Current sensor optimization based on simulated transfer function under partial discharge pulses

ContentslistsavailableatScienceDirect

Sensors

and

Actuators

A:

Physical

j o u r n a l ho me p a g e :w w w . e l s e v i e r . c o m / l o c a t e / s n a

Current

sensor

optimization

based

on

simulated

transfer

function

under

partial

discharge

pulses

夽

Douglas

Nascimento

_,

_Shady

_S.

_Refaat

_,

_Hermes

_Loschi

_,

_Yuzo

_Iano

_,

Euclides

Chuma

_,

_Waseem

_El-Sayed

_,

_Amr

_Madi

a_{FacultyofComputer,ElectricalandControlEngineering,UniversityofZielonaGora,ZielonaGora,Poland}

b_{FacultyofElectricalEngineering,MathematicsandComputerScience(EEMCS),UniversityofTwente,Enschede,Netherlands} c_{ElectricalandComputerEngineeringDepartment,TexasA&MUniversityatQatar,Doha,Qatar}

d_{DepartmentofElectricalandElectronicEngineering,UniversityofNottingham,Nottingham,UnitedKingdom} e_{SchoolofElectricalandComputerEngineering,UniversityofCampinas,SãoPaulo,Brazil}

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received19November2020 Receivedinrevisedform23April2021 Accepted7May2021

Availableonline11May2021 Keywords:

High-frequencycurrenttransformer Partialdischarges

Sensormodelling Physicaleffects

a

b

s

t

r

a

c

t

Thetimemeasurementefficiencyofthepartialdischarge(PD)reliesonthesignal-to-noiseratio(SNR)

andgainofthehigh-frequencycurrenttransformer(HFCT)sensor.However,thePD’stimemeasurement

efficiencydecreaseswiththenoisecoupledtotheHFCTinonsitemeasurements.Toovercomethat

set-back,thispaperproposesonepre-processing,throughmodellingandsimulation,consideringthephysical

effects,featuresoftheelectricalcircuitandcoilconstructionparametersoftheHFCT.Themaingoalisto

reachreasonablehighSNRunderthestronginfluenceofbackgroundnoises.Thisinvestigationaimsto

validatethehypothesisofimprovementordeteriorationoftheHFCTsignalresponsethroughatransfer

functionoptimization.Thisresearcheffort’scontributionsarethreefold:1.GenerationofPDpulse

sig-nalandnoiseaddition;2.HFCTmodelling,simulation,andfrequencyresponseanalysis;and3.Models

performanceevaluationandvalidationofhypothesis.Inconclusion,thepre-processingapproachstands

outasameanstorobustifyandprovidefreedomtotheelectricutility,makingupforaneventualneedto

redefinethephysicalandgeometricalparametersoftheHFCTsensorunderspecificbackgroundnoisefor

maintenancetestspurpose.Accordingtoacyber-physicalsystemframework,experimentscorroborate

theproject’sgoalstocontributetothePDpatternmonitoringinonsitemeasurementsandincorporate

robustnesstosignalswithlowSNRs.

ﾩ2021TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY

license(http://creativecommons.org/licenses/by/4.0/).

1. Introduction

Thedielectricmaterialdegradationinelectricalsystemsis gen-erally associatedwiththepartialdischarges(PD)[1],unleashed withinvoids,andcracksinconductor–dielectricinterfacesinsolid insulation systems(bubbles), inthecase ofliquid dielectricsor corona,ingaseous[2].Undertheelectricinsulationsystem’s oper-atingstressconditions,thevoltageacrossthedamagedinsulation,

夽 ThispublicationwasmadepossiblebytheUniversityofTwente.Thestatements madehereinaresolelytheresponsibilityoftheauthor.

∗ Correspondingauthor.

E-mailaddresses:eng.douglas.a@ieee.org(D.Nascimento),

shady.khalil@qatar.tamu.edu(S.S.Refaat),eng.hermes.loschi@ieee.org(H.Loschi), yuzo@decom.fee.unicamp.br(Y.Iano),euclides.chuma@ieee.org(E.Chuma), waseem.elsayed@ieee.org(W.El-Sayed),amr.madi@ieee.org(A.Madi).

URLs:http://www.uz.zgora.pl(D.Nascimento),http://www.loschihermes.com (H.Loschi).

withinbubbles,cracks,voids,mayexceeditsdielectric strength leadingtoelectricdischargesinthedielectric,reducingthe stiff-nessandfinallyleadingtototalorpartialfailureoftheinsulation [3].

