Classification of Underlying Causes of Power Quality

20 Pages·1.757 MB·English

by  Math H.J. Bollen, Irene Y.H. Gu, Peter G. V. Axelberg and Emmanouil Styvaktakis

HindawiPublishingCorporation
EURASIPJournalonAdvancesinSignalProcessing
Volume2007,ArticleID79747,17pages
doi:10.1155/2007/79747
Research Article
Classification of Underlying Causes of Power Quality
Disturbances: Deterministic versus Statistical Methods
MathH.J.Bollen,1,2IreneY.H.Gu,3PeterG.V.Axelberg,3andEmmanouilStyvaktakis4
1STRIAB,77180Ludvika,Sweden
2EMC-on-Site,Lulea˚UniversityofTechnology,93187Skelleftea˚,Sweden
3DepartmentofSignalsandSystems,ChalmersUniversityofTechnology,41296Gothenburg,Sweden
4TheHellenicTransmissionSystemOperator,17122Athens,Greece
Received30April2006;Revised8November2006;Accepted15November2006
RecommendedbyMoise´sVidalRibeiro
This paper presents the two main types of classification methods for power quality disturbances based on underlying causes:
deterministicclassification,givinganexpertsystemasanexample,andstatisticalclassification,withsupportvectormachines(a
novelmethod)asanexample.Anexpertsystemissuitablewhenonehaslimitedamountofdataandsufficientpowersystem
expertknowledge;however,itsapplicationrequiresasetofthresholdvalues.Statisticalmethodsaresuitablewhenlargeamount
ofdataisavailablefortraining.Twoimportantissuestoguaranteetheeffectivenessofaclassifier,datasegmentation,andfeature
extractionarediscussed.Segmentationofasequenceofdatarecordingispreprocessingtopartitionthedataintosegmentseach
representingadurationcontainingeitheraneventoratransitionbetweentwoevents.Extractionoffeaturesisappliedtoeach
segmentindividually.Someusefulfeaturesandtheireffectivenessarethendiscussed.Someexperimentalresultsareincludedfor
demonstratingtheeffectivenessofbothsystems.Finally,conclusionsaregiventogetherwiththediscussionofsomefutureresearch
directions.
Copyright©2007HindawiPublishingCorporation.Allrightsreserved.
1. INTRODUCTION andsubbandfilters)orfromtheparametersofsignalmodels
(e.g., sinusoid models, damped sinusoid models, AR mod-
With the increasing amount of measurement data from els).Thesefeaturesmaybecombinedwithneuralnetworks,
powerqualitymonitors,itisdesirablethatanalysis,charac- fuzzy logic, and other pattern recognition methods to yield
terization,classification,andcompressioncanbeperformed classificationresults.
automatically [1–3]. Further, it is desirable to find out the Among the proposed methods, only a few systems have
cause of each disturbance, for example, whether a voltage shown to be significant in terms of being highly relevant
dipiscausedbyafaultorbysomeothersystemeventsuch and essential to the real world problems in power systems.
asmotorstartingortransformerenergizing.Designingaro- Forclassificationandcharacterizingpowerqualitymeasure-
bust classification for such an application requires interdis- ments, [6, 15, 16] proposed a classification using wavelet-
ciplinaryresearch,andrequireseffortstobridgethegapbe- basedANN,HMM,andfuzzysystems;[19,20]proposedan
tween power engineering and signal processing. Motivated event-based expert system by applying event/transient seg-
bytheabove,thispaperdescribestwodifferenttypesofauto- mentationandrule-basedclassificationoffeaturesfordiffer-
maticclassificationmethodsforpowerqualitydisturbances: ent events; and [13] proposed a fuzzy expert system. Each
expertsystemsandsupportvectormachines. of these methods is shown to be suitable for one or several
There already exists a significant amount of literature applications,andispromisingincertainaspectsintheappli-
on automatic classification of power quality disturbances, cations.
amongothers[4–24].Manytechniqueshavefurtherbeende-
velopedforextractingfeaturesandcharacterizationofpower 1.1. Somegeneralissues
quality disturbances. Feature extraction may apply directly
totheoriginalmeasurements(e.g.,RMSvalues),fromsome Despitethevarietyofclassificationmethods,twokeyissues
transformed domain (e.g., Fourier and wavelet transforms, areassociatedwiththesuccessofanyclassificationsystem.
2 EURASIPJournalonAdvancesinSignalProcessing
v(t) Event 1.2. Deterministicandstatisticalclassifiers
i(t) segments Features Class
Segmen- Feature Classifi-
tation extraction cation Thispaperconcentratesondescribingthedeterministicand
statistical classification methods for power system distur-
bances. Two automatic classification methods for power
Additional
qualitydisturbancesaredescribed:expertsystemsasadeter-
Transition processing
segments ministicclassificationexample,andsupportvectormachines
asastatisticalclassificationexample.
(i)Rule-basedexpertsystemsformadeterministicclas-
Figure 1: The processes of classification of power quality distur-
bances. sification method. This method finds its application when
there is a limited amount of data available, however, there
existsgoodpriorknowledgefromhumanexperts(e.g.,from
previously accumulated experience in data analysis), from
whichasetofrulescanbecreatedbasedonsomeprevious
expertisetomakeadecisionontheoriginsofdisturbances.
