IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 15, NO. 1, JANUARY 2000 247

Characterization of Distribution Power QualityEvents with Fourier and Wavelet Transforms

Surya Santoso, Member, IEEE, W. Mack Grady, Senior Member, IEEE, Edward J. Powers, Fellow, IEEE,Jeff Lamoree, Member, IEEE, and Siddharth C. Bhatt, Member, IEEE

AbstractIt is the objective of this paper to present unique fea-tures that characterize power quality events and methodologiesto extract them from recorded voltage and/or current waveformsusing Fourier and wavelet transforms. Examples of unique featuresinclude peak amplitudes, RMS, frequency, and statistics of wavelettransform coefficients. These features are derived from well docu-mented theories, power engineers heuristics gained through longyears of experience, and power quality data collected in recentyears. Converter operation, transformer energization, and capac-itor energization (which includes normal, back-to-back, and re-strike on opening energization), representing three common powerquality events at the distribution level, are presented. These exam-ples provide the basis for further characterization of other powerquality events.

Index TermsFourier and wavelet transforms, identifying fea-tures, power quality.

I. INTRODUCTION

STUDIES of power quality phenomena have emerged as animportant subject in recent years due to renewed interest inimproving the quality of the electricity supply. As sensitive elec-tronic equipment continues to proliferate, the studies of powerquality will be further emphasized. According to the ElectricPower Research Institute, in 1985 20% of the total electric loadin the US was electronic, however this number will jump to ap-proximately 5060% by the year 2000 [1].

In recent years, power quality phenomena have been inves-tigated directly from actual recorded disturbance waveformsthanks to widely available power monitor equipment. Thesedisturbance recordings are stored as three-phase voltage andcurrent time-series which bring a wealth of information aboutthe characteristics of the associated power quality events.Since these characteristics are unique to each power qualityevent, they are useful to portray the process of power qualitydisturbances and to pinpoint their causes.

In this paper, we present unique features that characterizepower quality events and methodologies in order to extractthem from recorded waveforms. We unify the use of one of themost important mathematical transforms in power engineering,

Manuscript received July 31, 1997; revised September 18, 1998.S. Santoso was with the Department of Electrical and Computer Engineering,

The University of Texas at Austin, Austin, TX 78712-1084 and is now withElectrotek Concepts, Inc., Knoxville, TN 37923.

W. M. Grady and E. J. Powers are with the Department of Electrical andComputer Engineering, The University of Texas at Austin, Austin, TX 78712-1084.

J. Lamoree is with Electrotek Concepts, Inc., Knoxville, TN 37923.S. C. Bhatt is with EPRI Customer Systems Group, Palo Alto, CA 94523.Publisher Item Identifier S 0885-8977(00)00564-1.

the Fourier transform, with a newer transform, the wavelettransform, to extract characterizing power quality features.The Fourier transform is used to characterize steady state phe-nomena, whereas the wavelet transform is applied to transientphenomena. We also make use of other mathematical analysistechniques such as curve-fitting techniques to estimate suddenvoltage step changes. While theories of Fourier and wavelettransforms are not presented here due to space limitation, [2],[3], [7] provide excellent overviews in these subjects.

Power quality events are characterized by their maximum am-plitudes, crest voltages, RMS, frequency, statistics of wavelettransform coefficients, instantaneous voltage drops, number ofnotches, duration of transients, etc. These characteristics are dif-ferent for each power quality event, thus they are unique identi-fying features.

In Section II, characteristics of three common power qualityevents at the distribution level are presented. They are converteroperation, transformer energization, and capacitor energization(which is further broken down into normal, back-to-back, mag-nification, and restrike on opening energization). These exam-ples provide the basis for further characterization of other powerquality events. Utilizing characteristics described in Section II,Section III concludes this paper with an application to build anevent identification module.

II. PQ EVENTS AND THEIR FEATURESUnique features characterizing the three events mentioned

above are presented in this section. These identifying featuresare derived from well documented theories [3][6], power engi-neers heuristics gained through long years of experience, andpower quality data collected in recent years.

In performing wavelet transformations, a given signal is de-composed into four decomposition scales with a Daub4 waveletas a mother wavelet. A Daub4 wavelet is a Daubechies waveletwith 2 vanishing moments [2], [8], [9].