Thus,itisrecommendedtomakequalityandcompliancetests by PDanalysis. Also, considering cyber-physical system frame-works (e.g. [4]), the analysis of PD can be extrapolated as an redundantcomponent of power systems onalerting the active agents(electricalutilities,stakeholders,powersystemcompanies) inadvancewhenanycomponentitisabouttocollapseduetoPD. ThePDtestsareclassifiedaccordingtothemeasuringtechnique, andelectricmethodsarewidelyused[1].Electricalmethodscan beperformedonhighvoltageelectricalequipmentsuchaspower transformers,instrumenttransformers,medium,highand extra-highvoltagecables,highvoltagebushingsandrotarymachines[5]. Furthermore,theelectricalmethodsaredividedintoconventional andnon-conventional.ConventionalPDmethodsareperformed followingIEC60270-HighVoltagetestingtechniques:Partial Dis-https://doi.org/10.1016/j.sna.2021.112825

ingthroughtheinductivecouplingofelectriccurrentistheHigh FrequencyCurrentTransformer(HFCT)[7].

The time measurement efficiency of the PD relies on the signal-to-noise (SNR) ratio and gain of theHFCT sensor. How-ever, the PD’s time measurement efficiency decrease with the noisecoupledtotheHFCTinonsitemeasurements.Traditionally, thePDmeasurementapproachconsidersthenoiseremovalusing mathematical algorithmsandefficientsoftwareinthetimeand frequency domain,suchasspectral subtractiondenoising(SSD), discrete wavelet transform(DWT),wavelet shrinkagedenoising (WSD),PrincipalComponentAnalysis(PCA)[10,11],andComplex DaubechiesWavelet(CDW)[12,13].Overall,enablingthecorrect understandingofthePDphenomenonmagnitudeinonsite mea-surements.

However,thispaperaimstovalidatethehypothesisof improve-ment or deterioration of the HFCT signal response, through a transferfunctionoptimization,foraneventualredefinitionof phys-icalandgeometricalparametersoftheHFCTsensor.Thus,through theinvestigationofthephysicaleffects,modelling,andsimulation oftheHFCT,appliedtotimemeasurementsofthePDunderthe stronginfluenceofbackgroundnoises,expectedtoreach reason-ablehigherSNR.Therefore,themethodologyproposedinthispaper goesbeyondatraditionalsensoroptimizationapproach[14].It’s consideredHFCT’soptimizationandon-fieldemulationtaskstothe PDmeasurementsbyimplementingadditivewhiteGaussiannoise (AWGN)miscellaneous.

Theproposedmethodologywasdividedanddevelopedlinearly basedonthreestepsasshown inFig.1: 1.PDpulsegeneration andnoiseaddition;2.ModellingoftheHFCTsensor;and3. Per-formanceevaluation.Step1comprisesthePDsignalgeneration, modeledbytravelingwavesmethod[15]andapplicationof char-acteristicbackgroundnoisethroughAWGNtothesignalgenerated [1].Instep2,HFCTsensormodellingwasperformed,basedonthe ElectromagnetismLaws,accordingto[16],whereasthefrequency responseswerecarriedoutbasedon[14].Instep3,HFCTmodels werecreatedbasedonthevariationofconstructiveandelectrical parametersandsubsequentevaluationofTFs(TransferFunctions) performance[12].InFig.1s(i)representsthePDinputsignal,r(i) denotesnoise(AWGN),Z(i)meanstheTFsoftheHFCTmodels(g(s)) underanalysisand,iisthediscretetimeindex.

Traditionally,thedesignprocessofasensorusesstatistical oper-atorscustomarilyappliedasthelastevaluationstep,i.e.,step3of Fig.1.Themaingoalofstatisticaloperatorsistoevaluatethe sen-sorresponseperformanceregardingthesimilarityandprediction quality.Itisdonebycomparingtheoutput“pre-processed”signal fromthesensorandtheexactinputsignal(inthispaper,PDpulse) [12,13,17,18].Thereforeinthispaper,theHFCTsensorperformance was evaluatedbymean squarederror(MSE) and cross-relation (XCORR).AnoptimalresponsenearzeroisexpectedforMSEand oneforXCORR,consideringthenormalization.Thereby,the predic-tionandsimilarityofHFCTsensorperformancedrivethedecision onwhichisthebestmodel,bothintermsofelectricaland geomet-ricalparameters,i.e.,thebestfittedHFCTsensormodel.