(i) Properlyhandlingthedatarecordingssothateachin-
Theperformanceoftheclassificationismuchdependenton
dividualevent(theterm“eventsegment”willbeused
theexpertrulesandthresholdsettings.Thesystemissimple
later)isassociatedwithonlyone(classof)underlying
andeasytoimplement.Thedisadvantageisthatoneneedsto
cause. The situation wereone event (segment) is due
finetuneasetofthresholdvalues.Themethodfurtherleads
toasequenceofcausesshouldbeavoided.
toabinarydecision.Thereisnoprobabilityonwhetherthe
(ii) Selecting suitable features that make the underlying
decisionisrightorwrongorontheconfidenceofthedeci-
causeseffectivelydistinguishablefromeachother.Itis
sion.
counter-productivetousefeaturesthathavethesame
(ii) Support vector machine classifiers are based on the
rangeofvaluesforallclasses.
statisticallearningtheory.Themethodissuitableforappli-
cationswhentherearelargeamountsoftrainingdataavail-
Extracting“good”featuresisstronglydependentonthe
able. The advantages include, among others, that there are
available power system expertise, even for statistical classi-
no thresholds to be determined. Further, there is a guaran-
fiers. There exists no general approach on how the features
teed upper bound for the generalization performance (i.e.,
shouldbechosen.
theperformanceforthetestset).Thedecisionismadebased
It is worth to notice a number of other issues that are
onthelearnedstatistics.
easily forgotten in the design of a classifier. The first is that
the goal of the classification system must be well formu-
1.3. Structureofthepaper
lated: is it aimed at classifying the type of voltage distur-
bance, or the underlying causes of the disturbances? It is a
InSection2,segmentationmethods,includingmodelresid-
common mistake to mix the types of voltage disturbance
ual and RMS sequence-based methods, are described.
(or phenomena) and their underlying causes. The former
Through examples, Section3 serves as the “bridge” that
can be observed directly from the measurements, for ex-
translates the physical problems and phenomena of power
ample, interruption, dip, and standard classification meth-
qualitydisturbancesusingpowersystemknowledgeintosig-
ods often exist. While determining, the latter is a more dif-
nal processing “language” where feature-based data char-
ficult and challenging task (e.g., dip caused by fault, trans-
acterization can then be used for distinguishing the un-
former energizing), and is more important for power sys-
derlying causes of disturbances. Section4 describes a rule-
tem diagnostics. Finding the underlying causes of distur-
basedexpertsystemforclassificationofvoltagedisturbances,
bances not only requires signal analysis, but often also re-
as an example of deterministic classification systems. Next,
quires the information of power network configuration or
Section5presentsthestatistical-basedclassificationmethod
settings. Further,manyproposed classification methods are
usingsupportvectormachinesalongwithanovelproposed
verifiedbyusingsimulationsinapower-systemmodel.Itis
method,whichservesasanexampleofthestatisticalclassifi-
importanttonoticethatthesemodelsshouldbemeaningful,
cationsystems.SomeconclusionsarethengiveninSection6.
consistent,andclosetoreality.Deviatingfromsuchaprac-
tice may make the work irrelevant to any practical applica-
2. SEGMENTATIONOFVOLTAGEWAVEFORMS
tion.
Itisimportanttoemphasizetheintegrationofessential For analyzing power quality disturbance recordings, it is
steps in each individual classification system as outlined in essential to partition the data into segments. Segmentation,
theblockdiagramofFigure1. which is widely used in speech signal processing [25], is
Beforetheactualclassificationcantakeplace,appropriate foundtobeveryusefulasapreprocessingsteptowardsan-
features have to be extracted as input to the classifier. Seg- alyzing power quality disturbance data. The purpose of the
mentation of the voltage and/or current recordings should segmentationistodivideadatasequenceintostationaryand
takeplacefirst,afterwhichfeaturesaremainlyobtainedfrom nonstationary parts, so that each segment only belongs to
the event segments, with additional information from the one disturbance event (or one part of a disturbance event)
processingofthetransitionsegments. which is caused by a single underlying reason. Depending
MathH.J.Bollenetal. 3
on whether the data within a segment is stationarity, dif- 2.2. Segmentationbasedontime-dependent
ferent signal processing strategies can then be applied. In RMSsequences
[20], a typical recording of a fault-induced voltage dip is
splitintothreesegments:before,during,andafterthefault. In case only RMS voltage versus time is available, segmen-
Thedivisionsbetweenthesegmentscorrespondtofaultini- tationremainspossiblewiththesetime-dependentRMSse-
tiation and fault clearing. For a dip due to motor starting, quenceasinput.AnRMSsequenceisdefinedas
the recording is split to only two segments: before and af- (cid:8)(cid:9)
tertheactualstartinginstant.Thestartingcurrent(andthus (cid:3) (cid:4) (cid:9)(cid:9)1 (cid:2)tk
thevoltagedrop)decaysgraduallyandsmoothlytowardsthe VRMS tk =(cid:10)N v2(t), tk =t0,t1,..., (3)
newsteadystate. t=tk−N+1
Figure2 shows several examples where the residuals of where v(tk) is the voltage/current sample, and N is the size
Kalman filter have been used for the segmentation. The
of the sliding window used for computing the RMS. Rms
segmentationproceduredividesthevoltagewaveformsinto
sequence-based segmentation uses a similar strategy as the
partswithwell-definedcharacteristics.
method discussed above; however the measure of change is
computedfromthederivativesofRMSvaluesinsteadoffrom
2.1. Segmentationbasedonresidualsfrom model residuals. The segmentation can be described by the
thedatamodel followingsteps.