We shall now begin our discussion starting with transformerenergization, followed by converter operation and capacitor en-ergizing events.

A. Transformer EnergizingTransformer energizing events are caused by magnetizing in-

rush current when a transformer is energized. The inrush cur-rent can be significantly higher than the rated load current. Dueto saturation effects in the transforme iron core, inrush currentsare rich in both odd and even harmonics, particularly the 2ndthrough 5th harmonics. These harmonics are also reflected inthe voltage waveforms.

08858977/00$10.00 2000 IEEE

248 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 15, NO. 1, JANUARY 2000

Fig. 1. Typical waveforms of a transformer energizing event in phases (a) A,(b) B, and (c) C.

Fig. 1 shows the three-phase voltage for a transformer ener-gizing event. The energization event occurs on all phases simul-taneously. In the following, characteristics of transformer ener-gizing are presented.

1) Waveshape Before Transformer Energization: The wave-shape before the energization is very smooth and sinusoidal. Thewavelet transform variables in terms of squared wavelet trans-form coefficients (WTC) are utilized to determine the smooth-ness of the waveshape before transformer energization. As acase study, we analyze the phase A voltage waveform shown inFig. 1(a) which is also shown in Fig. 2(a). The squared wavelettransform coefficients at scales 1, 2, 3, and 4 of the transformare shown in Fig. 2(b)(e), respectively.

The starting time of energizing event can be located byfinding the maximum value of the squared WTC1 or squaredWTC2, or both depending on the tiny transient that occurs at theenergizing instant. Fig. 2(b) and (c) indicates that the startingtime is found by locating the maximum value of the squaredWTC1 because it occurs earlier than that of squared WTC2. Theenergizing instant is at ms.

The smoothness of the waveform prior to energizing (014ms) can be investigated through the statistics of the squaredWTC3 and squared WTC4. For phase A voltage, the max-imum value of squared WTC3 before the energizing time

is , and the average valueof the largest 30 coefficients of the squared WTC3 beforethe energizing time is .The wavelet statistics for squared WTC4 are for

and ,respectively.

2) Waveshape During Transformer Energization: Unlikethe waveshape before energization where there was no signifi-cant activity detected by the wavelet transform, the waveshapeduring the energization is loaded with disturbance activity,which is picked up by the wavelet transform. There areadditional high values of squared WTCs scattered over the

Fig. 2. The wavelet transform of a transformer energizing waveform. (a) Thetime domain signal. (b)(e), squared WTCs at scales 1, 2, 3, and 4, respectively.

energization period which are associated with the harmonicdistortion.

The statistics of squared WTC3 and squared WTC4 duringthe energization are quite different compared to those beforeenergization. The maximum squared WTTC3 during theenergization is 0.0108, which is54 times . The average of the largest30 coefficients of squared WTC3 during the energization

is 0.004, which is 40 times. For squared WTC4, the values

for andare 0.0609 and 0.0202, which are 122 and 200 times the beforeenergization values, respectively.

3) Harmonic Voltage: During the transformer energization,the voltage waveforms are contaminated with harmonics, in par-ticular the 2nd through 5th harmonics. A Fourier transform isperformed to find the harmonic voltage for the waveform duringthe energization. The second harmonic voltage is the predorni-nant one, as shown in Fig. 3.

B. Converter Operation

Notching in a voltage waveform is characteristic of converteroperation. These notches are the result of commutation duringa multiphase converter operation. During this period, a momen-tary phase-to-phase short circuit occurs and pulls the voltagephases as close as possible to zero. The phase-to-phase short cir-cuit causes the notches in the voltage waveforms. Fig. 4(a)(c)show three phase voltage notching waveforms for phases A, B,and C, respectively, in which there are 6 notches in every cycle.The following are the unique identifying features for voltagenotching waveforms.

1) Number of Notches per Cycle: Notches appear period-ically throughout the waveform as a result of commutationduring multiphase converter operation. In a conventionalsix-pulse rectifier, the current is commutated six times fromone phase to another in one cycle to produce a dc voltage on its

SANTOSO et al.: CHARACTERIZATION OF DISTRIBUTION POWER QUALITY EVENTS WITH FOURIER AND WAVELET TRANSFORMS 249

Fig. 3. Harmonic voltages of a transformer energizing waveform.

