PrognosticsofTransformerPaperInsulationusingStatisticalParticleFilteringofOn-LineData

Keywords:transformer,prognostics,paperinsulation,lifeestimation,conditionmonitoring

V.M.Catterson(1),J.Melone(2),andM.SegoviaGarcia(2),(1)InstituteforEnergyandEnvironment,UniversityofStrathclyde,UK(2)PowerNetworkDemonstrationCentre,UniversityofStrathclyde,UK

Prognosticsoftransformerremaininglifecanbeachievedthroughastatisticaltechniquecalledparticlefiltering,whichgivesamoreaccuratepredictionthanstandardmethodsbyquantifyingsourcesofuncertainty.

IntroductionThe adoption of prognostics for critical assets has the potential to advance assetmanagement in the power industry significantly. While diagnostic techniques canidentifythepresenceofincipientfaults,prognosticsaimstopredictthefuturestateofagivenasset[1],[2].Prognosticscanthereforebeusedtoestimatetheremainingusefullife(RUL)oftheasset,andhelpplanmaintenancewhileminimizingtheriskoffailureinservice.Prognostics requires a goodmodelof theprocessof deterioration, from inceptionthroughtofailure[1]-[3].Deteriorationmaybeduetoaging,asinthecaseofpaperinsulation, or it may be due to a fault. Regardless of the cause of deterioration,prognostics is useful only if the deterioration is slow enough that maintenance(repair or replacement) can be scheduled during the predicted RUL. Thusprognosticsisnotsuperiortodiagnosticsifthedeteriorationissorapidthatfailurecannotbeprevented.Adeteriorationmodelcantaketheformofaphysics-of-failure(PoF)model,oritcanbederivedfromdata[3].Withinthepowerindustry,amajordifficultyofthelatteris‘hazardcensoring’,wherelittledatarelatingtoassetfailuresisavailablebecausemost assets are removed from service before failure. A PoF model may bepreferable since it can offer some quantitative support for the RUL prediction. Ineithercase,thereisalwayssomeuncertaintyaboutanasset’sfuturedeterioration.Aprognosticssystemshouldideallyquantifythisuncertaintyaswellasmodelingthedeterioration.Severaltechniquescanbeusedforprognostics[3].Thosemorefamiliarasdiagnostictechniques can also be used for prognostics, e.g., neural networks [4] or supportvectorregression[5].Techniqueswhicharecommonlyusedforforecasting,suchaslinearregression[6],[7],orautoregressiveintegratedmovingaverage[8],canalsobeused. Those specific to prognostics include similarity-based prognostics [9] or

particle filtering [10]-[12]. Of the latter, a statistical filtering technique called theparticlefilterisoneofthemostversatile,asitplacesfewconstraintsontheformofthe deterioration function, and incorporates explicit handling of uncertainty. Itshould be noted that, in this context, a “particle” is a system simulation, not aphysicalparticle(impurity)intransformeroil.Prognosticsismorewidespreadinindustrieswherethesafety-relatednatureoftheapplication leads to higher levels of component monitoring than in the powerindustry.Inparticular,theparticlefilteringapproachhasbeenappliedtomechanicalfaults in aerospace assets, e.g., crack growth propagation [10] and impeller wear[11].However,withgrowingvolumesofdatabeingcollectedfrompowernetworks,following increasedadoptionofsmartgridtechnologiesand lowercostsofsensorsandstorage,onlineprognosticsisnowbecomingmorecommonforelectricalassets.In this article the particle filter as amethod of prognostics for transformer paperagingisdescribed.ThePoFmodelofdeteriorationatthecoreoftheparticlefilterisderived from thewidelyaccepted IEEE standardC57.91.Thekeyadvantageof theparticle filter approach is that it quantifies various sources of uncertainty in thepaperagingprocess,fromuncertaintyinthemeasurementsusedtoderivehotspottemperature to uncertainty in the activation energy required to break cellulosechains in the insulation paper of a given transformer. Over the course of atransformer’sservicelife,thesesmallsourcesofuncertaintymayleadtosignificantprognostic error. By adding a probabilistic layer of analysis to the deterministicequationsinC57.91,theparticlefiltercanprovideautilitywithamoreinformativebutlesspreciseestimateofremainingpaperlifetime.

