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

Induction Motor Thermal Aging Caused by Voltage Distortion and Imbalance: Loss of Useful Life and Its Estimated Cost Jose Policarpo G. de Abreu and Alexander Eigeles Emanuel, Fellow, IEEE

Abstract—This paper reports the effect of voltage distortion and imbalance (VDI) on the thermal aging of the insulation of lowvoltage induction motors. The study is based on a detailed thermal modeling of actual motors in the 2–200-hp range. The dollar value of the useful life lost was estimated for different VDI conditions. Two important conclusions were reached. First, voltage subharmonics have a dramatic effect on motor thermal aging. Second, the overall cost of motor loss of life due to harmonic pollution and voltage imbalance, in the U.S. today, is estimated to be in the range of 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 simultaneously on 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 significant additional power losses, thus increasing the steady-state temperature rise of the windings. During the starting time, the heating process of rotor bars and rings is nearly adiabatic; the upper region of the bars, where the current density is larger, is reaching higher temperatures than the lower region of the bars. The significant temperature rise during the motor starting, the

differences between the expansion coefficients of the conductors and silicon steel cause tremendous mechanical stresses that lead to metal fatigue and eventual fractures. Moreover, under unbalanced or distorted voltage the electromagnetic torque developed is smaller than the torque developed under ideal conditions; consequently, the starting time is larger, hence, the fatigue process is accelerated. Voltage harmonics are known to cause torque pulsations that may affect the life span of bearings, couplings, or gears. The engineering literature is rich on papers that report the effect of VDI on induction motors. The earlier papers were mainly focused on motor losses [5], [6], but more recent works have expanded the scope to motor derating and thermal aging [7]–[9]. The advent of adjustable speed drives (ASDs) has stirred renewed enthusiasm for this topic [10]. However, a matter that still remains to be examined in more detail is the loss of useful life of motors caused by VDI and the economics of this issue. The goal of this paper is to report the preliminary results of a study focused on the stator thermal insulation aging in function of VDI. The work is limited to integral horsepower motors supplied directly from the power system. Voltage surges and mechanical or chemical deterioration of the insulation are not taken into consideration. The motors are assumed to operate at steady state with a constant mechanical load. II. EFFECT OF VDI 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

Paper ICPSD 01–26, presented at the 2001 IEEE/IAS Industrial and Commercial Power Systems Technical Conference, New Orleans, LA, May 13–17, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Power Systems Protection Committee of the IEEE Industry Applications Society. Manuscript submitted for review May 15, 2001 and released for publication October 10, 2001. This work was supported by the EFEI, CAPES, and Rotary Foundation. J. P. G. de Abreu is with the Electrical and Computer Engineering Department, Worcester Polytechnic Institute, Worcester, MA 01609-2280 USA, on leave from the Escola Federal de Engenharia de Itajubá, 37500-903 Itajubá, Brazil ([email protected]). A. E. Emanuel is with the Electrical and Computer Engineering Department, Worcester Polytechnic Institute, Worcester, MA 01609-2280 USA ([email protected]). Publisher Item Identifier S 0093-9994(02)00603-5.

is (2)

with the peak value (3) and are the fundamental where is the harmonic order, and the th-order harmonic voltage, respectively (rms values), is the angular frequency. and

0093–9994/02$17.00 © 2002 IEEE

ABREU AND EMANUEL: INDUCTION MOTOR THERMAL AGING CAUSED BY VDI

The rated line-to-neutral sinusoidal voltage peak rated flux linkage

produces a

13

and

and

are equivalent impedances

(10)

(4) If the rms value voltage,

of the nonsinusoidal voltage equals the rated

(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 power the ratio systems, where the higher harmonics . Such voltage distortions have an insignificant effect on the iron losses [11]. However, (6) serves as an . For example, if important warning concerning (2.4 Hz) and , the peak flux could increase by 20%, causing eventual saturation. The presence of the negative-sequence fundamental voltage is causing voltage imbalance. The definition of voltage imbalance used in this paper is (7) is the positive-sequence fundamental voltage. For where , the voltage imbalance has practical situations where but a minute effect on the core losses. The slightly elliptical rotating field causes some regions of the stator core to experience a minor increase of magnetic flux density, while in the rest of the core the opposite is true.