Fig. 4. Typical waveform of a voltage notching event in phases (a) A, (b) B,(c) C.

output. This operation gives rise to six notches per cycle whichappear periodically throughout the waveform. Likewise, in atwelve-pulse rectifier, there will be twelve notches per cycle.

We shall now discuss the procedure to count the number ofnotches per cycle. For this purpose, the phase A voltage wave-form shown in Fig. 4(a) [also shown in Fig. 5(a)] is chosenas a study case. The wavelet transform is utilized to count thenumber of notches per cycle. The wavelet transform of the phaseA voltage is shown in Fig. 5(b)(e) for scales 14, respec-tively.

High magnitudes of squared WTC1 in Fig. 5(b) clearly indi-cate the occurrence of the notches. Squared WTC1 associatedwith notches at the peaks of the waveform are much higher thanthose of associated with notches between peaks because of latterare less severe. They all appear as perodic impulses. However,squared WTC2, squared WTC3, and squared WTC4 are not souseful to estimate the number of notches per cycle because theimpulse pattern does not clearly stand out. From our experience,it is sufficient to estimate the number of notches from squaredWTC1 only.

The number of notches per cycle is found usingthe following relation,

(1)

Fig. 5. Wavelet transform for phase A voltage. (a) The voltage waveform,(b)(e) are the squared WTCs at scales 14, respectively.

where and , are the number of notches and thenumber of cycles in the voltage waveform, , respectively.The number of notches in the waveform can be found by simplycounting the number of impulses in the squared WTC1. Thenumber of cycles in the waveform can be estimated simply usingthe following relationship,

(2)

where is the time duration of the waveform in ms.For the voltage waveform shown in Fig. 5(a), ms

and the number of notches is . Therefore using (1),the number of cycles in is cycles. Finally, using(2), the number of notches per cycles can be computed whichis . This number indicates that the voltagenotching waveform is due to a six-pulse rectifier operation.

2) Harmonic Voltages: Voltage notching waveforms arerich in harmonics. In a six-pulse rectifier, the voltage waveformsare rich in harmonics, where . In a twelve-pulserectifier, the voltage waveforms are rich in harmonics,where . Voltage waveforms in a twelve-pulse rectifiercontain 12 notches in every cycle.

Fig. 6 shows the harmonic voltages up to the 25th harmonic.The predominant harmonic voltages are the 5th, 7th, 11th,13th, 17th, 19th, 23rd, and 25th. The 13th harmonic, however,is rather small. This harmonic voltage spectrum providesfurther evidence about the nature of the notching waveform.If the waveform is due to a six-pulse rectifier, the ( )thharmonics should be present. However, due to imperfectionsin the converter systems, some of these harmonics may notreally stand out, but the majority of the ( )th harmonicsdo appear.

C. Capacitor EnergizingCapacitor energizing transient events are one of the most

common transient events present in power systems. Thetransient events occur when a capacitor is switched on.At the switching instant, a fast change in the bus voltage

250 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 15, NO. 1, JANUARY 2000

Fig. 6. Harmonic voltages for phase A voltage waveform.

occurs because the voltage in the capacitor cannot changeinstantaneously. The transient frequency is determined by thecombination of the capacitance of the capacitor bank and thesystem inductance. The oscillation frequency in the voltagewaveform is typically between 3001000 Hz and lasts for lessthan half a cycle of the power frequency.

There are several kinds of capacitor energizing events. Weshall present normal energizing, back-to-back energizing, andrestrike on capacitor opening events. We shall discuss each ofthese categories and formulate a procedure to extract these iden-tifying features.

