 5, 7, 11, and 13. The labels “n” and “p” mean nega-tive and positive sequence. The imbalance voltage correspondsto n (negative sequence). The impact of subharmonicsis quite dramatic; for example, for a trace as small as

% causes 17% loss of useful life. This means thatfor a 0.25% voltage subharmonic of order , a voltage

Fig. 6. 100-hp motor with 1% imbalance: percent loss of life versus percentvoltage harmonics (TEFC motors).

Fig. 7. Percent loss of life versus percent fifth harmonic voltage (TEFC motorswith 1% voltage imbalance).

imbalance of 1.8%, or a 6% fifth harmonic, all three will causethe same thermal aging.

When imbalance and voltage distortion are both present,Fig. 6, the curves loss of life versus are biased riding overthe imbalance curve shown in Fig. 5. The effect of the fifthvoltage harmonic in the presence of 1% imbalance is depictedin Fig. 7 All these results show that there is not a simplecorrelation among the loss of life, VDI, and motor power. Thefact that the 200-hp motor is less affected by the VDI thanthe 100-hp one is due mainly to the differences between thepreviously mentioned ratios (26), with the actual values

The effect of negative-sequence subharmonic of order 0.1 su-perposed with 1% imbalance is presented in Fig. 8. For the DPmotors the loss of useful life can be estimated using a correctionfactor .


Fig. 8. Percent loss of life versus percent 0.1th subharmonic voltage (TEFCmotors with 1% voltage imbalance).

V. ECONOMICAL ANALYSIS

We will assume a motor with an expected useful lifeyearsand the purchase cost, a combined interest-inflation rate,and a straight-line depreciation rate. For a loss of useful lifeyears, it results that in the year the financial loss is

where the first component is due to the book value lost

and the second component is due to the earlier replacement ofthe motor

The present value of the lost capital is

that yields

(27)

The above analysis is correct for a continuous 24 h/day motoroperation. Usually, motors operate of the time, where

is the expected life of the motor, . In this case, (27)remains valid if and are replaced with and

, respectively.This model was used to observe the effect of different

VDIs. The spectra of the tested voltage waveforms are givenin Table VI. Spectrum A has a THD of 3%, and is typical forvoltages measured in the 1980s/1990s, while spectrum B has6% and is typical for higher end situations. Spectrum C isan extreme case that may occur more frequently in the nearfuture if the proliferation of current harmonics is not properly

TABLE VIVOLTAGE SPECTRAUSED IN THIS STUDY. PERCENTHARMONICS AND TOTAL

HARMONIC DISTORTION

TABLE VIIMOTOR LOSS OFUSEFUL LIFE (YEARS)

controlled. The fact that the three spectra are proportionalenables to graph the results in function of the THD.

The computed losses of useful lives are summarized inTable VII. For comparison, the no-harmonic case (labeled O)was added. It is found that at 1% imbalance with no voltageharmonics, the loss of life is 0.59–1.21 years out of 20 usefulyears. At 2% imbalance, the loss of life quadruples, reaching4.44 years for the 100-hp motor. When the spectrum A har-monics are combined with 1% voltage imbalance, the motorslose 0.99–2.25 years. When the imbalance is doubled to 2%,the lost life is found in the range 2.63–5.30 years. For the sameconditions, spectrum B with 1% imbalance causes 2.13–5.04lost years and 3.67–7.60 years for 2% imbalance. A dramaticloss of life is caused by spectrum C. The 100-hp motor will lose8.76 years with 1% imbalance and more than half of its usefullife with 2% imbalance. Even the 2-hp motor, the least-affectedunit, will lose more than a quarter of its useful life with 2%unbalance plus spectrum C.

These results were translated into capital lost per motor peryear for each type of motor studied (Fig. 9). The graphs wereobtained from (27) assuming .

These observations were extended to the motor population ofthe U.S. [16], [17] to estimate the impact of the VDI at a nationallevel. In Table VIII are summarized five groups of motors, theirpopulation, and average cost per unit. It was assumed that at thebeginning of the first year one out of motors wasreplaced with a new motor. The estimated total capital lost dueto thermal aging caused by VDI is plotted in Fig. 10.

For the conservative range of voltage imbalance2% andvoltage distortion 5%, the capital lost may reach 1.8 billiondollars. These curves demonstrate the good engineering insightfor recommending voltage imbalance less than 1% (NEMA12.45) and voltage distortion less than 5% (IEEE Std. 519).


Fig. 9. Capital lost per motor per year versusTHD .

TABLE VIIIMOTORS’ POPULATION IN U.S. [16], [17]: MEAN HORSEPOWER ANDCOST

Fig. 10. Total yearly capital lost in U.S. versusTHD .

VI. CONCLUSIONS

The susceptibility to VDI is dependent on size and designof the motor. Smaller motors are less susceptible than largermotors. The ultimate factors that control the thermal aging ofthe stator insulation are the type of insulation, the equivalent pumotor impedance, stator resistance, and the equivalent thermalresistance . The thermal aging of the motor insulation is sig-nificantly affected by subharmonics. This result should alert allthe engineers responsible for standards, recommendations, orguidelines for harmonic limitations.