(11) is the rotor slip for the th-order where harmonic rotating field, is the slip at the fundamental rotating is the rotor slip for the negative-sequence rofield, is the stator reactance at fundamental frequency, tating field, are the dc rotor resistance and inductance transferred are the skin-effect coefficients of the to the stator, and rotor resistance at the rotor frequency , respectively, and are the skin-effect coefficients for the rotor reactance at the rotor harmonic frequenand , respectively. cies When computing the skin-effect coefficients for the rotor resistance and inductance [12], it is imperative to take into account both the bars and the rings. Keeping in mind that the motor operates at the slip , a harmonic voltage with the frequency Hz, will cause a rotor frequency

that corresponds to a rotor harmonic

with the sign for the positive-sequence harmonics and for the negative-sequence harmonics. Since , the rotor . skin-effect coefficients must be computed at the frequency will cause If one uses the frequency , the difference large errors at lower order harmonics, especially at subharmonic is comorder. The stator winding skin-effect coefficient puted at harmonic order . A careful computation accounts for the fact that the skin-effect coefficient for the end windings differs from the skin-effect coefficient for the slot winding. In a reliable heat-flow simulation, the end-winding losses are separated from the slot-winding losses. The total rotor cage losses are

B. Stator Winding and Rotor Cage Losses (12)

The additional power loss in the stator windings, caused by imbalance and harmonics, is (8) is the dc resistance of stator winding, is where the skin-effect coefficient at harmonic of order and at funda), is the rms current caused by the mental frequency ( is the rms harfundamental negative-sequence voltage, and monic current of order . The components of the stator current are (9)

In the thermal model, the cage power loss is also divided into ring and bars losses. C. Interbar (Transversal) Power Loss When the voltage developed between adjacent bars is large enough stray currents will flow via the rotor laminations that bridge the adjacent bars. These additional losses due to the interbar currents are hard to predict, they are strongly dependent on the contact resistance between the bar and the laminations, and can be assumed to be distributed within the rotor teeth. An approximate expression [13] for the ratio of the interbar losses

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

(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 at standstill rated conditions with sinusoidal voltage is (13) is the number of rotor teeth. For a voltage distortion where , the contribution usually encountered, when of harmonics to the transversal losses is not negligible. For ex, , and ample, assuming results in . D. Surface and Pulsating Losses These are iron losses due to the high frequencies of the air-gap induction, and are located at the surface and within the rotor teeth. The general expression [9] is (14) is a constant that depends on the geometry of the mawhere chine and the number of teeth and it is proportional to , (

is the velocity of the rotor in ). is the stator fundais the no-load current and is the peak mental current, air-gap magnetic induction. Voltage harmonics, for waves with , do not affect . In modern designs, with is contained mainly in the rotor nearly closed rotor slots, teeth. III. THERMAL EQUIVALENT CIRCUIT The thermal aging of the stator insulation is a function of the stator winding temperature that can be estimated by means of modeling the heat flow through the motor [10]. The complete thermal equivalent circuit of an induction motor for steady-state operation is shown in Fig. 1(a). The local losses, modeled by current sources, are labeled as in Table I. The heat is dissipated via two major paths. First is a radial path, that leads to the external surface of the motor housing. The second path is axial, or the lateral flow where the heat is ultimately dissipated through the lateral end shields or ports. Segments of these paths can be modeled by means of pi-equivalent cells of transmission lines. The circuit shown in Fig. 1(a) is the very basic circuit where groups of thermal resistances are

ABREU AND EMANUEL: INDUCTION MOTOR THERMAL AGING CAUSED BY VDI

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TABLE I STATOR AND ROTOR POWER LOSS SOURCES

TABLE II STATOR THERMAL RESISTANCES

Fig. 2. Hot spots M;

N

and the critical spot C .

where is the hot-spot temperature of the stator is the ambient temperature, and is the teminsulation, perature rise determined from the heat transfer model. For C and C results an expected useful life years. If additional losses cause an additional temof , the hot-spot temperature will reach perature rise and the corresponding percent loss of life is (16) TABLE III ROTOR THERMAL RESISTANCES