1) Normal Energizing of Utility Capacitors: Energizationof utility capacitors is a daily operation in the utility system.They are switched into the system in anticipation of load in-crease at a customer site, to correct power factor, to supportvoltage on the system, and so on. These energization of utilitycapacitors are considered normal energizing. The following arethe identifying features for normal capacitor switching.

a) Overvoltage: At the switching instant, the voltage inthe capacitor cannot change instantaneously. The bus voltage ispulled down, and then rises as the capacitor begins to charge.During the process, the capacitor voltage may overshoot andring at the natural frequency. The overvoltage in normal en-ergizing is usually between 1.11.4 p.u. Figs. 7 and 8 showtwo typical normal energization of utility capacitors. The over-voltage is not larger than 1.1 p.u in either case.

b) Polarity and Magnitude of the Step Voltage: One ofthe most common identifying features for normal energizing ofutility capacitors is the polarity of the step voltage. The be-havior of this feature and how it relates to normal energizing ofcapacitors axe illustrated using the above two normal switchingcases.

If the power quality monitor is located at or near capacitorsthat have no series reactor, a fast initial voltage step will be ob-served. The voltage step at the instant of closing cannot go be-yond zero if the capacitor has no initial net charge at the closinginstant or if the capacitor is grounded. If the power quality mon-itor is located farther away from the capacitor, the voltage stepchange may not be observed, or at least it is not as prominent.These situations are depicted in Figs. 7 and 8, respectively. Inany event, sudden changes of voltages never go across the zeroline, i.e., they do not change polarity. This behavior is exhibitedin nearly all normal energizing of utility capacitors.

Now let us consider phase C voltage shown in Fig. 7(c) asa study case. The first 22 ms of this voltage are also shown inFig. 9 for the sake of clarity. When the switch is closed on this

Fig. 7. Typical waveforms of normal energizing of utility capacitors in phases(a) A, (b) B, and (c) C. PQ monitor is located near or at the capacitors.

Fig. 8. Typical waveforms of normal energizing of utility capacitors in phases(a) A, (b) B, and (c) C. PQ monitor is located faraway from the capacitors.

phase, the sudden step voltage change occurs. The voltage inphase C at the closing instant is 1.5 at point . The utility ca-pacitor pulls the system voltage down to point , but the voltagedoes not pass zero. The polarity of the voltage at point is thesame as that of point . The voltages at points and are

p.u and p.u, respectively. They areseparated by , which is 0.325 ms.

The voltage change can be computed by taking the abso-lute difference of to . The slope of the step voltageis then computed by taking the ratio of to . For the aboveexample, the voltage change and its slope are 0.929p.u and 2.85 103 p.u/s, respectively.

c) Oscillation Frequency of the Energizing Event in thePhase Voltage: The oscillation frequency of any kind of ca-pacitor energizing in the phase voltage is generally between3001000 Hz. Thus, the frequency of oscillation is helpful inidentifying capacitor energizing in general, but it cannot be used

SANTOSO et al.: CHARACTERIZATION OF DISTRIBUTION POWER QUALITY EVENTS WITH FOURIER AND WAVELET TRANSFORMS 251

Fig. 9. The first 22 ms of phase C voltage shown earlier in Fig. 7(c).

to discriminate normal energizing versus other types of capac-itor energizing.

Extracting the oscillation frequency from the capacitor en-ergizing transients is difficult. First, the transient event from agiven voltage waveform has to be localized using the squaredwavelet transform coefficients. Once it is localized, the sinu-soidal part has to be removed. The solid line waveform shownin Fig. 10(a) is the first 22 ms of phase C voltage shown earlier inFig. 7(c). The dotted line waveform in Fig. 10(a) is a curve-fittedwaveform which is found using a polynomial curve-fittingtechnique. The transient event can now be removed fromby subtracting from it. The removed waveform is nowshown in Fig. 10(b).

The frequency of the transient event in the voltage phase isnow estimated by counting the number of crest voltages thatare larger than 0.1 p.u and the duration of the correspondingcrest voltages. This method does not always work if the removedwaveform is very small in magnitude. In such a case, theoscillation frequency feature from the phase voltagecannot be extracted. In this example, the estimated oscillationfrequency is Hz. Whereas the estimated oscil-lation frequency for the waveform shown in Fig. 8(c) using theabove technique is Hz.

d) Wavelet Transform Coefficients: The wavelet trans-form is utilized to provide additional features in identifyingnormal capacitor switching. Consider the phase C voltageshown in Fig. 7(c). We shall perform the wavelet transformsat scales 14. The WTCs for these scales are now shownin Fig. 11(b)(e), respectively. Fig. 11(a) shows the phase Cvoltage waveform which was shown earlier in Fig. 7(c).