The results discussed in this paper point to the fact that VDIis a liability that costs end users a significant amount of money.The exact calculation of the cost of the useful life is a chal-lenging task, nevertheless, the preliminary calculations revealthat VDI costs the U.S. community as much as 1.8 billion dollarsper year. The existing recommendations for voltage imbalanceand distortion are not overconservative and must be upheld.

ACKNOWLEDGMENT

The authors’ wholehearted feelings of gratitude go to WEGengineers who generously have shared their experience and keyinformation with them. Few manufacturers would do so muchfor students and for science.

REFERENCES

[1] IEEE Motor Reliability Working Group, “Report on large motors reli-ability survey of industrial and commercial installations, Part I,”IEEETrans. Ind. Applicat., vol. 21, pp. 853–864, July/Aug. 1985.

[2] IEEE Motor Reliability Working Group, “Report on large motors reli-ability survey of industrial and commercial installations, Part II,”IEEETrans. Ind. Applicat., vol. 21, pp. 865–872, July/Aug. 1985.

[3] O. V. Thorsen and M. Dalva, “Failure identification and analysis forhigh-voltage induction motors in the petrochemical industry,”IEEETrans. Ind. Applicat., vol. 35, pp. 810–818, July/Aug. 1999.

[4] R. H. Engelmann and W. H. Middendorf,Handbook of Electric Mo-tors. New York: Marcel Dekker, 1995.

[5] G. C. Jain, “The effect of voltage wave-shape in the performance ofthree-phase induction-motor,” presented at the IEEE Winter PowerMeeting, New York, NY, Feb. 1964, Paper 64–96.

[6] B. J. Chalmers, “Induction-motor losses due to nonsinusoidal supplywaveforms,”Proc. Inst. Elect. Eng., vol. 115, no. 12, pp. 1777–1782,Dec. 1968.

[7] P. G. Cummings, “Estimating the effect of system harmonics on lossesand temperature rise of squirrel-cage motors,”IEEE Trans. Ind. Ap-plicat., vol. 22, pp. 1121–1126, Nov./Dec. 1986.

[8] E. F. Fuchs, D. J. Roesler, and K. P. Kovacs, “Aging of electrical ap-pliances due to harmonics of the power system’s voltage,”IEEE Trans.Power Delivery, vol. 1, pp. 301–307, July 1986.

[9] P. K. Sen and H. Landa, “Derating of induction motors due to wave-form distortion,” IEEE Trans. Ind. Applicat., vol. 26, pp. 1102–1107,Nov./Dec. 1990.

[10] R. de Doncker, A. Vandenput, and W. Geysen, “Thermal models ofinverter fed asynchronous machines,” inConf. Rec. IEEE-IAS Annu.Meeting, 1986, pp. 132–139.

[11] M. Amar and R. Kaczmareck, “A general formula for prediction ofiron losses under nonsinusoidal forms,”IEEE Trans. Magn., vol. 31, pp.2504–2509, Sept. 1995.

[12] M. M. Liwshitz-Garik, “Computation of skin effect in bars ofsquirrel-cage rotors,”Trans AIEE, pp. 768–771, Aug. 1955.

[13] B. Heller and V. Hamata,Harmonic Field Effects in Induction Ma-chines. Amsterdam, The Netherlands: Elsevier, 1977.

[14] D. E. Metzger and N. H. Afgan,Heat and Mass Transfer in RotatingMachinery. Bristol, PA: Hemisphere, 1984.

[15] E. Brancato, “Estimation of lifetime expectancies of motors,”IEEEElect. Insul. Mag., vol. 8, pp. 5–15, May/June 1992.

[16] “Classification and evaluation of electric motors and pumps,” Arthur D.Little Inc., Cambridge, MA, DOE/TIC-11339, 1980.

[17] A. H. Bonnett, “An overview of how AC induction motor performancehas been affected by the October. 24, 1997 implementation of the EnergyPolicy Act of 1992,”IEEE Trans. Ind. Applicat., vol. 36, pp. 242–256,Jan./Feb. 2000.

Jose Policarpo G. de Abreuwas born on MadeiraIsland, Portugal, in 1952. He received the B.S.E.E.and M.Sc. degrees from the Escola Federal de En-genharia de Itajubá, Itajubá, Brazil, and the D.Sc. de-gree in electrical engineering from the University ofCampinas, Campinas, Brazil.

He is a full Professor at the Escola Federal de En-genharia de Itajubá, where he also serves as the PowerQuality Study Group Coordinator. He is currently onleave at Worcester Polytechnic Institute, Worcester,MA. His research interests include power quality is-

sues, such as power definitions, harmonics, imbalance, and voltage sags. Induc-tion motors, transformers, and converter transformers are other interests.

Prof. de Abreu has been nominated for the Chairmanship of the 10th IEEEPES ICHQP, to be held in Rio de Janeiro, Brazil, in October 2002.


Alexander Eigeles Emanuel (SM’71–F’97) re-ceived the B.Sc., M.Sc., and D.Sc. degrees fromthe Technion, Israel Institute of Technology, Haifa,Israel, in 1963, 1965, and 1969, respectively.

From 1969 to 1974, he was a Senior R&DEngineer with the High Voltage Power Corporation.In 1974, he joined Worcester Polytechnic Institute,Worcester, MA, where he teaches electrical engi-neering and conducts research in the areas of powerquality and power electronics.

induction motor thermal aging caused by voltage distortion and imbalance.pdf

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