Sensors and Actuators A: Physical

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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

^a,b

, Shady S. Refaat

^c

, Hermes Loschi

^a,b,d,∗

, Yuzo Iano

^e

, Euclides Chuma

^e

, Waseem El-Sayed

^a,b

, Amr Madi

^a,b

aFacultyofComputer,ElectricalandControlEngineering,UniversityofZielonaGora,ZielonaGora,Poland

bFacultyofElectricalEngineering,MathematicsandComputerScience(EEMCS),UniversityofTwente,Enschede,Netherlands

cElectricalandComputerEngineeringDepartment,TexasA&MUniversityatQatar,Doha,Qatar

dDepartmentofElectricalandElectronicEngineering,UniversityofNottingham,Nottingham,UnitedKingdom

eSchoolofElectricalandComputerEngineering,UniversityofCampinas,SãoPaulo,Brazil

a rt i c l e i nf o

Articlehistory:

Received19November2020 Receivedinrevisedform23April2021 Accepted7May2021

Availableonline11May2021

Keywords:

High-frequencycurrenttransformer Partialdischarges

Sensormodelling Physicaleffects

a b s t ra c t

Thetimemeasurementefficiencyofthepartialdischarge(PD)reliesonthesignal-to-noiseratio(SNR) andgainofthehigh-frequencycurrenttransformer(HFCT)sensor.However,thePD’stimemeasurement efficiencydecreaseswiththenoisecoupledtotheHFCTinonsitemeasurements.Toovercomethatset- back,thispaperproposesonepre-processing,throughmodellingandsimulation,consideringthephysical effects,featuresoftheelectricalcircuitandcoilconstructionparametersoftheHFCT.Themaingoalisto reachreasonablehighSNRunderthestronginfluenceofbackgroundnoises.Thisinvestigationaimsto validatethehypothesisofimprovementordeteriorationoftheHFCTsignalresponsethroughatransfer functionoptimization.Thisresearcheffort’scontributionsarethreefold:1.GenerationofPDpulsesig- nalandnoiseaddition;2.HFCTmodelling,simulation,andfrequencyresponseanalysis;and3.Models performanceevaluationandvalidationofhypothesis.Inconclusion,thepre-processingapproachstands outasameanstorobustifyandprovidefreedomtotheelectricutility,makingupforaneventualneedto redefinethephysicalandgeometricalparametersoftheHFCTsensorunderspecificbackgroundnoisefor maintenancetestspurpose.Accordingtoacyber-physicalsystemframework,experimentscorroborate theproject’sgoalstocontributetothePDpatternmonitoringinonsitemeasurementsandincorporate robustnesstosignalswithlowSNRs.

©2021TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).

1. Introduction

Thedielectricmaterialdegradationinelectricalsystemsisgen- erally associatedwiththepartialdischarges(PD)[1],unleashed withinvoids,andcracksinconductor–dielectricinterfacesinsolid insulation systems(bubbles), inthecase ofliquid dielectricsor corona,ingaseous[2].Undertheelectricinsulationsystem’soper- 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,reducingthestiff- nessandfinallyleadingtototalorpartialfailureoftheinsulation [3].

Thus,itisrecommendedtomakequalityandcompliancetests by PDanalysis. Also, considering cyber-physical systemframe- 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,highandextra- highvoltagecables,highvoltagebushingsandrotarymachines[5].

Furthermore,theelectricalmethodsaredividedintoconventional andnon-conventional.ConventionalPDmethodsareperformed followingIEC60270-HighVoltagetestingtechniques:PartialDis-

https://doi.org/10.1016/j.sna.2021.112825

0924-4247/©2021TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).

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 understandingofthePDphenomenonmagnitudeinonsitemea- surements.