In identifying normal energization of utility capacitors, weutilize only results from the wavelet transform at scales 1and 2. The maximum squared magnitude at scales 1 and 2

and , respectively, indicatethe onset of the disturbance and its disturbance activity. Theduration of the transient is estimated using WTC1 or WTC2.The small oscillating wave following the spike-like event inWTCI and/or WTC2 provides an estimate of the energizingtransient duration.

In this example, the maximum values of the squared WTC1and squared WTC2 are and

, respectively. The duration of thetransient event estimated using WTC1 iscycle.

Fig. 10. Oscillation frequency of capacitor energizing is estimated with thehelp of curve-fitting technique.

Fig. 11. The wavelet transform coefficients for phase C voltage waveformshown in Fig. 8(c).

The maximum values of the squared WTC1 and squaredWTC2 can always be found; however, the duration of thetransient event may not always be found. Thisis especially true when the transient frequency is very low.Under this circumstance, both the oscillation frequency in thephase voltage and the duration of the transient event

cannot be extracted. The duration of the capacitorenergizing transient for phase C voltage shown in Fig. 8 is also0.49 cycle, whereas the maximum values of the squared WTC1

and squared WTC2 areand , respectively. These three features

from the wavelet transform will be utilized as identifyingfeatures when available.

e) Oscillation Frequency of the Energizing Event in thePhase Current: As described earlier, the oscillation frequencyof the capacitor transient event in the phase voltage is

252 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 15, NO. 1, JANUARY 2000

very helpful in discriminating capacitor energizing events fromother events. However, the frequency feature from the phasevoltage cannot be used to distinguish normal capac-itor energizing from other types of capacitor energizing distur-bances. Fortunately, the oscillation frequency of the transientevent at the phase current for the normal energizingis very distinct from other types of capacitor energizing distur-bances. The frequency of the phase current during the energiza-tion is typically between 3001000 Hz.

Consider the phase C voltage shown in Fig. 8(c) and its phasecurrent shown in Fig. 12(c). The oscillation frequency of thephase current is computed using the Fourier transformonce the transient event is localized by the wavelet transform.For this example, the frequency is 395.6 Hz.

2) Back-to-Back Capacitor Energizing: Back-to-backenergizing of utility capacitors occurs when the capacitorbeing switched into the utility system is located near analready energized capacitor. The voltage waveforms of theback-to-back energizing events look very much the same asthose in normal energizing. Almost all features of the normalenergizing apply to back-to-back energizing. Therefore, dis-criminating back-to-back energizing events against normalones is a very delicate task. Fig. 13 shows a three-phase voltageof back-to-back energizing of utility capacitors. The associatedphase currents are shown in Fig. 14.

In the following we shall present two key features that mayhelp distinguish back-to-back from normal energizing; the stepvoltage change and the oscillatory frequency of the phase cur-rent.

f) Step Voltage: Back-to-back energizing transientsinvolve two capacitors in close vicinity. One of them is fullyenergized and the other is switching on. The resulting stepvoltage is not as large as if the fully energized bank did notexist. Furthermore, the voltage at point , defined earlier (seeFig. 9) does not drop close to zero as in the previous case. Inother words, during the energization process, the bus voltagecannot drop to zero (although the capacitor has no net charge)because a nearby fully energized capacitor supports the busvoltage. This feature may not always be able to be used todifferentiate back-to-back from normal energizing because thestep voltage in back-to-back energizing behaves exactly likethat in normal energizing when the power quality monitor islocated faraway from the capacitor.

Based on our observations, the voltage change inback-to-back capacitor energizing is typically no largerthan 0.5 p.u. None of the step voltages in phases A, B, and C inFig. 13 are larger than 0.5 p.u.

g) Oscillation Frequency of the Energizing Event at thePhase Current: The frequency of the phase current,provides distinct evidence for the back-to-back energizingevent. The typical frequency for back-to-back in the phasecurrent is larger than 1000 Hz, whereas that for thenormal energizing is less than 1000 Hz. Fig. 14 shows theenergizing transient in the phase current. The frequency in thesephase currents is obviously higher than those in normal ener-gizing shown in Fig. 12. The frequency of the transient eventin the phase current is therefore very useful to distinguishingback-to-back from normal energizing events.