Onewaytosegmentagivendisturbancerecordingistouse
(1)DownsamplinganRMSsequence
the model residuals, for example, the residuals from a si-
nusoid model, or an AR model. The basic idea behind this
Sincethetime-resolutionofanRMSsequenceislowandthe
methodisthatwhenasuddendisturbanceappears,therewill differencebetweentwoconsecutiveRMSsamplesisrelatively
beamismatchinthemodel,whichleadstoalargemodeler-
small, the RMS sequence is first downsampled before com-
ror(orresidual).Considertheharmonicmodeltodescribe
putingthederivatives.Thiswillreduceboththesensitivityof
thevoltagewaveform:
thesegmentationtothefluctuationsinRMSderivativesand
(cid:2)N (cid:3) (cid:4) thecomputationalcost.Ingeneral,anRMSsequencewitha
z(n)= Aicos 2πnfk+φk +v(n), (1) largerdownsampleratewillresultinfewerfalsesegments(or
k=1 split of segments) however with a lower time resolution of
where fk =2πkf0/fsisthekthharmonicfrequency, f0isas- saegsmmaelnletrbdoouwndnasraimesp.lCeornavtee,rstehley,ofoprpaonsitReMhSolsdesq.uPernacceticwailtlhy
sumed to be the power system fundamental frequency, and
fs thesamplefrequency.Here,themodelorderN shouldbe athmepdleo,wfnorsatmhepleexaramteplmesiisnotfhteisnscuhbosseecntioenm,pmiri∈cal[lyN,/f1o6r,eNx]-
selected according to how many harmonics are required to
is chosen (N is the number of RMS samples in one cycle).
accommodateasbeingnonsignificantdisturbances.
InmanycasesonlyalimitednumberofRMSvaluespercy-
Todetectthetransitionpoints,thefollowingmeasureof
clearestored(twoaccordingtothestandardmethodinIEC
changeisdefinedandusedtoextracttheaverageKalmanfil-
terresiduale(n)=z(n)−z(cid:5)(n)withinashortwindowofsize 61000-4-30)sothatfurtherdownsamplingisnotneeded.For
wasfollows: notationalconveniencewedenotethedownsampledRMSse-
quenceas
(cid:6) (cid:7)
d(n)= w1 i=nn+(cid:2)−ww/2/2(cid:3)z(i)−z(cid:5)(i)(cid:4) 2, (2) VRMS(cid:3)(cid:11)tk(cid:4), (cid:11)tk = mtk. (4)
wherez(cid:5)(n)istheestimatez(n)fromtheKalmanfilter.Ifd(n)
(2)Computingthefirst-orderderivatives
is prominent, there is a mismatch between the signal and
the model and a transition point is assumed to have been
Astraightforwardwaytodetectthesegmentationboundaries
detected. Figure3 shows an example where the transition
is from the changes of RMS values, for example, using the
pointswereextractedbyutilizingtheresidualsofaKalman
first-orderderivative
filter of N = 20. This is a recording of a multistage voltage
(cid:3) (cid:4) (cid:12) (cid:3) (cid:4) (cid:3) (cid:4)(cid:12)
dipasmeasuredinamediumvoltagenetwork. MRjMS (cid:11)tk =(cid:12)VRjMS (cid:11)tk −VRjMS (cid:11)tk−1 (cid:12), (5)
Thedetectionindexd(n)isobtainedbyusingtheresid-
uals of three Kalman filters (one for each phase). Then the where j = a,b,c indicate the different phases. Consider ei-
three detection indices are combined into one by consider- therasingle-phaseorathree-phasemeasurement,themea-
ing at each time instant the largest of the three indices. In sureofchangesMRMSinRMSvaluesisdefinedby
suchaway,therecordingsaresplittoeventsegments(where (cid:3) (cid:4)
M (cid:11)t
thedetectionindexislow)andtransitionsegments(wherethe RMS⎧ k
(cid:3) (cid:4)
dlceaecuttesecedtdiaobsnybeienvindengextasbilsilkehetiotgrhaa)nc.csoTfomhremmoeorrddsaeatrteuotrhfaetKiohanlamromarnoarnficiilctnsegrt,shwaisthiascerhe- =⎨⎩MmaRaxM(cid:3)S(cid:3)M(cid:11)tkRaMS,MRbMS,MRcMS(cid:4)(cid:3)(cid:11)tk(cid:4)(cid:4) ffoorr13pphhaassee,s.