Therestofthispaperisorganizedasfollows.Section2addresses thePDmechanisms,itsgeneration,andnoiseaddition,andin Sec-tion3isexplainedtheHFCTmodellingandsimulation.Section4

tothePDpulsesareestablishedinstandard[6],e.g.apparentload (q),pulserepetitionrate(n),phaseangle()andtime(t)ofpulse occurrence.

Therepresentationof PDsignals isconductedthrough three categoriesofstandards[19]:1.resolvedphasedata,suchasthe −q−ndiagram(Fig.2a.);2.resolvedtimedata,i.e.q−t wave-form–whereqistheloadmagnitudeandttheanalysisinterval,or V−t–whereVrepresentsthevoltageovertimet;3.signaldata thatareneitherresolvedphasenorresolvedtime,e.g.theq−V diagram–magnitudevariationofdischargepulsebytestvoltage amplitudeorthePulseSequenceAnalysis(PSA)diagram–inthat datarelatedtoPDpulsesshouldbesavedasasequence[3]. 2.1. PDpulse

The characteristics of PD current pulse are analyzed using parametersrisetime(Tr),pulsewidth(Tw)andfalltime(Tf).All thePDcurrentpulsesarefromtheorigintimet0 ofthevoltage step,whichreferstothetimewhentheincreasingvoltagehas10% ofinitialvoltage(V0).Thatis,Trregardsthetimeintervalbetween 10%and90%ofthepulseamplitude,Tfisthetimeintervalbetween 90%and10%ofthepulseamplitude,andTwisthetimeinterval between50%oftherisingsignaland50%ofthefallsignal,pulse height,andmaximumpulseamplitude(100%ofthepulse magni-tude)[19].Therefore,thePDcurrentpulseexpressedbyequation (1)isbasedonthemodelingofthetravelingwavesconceptofPD pulsesinhighvoltagecables[15]:

V (t)=V0.(10−˛t−10−ˇt), (1)

where˛andˇaretimeconstantsparametersrelatedtothecable signalwaveform[15].Thus,consideringOHM’sLawI(t)=U(t)/R andresistanceas1,thePDcurrentpulse’sinitialvaluewaswith themagnitudearound200mA,asdescribedinstudiesaddressing PDpulses[16].Therefore,thepulseparametersassumed inthis paperare:peakat246mA,Trof0.34435s,Tf =3.2174s,Twof 1.8503s,˛as7.108,andˇas3.109.

2.2. AdditivewhiteGaussiannoise

InPDanalysisthebackgroundnoiseisthesignalsdetected dur-ingits onsite measurement. However,external totheDUT [6]. Accordingtothecharacteristics of time–frequencydomain,the disturbancescanbeclassifiedaswhitenoise(WN),Discrete Spec-tralInterference(DSI),periodicpulseinterference(PPI),stochastic pulseinterference(SPI)[20].ConsideringPDaspulsesofa stochas-ticandnon-stationarynature[21]andthat,consequently,thenoise acquiredintheonsitemeasurementsignalhasarandom charac-teristic,itisimportanttoinserttheconceptofGaussianProcess.

AssumingthattheGaussianprocess(orrandomprocess)is rep-resentedbyX(t)intheintervalof[0,T ],withtheweightofX(t)over certainfunctiong(t)andintegratingtheproductofg(t)X(t)within thatinterval,itisexpressedas:

Y=



0

Fig.1. Overallchartflowoftheproposedmethodology.

Fig.2. OnlinemeasuringofPDbyusingHFCT:a)ExampleofonsitePDtest;b)SchematicrepresentationofthePDonsitemeasuring.

inwhichthemean-squarevalueofY(linearfunctionalvariableof X(t))asfiniteforcertainweightingfunctiong(t),Y issaidtobe Gaussian-distributedrandomvariableforeveryg(t)inthis class offunctions.Thatis,X(t)isaGaussianprocessifeveryY (t)isa Gaussianrandomvariable.Then,YrandomvariablehasaGaussian distributionifitsPDF(ProbabilityDensityFunction)hastheform givenbyEq.(3): PDFY= √ 1 2..Y exp





whereY isthemean,Y isthestandarddeviation,and_Y2isthe varianceofarandomYvariable.WhentheGaussianrandom vari-ableYisnormalizedtohaveY equals0andvarianceY2as1,the normalizedGaussiandistributioniscommonlywrittenasN(0.1) andthevalueofthesignalwillbefoundin±3for99.7%ofthe consideredtimeinterval.