The halving interval, i.e., the temperature , is , (for class F insulation (16) can be approximated with

that yields C), and

(17) For small temperature excursions, the thermal equivalent circuit is linear and the temperature rise at any location (node ) for the steady-state operating motor is expressed by a linear equation lumped into one equivalent component. One will observe from Fig. 1(b), that the radial heat flow is divided in two parallel paths ). or sectors, the tooth sector and the slot sector ( The main thermal resistances of the stator are labeled as in Table II. help make the The equalizing thermal resistors thermal model more accurate. All the lateral heat flows through [Fig. 1(a)] computed from [14]. In the thermal resistance the rotor, we have the thermal resistances listed in Table III Totally enclosed fan-cooled (TEFC) motors transfer 65%–85% of the heat through the stator cover surface and the remainder through the end shields. The drip proof (DP) motors dissipate 60%–80% of the heat via the end-shield ports and the rest through the outer surface of the stator. The stator hottest or (Fig. 2). For TEFC motors, spot is found at the points is the hottest spot, and 5%–15% of the total heat flows . For the DP design, is the critical spot and from . 4%–11% of the total heat flows from This work is based on the experimental motor aging curves detailed by Brancato [15] and the IEEE Std. 117. According to [15], the life of a class F insulation motor can be estimated with the expression (years)

(15)

(18) is the power loss dissipated at node (W), and where are equivalent thermal resistances ( C/W). From (18), it results that

or (19) that is the incremental change in temperature at node caused . by the incremental change in power loss One of the most critical spots where insulation failure occurs is the point (Fig. 2). At this particular location, the insulation aging is affected by a multitude of factors: the basic thermal aging, the edge effect that causes electric field stress amplifications, and high mechanical stresses due to time-varying shearing at the critical forces. The incremental temperature change spot can be estimated from the expression (20)

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

where (21) and , are the incremental temperature rises at the points respectively. The total VDI-caused stator winding power loss is the sum of the VDI power loss in the end windings and in the slots (22) Based on the fact that

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

Fig. 3. Equivalent thermal resistances for low-voltage motors. TABLE IV COEFFICIENTS a FOR POSITIVE-SEQUENCE HARMONICS AND SUBHARMONICS)

indicating that the incremental temperature rise at the critical point is proportional with the incremental increase in power . This proportionality constant is loss in the stator winding an 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 normalized thermal resistance (pu)

TABLE V COEFFICIENTS a FOR NEGATIVE-SEQUENCE HARMONICS AND SUBHARMONICS)

(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 impedances . to a base impedance Equation (25) shows that the loss of life due to thermal aging is a quadratic function of the unbalance and harmonic voltage. is an indiIt is learned from (26) that the ratio cator of the motor susceptibility to VDI-caused thermal aging. This important conclusion is reflected in the following section.

IV. RESULTS The data obtained for this study is based on the thermal modeling of five modern squirrel-cage motors, 460 V, 60 Hz, four poles, class F insulation, rated 2, 10, 30, 100, and 200 hp. All years when motors were assumed to have a useful life operating continuously at 75% rated load with a 30 C ambient temperature. In Fig. 3 is presented the graph of the versus the rated mechanical power of the studied motors. The normalized thermal resistance of the DP motor is smaller than the TEFC motor’s, hence, for the same electrical parameters and VDI, the DP motor will suffer smaller loss of useful life than the TEFC motor. The percent values of the coefficients for TEFC motors are presented in Tables IV and V. One will readily observe that for all the subharmonics and all the motors, the positive-sequence coefficients are larger than the negative-sequence coefficients. The explanation is found in the expression of the transferred , more precisely the expression of rotor resistance , with the sign for the positive the rotor slip sequence.

ABREU AND EMANUEL: INDUCTION MOTOR THERMAL AGING CAUSED BY VDI

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

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

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

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

For positive sequence and , , thus yielding a the negasmaller motor equivalent impedance (10). For tive-sequence is larger than the positive-sequence and the trend is reversed, i.e., for equal harmonic orders the motors are more susceptible to the negative-sequence harmonic. In Figs. 4–8 are presented the graphs that summarize the results of this study. The effect of voltage imbalance on TEFC motors 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 by the approximation (17) becomes noticeable. In Fig. 5 is shown 0.1, the effect of voltage distortion on the 100-hp motor for 0.5, 1, 3, 5, 7, 11, and 13. The labels “n” and “p” mean negative and positive sequence. The imbalance voltage corresponds n (negative sequence). The impact of subharmonics to a trace as small as is quite dramatic; for example, for % causes 17% loss of useful life. This means that , a voltage for a 0.25% voltage subharmonic of order

imbalance of 1.8%, or a 6% fifth harmonic, all three will cause the same thermal aging. When imbalance and voltage distortion are both present, are biased riding over Fig. 6, the curves loss of life versus the imbalance curve shown in Fig. 5. The effect of the fifth voltage harmonic in the presence of 1% imbalance is depicted in Fig. 7 All these results show that there is not a simple correlation among the loss of life, VDI, and motor power. The fact that the 200-hp motor is less affected by the VDI than the 100-hp one is due mainly to the differences between the previously mentioned ratios (26), with the actual values

