on wavelet transform A high speed noncommunication protection scheme for power transmission linesbased Electric Power Systems Research

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Electric Power Systems Research

j o ur na l ho me p ag e : w w w . e l s e v i e r . c o m / l o c a t e / e p s r

A high speed noncommunication protection scheme for power transmission lines based on wavelet transform

Ammar A. Hajjar

ElectricalPowerDepartment,FacultyofMechanicalandElectricalEngineering,TishreenUniversity,Latakia,Syria

a r t i c l e i n f o

Articlehistory:

Received30January2012

Receivedinrevisedform5October2012 Accepted30October2012

Available online 23 December 2012

Keywords:

Wavelettransform High-speedprotection Noncommunicationscheme Transmissionlines Transientcurrents

a b s t r a c t

Thispaperpresentsahigh-speedprotectionschemeforpowertransmissionlinesbasedonwavelet transform(WT).Itisanoncommunicationprotectionschemeasitdependscompletelyonlocallymea- suredcurrents.ItutilizesWT,whichactsasamulti-levelbandpassfilter,toextracttwodistinctbands offrequencyfromthefaultinducedhighfrequency(HF)transientcurrents;thefirstbandishighwhile thesecondbandisrelativelylower.Thespectralenergiesoftheextractedsignalsarethencalculatedto formtwodiscriminatingsignalsoftherelay(operativeandrestraint).Basedontheratiobetweenthese discriminatingsignalstherelaycandistinguishwhetherafaultisinternalorexternaltotheprotected line.

Theperformanceoftheintroducedprotectionschemewasevaluatedbysimulatingseveralfaultson 400kV–50Hztransmissionsystemusinganelectromagnetictransientprogram(EMTDC).Thesimulation resultsshoweddistinctperformanceoftheschemeirrespectiveofthefaulttype,faultinceptionangle, faultpositionandfaultresistance.Moreover,itisnotaffectedbyasystemconfigurationandsystem sourceparameters.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

EHVtransmissionlines protectionschemes canbeclassified intotwomaincategories:thecommunicationandnoncommunica- tionprotectionschemes.However,eachoftheaforesaidprotection schemeshasitsownproblems.Inthisrespect,theproblemsofthe noncommunicationprotectionschemes,suchasdistanceprotec- tion,are:itcannotprotecttheentirelineanditssettingisnoteasy.

Inthiscontext,thecommunicationprotectionschemes,suchasdif- ferentialprotection,weresolvedtheaforesaidproblems,butthey needanexpensiveandcomplicatedcommunicationsystem.Fur- thermore,thereliabilityandcostofthecommunicationprotection schemesarefunctionofthereliabilityandcostoftheusedcom- municationsystems[1].Hence,ahigh-speed,lowcostandreliable noncommunicationprotectionschemefortheentiretransmission lineprotectionisrequired.

Inthisrespect,thecommunicationprotectionschemes[2,3]and noncommunicationprotectionschemes[4,5]based ontransient componentswereoffereda high-speedprotectionof theentire line.However,theysufferedfromseverallimitations,suchasnot beingabletodetectfaultswithzerophaseinceptionangles,high resistancefaultsandareaffectedbyanychangeinasystemconfig- urationandsystemsourceparameters.

E-mailaddresses:ammarhajjar@hotmail.com,ammarhajjar@tishreen.edu.sy

Togetridoftheaforesaidlimitations,theauthorsof[6,7]pre- sentedanoncommunicationprotectionschemebasedoncapturing thefaultgeneratedHFtransientvoltageswiththehelpoflinetraps andstacktuners.Theydesignedspecialbandpassfilters,with17 floatingpointcoefficients,toextracttwodistinctsignalsfromthe capturedsignalsinordertoformtheoperativeandrestraintsignals andhencetodistinguishwhetherthefaultisinternalorexternalto theprotectedline.However,installinglinetrapsandstacktuners ateachendofthelineincreasesthecostandlimitstheapplica- tionofthescheme.Tosolvetheaforesaidproblemtheauthorof [8]presentedanalternativeformofnoncommunicationprotection schemebasedonthefaultgeneratedHFtransientcurrentsthatdoes notrequirelinetrapsandstacktuners.However,thetechniquein [8]alonehasdifficultyindistinguishingbetweenafaultontheline closetoremotebusbarwithintheprotectedzoneandonthebus- barorclosetothebusbaroutsidetheprotectedzone.Inaddition, theuseoftwoneedlessmodalsignalsin[8]tocoveralltypesof faultsatlowspeedspeciallydesignedmultichannelsfilter,with8 floatingpointcoefficients,maylimititsapplication.Theauthorsof [9]usedtheso-called‘Chaari’recursivecomplexWT[10]toextract theaforesaidtwodistinctbandsoffrequency.However,therecur- siveWTrequireshistorical andfuturedataandrequiresa large numberofcomputations;e.g.,itneeds36realmultiplicationsand 35realadditionsforeach sample[10].Theauthorsof[11]used the‘db4’wavelet,whichhasabandpassfilterof8floating-point coefficients,toextract theabovementionedbands offrequency.