TheWNisakindofGaussianprocess,withPSD(Power Spec-trumDensity)constantregardlessofthefrequency.Thus,thewhite GaussiannoiseisusedasanAWGNofPDfromthepulse genera-tor,inordertoemulatetheononsitecharacteristics.Therefore, knowingthattheSNRisgivenby20.log10Avs/Avn[12]–whereAvs

Table1

ClassificationofthemodelsbasedontheSNRinputlevels.

Label SNR(dB) AV NoiseAmp PD1 −3 0.708 0.3474576 PD2 3 1.414 0.1739745 PD3 6 1.995 0.1233083 PD4 20 10 0.0246 PD5 40 100 0.00246 PD6 60 1000 0.000246

representstheinputDPsignalandAvndenotesnoise–sixdifferent

conditionsofnoise.Fig.3showthenoisecondition(PD1toPD6),

from−3dB(harshenvironment)to60dB(idealconditions)aswell astherespectivenormalizedfrequencysinglesidespectrumband (SSB)representedas|P1(f)|.

Table1showstheinputsignal246mAmixedon347mAaverage signal(AV)forPD1,wheretheSNR=−3dBintheworsescenario (distortedsignal).Whereas,thePDpulseismixedonidealnoise amplitudeinorderof10−6(PD6,SNR=60dB)(cleansignal). There-fore,thenoiselevelcontrolparameteristheSNRindB.Inthiscase, thevaluesofsignalswithAWGNwereusedasinputsignalstothe HFCTmodel.

Fig.4.SchematicoftheHFCTsensormodel.

3. HFCTmodellingandsimulation

ThephysicalgeometryparametersoftheHFCTsensorisrelated toatoroidalcoilwrappedinacoreofhighrelativepermeability. Theelectrical responseoftheHFCTsensor isbasedonthe con-structiveandelectricalaspects,givenby:geometry,thenumberof turns,ferromagneticcorematerialandloadresistance(terminal) [22].Therefore,thedependentcharacteristicsoftheHFCTgeometry aresecondarywindingresistance,parasiticcapacitanceand leak-ageinductance[22].Theelectricalandconstructiveparametersof theHFCTsensorarehighlightedinFig.4.

whereRListheterminalloadresistance,riistheinternalradius, roistheexternalradius,risthesensorradius(concentricraysat pointO),rcistheradiusofthecore,Nisthenumberofturnsof thesensorcoil(secondarycircuit),Ac isthecross-sectionalarea, lmisthepathofthemagneticflux(c),I(t)isthecurrentofthe secondarycircuitandVo(t)istheoutputvoltageofthecircuit,i.e., theHFCTsensoroutputsignal.

3.1. Constructiveaspectsbasedongeometry

Thecalculationofelectricalparameterswerecarriedon con-sideringthereferences[16,22],andFig.4.Therefore,theradiusof theHFCTsensorisestimatedas,r=(ri+ro)/2,thelengthofflow pathisgivenby,lm=2..randtheradiusofthenucleusisgiven by,rc=(ro−ri)/2.Thediameterisexpressedasdrc=2.rc[m],the cross-sectionalareaofthecoreisAc=pi.rc2[m2],thelengthofthe windingpw=rc[m](thelengthofthewindingwasusedasthe samelengthasrc).Thecrosssectionalareaofthecoilwireisthe sameasAcforconvenience(hereisusedforsimulationpurpose only),thelengthofasinglecoilislc=2.pi.rc[m],andthelengthof thecompletecoilislw₌lc.N[Nm](turn.meter).

3.2. Electricalparameters

TheelectricalcircuitoftheHFCTwasanalyzedusinggrouped parameters originating in Fig. 4, and reduced to the electrical schemeshowninFig.5[23].

Inaddition,theelectricalparametersareprovidedinTable2. Furthermore,thecorematerialelectricandmagneticspecification defined as: of1.6800×10−8 [.m](Cooper resistance),r of 2000(Relativepermeability),0 of4×10−7 [H/m](freespace permeability), of 0.0025[H/m] (absolute permeability),e0 of 8.8540×10−12[F/m](freespaceelectricpermittivity),anderof1 (relativepermittivity),i.e.eisequalto8.8540×10−12[F/m]

(abso-Fig.5.S-domaincircuitmodeled.

Table2

Modelingconstructiveparametersused.