The effect of negative-sequence subharmonic of order 0.1 superposed with 1% imbalance is presented in Fig. 8. For the DP motors the loss of useful life can be estimated using a correction . factor

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

TABLE VI VOLTAGE SPECTRA USED IN THIS STUDY. PERCENT HARMONICS AND TOTAL HARMONIC DISTORTION

TABLE VII MOTOR LOSS OF USEFUL LIFE (YEARS)

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

V. ECONOMICAL ANALYSIS We will assume a motor with an expected useful life years and the purchase cost , a combined interest-inflation rate , and a straight-line depreciation rate. For a loss of useful life years, 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 of the motor

The present value of the lost capital is

that yields (27) The above analysis is correct for a continuous 24 h/day motor of the time, where operation. Usually, motors operate is the expected life of the motor, . In this case, (27) and are replaced with and remains valid if , respectively. This model was used to observe the effect of different VDIs. The spectra of the tested voltage waveforms are given in Table VI. Spectrum A has a THD of 3%, and is typical for voltages measured in the 1980s/1990s, while spectrum B has 6% and is typical for higher end situations. Spectrum C is an extreme case that may occur more frequently in the near future if the proliferation of current harmonics is not properly

controlled. The fact that the three spectra are proportional enables to graph the results in function of the THD. The computed losses of useful lives are summarized in Table VII. For comparison, the no-harmonic case (labeled O) was added. It is found that at 1% imbalance with no voltage harmonics, the loss of life is 0.59–1.21 years out of 20 useful years. At 2% imbalance, the loss of life quadruples, reaching 4.44 years for the 100-hp motor. When the spectrum A harmonics are combined with 1% voltage imbalance, the motors lose 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 same conditions, spectrum B with 1% imbalance causes 2.13–5.04 lost years and 3.67–7.60 years for 2% imbalance. A dramatic loss of life is caused by spectrum C. The 100-hp motor will lose 8.76 years with 1% imbalance and more than half of its useful life with 2% imbalance. Even the 2-hp motor, the least-affected unit, 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 per year for each type of motor studied (Fig. 9). The graphs were . obtained from (27) assuming These observations were extended to the motor population of the U.S. [16], [17] to estimate the impact of the VDI at a national level. In Table VIII are summarized five groups of motors, their population, and average cost per unit. It was assumed that at the motors was beginning of the first year one out of replaced with a new motor. The estimated total capital lost due to thermal aging caused by VDI is plotted in Fig. 10. For the conservative range of voltage imbalance 2% and voltage distortion 5%, the capital lost may reach 1.8 billion dollars. These curves demonstrate the good engineering insight for recommending voltage imbalance less than 1% (NEMA 12.45) and voltage distortion less than 5% (IEEE Std. 519).

ABREU AND EMANUEL: INDUCTION MOTOR THERMAL AGING CAUSED BY VDI

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ACKNOWLEDGMENT The authors’ wholehearted feelings of gratitude go to WEG engineers who generously have shared their experience and key information with them. Few manufacturers would do so much for students and for science. REFERENCES

Fig. 9.

Capital lost per motor per year versus

THD

.

TABLE VIII MOTORS’ POPULATION IN U.S. [16], [17]: MEAN HORSEPOWER AND COST

Fig. 10.

Total yearly capital lost in U.S. versus

THD

.

VI. CONCLUSIONS The susceptibility to VDI is dependent on size and design of the motor. Smaller motors are less susceptible than larger motors. The ultimate factors that control the thermal aging of the stator insulation are the type of insulation, the equivalent pu motor impedance, stator resistance, and the equivalent thermal resistance . The thermal aging of the motor insulation is significantly affected by subharmonics. This result should alert all the engineers responsible for standards, recommendations, or guidelines for harmonic limitations. The results discussed in this paper point to the fact that VDI is a liability that costs end users a significant amount of money. The exact calculation of the cost of the useful life is a challenging task, nevertheless, the preliminary calculations reveal that VDI costs the U.S. community as much as 1.8 billion dollars per year. The existing recommendations for voltage imbalance and distortion are not overconservative and must be upheld.