Theauthorsof[12]augmentedtheschemeof[8]withlinetraps 0378-7796/$–seefrontmatter© 2012 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.epsr.2012.10.018

icaldata.Moreover,theyusedphaseinformationtodiscriminate thefaultedline.However,inadditiontoalargenumberofcompu- tationsrequiredbythescheme,installinglinetrapsincreasesthe schemecostandlimitsitsapplication.

Itisobviousfromtheabovesurveythatthefilteringalgorithm isthecoreofthenon-communicationprotectionscheme.Hence, suitablechoiceofthefilteringalgorithm,intermsofspeedandtime frequencylocalization,playsavitalrole.Therefore,thispaperusesa high-speedwavelet“PiecewiseLinearSplineWavelet”,whichhas abandpassfilterwith3coefficients,fordevelopingahigh-speed noncommunicationprotectionschemeforEHVtransmissionlines.

Inthisrespect,theWTwasusedtocapturetwobandsoffrequencies fromthefaultinducedHFtransientcurrents.Thespectralenergies ofthesebandswereusedforfaultedlinediscrimination.Computer simulationoftheschemeshowedthattheschemehasahigh-speed responseanddistinctperformanceirrespectiveofthefaulttype, faultinceptionangle,faultpositionandfaultresistance.

2. Theoryofwavelettransform

Waveletisawaveformofeffectivelylimiteddurationthathas anaveragevalueofzero.WTisrelativelyanewsignalprocessing toolfortransientsignalsanalysis.Itbreaksupasignalintoshifted andscaled(compressedordilated)versionsofthemotherwavelet (basisfunction).WThassomeuniquefeaturesthatmakeitmore suitablefortransientsignalsanalysisinapowersystem[9–13], suchas:

䊉It hasthepropertyof time-frequencylocalization,even, of a smalldisturbanceinasignal.

䊉WT has a strong capability of extracting the signal compo- nentsunderdifferentfrequencybandswhileretainingthetime domaininformation.

ThecontinuousWT(CWT)ofatime dependentsignalf(t), is definedasthesumoveralltimesofasignalf(t)multipliedbya scaledandshiftedversionsofamotherwavelet (t).Themother wavelet (t)canbedefinedasfollows:

b,a(t)= 1

√a

_t−b

a

(1) where“a”and“b”representthetimescalingandshifting,respec- tively.Thecoefficients C_f (a,b),or theCWT, aredefinedbythe followinginnerproduct:

Cf(a,b)=

_+∞

−∞

f(t)· ^∗_b,a(t)·dt (2) where“*”referstoacomplexconjugate.

WTofasampledsignalcanbeobtainedusingthediscreteWT (DWT)relation:

DWT(m,n)= 1

a^m₀

k

f(k) ^∗

n−ka^m₀ a^m₀

(3)

where theparameters a and bin (1) are replaced bya^m₀,ka^m₀, respectively,n,k,a₀areintegers;a₀issomeselectedspacingfactor (usuallychosenequalto“2”fordyadicgrid),andmisthescaling index0,1,2,3,....

Generally,WTconsistsofsuccessivepairsoflowandhighpass filters[14,15].Foreachpairthehigh-scale,lowfrequencycompo- nentsofthesignalf(t)arecalledapproximations(CA),whilethe low-scale,highfrequencycomponentsofthesamesignalf(t)are calleddetails(CD).Aftereachfilteringstage,everyseconddata pointisthrownawaytoavoidredundantdata.Fig.1depictsthe twostagesfilteringprocessofasignalf(t).

f(t)

High pass filter

CA1

High pass filter CD1

Low pass filter

Low pass filter

CD2

CA2

Fig.1.Twostagesfilteringprocessofasignalf(t).

