FAULTDETECTIONANDIDENTIFICATIONINPERMANENTMAGNETSYNCHRONOUSMACHINESByReemonZakiSaleemHaddadADISSERTATIONSubmittedtoMichiganStateUniversityinpartialentoftherequirementsforthedegreeofElectricalEngineering-DoctorofPhilosophy2016ABSTRACTFAULTDETECTIONANDIDENTIFICATIONINPERMANENTMAGNETSYNCHRONOUSMACHINESByReemonZakiSaleemHaddadPermanentMagnetSynchronousMachinesaresubjecttoavarietyoffailuresinvariouspartsoftheirstructure.Thesefaultscausetandindependentchangestothemotorparametersanditsresponsebehavior.Thisrequirestdetectionandmitigationmeth-odsbasedonthefaulttype,location,andseverity.Therefore,aneefaultdetectionandidenmethodisrequired,notonlytoidentifyifthemotorishealthyorfaulted,buttodetectthefaulttype,separateitfromothers,andestimateitsseverity.Inthisresearch,analgorithmisproposedtodetectandseparatebetweentfaultsinPermanentMagnetSynchronousMachinesundertoperatingconditions.Theincrementalinductanceapproachisproposedwhenthemotoritatstandstill.Thismethodusesthechangesinthemachinesaturation,duetothepresenceoffaults,asafaultindicator.Understeadystateoperation,thechangeinthemachinecommandedvoltagesisproposedasafaultindicator.However,ifthemotorisoperatingatsteadystatewithhightorque,themotorcurrentorvoltagesignatureanalysisisproposed.Themainadvantageoftheproposedmethodisthatitdoesn'trequireanyadditionalhardwarecomponents.Thesamesignalsthatareusedforthecontrollercanbeusedforfaultdetection,separation,andestimation.Theproposedmethodsalsodoesnotrequireacomplicatedsignalprocessingtechniques.Thismakestheproposedmethodsfast,costtandeasytoimplement.ThreecommonfaultsinPermanentMagnetSynchronousMachinesarediscussedinthiswork:staticeccentricity,partialdemagnetizationandturn-to-turnshortcircuitfaults.FiniteElementAnalysissimulationsandexperimentaltesteswerecarriedoutforthreePermanentMagnetSynchronousMachinesunderhealthyandthefaultedconditions.Thebetweenthemotorsarethewindingtopology,theinput/outputpower,andtheslot/polecombination.Themotorisa12poles,72slotswithadistributedwindings,thesecondmotorisa16poles,48slotswithaconcentratedwindings,themachineisa10poles,12slotsfractionalslotsconcentratedwindingmachine.Bothsimulationsandexperimentalresultsshowedthattheproposedmethodswereabletoseparatebetweenthetfaultswithahighlevelofaccuracy.CopyrightbyREEMONZAKISALEEMHADDAD2016IdedicatethisDissertationtothememoryofmybelovedfather,ZakiHaddadwhohelpedduringeverystageofmylife.Aspecialgratitudetomylovingmother,AsmaDababneh,andmyfamilymembers,RwenaHaddad,RamiHaddad,RaniHaddadandRenadaHaddad,whomeunconditionalloveandsupportduringmystudy.Iwouldlikealsotodedicatethisworktomyfuturewife,MingmingZhouherpatienceandsupportwasmyinspirationandmotivation.Thankyouforallthatyoudoandallthatyouare.vACKNOWLEDGMENTSFirstandaboveall,IpraiseGodforprovidingmethisopportunityandforthehealth,abilityandstrengthtobewhereandwhoIamnow.IwouldliketoexpressmyspecialappreciationandthankstomyresearchadvisorPro-fessorEliasG.Strangas,forhissupport,assistance,guidance,andmotivationtopursueandcompletemydoctoraldegree.Also,Iwouldlikethankmygraduatecommittee;Prof.JoseAntoninoDaviu,Prof.SelinAviyente,andDr.ShanelleFoster,fortheirguidanceandsupport.AspecialthankstomyfriendsatMichiganStateUniversity,especiallyintheElectricalMachinesandDrivesLaboratory.IamgratefultohavetheopportunitytomeettheseamazingpeoplewhohelpedmeduringmyPhDstudy.IwouldliketothankCristianLopez-Martinez,RodneySingleton,ThangPham,WilliamJensen,SteveHayslett,Dr.AndrewBabel,Dr.JorgeG.Cintron-Rivera,EduardoMontalvo-Ortiz,ArslanQaiser,MuhammadJawadZaheer,andZaidBataineh.Theirhelp,support,andadvicemadethisworkpossible.IwouldalsoliketothankJordanUniversityofScienceandTechnologywhosupportedmeduringmystudy.Finally,Iwouldliketothankmymotherandmyfamilymembers,whoencouragedmetostartmyPh.Dandcontinuestosupportthroughoutmyfuturegoalsandcarrier.Iwouldhaveneverreachedthispointwithouttheirloveandsupport.viTABLEOFCONTENTSLISTOFTABLES....................................ixLISTOFFIGURES...................................xiChapter1Introduction...............................11.1Motivation.....................................11.2ProblemStatement................................21.3LiteratureReview.................................21.4ProposedMethods................