TheParticleFilterAparticlefilterisaprobabilisticsimulationofasystem—inthecaseofprognostics,the deterioration of a component [13]. Within the filter, a large number ofsimulations (called ‘particles’) are run in parallel with slightly different initialconditions and probabilistic state transitions. Each particle captures one possiblefault trajectory.Onceoneormoremeasurementsof the systemhavebeenmade,eachparticleisgivenaweightingbasedonthelikelihoodofitrepresentingthetruestateof thesystem.Thepredictionof thetimetoreachagivenstate,e.g., failure,emergesthroughagreementbetweenthemajorityofhighly-weightedparticles.The system is modeled as two parts, namely the process model f and themeasurementmodelh[14]:

𝑥! = 𝑓(𝑥!!!,𝑢!) (1)𝑦! = ℎ(𝑥! , 𝑣!) (2)

wherextisthesystemstateattimet,ytarethemeasurementsattimet,anduandvarenoiseterms.Theprocessmodelfcapturestheunderlyingdeteriorationofthesystem, which must be Markovian, i.e., the system state depends only on its

immediatepreviousstateandcurrentconditions,andnotonhistorical states [13].Themeasurementmodelh represents thedifferencebetweenmeasurements andthetruestateofthesystem,duetonoiseorknownbiasesintheinstrumentation,orbecausethesystemstateisnotdirectlyobservableandmustbeinferredfromproxyvariables.Ateachtime-step,twocalculationsaremadeforeachparticlei :

1. Simulationofthenewsystemstate𝑥!!,giventheprevioussystemstate𝑥!!!! : 𝑥!! = 𝑓 𝑥!!!! ,𝑢! ∀𝑖 (3)

2. Weightingoftheparticlelikelihood𝑤!!,giventheprobabilityofnewmeasurementvaluesoccurringifthisparticlerepresentsthetruesystemstate𝑝 𝑦! 𝑥!!),combinedwiththeweightofthisparticleattheprevioustimestep𝑤!!!! : 𝑤!! = 𝑝 𝑦! 𝑥!! × 𝑤!!!! ∀𝑖 (4)

Equation(3)providesprognosticcapability,asitpredictsthenexttimestep.Equation(4) is a diagnostic step, as it usesmeasurements to adjust the probability of eachparticle representing the true current state of the system. Predictions at longertimes can be generated by repeated use of (3), with predicted outputs being fedbackasinputsforsubsequenttimesteps.Theresultgeneratedbytheparticlefilterisderivedfromthestateofallparticles.Acommonapproachistolookatthespreadofpossiblestatesatagivenfuturetime,as in [11]. In that case all particles simulate health in, say, a year’s time, and theexpected distribution of RUL values at that time is calculated from individual RULvaluesineachparticle.ImportantparametersofthisdistributionincludethemedianRUL(the50thpercentile),andexpectedupperandlowerlimitsonRULsuchasthe5thand95thpercentilebounds.

ApplicationtoTransformerPaperAgingTransformersarethemostexpensivesingleassetinthepowersystem,andarecriticaltonetworkperformancetargetsbeingmet.Itcanthereforebecost-effectivetoinstallmonitoringequipmentandtracktheconditionofkeytransformers,withtheaimofdelayingrepairorreplacementuntiltheyareessential.Asaresult,alargebodyofresearchandpracticehasfocusedontransformermonitoringanddegradationmechanisms,sothatsignificantscopefortheapplicationofprognosticstotransformersnowexists.Thelife-limitingparameterforatransformeristhedegreeofpolymerization(DP)ofthepaperinsulationatitsmostagedlocation.NewpaperhasaDPofapproximately1000–1200 [15],while end of life is typically considered to beDP = 200 [16]. The