wassuggestedasN =20in[20]. (6)
4 EURASIPJournalonAdvancesinSignalProcessing
1.2
1 1
Magnitude(pu) 0.5 Magnitude(pu) 000...468
0.2
0 0
0 100 200 300 400 500 0 50 100 150 200 250 300 350 400
Time(ms) Time(ms)
(a) (b)
1.05 1.05
1 1
u) u)
p p
( (
e e
ud 0.95 ud 0.95
nit nit
g g
a a
M M
0.9 0.9
0.85 0.85
0 20 40 60 80 100 120 140 160 180 200 0 50 100 150 200 250
Time(ms) Time(ms)
(c) (d)
1.05 1.2
1.1
1
u) 1 u)
(p (p 0.9
e e
d d
u u
nit nit 0.8
g g
Ma 0.95 Ma
0.7
0.6
0.9 0.5
0 50 100 150 0 50 100 150 200 250 350
Time(ms) Time(ms)
(e) (f)
Figure2:RMSvoltagevaluesversustime(shadowedparts:transitionsegments).(a)–(f):(a)aninterruptionduetofault;(b)nonfault
interruption;(c)inductionmotorstarting;(d)transformersaturation;(e)stepchange;and(f)singlestagevoltagedipduetofault.
(3)Detectingtheboundariesofsegments whereδisathreshold.Atransitionsegmentstartsatthefirst
(cid:11)tk forwhichH1 issatisfied,andendsatthefirst(cid:11)tk forwhich
A simple step is used to detect the boundaries of segments MRMS((cid:11)tk)<δoccursafteratransitionsegmentisdetected.
undertwohypotheses: Itisrecommendedtousewaveformdataforfeatureex-
(cid:3) (cid:4)
H0(event-segment):MRMS (cid:11)tk <δ, traction whenever available, as extracting features from the
(cid:3) (cid:4) (7) RMSvoltagesleadstolossofinformation.Itishoweverpos-
H1(transition-segment):MRMS (cid:11)tk ≥δ, sible, as shown in [20], to perform segmentation based on
MathH.J.Bollenetal. 5
1 1
pu) 0.5 pu) 0.5
( (
e 0 e 0
g g
Volta (cid:0)0.5 Volta (cid:0)0.5
(cid:0)1 (cid:0)1
0 200 400 600 800 1000 0 20 40 60 80 100 120 140 160 180 200 220
Time(ms) Time(ms)
(a) (a)
pu) 1 pu) 1
nitude( 0.8 Voltagenitude(0.95
g g
Ma ma 0.9
0.6
0 200 400 600 800 1000 0 20 40 60 80 100 120 140 160 180 200 220
Time(ms) Time(ms)
(b) (b)
50
x
de Figure4:Inductionmotorstarting:(a)voltagewaveforms;(b)volt-
n
i agemagnitude(measurementina400Vnetwork).
on 25
cti
e
et
D
0
0 200 400 600 800 1000 ing and previous knowledge of disturbances in power sys-
Time(ms) tems.Anautomaticclassificationsystemshouldbebasedat
least in part on this human expert knowledge. The inten-
(c)
sionistogivesomeexamplesofvoltagedisturbancesthatare
Figure3:UsingtheKalmanfiltertodetectsuddenchanges(N = causedbydifferenttypesofunderlyingreasons.Oneshould
20):(a)originalvoltagewaveformsfrom3phases;(b)thedetected be aware that this list is by far complete. It should further
transition points (marked on the fundamental voltages) that are be noted that the RMS voltage as a function of time (or,
usedastheboundariesofsegmentedblocks;(c)thedetectionin- RMSvoltageshape)isusedheretopresenttheevents,even
dexbyconsideringallthreephases. though the features may be better extracted from the ac-
tual waveforms or from some other transform domain. We
willemphasizethatRMSsequencesarebyfartheonlytime-
dependentcharacteristicstodescribethedisturbances;many
recorded RMSsequences.Theperformanceof the resulting
othercharacteristicscanalsobeexploited[5].
classifier is obviously less than that for a classifier based on
thefullwaveformdata.
Inductionmotorstarting
3. UNDERSTANDINGPOWERQUALITY ThevoltagewaveformandRMSvoltagesforadipduetoin-
DISTURBANCES:UNDERLYINGCAUSES ductionmotorstartingareshowninFigure4.Asharpvolt-
ANDTHEIRCHARACTERIZATION age drop, corresponding to the energizing of the motor, is
followed by gradual voltage recovery when the motor cur-
Characterizingtheunderlyingcausesofpowerqualitydistur- rentdecreasestowardsthenormaloperatingcurrent.Asan
bancesandextractingrelevantfeaturesbasedontherecorded inductionmotortakesthesamecurrentinthethreephases,
voltagesorcurrentsisingeneraladifficultissue:itrequires thevoltagedropisthesameinthethreephases.
understandingtheproblemsandphenomenaofpowerqual-
itydisturbancesusingpowersystemknowledge.Acommon Transformerenergizing
andessentialstepforsuccessfullyapplyingsignalprocessing
techniques towards any particular type of signals is largely Theenergizingofatransformergivesalargecurrent,related
dependentonunderstanding thenatureof thatsignal(e.g., tothesaturationofthecoreflux,whichresultsinavoltage
speech, radar, medical signals) and then “translating” them dip.AnexampleisshowninFigure5,whereonecanobserve
into the problems from signal processing viewpoints. This thatthereisasharpvoltagedropfollowedbygradualvoltage
section,throughexamples,contributestounderstandingand recovery.Asthesaturationisdifferentinthethreephases,so
“translating”severaltypesofpowerqualitydisturbancesinto isthecurrent.Theresultisanunbalancevoltagedip;thatis,a
the perspective of signal processing. With visual inspection dipwithdifferentvoltagemagnitudeinthethreephases.The
of the waveform or the spectra of disturbances, the suc- dip is further associated with a high harmonic distortion,
cessrateisverymuchdependentonaperson’sunderstand- includingevenharmonics.