Fig. 12. Current waveforms at phases A, B, and C of the voltage waveformsshown in Fig. 8.

The oscillation frequency of the energizing event in the phasecurrent is computed using the technique described in the ear-lier section. The frequency for phases A, B, and C cur-rents shown in Fig. 14(a)(c), are 1.09, 2.28, and 2.40 KHz, re-spectively. These frequencies are certainly higher than those innormal energizing events.

3) Capacitor Switch Restrike on Opening: Switching off acapacitor (i.e., capacitor de-energizing) does not usually resultin any transient oscillation. However, the bus voltage may dropslightly due to loss of voltage support from the capacitor. Duringthe deenergizing process, the contactor of a capacitor opens anddiscontinues the flow of current. If the contactor does not opensuccessfully, an arc will be established between the contactsand the capacitor will be re-energized. The voltage at the in-stant of restrike will oscillate at the natural frequency character-ized by the capacitance of the capacitor and the system induc-tance. Fig. 15 shows a three-phase voltage of restrike transientsof utility capacitors. The restrikes occur on phases A and B only.Phase C voltage shows no transient because the utility capacitoron phase C successfully de-energized.

Features of capacitor restriking on opening are similar toother capacitor energizing transients. However, discriminatingcapacitor switch restrike on opening events from the previousthree capacitor switching events are quite straightforward.The following are identifying features for capacitor switchingrestrike transients.

h) Polarity of the Voltage Step: Consider phase A voltageshown in Fig. 15(a). The magnified version of the transient isshown in Fig. 16. The voltage change from point and pointis quite dramatic. The voltage at points and arep.u and p.u, respectively. Unlike step voltages fromthe previous two energizing transients, the step voltages of therestrike transients do change polarity. If the voltage at point ispositive then the voltage at point is negative, and vice versa.The change of polarity is attributed to trapped charges in thecapacitor. This is the unique feature associated with capacitorrestrike transients.

SANTOSO et al.: CHARACTERIZATION OF DISTRIBUTION POWER QUALITY EVENTS WITH FOURIER AND WAVELET TRANSFORMS 253

Fig. 13. Typical waveforms of back-to-back energizing of utility capacitors inphases (a) A, (b) B, and (c) C.

Fig. 14. Current waveforms at phases A, B, and C of the voltage waveformsshown in Fig. 13 (only the first ee ms is shown).

i) Squared WTCs: Since the voltage step is very dra-matic, the slope of the voltage step change is also verylarge. This condition translates to a very high magnitude ofsquared WTCs.

Fig. 17 shows squared WTCs at scales 14 for the phase Avoltage. The high magnitudes of the squared WTCs indicatelocation of step voltage. The maximum value of squaredWTC1 is 0.63 whereas that for scale 2

is 1.34. Features from these two scales aresufficient to identify the event.

III. APPPLICATION TO EVENT IDENTIFICATION MODULE

We have presented identifying features of three types ofpower quality events at distribution level. These identifyingfeatures are very useful to understand the physics underlyingthe disturbance processes.

Fig. 15. Capacitor switch restrike on opening at phases (a) A, (b) B, and (c) C.

Fig. 16. Voltage waveform of phase A in detail.

Fig. 17. The squared WTC of voltage waveform (a) at scales (b) 1, (c) 2, (d)3, and (e) 4.

We utilized these identifying features to build an event iden-tification module. The identification module extracts relevantidentifying features using the above methodologies. In orderto identify the PQ events, we made use of a rule-based expertsystem as a reasoning paradigm. The identifying features pre-sented in the previous section were incorporated into expertsystem knowledge bases. The module was designed to mimicpower quality engineers thought process and conversely, the

254 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 15, NO. 1, JANUARY 2000

module permits power engineers to follow its reasoning processand how it reaches its decision. These features are important toassist power engineers in pinpointing the cause of a disturbanceevent. The event identification module is described in [8].