factorswithmostinfluencepaperDParethoughttobetemperature,moistureandoxygencontent,andtoalesserextentacidandcontaminantcontent[16],[17].Themainmechanismsofpaperbreakdownarehydrolysis,oxidation,andpyrolysis,which occur at different rates depending on temperature, moisture, and oxygenlevelswithinthepaper[16].Pyrolysisrequiresextremetemperatures(greaterthan140oC),andcanthereforebe largelydiscountedundernormaloperation[16],[17].Oxidationrequiresthepresenceofoxygen,andmaythereforebeconsideredhighlyimportantforfree-breathingtransformersandlesssoforsealedunits[16].However,overthelifeofasealedtransformer,oxidationcanplayanimportantrolebecauseitleads to the generation of acids, which catalyze deterioration [16]. Hydrolysis isdependentontemperatureandthepresenceofmoisture.Since thepaper isdriedduringtransformerconstructionandmoisturelevelstendtoincreaseduringservice,therateofhydrolysisisgenerallyexpectedtoincreaseasthetransformerages[16].For a newly-built sealed transformer, the main deterioration mechanism ishydrolysis,and the rateofagingonaday-to-daybasis isdominatedbychanges intemperature rather than by changes inmoisture content. Amodelwhich relatestemperature to rateof changeof paperDP is found in IEEE StandardC57.91 [18],whichdefinesanagingaccelerationfactor𝐹!!

𝐹!! = 𝑒!"###!"! !

!"###!"#!!! (5)

whereΘ!isthetemperature(inoC)ofthetransformerhotspot.C57.91statesthatthetransformerpaperwillreachend-of-lifeDPafter180,000hoursat110oC.Agingisfasterandlifetimeisshorterathighertemperatures.(5)canberearrangedbyconvertingitintoarecurrencerelationforremainingpaperlifetime:

𝑙! = 𝑙!!! − exp (15000+ 𝑢!)!!"!

− !!"#! !!!

(6)

where𝑡is the time in service in hours,𝑙!is the RUL at time𝑡,Θ!! is the hotspottemperature at time𝑡, and𝑢! is process noise. There are two main sources ofuncertaintyinthismodel,namelytheinitialcondition𝑙!,whichistheinitialnumberofhoursofexpectedservicelifecorrespondingtotheinitialDPofthepaper,andtheprocessnoisewhich is theslightvariation in lifetimereduction foragivenhotspottemperature.Thelatterisduetosmalldifferencesintheactivationenergyrequiredtobreakcellulose(paper)chains.The measurement model must capture the relationship between hotspottemperature and transformer measurands, and measurement noise. Since thetransformerhotspottemperatureisnotdirectlyobservable,itmustbeinferredfromother parameters. C57.91 [18] gives an equation for hotspot temperatureΘ! ,assuming a known ambient temperatureΘ! , a known top oil temperature rise

ΔΘ!"/! relativetoΘ!,andaknownhotspottemperatureriseΔΘ!/!"relativetotopoiltemperatureΘTO:

Θ! = Θ! + ΔΘ!"/! + ΔΘ!/!" (7)Thesteady-statetopoiltemperatureriseoverambientcanbecalculatedas:

ΔΘ!"/! = ΔΘ!",!!!!!!!!!

! (8)

whereΔΘ!",! and𝛾are respectively the topoil temperature riseover ambient atthe transformer rated load and the ratio of load loss at rated load to loss at zeroload,𝐾istheratioofmeasuredloadtoratedload(𝐿/𝐿!),and𝑛isaconstantforagivencoolingmode.Thehotspottemperatureriseovertopoilcanbecalculatedas:

ΔΘ!/!" = ΔΘ!,! × 𝐾!! (9)whereΔΘ!,! isthetransformerdesignparameterhotspottemperatureriseovertopoilatratedload,𝐾isasdefinedimmediatelyabove,and𝑚isanotherconstantforagivencoolingmode.Hotspottemperaturecanbecalculatedfrommeasurementofambienttemperatureandload,incombinationwithanumberofdesignparametersandconstants.Thefinalstepinbuildingaparticlefiltermeasurementmodelistoincorporatethesensornoise𝑣!and𝑣! superimposedonmeasurementsofambienttemperatureandloadrespectively:

Θ! = (Θ! + 𝑣!)+ ΔΘ!",!!!!!!!!!