6 EURASIPJournalonAdvancesinSignalProcessing
1 1
pu) 0.5 pu) 0.5
( (
e 0 e 0
g g
Volta (cid:0)0.5 Volta (cid:0)0.5
(cid:0)1 (cid:0)1
0 50 100 150 200 250 300 0 20 40 60 80 100 120 140 160 180 200
Time(ms) Time(ms)
(a) (a)
1.1 1.08
pu) 1 pu) 1.06
Voltageagnitude( 00..89 Voltageagnitude( 11..00241
m m
0.7 0.98
0 50 100 150 200 250 300 0 20 40 60 80 100 120 140 160 180 200
Time(ms) Time(ms)
(b) (b)
Figure 5: Voltage dip due to transformer energizing: (a) voltage Figure7:Voltagedisturbanceduetocapacitorenergizing:(a)volt-
waveforms;(b)voltagemagnitude(EMTPsimulation). age waveforms; (b) voltage magnitude (measurement in a 10kV
network).
1
u) 0.5
p
(
e 0
g
a
Volt (cid:0)0.5 transient,andoftenachangeinharmonicspectrum.Capac-
1 itor banks in the public grid are always three phase so that
(cid:0)
0 20 40 60 80 100 120 140 160 180 200 the same voltage rise will be observed in the three phases.
Time(ms) The recording shown here is due to synchronized capaci-
tor energizing where the resulting transient is small. Non-
(a)
synchronizedswitchinggivesseveretransientswhichcanbe
1.05 usedasafeaturetoidentifythistypeofevent.Severaltypes
pu) 1 ofloadsareequippedwithacapacitor,forexample,aspart
Voltageagnitude( 00.9.95 owpfailctlhitseohirrodwEeM-seiImn-efiirllagterizrc.ihnTaghrweacieltvleegrniisvtteidcausdetortoocpasipwnaicvtciotholtiranggeenoienfrtgmhizeoisnsetglc.oaCasdae-ss
m
0.85 withoutanynoticeabletransient.
0 20 40 60 80 100 120 140 160 180 200
Time(ms)
Voltagedipduetoathree-phasefault
(b)
Figure6:Voltagedisturbanceduetoloadswitching:stepchange The most common cause of severe voltage dips in distri-
measurement:(a)voltagewaveforms;(b)voltagemagnitude(mea- butionandtransmissionsystemsaresymmetricalandnon-
surementinan11kVnetwork). symmetrical faults. The large fault current gives a drop in
voltagebetweenfaultinitiationandtheclearingofthefault
bytheprotection.Anexampleofavoltagedipduetoasym-
Loadswitching metrical (three-phase) fault is shown in Figure8: there is a
sharpdropinvoltage(correspondingtofaultinitiation)fol-
Theswitchingoflargeloadsgivesadropinvoltage,butwith- lowedbyaperiodwithconstantvoltageandasharprecov-
outtherecoveryafterafewseconds,seeFigure6.Theequal ery(correspondingtofaultclearing).Thechangeinvoltage
dropinthethreephasesindicatesthatthiseventwasdueto magnitudehasarectangularshape.Further,allthreephases
theswitchingofathree-phaseload.Thedisconnectionofthe areaffectedinthesamewayforathree-phasefault.
loadwillgiveasimilarstepinvoltage,butintheotherdirec-
tion. Voltagedipduetoanasymmetricfault
Capacitorenergizing Figure9 shows a voltage dip due to an asymmetric fault (a
faultinwhichonlyoneortwophasesareinvolved).Thedip
Capacitor energizing gives a rise in voltage as shown in in the individual phases is the same as for the three-phase
Figure7,associatedwithatransient,inthisexampleaminor fault,butthedropinvoltageisdifferentinthethreephases.
MathH.J.Bollenetal. 7
1
1
pu) 0.5 pu) 0.5
( (
e 0 e 0
g g
Volta (cid:0)0.5 Volta (cid:0)0.51
1 (cid:0)
(cid:0)
0 50 100 150 200 250 300 350 0 20 40 60 80 100 120 140
Time(ms) Time(ms)
(a) (a)
1.2 1.3
pu) 1 pu) 1.2
Voltagenitude( 00..68 Voltagenitude( 01..191
ag 0.4 ag 0.8
m m
0.2 0.7
0 50 100 150 200 250 300 350 0 20 40 60 80 100 120 140
Time(ms) Time(ms)
(b) (b)
Figure8:Voltagedipduetoasymmetricalfault:(a)voltagewave- Figure 10: A self-extinguishing fault: (a) voltage waveforms; (b)
forms;(b)voltagemagnitude(measurementinan11kVnetwork). voltagemagnitude(measurementina10kVnetwork).
