Engineering5(2019)795–802Contents lists available at ScienceDirectEngineeringResearch
CleanEnergy—Article
AComprehensiveApproachfortheClusteringofSimilar-PerformanceCellsfortheDesignofaLithium-IonBatteryModuleforElectricVehicles
WeiLia,SiqiChenb,XiongbinPengb,MiXiaoa,LiangGaoa,?,AkhilGargb,NengshengBaobabStateKeyLabofDigitalManufacturingEquipmentandTechnology,HuazhongUniversityofScienceandTechnology,Wuhan430074,ChinaKeyLabofMechatronicSystemsIntelligentIntegrationTechnology,MinistryofEducation,ShantouUniversity,Shantou515063,Chinaarticleinfoabstract
Anenergy-storagesystemcomprisedoflithium-ionbatterymodulesisconsideredtobeacorecompo-nentofnewenergyvehicles,asitprovidesthemainpowersourceforthetransmissionsystem.However,manufacturingdefectsinbatterymodulesleadtovariationsinperformanceamongthecellsusedinseriesorparallelcon?guration.Thisvariationresultsinincompletechargeanddischargeofbat-teriesandnon-uniformtemperaturedistribution,whichfurtherleadtoreductionofcyclelifeandbatterycapacityovertime.Tosolvethisproblem,thisworkusesexperimentalandnumericalmethodstocon-ductacomprehensiveinvestigationontheclusteringofbatterycellswithsimilarperformanceinordertoproduceabatterymodulewithimprovedelectrochemicalperformance.Experimentswere?rstper-formedbydismantlingbatterymodulesforthemeasurementofperformanceparameters.Thek-meansclusteringandsupportvectorclustering(SVC)algorithmswerethenemployedtoproducebatterymodulescomposedof12cellseach.Experimentalveri?cationoftheresultsobtainedfromtheclusteringanalysiswasperformedbymeasuringthetemperatureriseinthecellsoveracertainperiod,whileaircoolingwasprovided.ItwasfoundthattheSVC-clusteredbatterymoduleinCategory3exhibitedthebestperformance,withamaximumobservedtemperatureof32°C.Bycontrast,themaximumobservedtemperaturesoftheotherbatterymoduleswerehigher,at40°CforCategory1(manufacturer),36°CforCategory2(manufacturer),and35°CforCategory4(k-means-clusteredbatterymodule).ó2019THEAUTHORS.PublishedbyElsevierLTDonbehalfofChineseAcademyofEngineeringandHigherEducationPressLimitedCompany.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).Articlehistory:Received28August2018Revised25October2018Accepted3June2019Availableonline10July2019Keywords:ClusteringalgorithmBatterymoduleEqualizationElectricvehicle1.IntroductionEnergy-storagesystemssuchasbatterymodulesfornewenergyvehicles(NEVs)aregainingextensiveattention[1,2]asameansofreplacingtraditionalgas(petrol/diesel)-operatedvehiclesandtherebypromotingacleanerenvironment.Theperformanceparametersoflithium(Li)-ionbatterymodulesincludeenergydensity,capacity,andspeci?cpower.TomeetthepowerdemandrequiredforthetransmissionsystemsofNEVs,severalsmallbat-terymodulesareusedinseriesorparalleltoformalargebatterymodule(alsoknownasabatterypack).Abatterymoduleconsistsofanumberofcellsconnectedinseriesandparallel.TherangeofanNEVdependsontheperformanceofitsbatterymodule,andtheperformanceofabatterymoduledependsontheindividualperfor-manceofeachcellandonthecon?gurationofthecellsinseriesorparallel.Theidealperformanceofabatterymoduleshouldfollow?Correspondingauthor.E-mailaddress:gaoliang@mail.hust.edu.cn(L.Gao).thecriteriaofuniformityandequalization;however,thesecriteriahavenotyetbeensatisfactorilymet.Duringthemassmanufacturingofcellsandtheassemblyofcellsintomodules,slightvariationsoccurduetouncertaintiesintheoperatingmanufacturingconditions[3];thesemayincludeaperformancedifferenceoftheelectrodematerials,achangeofoperatingconditions,orgeometricalvariationcausedbymachin-ingerrors[4].Theseuncertaintiescancausedefectsinthebatterymodulessuchassurfacescratches,exposedfoils,andcracks.Manufacturingdefectsinbatterymodulesleadtovariationsinper-formanceamongthecellsusedinseriesorparallelcon?guration,whichinturnmayleadtovariationsintheperformanceparame-ters(i.e.,capacityandvoltage)ofeachcellinamodule.Overaperiodoftime,thisproblemaccumulates,resultinginuneventem-peraturedistributionandincompletecharge/dischargeofseveralcellsinthemodule.Theseproblemsleadtolesscapacitybeingavailable[5–7].Uniformityandequalizationcriteria—ifadaptedduringthedesignandmanufacturingofabatterymodule—canavoidthe796W.Lietal./Engineering5(2019)795–802problemsofoverheating,thermalrunaway,andsoforth,andthusincreasethelifeofthebatterymodule[8–12].Inordertosolvetheseproblems,somebattery-sortingmethodshavebeenresearched[13–15].Gallardo-Lozanoetal.[16]summa-rizedthedifferentactivemethodsforabatteryequalizationsystem,andconcludedthattheswitchedcapacitoranddouble-tieredswitchingcapacitormethodsarethebestsortingmethods.Kimetal.[17]proposedanapproachbasedonascreeningprocess(capacityscreeningandresistancescreening)toimprovetheutilityofaLi-ionseriesbatterymodule.Insubsequentresearch,theypro-posedapracticaluniversalmodelingofmulti-cellbatterystringsarrangedinseriesandparallelcon?gurations[18].Kimetal.[19]proposedamodularizedtwo-stagechargeequalizerwithcellselectionswitches.TheadvantageofthissortingmethodisthatitcanbewidelyusedforalargenumberofLi-ioncellsinahybridelectricvehicle(HEV).Inaddition,?vesortingmethods—namely,capacityandalternatecurrentinternalresistance,electrochemicalimpedancespectroscopy(EIS),voltagecurve,dynamicsparame-ters,andthermalbehavior—arecomparedinRef.[20].Itwasfoundthatlow-frequencybatteryimpedanceisthemostsuitablemethodforsortingbatteriesbytheirdynamiccharacteristics.Previousstudies[21–36]haveconductedtheselectionandclas-si?cationofhomogenouscells.Basedonexperimentalveri?cation,thesortedcellshaveamoreconsistentperformanceintermsofvoltage,temperature,andcapacityincomparisonwithunsortedcells.However,littleresearchhasfocusedonconductingexperi-ments.Therefore,thepresentworkcombinesexperimentalandnumericalmethodstoconductacomprehensiveinvestigationontheclusteringofbatterycellswithsimilarperformanceinordertodesignabatterymodulewithhigherelectrochemicalperfor-mance.Fig.1illustratestheproceduresthatwereusedtoperformtheclusteringanalysisandverifytheperformanceofthedesignedmodules.Charging–dischargingtestswereconductedon48Li-ioncellstomeasuretheirvoltage,temperature,andcapacity.Thek-meansclusteringandsupportvectorclustering(SVC)algorithmswereusedtogroupcellswithsimilarperformanceinordertopro-duceabatterymodule.Acomparisonanalysiswasperformedontheperformanceofthebatterymodulesproducedinthisresearchandtheperformanceofthosepurchasedfromamanufacturer.2.ExperimentalsetupfordatameasurementThissectiondescribesthecharging–dischargingteststhatwereconductedon48Li-ioncellsforthemeasurementofdata(voltage,temperature,andcapacity).The48cellswereobtainedbydisman-tlingthebatterypackshowninFig.2(a).Thedisassemblyprocessofthebatterymoduleswasperformedinfoursteps:Step1:Obtaininformationonthebatterymodulessuchascapacity,cellnumbers,andconnectionmodesbetweencells.Step2:Identifytheoutputterminalofthebatterymoduleoncethemoduleisunpacked.Thisstepshouldbedonecarefullytoavoidanyconnectionbetweenthenegativeandpositivepolesofthebatterymodule.Step3:Breaktheseriesconnection?rst.Inordertoensuresafety,thebatterymodulewassplitupintosmallpartsbydestroy-ingtheseriesandparallelconnections.Step4:Splitthesmallpartsintocells.Afterdismantlingthebatterymodule,charging–dischargingtestswereconductedbymeansofabattery-testingsystem(Fig.2(b)).Thebattery-testingsystemmainlyincludethebattery-testingdevice,adata-collectingsystem,Li-ioncells,etc.Thebattery-testingdevicewaspurchasedfromNewwareLtd.Ithaseightchannelsandcansavedataautomatically.Thestepsfortestingthecharging