!+ ΔΘ!,! × 𝐾!!,𝐾 =

(!!!!)!!

(10)

Thismeasurementmodelassumesthatasimulationtime-stepislongenoughforthehotspottemperaturetobetakenasitssteadystatevalue.

CaseStudyExampleThe Power Networks Demonstration Centre (PNDC) is an 11kV/400V test facilitylocated near Glasgow, UK, used for trial and demonstration of smart gridtechnologies. It was built to resemble a distribution network of the future, withsignificantlevelsofautomationandcommunications,embeddedgeneration,andthecapabilitytogenerateresistivebalancedandunbalancedfaults[19].Thesiteisfedthroughan11kV/11kV2MVAisolationtransformer.Thehealthofthistransformer is critical for the site, since any transformer downtime, e.g., formaintenance, means the site is offlineuntilmaintenance is completed.Given thehighdatacollectioncapabilityon-site,onlineprognosticsofthetransformercanbeachieved without additional instrumentation. The transformer parameters for themeasurementmodeloftheparticlefilteraregiveninTable1.

Table1:Transformerparametersformeasurementmodel

Parameter ValueRating 2MVACoolingmode ONANOiltemperatureriseover40oCambient 60oCNoloadlosses 3100WLoadlossesatratedcurrent 21000WTheparticlefilterwillnowbeusedtoexaminetwocases,firstlytheagingtoSeptember2015ofthetransformerinservice,followedbyitsexpectedagingoverthenextfiveyears.

AgingtodateThePNDCsitewascommissionedinJanuary2014.Theon-siteloadisatypicalforadistributionfeeder,sinceitislimitedalmostentirelytoweekdaybusinesshours.Dueto the testing of equipment, including novel protection devices, the networkmayexperience a higher number of faults than a utility would consider acceptable.However, the duration of fault current is limited by standard backup protectionschemes,andconsequentlywillnotcausesignificantheatinginthetransformer.AdatasetofloadandtemperaturebetweenJanuary2015andSeptember2015wasgenerated. Loadwasmeasured using ameasurement class 1 current transformer,withautomatic logginginitiatedinJanuary2015.Priortothis, loggingwasinitiatedmanually and consequently some service data were not recorded. However, nosignificanttransformer loadingoccurredin2014asthesitewentthroughstagesofequipmentcommissioning.Ambienttemperaturedatawerecollectedfromanearbyairportweatherstation.Minimum,mean,andmaximumwere loggedatbothdailyandhourlyintervals.Thenetworkisusuallyde-energizedovernight,withexperimentalworkbeginningat0900h.Itisusedforvariousexperimentsuntiltheworkingdayendsat1700h,whenit is again de-energized. The current measured at the isolation transformer istypically 20–30 A, and fluctuates due to network reconfiguration and changingloadbank settings. On multiple occasions current peaked at 80-105 A, andinterruptionsoccurredduetointroductionoffaults.Theparticle filterwas initializedwith 1000particles, eachwith theprocessmodelfromequation(6),themeasurementmodelfromequation(10),andtheinitiallifeoftheinsulationpaper𝑙!drawnfromanormaldistributionwithameanof180,000handastandarddeviationof500h (𝒩(180000, 500)). This standarddeviationwasselectedbasedonengineeringjudgment.Ifhigheraccuracyweredesired,datafromthe paper supplier or from testing of samples could be used to refine thesedistributionparameters.