Parameter Value Specification

do 0.1[m] Outerdiameter

r0 0.05[m] Outerradius

di 0.065[m] Innerdiameter

ri 0.0325[m] Innerradius

Np 1 Primarycircuitturns

Ns 10 Secondarycircuitturns

dw 0.0005[m] Wirediameter rw 0.00025[m] Wireradius Ac 2.4053×10−4[m2] Corearea rc 0.0088[m] Careradius drc 0.0175[m] Corediameter r 0.0575[m] Sensorradius lm 0.3613[m] Fluxpath

Aw 2.4053×10−4[m2] Coilcross-sectionarea

lc 0.0550[m] Oneturnlength

pw 0.0088[m] Coilstepback

lutepermittivity).Oncethecopperresistivityis =1.68×10−8

.m,thewindingresistanceofthesecondarycircuitis[16,22]:

Rs= .lw Aw

. (4)

Thesecondarysensorvoltageisexpressedas:

v

dt . (5)

Mutualinductanceisgivenby[16]: Mc= N

2 s..Ac

lm

, (6)

whereisgivenby=r·o,inwhichristherelative per-meability(valueaccordingtothematerial)andoisthevacuum permeabilitywiththevalueof410−7H/m.TheNsisthenumberof turnsofthesecondary,i.e.windingofthesensor.Inleakage induc-tance(alsocalledauto-inductance)[24],thecircularcoilmethod wasusedforsingleturninductanceandforrwrc,thus,based on: Lloop=0.rc.log10







Theresultingleakageinductancefortheentirecoilis: Ls=N2

s.Lloop. (8)

SincetheapplicationisinHF,thevalueoftheparasitic capac-itance (Cs) of the secondary winding must be estimated. The parasiticeffectwasestimatedusingtheanalyticalapproachof[24], inwhich:e0=8.854.10−12(dielectricconstant),er=1(relative permittivityofair)ande=e0er(absolutepermittivity),therefore: Cs= lw.pi.e

AlthoughLsandCsareintrinsictotheHFCTsensor,requiring

thecalculationofthecapacitivenetworkandexperimental

calcu-lation oftheHFCTsensordimensions,asdemonstratedby[24].

ThispaperisrestrictedtotheanalyticalcalculationofCsandLs sincesuchparametersarenotthepresentstudy’sinitialobjective. Despitethis,thevaluesobtainedinthisstudywereconsistentwith [25].

Therefore,thefinalproposalTFconsideringthesecond-order polynomialexpressedbyequation(10)is:

F(s)= −sMc.Np.RL Cs.RL.(Ls+Mc).Ns s2_+s





Thefrequencyresonance(w0)inrad/s: w0=

RL Cs.RL.(Ls+Mc)

. (11)

Also,thedampingcoefficient(),givenb: = (Cs.RL.Rs+Ls+Mc)

Thevaluesofw0andprovidedataforsystembehaviorsince: >1providesaoverdampedresponse(realanddifferentrootsand productoftwo1st-orderpoles);<1determineaunderdamped response(complexroots)ofthesystem;=1resultsincritically dampedresponse(realandequalroots).Thus,Fig.4canbemodeled accordingtoFig.5inthesdomain.NotethatReq1andReq2are equiv-alentresistancesfromresistiveassociationsinseries(betweenRs andsLs)andinparallel(between1/sCsandRL),respectivelyand whosetotalequivalentresistanceisReq(seriesassociationbetween Req1andReq2).

3.3. Simulation

Inordertoassessthehypothesisofimprovementor deteriora-tionoftheHFCTsignalresponse,weconsidertheS-domainthrough a transfer function optimization, which means the frequency response.Fivedifferentmodelshavebeensettledasdescribedin Table3,whichweredividedintoreferenceandvariationgroups. Thereferencemodel(PAD)isthestandardmodel,whereasRL(load resistance),Ns(numberofsecondaryturns)andr(relative per-meability)arevariationmodels.Ontheotherhand,thevariation modelscalledN30,RL250,mur2300andRLNmurwereorganized totestthegeneralperformanceoftheHFCTsensor,withchanges initsparametersbasedonthePAD.

ThefiveTFs,consideringthecalculationsbasedonthespecified parametersinTable3,arepresentedinTable4.

TheBodediagramwasconsidered(Fig.6), toobtainthe fre-quencyresponseoftheHFCTsensormodels,throughsimulation withMatlabsoftware.