–dischargingprocessaresummarizedinTable1.Step1:Theconstantcurrentdischargewassetat1.3A.Step2:ThisstepbeganatthepointwhenthevoltageoftheLi-ionbatterywas2.75V,andinvolvedarestingtimeof30min.Step3:Aconstantcurrentandconstantvoltagechargeweresetwithacut-offvoltageof4.2V.Step4:Thisstepagaininvolvedrestingfor30min.Step5:Thenumberofcycleswassetas20.Throughouttheprocess,thevoltagewasnotpermittedtoexceedtherangeof2.65–4.3V.Eachcellwascharged–dischargedforatleast30cycles.ThedatacollectedfromtheexperimentareshowninTable2,whereFig.1.Acomprehensiveprocedureforthedesignandmanufactureofabatterymodule.W.Lietal./Engineering5(2019)795–802797Fig.2.(a)Dismantlinganddisassemblyprocessforbatterymodules;(b)battery–testingsystemusedforconductingcharging–dischargingtests.Table1
Stepsfortestingthe18650Li-ionbattery.Step12345StateConstantcurrentdischargeRestingConstantcurrentandconstantvoltagechargeRestingCycleValue1.3A30min1.3A4.2V30min20Cut-offvoltage2.75V4.2VThesumofsquareerrorsisacommonlyusedevaluationcrite-rionthatreferstothesumoftheEuclideandistancesfromthedatasamplesinoneclustertotheclustercenterml,whichcanbeexpressedasfollows:Eem1;m2;:::;mlT?kXXi?1j2clkxjàmlk2e1TMaximumsafetyvoltage:4.3V;minimumsafetyvoltage:2.65V;startexperimentsteps:constantcurrentdischarge.where{xj}#cisadataset,c#Xisthedatadomain,kisthenum-berofclusters,andclistheclusterdomainwhoseclustercenterisml.Theclusteringcentermlcanbecalculatedbythefollowing:‘‘zero”and‘‘full”refertofullydischargedandfullychargedstates,respectively.Thefollowingsectiondescribeshowclusteringalgo-rithmswereusedtoanalyzethecollectedexperimentaldata.3.ClusteringalgorithmsSupervisedlearningandunsupervisedlearningaretwocate-goriesofmachinelearningmethods.Supervisedlearningisgener-allyusedforclassi?cation,whileunsupervisedlearningisemployedforclustering.Clusteringalgorithmsareabroadsetoftechniquesforgroupingdataaccordingtodifferentrules;manyexcellentdescriptionscanbefoundinRefs.[37–39].Thepurposeofclusteringanalysisistogroupdataintoseveralclassesaccordingtocertainrules.Theseclassesarenotgiveninadvance,butaredeterminedbythecharacteristicsofthedata.Thedatainthesameclasstendtoresembleeachotherinasense,whereasthedataindifferentclassestendtobediscrepant.3.1.k-meansclusteringalgorithmMacQueenproposedthek-meansclusteringalgorithmin1967[39].Asthisalgorithmissimpleandeasytounderstandandhasarelativelyfastcalculationspeed,itisusuallyusedasthepreferredalgorithmfortheclusteranalysisoflargesamples[40].Themainstepsofthek-meansclusteringalgorithmareasfollows:Step1:ksamplesarerandomlyselectedastheinitialclustercenters.Step2:Thedistancesbetweenotherdataandeachinitialclus-tercenterarecalculated,andthedataaredividedintoclusterdomainsinwhichthenearestclustercenterislocated.Step3:Afterallthedataaresorted,theaverageofallthedataofeveryclusterisrecalculated,andthedatawheretheaverageislocatedbecomeanewclustercenter.Step4:Multipleiterationsareperformeduntilthecentersoftwoconsecutiveclustersarethesame,indicatingthatthedataareclassi?edintokclusters.ml?1XxjNlj2cle2TwhereNlisthenumberofdatasamplesinclusteringdomaincl.TheobjectivefunctionE(á)inEq.(1)representsthesumofthesquareerrorsbetweenallthedatainkclustersandtheirclustercenterml.AsmallervalueofE(á)indicatesbetterdataconcentra-tioninthecluster—thatis,abetterclusteringresult.Althoughthek-meansclusteringalgorithmispracticalandsim-pletoimplement,ithassomelimitations.First,determiningarea-sonablevalueofkisdif?cult.Second,therandomnessofselectinginitialclusteringcentersmayresultininstabilityoftheclusteringresults.Third,thisalgorithmissensitivetonoise.Aself-organizedmapbasedonaneuralnetworkcanalsobeusedforclustering.However,itisnecessarytotraintheneuralnetworks,whichcanmakethisprocesstime-consuming.Therefore,thenextsectionintroducesabetterandmoreef?cientclusteringalgorithm.3.2.TheSVCalgorithmIngeneral,asupportvectormachine(SVM)isadoptedforclas-si?cation(supervisedlearning).SVCisaslightlydifferentalgo-rithmfromanSVM.Infact,SVCisanunsupervisedlearningclusteringalgorithm.ThemainideaofSVCistomapdataspacetoahigh-dimensionalfeaturespaceusingaGaussiankernelfunction.Next,aspherewithaminimumradiusisobtainedandthespherecontainsmostofthemappeddata[41,42].Afterbeingmappedbacktothedataspace,thespherecanbeseparatedintoseveralparts,eachcontainingasingleclusterpointset.Inthispaper,arobustandef?cientclustermarkingmethodisadopted,whichisbasedonthetrainingkernelradiusfunction.Thismethodhastwostages.The?rststageinvolvesdividingthedatasetintoseveralmutuallyexclusivegroups,eachofwhichisacluster.Thesecondstageinvolvesmarkingalldatasamples.ThedescriptionofthedatasetsupportvectoristhefoundationoftheSVCalgorithm.Thedatasamplesaremappedtoahigh-dimensionalfeaturespacethroughnonlinearchanges,andthe798Table2
Dataobtainedfromcharging–dischargingtestsoncells.CellnumberDischargedstateZerovoltage(V)1234567891011121314151617181920212223242526272829303132333435363738394041424344454647483.39813.37513.40653.35573.40553.36003.36493.3981—3.41283.37743.37693.38843.34643.39083.41473.41033.40633.40893.39823.41823.39953.39393.40413.39673.40263.40113.39623.41543.28763.41223.41043.39373.37903.3902—3.40023.38513.42513.41003.35333.39603.39643.36013.40273.37473.3881—W.Lietal./Engineering5(2019)795–802ChargedstateZerotemperature(°C)25.626.826.626.526.726.125.825.6—28.027.928.027.926.827.126.925.324.223.725.124.223.823.222.928.329.323.828.323.828.829.930.125.025.124.8—23.823.823.824.725.325.325.425.223.923.824.2—Zerocapacity(Aáh)2.67832.71922.66692.69592.47732.64882.68452.6783—2.69412.66982.70422.68612.68292.67642.66172.54322.66202.67072.67082.51752.66422.67282.63482.64522.64132.68512.65602.57922.63312.59952.67472.65662.67882.6020—2.63942.64462.62282.59462.62932.67962.69172.69312.66432.67632.6236—Fullvoltage(V)4.18954.19114.18874.19224.19054.18824.19004.1895—4.19464.19624.19464.19414.19464.19494.19534.19544.19474.19384.19464.19414.19444.19514.19364.19664.19654.19624.19624.19504.19414.19444.19474.19454.19484.1951—4.19434.19564.19274.19534.19624.19584.19644.19524.19414.19524.1952—Fulltemperature(°C)26.026.926.926.526.826.226.126.0—26.627.327.026.726.326.726.424.823.624.023.024.122.422.722.928.629.024.329.623.730.530.130.124.824.224.4—23.823.523.724.725.124.625.224.423.523.723.6—Fullcapacity(Aáh)2.68472.72582.66832.70562.48432.65382.68582.6847—2.69342.65332.70802.68812.63492.65712.66462.54682.65942.67372.67172.51702.66342.67242.63232.64552.64342.68772.66342.58372.63642.59872.67902.65342.67562.6022—2.63862.64342.61922.59332.63102.67762.69552.69532.66632.67502.6268—minimumradiusofaspherecontainingallthemappeddatasam-plesisidenti?ed.Theabovestepsareequivalenttothefollowingoptimizationproblem:W?XàXáàáKxj;xjbjàbibjKxi;xjji;je5TàáPàá2PmaxW?UxjbjàbibjUexiTáUxjjAteachpointofxi,Wisde?nedastheWolfedualformofthedistancefromthecenterofthesphereinthefeaturespace.s:t:0 bj C;Pji;jbj?1;j?1;:::;Ne3TfexT?R2exT?kUexTàak2e6TwhereUeáTrepresentsthenonlinearmapping,bjistheLagrangemultiplier,andCisaregularizationconstant.Onlythesamplesthatsatisfytheconstraints0 bj