[1] IEEE Motor Reliability Working Group, “Report on large motors reliability survey of industrial and commercial installations, Part I,” IEEE Trans. Ind. Applicat., vol. 21, pp. 853–864, July/Aug. 1985. [2] IEEE Motor Reliability Working Group, “Report on large motors reliability survey of industrial and commercial installations, Part II,” IEEE Trans. Ind. Applicat., vol. 21, pp. 865–872, July/Aug. 1985. [3] O. V. Thorsen and M. Dalva, “Failure identification and analysis for high-voltage induction motors in the petrochemical industry,” IEEE Trans. Ind. Applicat., vol. 35, pp. 810–818, July/Aug. 1999. [4] R. H. Engelmann and W. H. Middendorf, Handbook of Electric Motors. New York: Marcel Dekker, 1995. [5] G. C. Jain, “The effect of voltage wave-shape in the performance of three-phase induction-motor,” presented at the IEEE Winter Power Meeting, New York, NY, Feb. 1964, Paper 64–96. [6] B. J. Chalmers, “Induction-motor losses due to nonsinusoidal supply waveforms,” Proc. Inst. Elect. Eng., vol. 115, no. 12, pp. 1777–1782, Dec. 1968. [7] P. G. Cummings, “Estimating the effect of system harmonics on losses and temperature rise of squirrel-cage motors,” IEEE Trans. Ind. Applicat., vol. 22, pp. 1121–1126, Nov./Dec. 1986. [8] E. F. Fuchs, D. J. Roesler, and K. P. Kovacs, “Aging of electrical appliances 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 waveform distortion,” IEEE Trans. Ind. Applicat., vol. 26, pp. 1102–1107, Nov./Dec. 1990. [10] R. de Doncker, A. Vandenput, and W. Geysen, “Thermal models of inverter fed asynchronous machines,” in Conf. Rec. IEEE-IAS Annu. Meeting, 1986, pp. 132–139. [11] M. Amar and R. Kaczmareck, “A general formula for prediction of iron 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 of squirrel-cage rotors,” Trans AIEE, pp. 768–771, Aug. 1955. [13] B. Heller and V. Hamata, Harmonic Field Effects in Induction Machines. Amsterdam, The Netherlands: Elsevier, 1977. [14] D. E. Metzger and N. H. Afgan, Heat and Mass Transfer in Rotating Machinery. Bristol, PA: Hemisphere, 1984. [15] E. Brancato, “Estimation of lifetime expectancies of motors,” IEEE Elect. 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 performance has been affected by the October. 24, 1997 implementation of the Energy Policy Act of 1992,” IEEE Trans. Ind. Applicat., vol. 36, pp. 242–256, Jan./Feb. 2000.

Jose Policarpo G. de Abreu was born on Madeira Island, Portugal, in 1952. He received the B.S.E.E. and M.Sc. degrees from the Escola Federal de Engenharia de Itajubá, Itajubá, Brazil, and the D.Sc. degree in electrical engineering from the University of Campinas, Campinas, Brazil. He is a full Professor at the Escola Federal de Engenharia de Itajubá, where he also serves as the Power Quality Study Group Coordinator. He is currently on leave at Worcester Polytechnic Institute, Worcester, MA. His research interests include power quality issues, such as power definitions, harmonics, imbalance, and voltage sags. Induction motors, transformers, and converter transformers are other interests. Prof. de Abreu has been nominated for the Chairmanship of the 10th IEEE PES ICHQP, to be held in Rio de Janeiro, Brazil, in October 2002.

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

Alexander Eigeles Emanuel (SM’71–F’97) received the B.Sc., M.Sc., and D.Sc. degrees from the Technion, Israel Institute of Technology, Haifa, Israel, in 1963, 1965, and 1969, respectively. From 1969 to 1974, he was a Senior R&D Engineer with the High Voltage Power Corporation. In 1974, he joined Worcester Polytechnic Institute, Worcester, MA, where he teaches electrical engineering and conducts research in the areas of power quality and power electronics.