Also,inFig.6,thefrequencyresponseallowedtheanalysisof magnitudedata(dB)andphase(degrees)inthefrequencydomain. Tables5and6showsthephysicalandelectricalparameters, respec-tively,calculatedandobtainedforallthemodels(PAD,N30,RL250, mur2300,andRLNmur),throughsimulationwithMatlabsoftware.

Fig.6.FrequencyresponseoftheHFCTsensormodels.

Table5

Performancebasedonthephysicalparametersobtainedforeachmodel.

Model Poles BW(Hz)

PAD s1=−2.92E+05 6.3104E+01 5.03E+09

s2=−4.65E+09

N30 s1=−3.24E+04 1.0930E+02 4.89E+08

s2=−1.55E+09

RL250 s1=−1.46E+06 1.2621E+01 1.32E+09

s2=−9.28E+08

mur2300 s1=−2.55E+05 6.7569E+01 4.95E+09

s2=−4.65E+09

RLNmur s1=−2.09E+05 3.0465E+01 1.32E+09

s2=−7.75E+08

Table6

Electricalstrayparametersobtainedforthemodels.

Model Rs() Ls(H) Cs(F)

PAD 3.84E-05 4.00E-06 4.30E-12

N30 1.15E-04 3.60E-05 1.29E-11

RL250 3.84E-05 4.00E-06 4.30E-12

mur2300 3.84E-05 4.00E-06 4.30E-12

RLNmur 7.68E-05 1.60E-05 8.60E-12

ThePAD’sgainreaches13.8dB(Fig.6),andintheresonance

frequency,thereisa180◦phaseshift,accordingtoLenz’sLaw.In thecaseofvariationmodels(N30,RL250,mur2300,andRLNmur), whicharedescribedinTables5and6.Sincethesizeofthecore (r_i,ro,r,andrc)wasmaintained,andtheRL,Nsandrwerealtered (Table3),distinctperformanceswereobtainedbetweentheHFCT sensormodels.

Fig.7. MSEoftheHFCTsensormodels.

TheBodediagram(Fig.6),showsthattheN30’sgainreaches 4.23dB.Also,Table5presentsthesmoothestresponseduetothe increaseintheto1.0930E+02.Inaddition,alsointheBode dia-gram(Fig.6),thereisaflattercurveatthecenterofphasecharge attributedtotheincrease(higherwindingturns)inthereactive characteristicsoftheCsandLsinrelationtothePAD.

UnlikemodelN30,themodelRL250hasadirectchangeinthe RL,i.e.,non-reactiveelectricalparameter.ComparativelytoPAD, theBodediagram(Fig.6),showsthehighergain(27.8dB). Con-sequently,Table5showstheRL250responseresultsinawider bandwidth,BW=1.32E+09Hz,anddecreasingon=1.2621E+ 01.

Inthemur2300,ther=2300,basedon[26],andbasedonthe Bodediagram(Fig.6),itisobservedthatthegainis13.8dB.The characteristic responseofmur2300isalmostthesamefor PAD, oncechangingr(Table3)doesnotchangethereactiveparameters (Tables5and6).Thus,thisendsupcausinganoverlappinginthe PADresponsecurve(Fig.6).

TheRLNmur’sgainreaches17.3dBintheBodediagram(Fig.6), corresponding to the intermediate response between the PAD, mur2300,andRL250models,regardingthecharacteristicsofthe reactiveparameters.

4. HFCTperformanceevaluation

BasedonthesimulationresultspresentedinSection3.3,Ithas beenconsideredadecreaseinmagnitudeandanincreaseinBW withincreasedwindingsinthesecondarycircuit(modelN30).In themodelN30, thereis aphase advanceconcerningfrequency. Also,itwasfoundthatincreasingthevalueofr,inthecaseof mur2300,didnotleadtoaconsiderablechangeinmagnitudeand phaseresponse,comparedtoPAD.However,tocomplementthe HFCT performance evaluation analysis,the meansquared error (MSE)andcross-relation(XCORR)wereconsidered.