3. Principleofthenoncommunicationprotection

IfafaultoccursonatransmissionlineawidebandofHFtran- sientcurrentsignalswillbeinducedatthefaultpoint,thenthey willtraveltowardtheline’sbusbars,whichconstituteadisconti- nuitypoints.Accordingly,partofthesignalswillcontinuealongthe adjacentline(s)whiletherestwillreflectbackandforthbetween afaultpointandtheline’sbusbarsuntilapostfaultsteadystateis reached.

Theprincipleofanoncommunicationprotectionschemecanbe explainedusinga400kVtransmissionsystem(showninFig.2);

thelengthsoflinesaregiveninfigure.Theprotectionrelay‘R_yzis assumedtobeinstalledonline‘L2’nearbusbar‘Y’,andisresponsi- blefortheprotectionoftheentireline‘L2’.CSrepresentsthestray capacitanceof thebusbar(typically0.1␮F [6–10])thathaslow impedanceathighfrequencyandhighimpedanceatlowfrequency.

In thiscontext, abusbaris normallyconnectedtomany power equipmentssuchaspowertransformersandgeneratingunits,the characteristicsoftheseequipmentswilldeterminethebusbarto groundimpedancethatisnormallyconductiveinnature.However, atsignificanthighfrequencies,thecapacitanceandcapacitivecou- plingbecomethedominantfactorinthebusbarimpedance[6,8].

Therefore,asignificantamountofthetransientcurrent,particu- larlythehigherfrequencycomponents,willbeshuntedtoground throughthebusbarcapacitance.Thisfeatureisthekeytodevelopa noncommunicationprotectionschemeinwhichthebusbarsatboth endsofaprotectedlinecanbeusedasboundariestotheprotected zone[8].Whenanexternalfaultoccursonatransmissionsystem showninFig.2,e.g.,atpointF₂online‘L₃’,thetransientcurrent signalI2,whichcontainswidebandofHFcomponents,willtravel towardbusbar‘Z’.Whenthissignalreachbusbar‘Z’partofit,I₁, willcontinuetotravelintoline‘L₂’,andtherest,Io,willbeshunted intogroundbyabusbarcapacitance.Asaresult,therelay‘Ryz’will measureanattenuatedcurrent,I₁,ratherthantheinitialcurrentI₂. However,theattenuationwillbelargerathigherfrequencythan thatatlowerfrequencysincethebusbarimpedanceintoground decreaseswithincreasingfrequency.Incontrast,thereisnosuch attenuationincaseofaninternalfault,e.g.,afaultatpointF₁on lineL2.Thisimportantfeaturecanbeusedtodiscriminatebetween internalandexternalfaults.

The introduced high-speed noncommunication protection schemedependsonusinghigh-speedWT,whichactsasamulti- levelbandpassfilter,tocapturetwodistinctbandsoffrequency, oneoflowfrequencylevelandtheotherofhigherfrequencylevel.

Theratioofthespectralenergiesofthehigherbandtothelower bandwillbeusedtodiscriminatebetweenexternalandinternal faults.

4. Relaydesigndescription

Ablockdiagramoftheintroducedprotectionschemeisshown inFig.3.

S2

S1

R_yz X

L₁=100 km ^Y

Z W

S4 I₁

F3

C_s

L2=120 km

C_s

S3

L3=140 km

C_s C_s

F₁ F₂

I₀I₂ I₁

Fig.2. Aonelinediagramofthestudiedtransmissionsystem.

4.1. Modalcurrentsignal

To eliminate any noise induced in the line due to mutual couplingbetweenadjacentparallellinesand/ormultiplecircuits sharingthesamerightofway,theoutputsoftheCT’s(Ia,IbandIc) arecombinedinordertoformamodalcurrentsignalasfollows:

Im=Ia−2Ib+2Ic (4)

Thismodalsignalissufficienttocoveralltypesoffaultsthat encounteredinpractice;andensuresimmunitytoalldisturbances otherthanthoseassociatedwiththeprotectedline.Itisworthmen- tioningthattheintroducedschemecanbeapplieddirectlytophase

Fig.3. Aflowchartofthedevelopedprotectionscheme.

currents(Ia,Ib andIc), butinsodoingthecomputationburden willbeincreased(threephasesignalswillbeprocessedinsteadof onemodalsignal).Moreover,therelaystabilitywillbejeopardized underexternalfaultsduetoamutualcoupling.