Clieontheboundaryofthesphere.Whenbj?C,thesamplesarelocatedoutsidetheboundary.TheGaussiankernelfunctionisusedtocalculatethedotproductàáUeXiTáUXj:whereR(á)isthedistancefromeachxitothecenterofthesphereandaisthecenterofthesphere.Consideringthekernelde?nition,thefollowingequationcanbeobtained:fexT?R2exT?Kex;xTà2XàXáàáKxj;xbjtbibjKxi;xjji;je7TKexi;xjT?eàqkxiàxjk2e4TwhereqisthewidthparameterandWcanbere-expressedasfollows:Anotablefeatureofthetrainedkernelradiusfunctionisthatthisclusterboundarycanbeconstructedfromasetofoutlinestono^?ReXiTforasup-^2,Rcontainsamplesindataspace:x:fexT?Rportvectorxi.feáTisseparatedintoseveraldisjointedsets:W.Lietal./Engineering5(2019)795–802799??2??no^?x:fexT?R^2?C1[:::[CnLfRe8TwhereCi(i=1,...,n)istheconnectionsetcorrespondingtodiffer-entclusters.Althoughitmaybedif?culttodeterminetheappropriatekernelparametersintheselectionofthemodel,SVChassomeobviousadvantagesoverotherclusteringalgorithms:①Itcangeneratearbitraryclusterboundaryshapes;②ithas?exibleboundarychangestohandleoutliers;and③itavoidsexplicitcalculationsandisthereforeeffectiveforlargedatasets.3.3.ClusteringresultsSupervisedlearningmethodsrequiretrainingsetsandtestsets.Thismethodidenti?estherulesinthetrainingsetandthenusestheserulesforthetestset.Incontrast,unsupervisedlearninghasnotrainingsetortestset;rather,itlooksforrulesonlyinasetofdata.Inthisresearch,thesixkindsofparametersofchargedanddischargedstateinTable2wereusedastheinputvectorstoconducttheclusteringanalysis.Theoutputistheclusteringresults,whichwereveri?edbyperformingexperimentalveri?cation.ThissectionmainlyfocusesontheclusteringanalysisofthedatainTable2.Inthisstudy,wechosevoltage,temperature,andcapacityastheinputs.Ofcourse,researcherscanalsochooseotherparameters,sothischoiceofinputsisjustoneoptionratherthanastandard.Inthispaper,thek-meansclusteringandtheSVCalgo-rithmsareconsidered.IntheSVCapproach,thekernelargumentqandtheregularizationconstantCaresetas0.2and1.2,respec-tively.Inthek-meansclusteringapproach,thenumberofclustersissetas4.TheresultsoftheclusteringanalysisareshowninTable3,wherethecolumnlabeled‘‘un-clustering”representsthecomparisongroupthatisproducedbyrandomlyselectedcellsoutofallthecells.Basedontheclusteringanalysisresults,thechangesinvoltage,temperature,andcapacityinthechargeanddischargeofthenewbatterymodulewerecalculated.Themeandifferenceandstandarddifferencewerecalculatedbythefollowing:Nàá1Xmv?FviàZviNi?1wheremvdenotesthemeandifferenceofthevoltage;FvandZvdenotethefullvoltageandzerovoltage,respectively;Nisthenum-berofcells;andsvdenotesthestandarddifferenceofthevoltage.TheresultsofthemeandifferenceandstandarddifferencearegiveninTables4and5,respectively.AscanbeseenfromTable4,themeandifferencesofthevoltage,temperature,andcapacityinthesortedbatterymoduleareobviouslysmallerthanthoseintheunsortedbatterymodule,indicatingthatthesortedcellsshareasimilarperformance.TheresultsinTables4and5arealsorepre-sentedinFigs.3and4,respectively.FromFig.3,itcanbeseenthattheSVCalgorithmperformedbetterthanthek-meansclusteringalgorithmintheclusteringanalysis,especiallyregardingtempera-turedifference.4.Experimentalveri?cationInordertoverifytheresultsoftheclustering,experimentalveri?cationwasperformed.Astemperatureisthemostimportantparameteraffectingthecapacityandlifeofabatterymodule,ananalysiswasperformedonthetemperatures(performanceparameter)ofthebatterymodulesproducedfromthefourdifferentTable3
Clusteringanalysisresults.ClusteringmethodUn-clusteringk-meansclusteringSVCCellnumber4,7,21,22,23,24,26,27,29,30,42,4418,19,22,23,27,29,37,38,39,45,46,4717,18,21,23,24,27,29,33,35,39,40,41Table4
Meandifferenceofbatterymodule.ClusteringmethodUn-clusteringk-meansclusteringSVCVoltage(V)0.81110.79460.7930Temperature(°C)0.55410.41830.2762Capacity(Aáh)0.00260.00220.0022e9TTable5
Standarddifferenceofbatterymodule.ClusteringmethodVoltage(V)0.03600.01420.0191Temperature(°C)0.53220.36520.2162Capacity(Aáh)0.00250.00130.0014v?????????????????????????????????????????????????uNu1Xàá2FviàZviàmvsv?tNi?1e10TUn-clusteringk-meansclusteringSVCFig.3.Meandifferenceofbatterymodule.
电动汽车锂电池模块设计中相似性能电池聚类的综合方法 - 图文