1.5
1
pu) 0.5 pu) 0.15
( (
Voltage (cid:0)0.05 Voltage (cid:0)0.051
(cid:0)1 1(cid:0).5
0 100 200 300 400 (cid:0) 0 100 200 300
Time(ms) Time(ms)
(a) (a)
1.1 1.4
pu) 1 pu) 1.2
Voltagemagnitude( 00000.....56789 Voltagemagnitude( 00..168
0 100 200 300 400 0 100 200 300
Time(ms) Time(ms)
(b) (b)
Figure 9: Voltage dip due to an asymmetrical fault: (a) voltage Figure11:Overvoltageswellduetoafault:(a)voltagewaveforms;
waveforms;(b)voltagemagnitude(measurementinan11kVnet- (b)voltagemagnitude(measurementinan11kVnetwork).
work).
Self-extinguishingfault Voltageswellduetoearthfault
Figure10 shows the waveform and RMS voltage due to Earthfaultsinnonsolidly-earthedsystemsresultinovervolt-
a self-extinguishing fault in an impedance-earthed system. ages in two or three phases. An example of such an event
The fault extinguishes almost immediately, giving a low- is shown in Figure11. In this case, the voltage rises in one
frequency (about 50Hz) oscillation in the zero-sequence phase, drops in another phase, and stays about the same in
voltage. This oscillation gives the overvoltage in two of the the third phase. This measurement was obtained in a low-
three-phasevoltages.Thiseventisanexamplewherethecus- resistance-earthed system where the fault current is a few
tomers are not affected, but information about its occur- timesthenominalcurrent.Insystemswithlowerfaultcur-
rence and cause is still of importance to the network oper- rents, typically both nonfaulted phases show an increase in
ator. voltagemagnitude.
8 EURASIPJournalonAdvancesinSignalProcessing
1 Explanation
(pu) 0.5 system Case-specific
ge 0 data
a
Volt (cid:0)0.5 User Inference
(cid:0)1 interface engine
0 100 200 300 400 500
Knowledge
Time(ms)
Knowledge base
(a)
baseeditor
1.1
pu) 1 Figure13:Blockdiagramofanexpertsystem.
agede( 0.9
Voltnitu 0.8
ag 0.7
m 0.6 theclassificationordiagnosticresultsaretheoutputthrough
0 100 200 300 400 500 theinterface(e.g.,acomputerterminal).
Time(ms)
(b) (ii)Inferenceengine
Figure 12: Voltage dip due to fault, with the influence of induc-
Aninferenceengineperformsthereasoningwiththeexpert
tionmotorloadduringafault:(a)voltagewaveforms;(b)voltage
systemknowledge(or,rules)andthedatafromaparticular
magnitude(measurementinan11kVnetwork).
problem.
(iii)Explanationsystem
Inductionmotorinfluenceduringafault
Anexplanationsystemallowsthesystemtoexplaintherea-
Induction motors are affected by the voltage drop due to a soningtoauser.
fault. The decrease in voltage leads to a drop in torque and
a drop in speed which in turn gives an increase in current (iv)Knowledge-baseeditor
taken by the motor. In the voltage recording, this is visible
as a slow decrease in the voltage magnitude. An example is Thesystemmaysometimesincludethisblocksoastoallow
showninFigure12:athree-phasefaultwithmotorinfluence ahumanexperttoupdateorchecktherules.
duringandafterthefault.
(v)Knowledgebase
4. RULE-BASEDSYSTEMSFORCLASSIFICATION
Itcontainsalltherules,usuallyasetofIF-THENrules.
4.1. Expertsystems
(vi)Case-specificdata
Astraightforwardwaytoimplementknowledgefrompower-
qualityexpertsinanautomaticclassificationsystemistode- This block includes data provided by the user and can also
velopasetofclassificationrulesandimplementtheserules include partial conclusions or additional information from
inanexpertsystem.Suchsystemsareproposed,forexample, themeasurements.
in[6,7,14,19,20].
This section is intended to describe expert systems
4.2. Examplesofrules
through examples of some basic building blocks and rules
upon which a sample system can be built. It is worth men- The heart of the expert system consists of a set of rules,
tioningthatthesampleexpertsystemdescribedinthissec- wherethe“realintelligence”byhumanexpertsistranslated
tionisdesignedtoonlydealwithacertainnumberofdistur- into“artificialintelligence”forcomputers.Someexampleof
bancetypesratherthanalltypesofdisturbances.Forexam- rules,usingRMSsequencesasinput,aregivenbelow.Most
ple,arcingfaultsandharmonic/interharmonicdisturbances of these rules can be deducted from the description of the
arenotincludedinthissystem,andwillthereforebeclassi- differenteventsgivenintheprevioussection.
fiedasunknown/rejectedtypebythesystem.
A typical rule-based expert system, shown in the block Rule1(interruption). IFatleasttwoconsecutiveRMSvolt-
diagramofFigure13,mayconsistofthefollowingblocks. agesarelessthan0.01pu,THENtheeventisaninterruption.