However,thispaperaimstovalidatethehypothesisofimprove- ment or deterioration of the HFCT signal response, through a transferfunctionoptimization,foraneventualredefinitionofphys- icalandgeometricalparametersoftheHFCTsensor.Thus,through theinvestigationofthephysicaleffects,modelling,andsimulation oftheHFCT,appliedtotimemeasurementsofthePDunderthe stronginfluenceofbackgroundnoises,expectedtoreachreason- 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]andapplicationofchar- 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,thedesignprocessofasensorusesstatisticaloper- atorscustomarilyappliedasthelastevaluationstep,i.e.,step3of Fig.1.Themaingoalofstatisticaloperatorsistoevaluatethesen- 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,thepredic- tionandsimilarityofHFCTsensorperformancedrivethedecision onwhichisthebestmodel,bothintermsofelectricalandgeomet- ricalparameters,i.e.,thebestfittedHFCTsensormodel.

Therestofthispaperisorganizedasfollows.Section2addresses thePDmechanisms,itsgeneration,andnoiseaddition,andinSec- 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−twave- 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(T_f).All thePDcurrentpulsesarefromtheorigintimet0 ofthevoltage step,whichreferstothetimewhentheincreasingvoltagehas10%

ofinitialvoltage(V₀).Thatis,Trregardsthetimeintervalbetween 10%and90%ofthepulseamplitude,T_fisthetimeintervalbetween 90%and10%ofthepulseamplitude,andT_wisthetimeinterval between50%oftherisingsignaland50%ofthefallsignal,pulse height,andmaximumpulseamplitude(100%ofthepulsemagni- 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,T_f =3.2174s,Twof 1.8503s,˛as7.10⁸,andˇas3.10⁹.

2.2. AdditivewhiteGaussiannoise

InPDanalysisthebackgroundnoiseisthesignalsdetecteddur- ingits onsite measurement. However,external totheDUT [6].

Accordingtothecharacteristics of time–frequencydomain,the disturbancescanbeclassifiedaswhitenoise(WN),DiscreteSpec- tralInterference(DSI),periodicpulseinterference(PPI),stochastic pulseinterference(SPI)[20].ConsideringPDaspulsesofastochas- ticandnon-stationarynature[21]andthat,consequently,thenoise acquiredintheonsitemeasurementsignalhasarandomcharac- teristic,itisimportanttoinserttheconceptofGaussianProcess.

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

Y=

T 0

g(t).X(t)dt, (2)

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

−^(Y−Y)2 22

Y

, (3)

whereY isthemean,Y isthestandarddeviation,and_Y²isthe varianceofarandomYvariable.WhentheGaussianrandomvari- ableYisnormalizedtohave_Y equals0andvariance_Y²as1,the normalizedGaussiandistributioniscommonlywrittenasN(0.1) andthevalueofthesignalwillbefoundin±3for99.7%ofthe consideredtimeinterval.

TheWNisakindofGaussianprocess,withPSD(PowerSpec- trumDensity)constantregardlessofthefrequency.Thus,thewhite GaussiannoiseisusedasanAWGNofPDfromthepulsegenera- 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(A_V)forPD1,wheretheSNR=−3dBintheworsescenario (distortedsignal).Whereas,thePDpulseismixedonidealnoise amplitudeinorderof10⁻6(PD6,SNR=60dB)(cleansignal).There- fore,thenoiselevelcontrolparameteristheSNRindB.Inthiscase, thevaluesofsignalswithAWGNwereusedasinputsignalstothe HFCTmodel.

Fig.3.PDpulsesgenerated(left)andtheirnormalizedfrequencysinglesidespectrumband–SSB(rightcolumn).

Fig.4.SchematicoftheHFCTsensormodel.

3. HFCTmodellingandsimulation

ThephysicalgeometryparametersoftheHFCTsensorisrelated toatoroidalcoilwrappedinacoreofhighrelativepermeability.