ACKNOWLEDGMENT

This work represents a concerted effort between The Uni-versity of Texas and Electrotek Concepts under the financialsupport of EPRI to develop an event identification module. Wewould like to thank Electroteks power engineers, especially, M.F. McGranaghan, R. F. Scott, and Dr. H. V. Nguyen in providingtechnical assistance. Valuable discussions with A. C. Parsons ofThe University of Texas at Austin are appreciated.

REFERENCES[1] R. J. Gilleskie, Utility expertise in providing power quality and other

engineering services, in Proceedings of the National Science Founda-tion Conference on Unbundled Power Quality Services in the Power In-dustry, Nov. 1996, pp. 2127.

[2] I. Daubechies, Ten Lectures on Wavelets. Philadelphia: SIAM, 1992.[3] J. Arrilaga, Power System Harmonics. Chichester (West Sussex)/New

York: Wiley, 1985.[4] G. T. Heydt, Electric Power Quality, 2nd ed. West Lafayette, IN: Stars

in a Circle Publications, 1991.[5] R. C. Dugan, M. F. McGranaghan, and H. W. Beaty, Electrical Power

Systems Quality. New York: McGraw-Hill, 1996.[6] A. Greenwood, Electrical Transients in Power Systems, 2nd ed. New

York: John Wiley & Sons, Inc., 1991.[7] G. P. Tolstov, Fourier Series. New York: Dover Publications, Inc.,

1976.[8] S. Santoso, E. J. Powers, and W. M. Grady, Wavelet-based power

quality event identification system, Part 1: The wavelet transform andfeature extraction of power quality disturbances and Part 2: Design andimplementation,, EPRI Report, Aug. 1997.

[9] S. Santoso, E. J. Powers, W. M. Grady, and A. C. Parsons, Power qualitydisturbance waveform recognition using wavelet-based neural classifier,Part 1: Theoretical foundation and Part 2: Applications,, IEEE Trans. onPower Delivery, PE-405-PWRD-0-01-1997 and PE-599-PWRD-0-01-1997, 1997.

Surya Santoso (M97) received the Ph.D. degree in electrical and computerengineering from The University of Texas at Austin in 1996. From January97August 97, he was a postdoctoral fellow under the auspices of the ElectricPower Research Institute. He is now with Electrotek Concepts, Inc, Knoxville,TN. His primary responsibility is to research, develop, and implement advancedalgorithms for the state-of-the-art power quality and energy monitoring instru-mentation. He is a Member of IEEE-PES and IEEE-SP.

W. Mack Grady (SM83) received the Ph.D. degree in electrical engineeringfrom Purdue University, West Lafayette, IN, in 1983. He is a Professor of elec-trical and computer engineering at The University of Texas at Austin. His areasof interest include power systems analysis, power system harmonics, powerquality, and short term load forecasting.

Edward J. Powers (F83) received the Ph.D. degree in electrical engineeringfrom Stanford University, Stanford, CA, in 1965. He is a Professor of electricaland computer engineering at The University of Texas at Austin. His currentinterests include wavelet and higher-order statistical signal processing and theirapplication to transient and nonlinear phenomena.

Jeff Lamoree (M90) received the M.E. degree in electric power engineeringfrom Rensselaer Polytechnic Institute, Troy, NY, in 1990. He is currently theGeneral Manager for Electrotek R&D at Electrotek Concepts, Inc., Knoxville,TN. He is responsible for the design, engineering, software development andproject management involved in Electroteks research and development projectarea. These projects focus primarily on the development of power quality anal-ysis tools for utility engineers and are typically funded by the Electric Power Re-search Institute. These tools include the PQ Database, the PQ Diagnostic Systemand the PQ Toolbox.

Siddharth C. Bhatt (M72) received the Ph.D degree in physics from Rensse-laer Polytechnic Institute, Troy, NY, in 1972. He was a Principal Engineer indesign, simulation, and computer products for 13 years with General Electric.He spent two years with Litton Industries in electronic warfare simulation anddiagnostics systems. He is currently with EPRI managing various R&D projectsinvolving power quality systems, power quality and load signature analysis, ad-vanced power quality monitoring projects using advanced technologies such aswavelets, artifical neural networks, and expert systems.