ApplicationofWaveletstoAnalyzePowerSystemTransients
Ö.N.Gerek*,D.G.Ece,
DepartmentofElectrical-ElectronicsEngineering,AnadoluUniversity,Eskişehir,Turkey
Abstract
Powersystemtransientsremaintobeanissueforenergydeliveryefficiency.Waveletshavebeenauseful
tooltoanalyzevarioussignalsandwaveformsforitsgoodtime-frequencyproperties,includingtheanalysis
ofpowersystemtransientsandpowerqualityproblems.Inmostoftheresearches,popularwaveletsare
selected, and it has been observed that the wavelet decomposition of transient waveforms at various
resolutionsprovideafairemphasisonthedetectionandclassificationofpowersystemabnormalities.Since
thetransformcoefficientsdepictthetransientwaveformcharacteristicsinatime-windowedmanner,these
coefficientsindicatethetimeperiodoverwhichatransienteventoccurs.Nevertheless,thechoiceordesign
ofthewaveletforthisparticularpurposehasnotbeenaddressedbefore.Thispaperprovidesresultsfor
variouschoicesofwavelets,andproposesaspecificfilterforthesubbanddecompositionanddetectionin
subbanddecompositionofvoltagewaveformsunderstagedincipientfaultsandspeeddrivestarting.
©2016IEESE.Allrightsreserved.
1.Introduction
TheImprovingcomputeranddigitalprocessingtechnologieshaveenabledmorepracticaluse
of automated computer based systems which digitally analyze the power system transients by
filtering and frequency domain methods. Recently wavelet analysis has been a very popular
methodinthisaspect[1]-[12].Itsabilitytodepictfrequencycontentatdifferentscalestogether
withpreservingtimelocalityinducesagreatpotentialforsignalanalysis.Unliketheshorttime
Fourier Transform (STFT), the wavelets can be selected, generated, or designed for satisfying
specificpropertiesoftheclassofsignalsunderconsideration.
Multiplelevelwaveletdecompositionisperformedtoselecttheenergycontentofthesignalina
specific frequency band. In this aspect, wavelets can be thought of as practical tools for
determiningthespectrumofthewaveforminatime-windowedmanner.Infact,mostresearchers
intheareaofpowerqualityanalysishaveconsideredandusedthewellknownwaveletsasaway
ofsplittingthefrequencyspectrumofthewaveformusinghigh-andlow-passfilterpairs.Ifonly
this property of the wavelet filter banks are considered, the choice of the wavelet becomes
irrelevant.Whentheideaistoselectgoodlow-andhigh-passfilters,thereislittlereasontoselect
the wavelets as Daubechies or Morlets, etc. However, wavelets have many other time-domain
properties.
Inthiswork,weinvestigatedwaysofgeneratingwaveletfilterbanksdependingontheirspectral
andtimedomainproperties,andcomparedthemtostandardwavelets.Twomethodsusedhere
to generate filter banks are; selection of a half band filter-pair due to its good band splitting
property,andselectingafilterwhichapproximatesthewaveformwithoutatransient.Filterswere
usedtoanalyzereallifecurrentwaveformdataacquiredfromaphaseofanexperimentallowvoltagesystemloadedwithanadjustablespeeddrive(ASD),resistiveandinductiveloadbanks.
Phase-to-phasestagedincipientfaultcurrentandASDstartingcurrentwaveformsareanalyzed.
It was observed that both filter banks generated in this work have on par, or better detection
propertiesthanthewellknownwavelets.
2.Half-BandFilterPairsversusDaubechiesFilters
Amajorobservationbetweennormalandfault-contaminatedvoltagesistheavailabilityversus
unavailabilityofparticularharmonicsasseeninFigure1.
*
Correspondingauthor:ongerek@anadolu.edu.edu.tr
Gerek&Ece/8thInternationalEgeEnergySymposiumandExhibition-2016
Fig1:(a)IncipientfaultcurrentwaveformofanASD,(b)Powerspectrumofthenoiselesspart,
(c)Powerspectrumoffaultycurrent.
Selectinglow-passandhigh-passfilterpairsisareasonableapproachtodistinguishbetween
frequencybandcharacteristicsofthetwospectra.Indeed,inmostoftherecentworks,wavelets
withgoodfrequencypropertieshavebeenused.However,onecanselectbetterfiltersthanthe
readilyavailablefilters(i.e.,Daubechies,Morlet,etc.)Mostofthepopularwaveletsaredesigned
forgeneralsignalprocessingpurposes,andtheymaylacksomeofthepropertieswhichmaybe
desirable for analysis of power system transients. For example, when incipient fault occurs,
frequencypeakscorrespondingto5thand6thharmonicsareemphasizedmoreinthenoisysignal.