4.2. Antialiasingfilter

Toavoidanyerrorinasubsequentdigitalsignalprocessingaris- ingduetosignalaliasing(arisingfalsefrequenciesinasignal)the modalsignalispassedthroughananalog2ndorderButterworth filterwithacutofffrequencyofaroundhalfthedigitalsampling frequency.Insodoing,anyunwantedhighfrequencies(noise)can beremovedbeforesampling.

4.3. Ahigh-speedwaveletfornoncommunicationprotection Digitaldecompositionfilterconstitutethemainpartofanon- communicationprotectionrelay.Therefore,suitablechoiceofthis filter,intermsofspeedandtime-frequencylocalization,playsan importantroleinrealizingahigh-speedrelay.Inthispaper,WTthat representsamulti-levelbandpassfilter,ischosen.Asuitablechoice ofamotherwaveletplaysalsoavitalroleintermsofspeedand time-frequencylocalization.Inthisrespect,theso-called“Piece- wiseLinearSplineWavelet”ischosensinceitismoresuitablefor transientsignalsanalysisinterms ofspeed andtime-frequency localization[15].Inthiscontext,thehigh-passfilterofthiswavelet has3coefficients,soitissimplerandspeederthanotherfilters usedin[6–12].Fig.4showstheaforesaidmotherwaveletwithits transfermodulus.

Thechosenwaveletistunedtoextracttwosignalsofdifferent bandsoffrequencies(I_H,I_L)fromthefault inducedHFtransient currentsignalinamodaldomain.Thefirstsignal,IH,hasfrequen- ciesbandof[50–100kHz],withcenterfrequencyof75kHz,which canbeobtainedbyapplyingtheDWTwithdetail1(d1),whilethe secondsignal,IL,hasfrequenciesbandof[6.25–12.5kHz],withcen- terfrequencyof9.37kHz,whichcanbeobtainedbyapplyingthe

Fig.4.Apiecewiselinearsplinewaveletwithitstransfermodulus.

transientsignalsarealsoinduced,buttheircontentsoffrequencies arelessthanthoseinducedbyafaultaswillbeshownlaterinthe simulationresults.Athresholdvalue‘ε’ischosentobecompared withd1coefficientstodetecttheabnormalcondition,ifawavelet coefficientofd1ismorethanthisthresholdthespectralenergy routinewillbetriggeredtocomputethespectralenergies(E_H,E_L) ofthecapturedsignals(IH,IL),respectively,overa1.5mswindow length(300samples),toproducetheoperative,E_op,andrestraint, Ere,signalsoftherelaythataregivenasfollows:

EH(n)=Eop(n)=S

n

k=n−m

IH²(k) (5)

EL(n)=Ere(n)=

n

k=n−m

I_L²(k) (6)

wherenrepresentstherecentsample,mrepresentsthenumber ofsamplesinachosenwindowandSrepresentsascalingfactor, whichischosentobe100inthisstudy.

Thediscriminatingsignals,EopandEre,arecomputedsample bysampleandconsequentlytheenergyratioiscomputedateach sampleasfollows:

Ratio(n)= Eop(n)

Ere(n) (7)

Iftheenergyratiois≥1for1ms(200sample),thentherelay discriminatesaninternalfaultandissuesatripsignal,elsetherelay discriminatesanexternalfaultandrestraint.

5. Protectionschemeperformanceevaluation

In order toevaluatetheperformance of thedeveloped pro- tectionschemeit isprogrammedinconjunctionwithWTusing MATLABenvironment.TheEMTDCprogram[16]isusedtosimu- latedifferenttypesoffaultsatdifferentpositions,faultresistances andfaultinceptionanglesonastudied400kV–50Hzpowertrans- missionsystem,showninFig.2.Thetransmissionlineisideally transposedandhasaflatconfigurationwith10mspacingbetween adjacentconductorsandagroundresistivityof100m.Theused transmission linemodel is frequency dependent, thearc resis- tanceisincludedinthefaultmodel,andthebusbarcapacitance is included in the network model. The impedances values of theequivalentsources S1, S2,S3,and S4 inohm are: Zs1=25, Zs2=25,Zs3=20,Zs4=15,respectively.Twoloadsof(300+j190) MVA/phaseareplacedattheeachend ofthelineL2 toinvesti- gatetheeffectofheavyloadswitchingontheperformanceofthe introducedscheme.Allfaultcurrentsareconsideredtobeseenby therelayRyz.Asamplingfrequencyof200kHzisusedinthisstudy andaDWTwithd1andd4isappliedtoextracttherequiredbands offrequencyfromfault inducedHFtransientcurrentsignalina modaldomain.