The measurement noise 𝑣! superimposed on the ambient temperaturemeasurement was chosen to be𝒩(0, 1), with a standard deviation of 1 oC toaccountforthetemperaturebeingmeasurednearbyratherthanonsite.Thenoise𝑣!superimposedonloadcurrentmeasurementsisduetothemeasurementclass1currenttransformersusedtodeterminethetransformerloading.Theprocessnoise𝑢,chosenas𝒩 0, 20 onthebasisofanassumeduncertaintyΔEAupto0.5kJ/molintheactivationenergyofthepaperdegradationprocess,causesavariationintheconstant15,000inequation(6).Thatvariationcouldbeupto

∆𝐸!𝑅 =

0.58.314 × 10!! = 60.1 Κ

where𝑅istheuniversalgasconstant.Thevalueof60.1Kwasassumedequivalenttothreestandarddeviationsinthevalueofthemeanactivationenergy(accountingfor over 99% of events). Thus the process noise u was drawn from a normaldistributionwithastandarddeviationofonethirdof60.1K.Startingfromtheseinitialconditions,theserviceconditiondatawerefilteredtogivea diagnosis of the health of the transformer paper in September 2015. Figure 1shows the resultingprobabilitydistribution functionsof theRUL,derived from thepredictionsofall1000particles.ThemedianRULatthestartoflifeisjustbelowthemean, at 179,986 hours, and is estimated to have dropped to 179,631 hours bySeptember2015.

Figure1:Theprobabilitydensityfunctionsofremainingusefullifeatthestartoflife(red)andafterninemonthsinservice(blue).

Therelativelylightloadingofthistransformercomparedtoitsratedloadmeansthatthelifeconsumptionofitspaperisslow,althoughstepchangesinRULcanbeseenwhentheloadcurrentapproachesitsratedvalue.Figure2showsatypicalnine-dayperiod of relatively light loading compared to rated load, where the decrease inmedianvalueofRULcanhardlybeseen.Incontrast,Figure3showsamuchhigherloadon3September,withareadilyvisiblereductioninRUL.

Figure2:Atypicalninedayperiodoftransformerloadcurrent(blue),withthecorrespondingRUL(red).

Figure3:AnexampleofhightransformerloadcausingastepchangeinRUL.

PrognosticsUnderNormalConditionsAfter determining RUL to September 2015, the particle filter was used to predictremaininglifeafterafurtherfiveyearsofoperation.Theexistingloadingdatawereassumedtoberepresentativeoffutureloading,andtheweatherdataforallof2014wereassumedtoberepresentativeoffutureweatherconditions.Figure4showstheprobabilitydensityfunction(PDF)oftheRULinSeptember2015inred,andthePDFofthepredictedRULinfiveyears’timeinblue.Itcanbeseenthattheoverallshapeof both distributions remains roughly the same, with similar variance, skew, andkurtosis.ThemedianRULispredictedtodropby1,952hoursto177,679hours.

Figure4:ProbabilitydensityfunctionsofRULinSeptember2015(red),andpredictedafterafurtherfiveyearsofservice(blue).

PrognosticsUnderOverloadConditionsThe particle filter can be used to explore the effects of various conditions ontransformer life. Inparticular, theeffectsofanoverloadforagivenperiodof timecanbevisualized.Thiscanhelpwithdecision-makingaboutwhetheritisadvisabletoallow an overload to occur. Figure 5 shows a load profile over a 20-hr periodcontainingacurrentspikewithamaximumcorresponding to1.6 timesrated load.Theeffecton themedianRUL isa step-reductionof385hoursoccurringoveronehourofoperation. The5th and95thpercentilesof theRUL fell by382and378hrsrespectively.

Figure5:Loadprofileovera20-hrperiodcontaininganoverload,withcorrespondingreductioninRUL.