Forillustrativepurposes,wecomparedthe15-taphalfbandlow-pass(Eq.1)andhigh-passfilter
pairwiththeDaubechies-4filterbank.
[0.0074,0,0.0328,0,0.1076,0,0.4352,0.7083,0.4352,0,0.1076,0,0.0328,0,0.0074](1)
Inananalysisof3-levelbalancedtreedecomposition,weobservethatthetwofilterbankcases
provide exactly the same subband sample variation for the eight subbands. The observation is
valid for both arcing faults and ASD motor start up. Hence, it is concluded that half band or
Daubechies filters do not provide any improvement for event detection. The experiments are
repeated for longer (hence sharper) half band filters and longer Daubechies wavelets, and
comparativeresultsdidnotchange.Thisobservationalsoimpliesthatwaveletsgoodforspecific
applicationsmaynotnecessarilycorrespondtogoodall-purposewavelets.
3.DesignofWaveletsforPowerTransientSignalAnalysis
In this work, we have adopted the Daubechies-type wavelet generation strategy to come up
withanalysisandsynthesisfilters.Sincetheapproximationsubspaceisgeneratedbythescaling
function,wehavestartedwithscalingfunction(low-pass)filterdesignbymimickingaperiodof
normalvoltagewavecycle,andincorporatedaspectralzeroat𝜔 = 𝜋,asrequiredforregularity.
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Gerek&Ece/8thInternationalEgeEnergySymposiumandExhibition-2016
Consequently,thehighpassfilterwasgeneratedtocomplementtheapproximationwithaspectral
zeroat𝜔 = 0.Theselectedscalingfunction(thefilter𝐻' )isshowninFigure2.
Fig2:Thelow-passfilterthatmimicsanormalvoltagewaveform,itself.
Again, wavelet decompositions are obtained and high frequency bands are investigated. In
Fig.3(a),wecanseethattheapproximationwaveformcontainsmostofthesignalpower,whereas
thedetailsignalsatvariousstagesarerathersmallforthenormalwaveform.Ontheotherhand,
forthewaveformwithincipientfault(Fig.3(b)),thedetailsignalsbecomelargeranditcanbe
better discriminated from the event free case than the detail signals using, for example,
Daubechieswavelets(Fig.3(c)).
Fig3:Pyramiddecompositionof(a)normalwaveform,(b)incipientfaultwaveformusingfilterinFig.2,
and(c)usingDaubechies-6wavelet.
Thesecondmethodtoobtainthepyramiddecompositionlowpassfilterisbasedontheadaptive
predictionofthetransientwaveformsamplesfromitsadjacentsamplesintime.Forthispurpose,
aLeastSquarestypeofadaptationwasappliedtothepartsofthewaveformwithoutatransient.
Thecoefficientsoftheresultingnon-causal13-tapFIRfilterwasobtainedas
[0.0029,0.0108,0.0297,0.0597,0.1066,0.3303,0.6836,0.3164,0.1201,0.0356,0.0332,0.0006,0.0049]
Whenthisfilterisusedwithreallifesignalscontaininganincipientfault,weobtaintheresultsas
showninFigure4(a).AswecanseeinFigure4(b),thisfilteremphasizesthefaultregionsbetter
thantheDaubechies-6filterbankacrosssecond,third,andfourthscales.
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Gerek&Ece/8thInternationalEgeEnergySymposiumandExhibition-2016
Fig4:Decompositionoftheincipientfaultwaveformusing(a)adaptedfilterbankand(b)Daubechies-6
wavelet.
4.Conclusions
Inthiswork,weillustratedanattempttoobtainwaveletfiltersspecificallyoptimizedforpower
system transient waveforms. Although it is true that wavelets constitute a nice way to detect
abnormalbehaviorinsignals,ratherlittleattentionispaidontheselection,betteryet,thedesign
of the wavelet suitable for the power system transient analysis. We proposed various ways to
selectordesignsubbandfilterbanksforwaveletanalysis.Forthereallifevoltagedatasamples,
weobtainedsuccessfulresultsthanconventionalandpopularwaveletsintermsofmoreapparent
subbandenergyforPQfaultsituations.Theresultsshowthatmoreattentionneedstobepaidon
thesignalcharacteristicsforselectingorgeneratingwaveletsforbetteroverallperformance.
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