(i)Userinterface Rule2(voltageswell). IFatleasttwoconsecutiveRMSvolt-
agesaremorethan1.10pu,ANDtheRMSvoltagedropsbe-
It is the interface where the data are fed as the input into a low 1.10pu within 1 minute, THEN the event is a voltage
system (e.g., from the output of a power system monitor), swell.
MathH.J.Bollenetal. 9
Rule3(sustainedovervoltage). IFtheRMSvoltageremains Self-extinguishing
Rectangular Durationless
above1.06pufor1minuteorlonger,ANDtheeventisnota voltagedips Faults than3cycles fault
Fuse-clearedfault
voltageswell,THENtheeventisasustainedovervoltage. Singlestage
Rule 4 (voltage dip). IF at least two consecutive RMS volt- Multistage Changeinthefault
agesarelessthan0.90pu,ANDtheRMSvoltagerisesabove Changeinthesystem
0.90puwithin1minute,ANDtheeventisnotaninterrup- Nonrectangular Transformer Normalswitching
tion,THENtheeventisavoltagedip. voltagedips saturation Duetoreclosing
Inductionmotor
Rule5(sustainedundervoltage). IFtheRMSvoltageremains starting
Stepchanges
below0.94pufor1minuteorlonger,ANDtheeventisnota Interruption Normaloperation
involtage
voltagedip,ANDtheeventisnotaninterruption,THENthe Duetofault
eventisasustainedundervoltage. Energizing
Rule 6 (voltage step). IF the RMS voltage remains between Loadswitching
0.90puand1.10puandthedifferencebetweentwoconsec-
Voltagecompensation
utive RMS voltages remains within 0.0025pu of its average
valueforatleast20secondsbeforeandafterthestep,andthe
eventisnotasustainedovervoltage,ANDtheeventisnota Figure14:Atreestructuredinferenceprocessforclassifyingpower
sustainedundervoltage,THENtheeventisavoltagestep. systemdisturbancerecordings.
Note that these rules do allow for an event being both
a voltage swell and a voltage dip. There are also events that
possiblydonotfallinanyoftheeventclasses.Theinference (vi) stepchange,
engineshouldbesuchthatbothcombinedeventsandnon- (vii) transformersaturationfollowedbyprotectionopera-
classifiable events are recognized. Alternatively, two addi- tion,
tionaleventclassesmaybedefinedas“combineddip-swell” (viii) singlestagedipduetofault,
and “other events.” For further classifying the underlying (x) Multistagedipduetofault.
causesofavoltagedip,thefollowingrulesmaybeapplied.
Somefurtheranalysisandclassificationarethenapplied,for
example,
Rule 7 (voltage dip due to fault). IF the RMS sequence has
a fast recovery after a dip (rectangular shaped recovery), (i) seventypesofdip(typeA,Ca,Cb,Cc,Da,Db,Dc,as
THENthedipisduetoafault(rectangularshapediscaused definedin[3]);
byprotectionoperation). (ii) stepchangeassociatedwithvoltageincrease/decrease;
(iii) overvoltage associated with energizing/transformer
Rule8(inductionmotorstarting). IFtheRMSsequencesfor
saturation/stepchange/faults;
allthreephasesofvoltagerecovergraduallybutwithapprox-
(iv) faultrelatedtostarting/voltageswell/clearing.
imatelythesamevoltagedrop,THENitiscausedbyinduc-
tionmotorstarting. The tree-structured inference process for classifying the
underlyingcausesisshowninFigure14.
Rule 9 (transformer saturation). IF the RMS sequences for Table1 shows the results from the expert system. Com-
allthreephasesofvoltagerecovergraduallybutwithdifferent paring with the ground truth (manually classified results
voltagedrop,THENitiscausedbytransformersaturation. frompowersystemexperts),theexpertsystemhasachieved
approximately97%ofclassificationrateforatotalof962dis-
turbancerecordings.
4.3. Applicationofanexpertsystem
Asimilarsetofrules,butusingwaveformdataasinput,has 5. STATISTICALLEARNINGANDCLASSIFICATION
beenimplementedinanexpertsystemandappliedtoalarge USINGSUPPORTVECTORMACHINES
number of disturbances (however, limited to 9 types), ob-
tainedinamedium-voltagedistributionsystem[19,20]. 5.1. Motivations
Theexpertsystemisdesignedtoclassifyeachvoltagedis-
AnaturalquestionarisesbeforewedescribeSVMclassifiers.
turbanceintooneofthe9classes,accordingtoitsunderly-
Why should one be interested in an SVM when there are
ingcause.Thelistofunderlyingcausesofdisturbancesbeing
manyotherclassificationmethods?Twomainissuesofinter-
consideredinthisexpertsystemincludes
estinSVMclassifiersarethegeneralizationperformanceand
(i) energizing, the complexity of classifier which is a practical implementa-
(ii) nonfaultinterruption, tionconcern.