4.1. Dataanalysisevaluationmetrics

Twometricshasbeenusedinthispaper,theMSEandXCORR, betweensignalsobtained(Z(i))andtheinputsignals(s(i))(referto Fig.1).TheMSEisgivenby[12]:

MSE= _N1 N

i=1

|z(i)−s(i)|2_{. (13)}

TheMSEis generallyusedtoassessthedegreeof distortion causedby removingnoise froma signal,sothelower theMSE value,thesmallertheerror.Incontrast,theXCORRcoefficient( sz) isexpressedby[12]:

sz(n)= N

i=0

s(i).z(i+n). (14)

TheXCORRcoefficientassessesthesimilarityintheshapeofthe signals’wave;itwasnormalizedinorderthatazeroXCORRfactor indicatestotal asymmetrywhileanXCORRfactorof1indicates completesymmetry.Therefore,theXCORRisappliedbetweenthe Z(i)ands(i)(seeFig.1)ondiscrete-time.Also,sincethisEq.(14) returnsavector,thesequencesoftheXCORRhavebeennormalized. TheMSEobtainedforallHFCTsensormodelsitisexpressedin Fig.7.TheMSEfortheRL250model(Fig.7)isthegreatestone.On theotherhand,increasingthenumberofwindings(N30model), thesimilaritybetweenthes(i)andtheZ(i)(HFCTsensorresponse) increases,giventhatthemutualinductanceisthehighestamong themodels,Mc=1.5mH,whileinthePADmodelthemutual induc-tanceisMc=0.17mH,i.e.,anincreaseof20inthenumberofturns ofthewindingresultsinanincreaseof8.82timesthevalueofMc (seeEq.(6)).Furthermore,ithasbeenobservedthatfromSNR=6 dB,theMSEremainsbelow1forallthemodelsexceptingRL250. Therefore,inthecaseofPAD,N30,mur2300,andRLNmurtheZ(i) mustbeatleast2twicethes(i)toreachanacceptablemeasurement error.

Fig.8. XCORRoftheHFCTsensormodels.

TheXCORRobtainedforallHFCTsensormodelsitisexpressed inFig.8.TheXCORRanalysis(Fig.8)reinforcesthattheTFsmodeled forHFCTsensormodels,providesagoodperformanceforanSNR above6dB(Fig.7),andXCORRcoefficientvaluesupper0.5(e.g. 0.7645forN30model).

5. Conclusionsandprospects

Thispaperaddressedthephysicaleffects,modelling,and simu-lationofthehigh-frequencycurrenttransformer(HFCT),appliedto timemeasurementsofthepartialdischarges(PD)underthestrong influenceofbackgroundnoises.

SeveralfactorslimitthefrequencyresponsesoftheN30,RL250, mur2300,andRLNmurmodels.IntherealHFCTsensor,the fre-quencyresponseentailsseveralparameters.Themainonesbeing reactive components with origin in construction and electrical phenomena since a coil has(i)capacitance and (ii)inductance, duetotheassociationofturns.Hence,thesereactivecomponents contribute to self-capacitanceand self-inductance, respectively. However,state-of-the-artstudiesdescribethattheloadresistance valuemustbe50,duetotheresistivecouplingwiththe measur-inginstruments,toeliminatelosses.Thepresentpaperemploysa variationofupto250toverifychangesinresponsetotheinput signalandperformanceevaluationundernoisyconditions.

Thus, thehypothesisofimprovement ordeterioration ofthe HFCTsignalresponse,throughatransferfunctionoptimization,for aneventualredefinitionofphysicalandgeometricalparametersof theHFCTsensor,canbevalidated,dependingonwhich parame-tersarechosentobechanged.Additionally,theHFCTmodelN30 providedmorereliableS-domainvaluesbyincreasingthenumber ofcoilturnsadaptivelytothenoisysignalcomparedtotheother modelsanalyzed,i.e.,RL250,mur2300,andRLNmur.

Therefore, the proposed transfer function optimization approachgivesarobustpre-processingbychangingthefeatures oftheHFCT’selectricalcircuitandcoilconstructionparametersto reachahighsignal-to-noise(SNR)ratio.Furthermore,thispaper

servesasaninspiration forpotentialsolutions throughartificial intelligence.In thisway,itis possibletooptimizetheelectrical parameterstoobtainidealcharacteristicsofmagnitudeandphase inthefrequency responsetorejectdifferentcharacteristic field noise(onsitemeasurement).

CRediTauthorshipcontributionstatement

DouglasNascimento:Conceptualization,Methodology, Inves-tigation, Data curation, Validation, Formal Analysis, Writing – original draft. Shady S. Refaat: Writing – review & editing, Resources, Project administration, Funding acquisition. Hermes Loschi:Datacuration,Visualization,Methodology,Writing– Orig-inal draft,Writing – review & editing.Yuzo Iano: Supervision, Writing–review&editing.EuclidesChuma:Writing–review& editing.WaseemEl-Sayed:Writing–review&editing.AmrMadi:

Writing-review&editing.