DiscussionTheparticle filter is a statistical toolwhich canpredict the futurehealthof assetsunderdifferentoperatingregimes.Whilethe IEEEequations for transformerpaperaginggiveninC57.91provideestimatesoftheeffectsofloadandtemperature,theydo not include uncertainty estimates. On the other hand the particle filter canenhancetheinformationavailablebyaccountingforuncertaintyinthepreciserateofdegradationandinthemeasurements.The approach shownhere canbe extended to include the effects of factors otherthantemperatureonpaperaging.Thusan increase in themoisturecontentof thepaperwouldaffecttheactivationenergyofthedeteriorationprocess,andthereforetheconstantvalue15,000 in (6).Thestatisticalparticle filteringapproachcouldbemodified to take account of online moisture sensor data through an appropriateexpansionof(6).Autilitymayalsoperiodicallygainupdatedinformationaboutthetruestateofthepaper in a transformer.Oneapproach is through sacrificial paper stripswithin thetransformer tank, which can be removed and the DP measured directly.Alternatively, thefurancontentof thetransformeroilcanbeusedtoestimatetheDPvalue[20].Thisinformationcanbecomparedagainstthepaperstateestimatedbythefilter,toassesshowaccuratelythelatteristrackingpaperaging.Additionally,the filterestimatecanbe incorporated in thevalueof𝑙!!!in (6), therebyensuringfuturepredictionsarebasedonthemostrecentinformation.

Theoutputofthefilterisaprobabilitydensityfunction,whichcapturestherangeofpossiblevaluesandtheirprobabilities.Adeterministicmodelsuchasthatdescribedin C57.91 will provide a very precise estimate, i.e., a single value, which mayhowever be in error. The probabilistic approach gives a range of values, which islikely to contain the true remaining life value. Further, theprobabilistic predictioncanbesettobepessimistic,suchastakingthe5thpercentile,inordertoerronthesideofavoidingafailureinservice.Prognostic information can assist with various types of decision making within autility.Mostobviously,assetmanagementcanbenefitfromthepredictedwindowoftime in whichmaintenance can successfully avoid a failure. However, prognosticscanalsobeuseful inanoperationalcontext,bygivingextra informationabouttheeffects of a possible overload on the health of the assets. Adopting prognosticswithinautilityofferscleargainsover relyingonexpert judgment,and this topic isexpected to drive further fundamental research, case studies, and adoption byindustryoverthecomingyears.

AcknowledgmentTheauthorsthanktheanonymousreviewersfortheirinsightfulcommentsandtheirguidanceonthequantificationofprocessnoiseinthisapplication.

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VictoriaM.Catterson(SM'12)receivedtheB.Eng.andPh.D.degreesfromtheUniversityofStrathclyde,Glasgow,U.K.in2003and2007respectively.SheiscurrentlyaLecturerintheInstituteforEnergyandEnvironment,UniversityofStrathclyde,andistheChairoftheIEEEDEISTechnicalCommitteeonSmartGrids.Herresearchinterestsincludedataanalyticsforconditionmonitoring,diagnostics,andprognosticsinthepowerindustry.

JosephMeloneisanR&DengineeratthePowerNetworksDemonstrationCentre,whichisajointventurebetweentheUniversityofStrathclyde,ScottishEnterprise,theScottishFundingCouncil,andUK-basedDistributionNetworkOperators.HeobtainedaPhDinNuclearPhysicsin2005fromtheUniversityofGlasgowandworkedasapostdocdevelopinghardwareandsoftwaresystemsforarangeofphysicsexperiments.In2011heshiftedfocustoenergysystemsaspartoftheRenew-NetKnowledgeExchangeinitiative,andin2014hestartedworkonacceleratingsmartgridtechnologyatthePNDC.Joseph'smainresearchinterestsareinpowersystemssimulation,dataanalysis,anddevelopmentofinnovativesensorsandmeasurementtechniques.

MariaSegoviareceivedherPhDinStatisticsandOperationalResearchin2009fromtheUniversityofGranada,Spain.Sheworkedasapostdoctoralresearcherinthedevelopmentofmodelstodescribesystemreliability,andcapturemaintenanceactionsefficiency,attheNuclearMetrologyDepartmentattheFreeUniversityofBrussels.In2013shejoinedthePowerNetworkDemonstrationCentre,UniversityofStrathclyde,Glasgow,UK,wheresheworksonindustryprojectsrelatedtohealthestimationandforecastingoftheremaininglifeofelectricalassets.Hermainresearchinterestsaremodelingofassetdeterioration,estimationoftheimpactofmaintenanceactions,anddataanalysis.