Theelectrical responseoftheHFCTsensor isbasedonthecon- structiveandelectricalaspects,givenby:geometry,thenumberof turns,ferromagneticcorematerialandloadresistance(terminal) [22].Therefore,thedependentcharacteristicsoftheHFCTgeometry aresecondarywindingresistance,parasiticcapacitanceandleak- ageinductance[22].Theelectricalandconstructiveparametersof theHFCTsensorarehighlightedinFig.4.

whereR_Listheterminalloadresistance,r_iistheinternalradius, 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

Thecalculationofelectricalparameterswerecarriedoncon- 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 samelengthasr_c).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:

vs(t)=−Mc.dip(t)

dt . (5)

Mutualinductanceisgivenby[16]:

Mc= N_s²..Ac

lm

, (6)

whereisgivenby=r·o,inwhichristherelativeper- meability(valueaccordingtothematerial)andoisthevacuum permeabilitywiththevalueof410⁻⁷H/m.TheNsisthenumberof turnsofthesecondary,i.e.windingofthesensor.Inleakageinduc- tance(alsocalledauto-inductance)[24],thecircularcoilmethod wasusedforsingleturninductanceandforrwrc,thus,based on:

Lloop=₀.rc.log₁₀

_8.r

c

r_w

−2

. (7)

Theresultingleakageinductancefortheentirecoilis:

Ls=N_s².L_loop. (8)

SincetheapplicationisinHF,thevalueoftheparasiticcapac- 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 acosh

_pw

2.rw

^{. (9)}

AlthoughLsandCsareintrinsictotheHFCTsensor,requiring thecalculationofthecapacitivenetworkandexperimentalcalcu- 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

Cs.RL.Rs+Ls+Mc Cs.RL.(Ls+Mc)

+_Cs.R^R_L^s_.(Ls+Mc)^+RL

. (10)

Thefrequencyresonance(w₀)inrad/s:

w0= R_L

Cs.R_L.(Ls+Mc). (11)

Also,thedampingcoefficient(),givenb:

= (Cs.RL.Rs+Ls+Mc)

Cs.RL.(Ls+Mc) 2.Cs.R_L(Ls+Mc)

R_L . (12)

Thevaluesofw0andprovidedataforsystembehaviorsince:

>1providesaoverdampedresponse(realanddifferentrootsand productoftwo1st-orderpoles);<1determineaunderdamped response(complexroots)ofthesystem;=1resultsincritically dampedresponse(realandequalroots).Thus,Fig.4canbemodeled accordingtoFig.5inthesdomain.NotethatR_eq1andR_eq2areequiv- alentresistancesfromresistiveassociationsinseries(betweenRs

andsLs)andinparallel(between1/sCsandRL),respectivelyand whosetotalequivalentresistanceisReq(seriesassociationbetween R_eq1andR_eq2).

3.3. Simulation

Inordertoassessthehypothesisofimprovementordeteriora- tionoftheHFCTsignalresponse,weconsidertheS-domainthrough a transfer function optimization, which means the frequency response.Fivedifferentmodelshavebeensettledasdescribedin Table3,whichweredividedintoreferenceandvariationgroups.

Thereferencemodel(PAD)isthestandardmodel,whereasRL(load resistance),Ns(numberofsecondaryturns)andr(relativeper- meability)arevariationmodels.Ontheotherhand,thevariation modelscalledN30,RL250,mur2300andRLNmurwereorganized totestthegeneralperformanceoftheHFCTsensor,withchanges initsparametersbasedonthePAD.

ThefiveTFs,consideringthecalculationsbasedonthespecified parametersinTable3,arepresentedinTable4.

TheBodediagramwasconsidered(Fig.6), toobtainthefre- 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,r_o,r,andr_c)wasmaintained,andtheR_L,N_sand_rwerealtered (Table3),distinctperformanceswereobtainedbetweentheHFCT sensormodels.

Fig.7. MSEoftheHFCTsensormodels.

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

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

Inthemur2300,the_r=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= 1 N

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

−n−1

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,whileinthePADmodelthemutualinduc- tanceisMc=0.17mH,i.e.,anincreaseof20inthenumberofturns ofthewindingresultsinanincreaseof8.82timesthevalueofM_c (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,andsimu- lationofthehigh-frequencycurrenttransformer(HFCT),appliedto timemeasurementsofthepartialdischarges(PD)underthestrong influenceofbackgroundnoises.

SeveralfactorslimitthefrequencyresponsesoftheN30,RL250, mur2300,andRLNmurmodels.IntherealHFCTsensor,thefre- 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,duetotheresistivecouplingwiththemeasur- inginstruments,toeliminatelosses.Thepresentpaperemploysa variationofupto250toverifychangesinresponsetotheinput signalandperformanceevaluationundernoisyconditions.