Figs.5–13showtherelayresponsecurvesforthestudiedcases.

Therearefourgraphsforeachstudiedcase:thefirsttwographsrep- resenttheDWToutputsatd1andd4,respectively.Thethirdgraph showsthediscriminating energysignals;where thesolidcurve representstheoperativesignalandthedottedcurverepresents therestraintsignal.Thesolidcurveinthefourthgraphrepresents theenergyratioandthestraitdashedlinerepresentsathreshold value(unity)fordiscriminatingbetweentheinternalandexternal faults.R_frepresentsthefaultresistanceandϕrepresentsthefault inceptionangle.

Fig.5depictsaninternalsinglephasetogroundfault‘a–g’at 50kmfrombus‘Y’atlineL₂.Theenergyratioindicatesclearlythat thereisaninternalfault.Asaresult,therelayissuesatripsignal.

4 4.5 5 5.5 6

-2 0 2

d1

4 4.5 5 5.5 6

-10 0 10

d4

4 4.5 5 5.5 6

0 1200

Energy Signals

4 4.5 5 5.5 6

0 1 2

time [ms]

Ratio

Fig.5.‘a–g’faultonlineL2at50kmfrombusbar‘Y’,Rf=0.5,ϕ=90^◦.

Fig.6depictsanexternalsinglephasetogroundfault‘a–g’at lineL₃at70kmfrombusbar‘Z’.Itisobviousthattheenergyratio islowerthanunity;therefore,therelayindicatesanexternalfault andrestraints.

Fig.7depictsanexternalsinglephasetogroundfault‘a–g’atline L3at200mfrombusbar‘Z’.Again,theenergyratioislowerthan unity,therefore,therelayindicatesanexternalfaultandrestraints.

Fig.8depictstherelayresponsetoasinglephasetogroundfault

‘a–g’atbusbar‘Z’.Sincebusbar‘Z’isoutoftheprotectionzone, thentheenergyratioislowerthanunityandtherelayindicatesan externalfaultandrestraints.

Fig.9,depictstherelayresponsetoaninternalsinglephaseto groundfault ‘a–g’atlineL2 at200mfrombusbar‘Z’.Since the energyratioismorethatunitytherelayindicatesaninternalfault andissuesatripsignal.

Theresultsofthelast threecasesprovethat theintroduced schemecandiscriminatebetweenfaultsonand/orclosetoremote busbar(internalorexternaltotheprotectedzone),incontrastto theprotectionschemeof[8].

Fig.10depictstherelayresponsetoaninternalhighresistance fault‘b–g’(R_f=300)atamidpointoflineL₂.Itisevidentthatthe energyratioismorethanunity;therefore,therelayindicatesan internalfaultandissuesatripsignal.Hence,theintroducedrelay isunaffectedbytheexistenceofhighresistanceinthefaultpath.

Fig.11depictstherelayresponsetoaninternal‘b–g’faultwith phaseinceptionangleϕ=0^◦atamidpointoflineL2.Asexpected, theWToutputsarereducedinmagnitudebuttheiruniquechar- acteristicsstillexist,hencetheenergyratioismorethanunity.As aresult,therelayindicatesaninternalfaultandissuesatripsig- nal.Hence,theintroducedrelayisunaffectedbythefaultinception angle.

Fig.12depictstherelayresponsetoanexternal‘a–b’faulton lineL₁at200mfrombusbar‘Y’,withphaseinceptionangleϕ=0^◦. Itisclearthattheenergyratioislowerthanunity;therefore,the relayindicatesanexternalfaultandrestraints.

4 4.5 5 5.5 6 -0.1

0 0.05

d1

4 4.5 5 5.5 6

-2 0 2

d4

4 4.5 5 5.5 6

0 60

Energy Signals

4 4.5 5 5.5 6

0 1

time [ms]

Ratio

Fig.6. ‘a–g’faultonlineL3at70kmfrombusbar‘Z’,Rf=0.5,ϕ=90^◦.

4 4.5 5 5.5 6

-0.2 0 0.2

d1

4 4.5 5 5.5 6

-10 0 10

d4

4 4.5 5 5.5 6

0 1000

Energy Signals

4 4.5 5 5.5 6

0 1

time [ms]

Ratio

Fig.7. ‘a–g’faultonlineL3at200mfrombusbar‘Z’,Rf=0.5,ϕ=90^◦.