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Biographies

DouglasNascimento,M.Sc.,receivedhis B.Sc.at Uni-versity ofWestSantaCatarinaand M.Sc.inElectrical EngineeringfromtheUniversityofCampinas.Currentlyis aPh.D.candidateandEarlyStageResearcherintheETOPIA (EuropeanTrainingNetworkofPhDResearcherson Inno-vativeEMIAnalysisandPowerApplications)Project,a jointdoctoralprogrammeunderTheEuropean Commis-sion Horizon 2020initiative, MarieSkłodowska-Curie Actions, atTheUniversityofZielonaGóraandatThe University ofTwente.Heisa memberofInstituteof ElectricalandElectronicEngineers(IEEE),and Electro-magneticCompatibilitySociety(EMC-S)workingonTC-7 (TechnicalCommittee).Hisresearchareasaddresselectric vehicles,smartcities,sensors,EMCandEMI.Hehasexperiencein electromag-neticmodeling,cableandsensordesign,simulationofelectriccircuits,andpartial dischargetests.

ShadyS.Reffat,Ph.D.,isapostdoctoralresearchassociate intheDepartmentofElectricalandComputer Engineer-ing,TexasA&MUniversityatQatar,amemberofthe InstituteofElectricalandElectronicEngineers(IEEE),a memberofTheInstitutionofEngineeringand Technol-ogy(IET),amemberoftheSmartGridCenter–Extension inQatar(SGC-Q),hehasworkedwithindustryforover fifteenyearsaselectricaldesignengineer.Hehas pub-lishedovertwentyjournalandconferencepapers.His researchinterestsincludeelectricalmachines,power sys-tem,smartgrid,energymanagementsystem,reliability ofpowergridandelectricmachinery,faultdetection,and conditionmonitoringinconjunctionwithfault manage-mentanddevelopmentoffaulttolerantsystems.Hehassuccessfullyrealizedmany potentialresearchprojects.

HermesLoschi,M.Sc.,wasbornin1990,SaoPaulo,Brazil. HereceivedhismasterdegreeinElectricalEngineeringat theUniversityofCampinasandhisbachelor’sdegreein ControlandAutomationEngineeringatthePaulista Uni-versity.SinceApril2019,hestartedasaPh.D.studentin “SmartCitiesEMCNetworkforTraining(SCENT)”project intheInstituteofAutomaticControl,Electronicsand Elec-tricalEngineeringattheUniversityofZielonaGora,Poland aswellasthefacultyofElectricalEngineering, Mathemat-icsandComputerScience(EEMCS)intheUniversityof Twente,Netherlands.Hisresearchareasarepower sys-tems,renewableenergies,sensors,EMCandEMI.

YuzoIano,Prof.Ph.D.,hasadegree(1972),amaster’s degree(1974)andadoctorate(1986)inElectrical Engi-neeringfromtheUniversityofCampinas(Unicamp).Since then, he wasa supervisorin 5postdoctoralprojects, 34doctoraltheses,59master’sdissertations,74 under-graduatestudies,48undergraduateresearch, and198 otherorientations(TeacherInternshipProgram,projects, etc.).Authorof2booksandauthor/co-authorof8book chapters,and300publishedarticles.Hereceivedtwo InnovationAwards,Category“LicensedTechnology”,from InovaUnicampintheyears2013and2018,anAward forTeachingExcellenceinUndergraduateEducation,from theFacultyofElectricalandComputerEngineering,from theUniversityofCampinas(2012)anda“LifeMember”honorgrantedbythe Inter-nationalInstituteofElectricalandElectronicsEngineers-IEEE(2018).Heiscurrently FullProfessorMS6inRDIDPofDecom/Feec/Unicamp.

EuclidesChuma,Ph.D.,iscurrentlyR&DManagerof Pho-tonicsInnovationInstitute.Hecompletedhisdegreein MathematicsfromtheUniversityofCampinas(UNICAMP) (2003),graduatedegreeinNetworkand Telecommuni-cationsSystemsfromINATEL(2015),MScinElectrical EngineeringfromUNICAMP(2017),andPhDin Electri-calEngineeringinUNICAMP(2019).Hisresearchinterests includeantennas,microwave,millimeterwave, photon-ics,sensors,wirelesspowertransfer,andsoftwaredefined radio.