Thus, thehypothesisofimprovement ordeterioration ofthe HFCTsignalresponse,throughatransferfunctionoptimization,for aneventualredefinitionofphysicalandgeometricalparametersof theHFCTsensor,canbevalidated,dependingonwhichparame- 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.atUni- versity ofWestSantaCatarinaand M.Sc.inElectrical EngineeringfromtheUniversityofCampinas.Currentlyis aPh.D.candidateandEarlyStageResearcherintheETOPIA (EuropeanTrainingNetworkofPhDResearchersonInno- vativeEMIAnalysisandPowerApplications)Project,a jointdoctoralprogrammeunderTheEuropeanCommis- sion Horizon 2020initiative, MarieSkłodowska-Curie Actions, atTheUniversityofZielonaGóraandatThe University ofTwente.Heisa memberofInstituteof ElectricalandElectronicEngineers(IEEE),andElectro- magneticCompatibilitySociety(EMC-S)workingonTC-7 (TechnicalCommittee).Hisresearchareasaddresselectric vehicles,smartcities,sensors,EMCandEMI.Hehasexperienceinelectromag- neticmodeling,cableandsensordesign,simulationofelectriccircuits,andpartial dischargetests.

ShadyS.Reffat,Ph.D.,isapostdoctoralresearchassociate intheDepartmentofElectricalandComputerEngineer- ing,TexasA&MUniversityatQatar,amemberofthe InstituteofElectricalandElectronicEngineers(IEEE),a memberofTheInstitutionofEngineeringandTechnol- ogy(IET),amemberoftheSmartGridCenter–Extension inQatar(SGC-Q),hehasworkedwithindustryforover fifteenyearsaselectricaldesignengineer.Hehaspub- lishedovertwentyjournalandconferencepapers.His researchinterestsincludeelectricalmachines,powersys- tem,smartgrid,energymanagementsystem,reliability ofpowergridandelectricmachinery,faultdetection,and conditionmonitoringinconjunctionwithfaultmanage- mentanddevelopmentoffaulttolerantsystems.Hehassuccessfullyrealizedmany potentialresearchprojects.

HermesLoschi,M.Sc.,wasbornin1990,SaoPaulo,Brazil.

HereceivedhismasterdegreeinElectricalEngineeringat theUniversityofCampinasandhisbachelor’sdegreein ControlandAutomationEngineeringatthePaulistaUni- versity.SinceApril2019,hestartedasaPh.D.studentin

“SmartCitiesEMCNetworkforTraining(SCENT)”project intheInstituteofAutomaticControl,ElectronicsandElec- tricalEngineeringattheUniversityofZielonaGora,Poland aswellasthefacultyofElectricalEngineering,Mathemat- icsandComputerScience(EEMCS)intheUniversityof Twente,Netherlands.Hisresearchareasarepowersys- tems,renewableenergies,sensors,EMCandEMI.

YuzoIano,Prof.Ph.D.,hasadegree(1972),amaster’s degree(1974)andadoctorate(1986)inElectricalEngi- neeringfromtheUniversityofCampinas(Unicamp).Since then, he wasa supervisorin 5postdoctoralprojects, 34doctoraltheses,59master’sdissertations,74under- 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”honorgrantedbytheInter- nationalInstituteofElectricalandElectronicsEngineers-IEEE(2018).Heiscurrently FullProfessorMS6inRDIDPofDecom/Feec/Unicamp.

EuclidesChuma,Ph.D.,iscurrentlyR&DManagerofPho- tonicsInnovationInstitute.Hecompletedhisdegreein MathematicsfromtheUniversityofCampinas(UNICAMP) (2003),graduatedegreeinNetworkandTelecommuni- cationsSystemsfromINATEL(2015),MScinElectrical EngineeringfromUNICAMP(2017),andPhDinElectri- calEngineeringinUNICAMP(2019).Hisresearchinterests includeantennas,microwave,millimeterwave,photon- ics,sensors,wirelesspowertransfer,andsoftwaredefined radio.

Twente,Netherlands.