(iii) faultinterruption, Whendesigningaclassificationsystem,itisnaturalthat
(iv) transformersaturationduetofault, onewouldliketheclassifiertohaveagoodgeneralizationper-
(v) inductionmotorstarting, formance(i.e.,theperformanceonthetestsetratherthanon
10 EURASIPJournalonAdvancesinSignalProcessing
Table1:Classificationresultsfor962measurements. Rm0 Φ((cid:0)) F f((cid:0)) Y
Numberofclassified Φ(x)
Typeofevents events x x xo Φ(xΦ)(xΦ)(xΦ)(x) Φ(o) C1
EI(nbntyeerfragruuizlpitnsti/gonnonfaults) 13 104 88 x xoxooo ox oo Φ(ΦΦx)((ox))ΦΦ((ooΦ))Φ(o(Φ)o)(Φo)(o) C2
Transformersaturation
119 6 Inputspace Featurespace Decisionspace
(normal/protectionoperation)
Stepchange
15 21 Figure15:Differentspacesandmappingsinasupportvectorma-
(increase/decrease)
chine.
Fault-dip(singlestage) 455
Fault-dip(multistage)
(fault/systemchange) 56 56 Then, another function f(·) ∈ F is applied to map the
high-dimensionalfeaturespaceF ontoadecisionspace,
Othernonclassified
16 13
(shortduration/overvoltage) (cid:3) (cid:4) (cid:3) (cid:3) (cid:4)(cid:4)
f :F −→Y Φ xi (cid:5)−→ f Φ xi . (9)
Thebestfunction f(·) ∈ Fthatmaycorrectlyclassifyaun-
seenexample(x,d)fromatestsetistheoneminimizingthe
the training set). If one uses too many training samples, a
expectederror,orthegeneralizationerror,
classifier might be overfitted to the training samples. How-
(cid:16)
ever,ifonehastoofewtrainingsamples,onemaynotbeable (cid:17) (cid:3) (cid:4) (cid:18) (cid:3) (cid:4)
toobtainasufficientstatisticalcoveragetomostpossiblesit- R(f)= l f Φ(x) ,d dP Φ(x),d , (10)
uations.Bothcaseswillleadtopoorperformanceonthetest
dataset.ForanSVMclassifier,thereisaguaranteeoftheup- wherel(·)isthelossfunction,andP(Φ(x),d)istheproba-
pererrorboundonthetestsetbasedonstatisticallearning bilityof(Φ(x),d)whichcanbeobtainediftheprobabilityof
theory. Complexity of classifiers is a practical implementa- generatingtheinput-outputpair(x,d)isknown.Aloss(or,
tionissue.Forexample,aclassifier,forexample,aBayesian error)isoccurredif f(Φ(x))(cid:6)=d.
classifier,maybeelegantintheory,however,ahighcompu- Since P(x,d) is unknown, we cannot directly minimize
tational cost may hinder its practical use. For an SVM, the (10).Instead,wetrytoestimatethefunction f(·)thatisclose
complexity of the classifier is associated with the so-called totheoptimalonefromthefunctionclassFusingthetrain-
VCdimension. ingset.Itisworthnotingthatthereexistmany f(·)thatgive
AnSVMclassifierminimizesthegeneralizationerroron perfect classification on the training set; however they give
the test set under the structural risk minimization (SRM) differentresultsonthetestset.
principle. According to VC theory [26–29], we choose a function
f(·) that fits to the necessary and sufficient conditions for
theconsistencyofempiricalriskminimization,
5.2. SVMsandthegeneralizationerror
(cid:19) (cid:20)
(cid:3) (cid:4)
One special characteristic of an SVM is that instead of di- limP sup R(f)−R (f) >ε =0, ∀ε>0, (11)
mension reduction is commonly employed in pattern clas- n→∞ f emp
sificationsystems,theinputspaceisnonlinearlymappedby
Φ(·) onto a high-dimensional feature space, where Φ(·) is wheretheempiricalrisk(orthetrainingerror)isdefinedon
a kernel satisfying Mercer’s condition. As a result of this, thetrainingset
classes are more likely to be linearly separable in the high-
dimensionalspaceratherthaninalow-dimensionalspace. 1 (cid:2)N (cid:3) (cid:3) (cid:3) (cid:4)(cid:4) (cid:4)
Letinputtrainingdataandtheoutputclasslabelsbede- Remp(f)= N l f Φ xi ,di (12)
scribedaspairs(xi,di),i=1,2,...,N,xi ∈Rm0 (i.e.,m0 di- i=1
mensionalinputspace)anddi ∈Y (i.e.,thedecisionspace). andN isthetotalnumberofsamples(orfeaturevectors)in
As depicted in Figure15, the spaces and the mappings for thetrainingset.Aspecificwaytocontrolthecomplexityof
anSVM,anonlinearmappingfunctionΦ(·)isfirstapplied functionclassFisgivenbyVCtheoryandthestructuralrisk
which maps the input-space Rm0 onto a high-dimensional minimization(SRM)principle[27,30].UndertheSRMprin-
feature-spaceF, ciple,thefunctionclassF(andthefunction f)ischosensuch
that the upper bound of the generalization error in (10) is
(cid:3) (cid:4) minimized.Forallδ>0and f ∈F,itfollowsthatthebound
Φ:Rm0 −→F xi(cid:5)−→Φ xi , (8) ofthegeneralizationerror
(cid:21)
(cid:3) (cid:4)
whereΦisanonlinearmappingfunctionassociatedwitha R(f)≤R (f)+ h ln(2N/h)+1 −ln(δ/4) (13)
emp N
kernelfunction.