4 4.5 5 5.5 6

-1 0 1

d1

4 4.5 5 5.5 6

-5 0 5

d4

4 4.5 5 5.5 6

0 300

Energy Signals

4 4.5 5 5.5 6

0 1

time [ms]

Ratio

Fig.8.‘a–g’faultonbusbar‘Z’,Rf=0.5,ϕ=90^◦.

4 4.5 5 5.5 6

-4 0 4

d1

4 4.5 5 5.5 6

-8 0 8

d4

4 4.5 5 5.5 6

0 0 2000

Energy Signals

4 4.5 5 5.5 6

0 1 5

time [ms]

Ratio

Fig.9.‘a–g’faultonlineL2at200mfrombusbar‘Z’,Rf=0.5,ϕ=90^◦.

4 4.5 5 5.5 6 -4

0 4

d1

4 4.5 5 5.5 6

-5 0 5

d4

4 4.5 5 5.5 6

0 2500

Energy Signals

4 4.5 5 5.5 6

0 10

time [ms]

Ratio

Fig.10.‘b–g’faultatmidpointoflineL2,Rf=300,ϕ=90^◦.

Fig.13depictstherelayresponsetoanexternal‘a–b–c–g’fault atamidpointoflineL₁.Itisclearthattheenergyratioislowerthan unity;therefore,therelayindicatesanexternalfaultandrestraints.

Hence,onecanconcludethattherelayresponseisunaffectedby thefaulttype.

6 6.5 7 7.5 8

-0.2 0 0.2

d1

6 6.5 7 7.5 8

-0.4 0 0.4

d4

6 6.5 7 7.5 8

0 7

Energy Signals

6 6.5 7 7.5 8

0 5 10

time [ms]

Ratio

Fig.11.‘b–g’faultatmidpointoflineL2Rf=0.5,ϕ=0^◦.

4.5 5 5.5 6 6.5

-0.5 0 0.5

d1

4.5 5 5.5 6 6.5

-20 0 20

d4

4.5 5 5.5 6 6.5

0 12000

Energy Signals

4.5 5 5.5 6 6.5

0 1

time [ms]

Ratio

Fig.12. ‘a–b’faultonlineL1at200mfrombusbar‘Y’,Rf=0.5,ϕ=0^◦.

Theeffectofnon-faulttransientsontheprotectionschemeis tested for several cases, for example,Fig. 14, depicts the relay responsetoaheavyloadswitchingatbusbar‘Y’.Itisclearthatthe energyratioislowerthanunity;hence,therelaycandiscriminate betweenfaultsandnon-faulteventssuccessfully.

4 4.5 5 5.5 6

-0.2 0 0.3

d1

4 4.5 5 5.5 6

-5 0 5

d4

4 4.5 5 5.5 6

0 700

Energy Signals

4 4.5 5 5.5 6

0 1

time [ms]

Ratio

Fig.13.‘a–b–c–g’faultatmidpointoflineL1,Rf=0.5,ϕ=90^◦.

9 10 11 12 -0.2

0 0.1

d1

9 10 11 12

-3 0 2

d4

9 10 11 12

0 100

Energy Signals

9 10 11 12

0 1

time [ms]

Ratio

Fig.14.Heavyloadswitchingatbusbar‘Y’.

6. Conclusion

This paper presented a high-speed noncommunication pro- tectionschemebased onWT, dedicatedfor entiretransmission linesprotection.Theschemehasthecommunicationprotection discriminative properties without the need for communication channelslinkingtheprotectionateachendofaline.Itthuselim- inatesanylossofreliability,whichmightotherwisearisebecause ofcommunicationchannelsfailure.The protectionschemeutil- izesa high-speedWTtoextracttwo signals,each withdistinct bandoffrequency,fromthefaultinducedHFcurrentsignalina modaldomain.Thespectralenergiesoftheextractedsignalsare

thenusedasthediscriminatingsignalsoftherelay(operativeand restraint).Basedontheratiobetweenthesediscriminatingsignals therelaycandistinguishbetweentheinternalandexternalfaults.

Theintroducedschemehastheabilitytodiscriminatethefaulted lineirrespectiveof thefaulttype, fault position,fault inception angle,andfaultresistance.Moreover,itdoesnotaffectedbyany changeinasystemsourceparametersandsystemsourceconfigu- ration.

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