................111.5Organization...................................13Chapter2TheoreticalBackground........................142.1HealthyPMSMModel..............................142.2PMSMUnderEccentricityFaults........................222.3PMSMUnderDemagnetizationFaults.....................282.4PMSMUnderTurn-to-TurnShortCircuitFault................30Chapter3ExperimentalandSimulationSetup................343.1AugmentedFiniteElementAnalysisSimulations................343.2FaultsImplementationinFEA..........................363.2.1ImplementingEccentricityFault.....................363.2.2ImplementingDemagnetizationFault..................363.2.3ImplementingTurn-to-turnShortCircuitFault............373.3ExperimentalSetup................................383.4FaultImplementationExperimentally......................413.4.1ImplementingEccentricityFault.....................413.4.2ImplementingTurn-to-turnShortCircuitFault............423.4.3ImplementingDemagnetizationFault..................43Chapter4TheIncrementalInductanceApproach...............454.1ofIncrementalInductance......................454.2ofFaultsontheIncrementalInductanceCurve.............474.3MethodstoGeneratetheIncrementalInductanceCurve...........484.4ComparisonBetweentheIncrementalInductanceApproaches........504.5SimulationandExperimentalResults......................534.6FaultDetectionandSeparationAlgorithm...................574.6.1k-NearestNeighbor............................594.6.2DiscriminantAnalysis..........................604.6.3MethodologyandResults.................61vii4.7ofParameterVariation..........................64Chapter5TheMC/VSAandLDAApproach........685.1AlgorithmforFaultDetectionandn................695.2SimulationandExperimentalResults......................715.2.1IdentifyingtheFaultType........................735.2.2DeterminingtheFaultSeverity.....................745.2.3ComparingFEAwithExperimentalData................765.2.4ofTemperature..........................81Chapter6TheCommandedVoltagesApproach................846.1VariationsofVdandVqUnderVariousFaults.................846.1.1VdandVqVariationsUnderEccentricityFault.............846.1.2VdandVqVariationsUnderDemagnetizationFault..........856.1.3VdandVqVariationsUnderTurn-to-turnShortCircuitFault.....866.2NumericalAndExperimentalResults......................896.2.1StaticEccentricityFaultResults.....................906.2.2PartialDemagnetizationFaultResults.................916.2.3Turn-to-turnShortCircuitFaultResults................926.2.4ofMagnetAngle..........................956.2.5ofSpeedandTemperature....................1006.3FaultDetectionandSeparationAlgorithm...................1026.3.1ProposedDetectionMethod.......................1026.3.2Implementation......................1066.3.3Results...........................107Chapter7Conclusion................................110BIBLIOGRAPHY....................................112viiiLISTOFTABLESTable1.1Comparisonoffaultdetectiontechniques...............7Table3.1Parametersforthetestedmachines..................36Table4.1resultsfortheconcentratedwindingmachine.....63Table4.2k-NNresultsfortheconcentratedwindingmachine..63Table4.3k-NNresultsfortheconcentratedwindingmachine..64Table4.4k-NNresultsfortheconcentratedwindingmachine..64Table4.5k-NNresultsunderparametersvariation........66Table5.1LDAresultsforfaultdetectionusingFEAresults.(Eachclasscontains11samplescorrespondtospeeds10002000rpm)...74Table5.2LDAresultstodetecttheseverityofstaticeccentricityfaultusingFEAresults.Eachclasscontains11samplescorrespondtospeeds10002000rpm).......................75Table5.3LDAresultstodetecttheseverityofturntoturnshortcircuitfaultusingFEAresults.(Eachclasscontains11samplecor-respondstospeeds10002000rpm)..................75Table5.4ComparisonofLDAresultsbetweenexperimentsandFEAtodetectthefaulttypeforthedistributedwindingmachine.Eachclasscontains11samplescorrespondtospeeds5001000rpm).77Table5.5ComparisonofLDAresultsbetweenexperimentsandFEAfortheconcentratedwindingmachine.Eachclasscontains11samplescorrespondtospeeds5001000rpm).............78Table5.6ComparisonofLDAresultsbetweenexperimentsandFEAtodetectthefaultseverityforthedistributedwindingmachine.Eachclasscontains11samplecorrespondstospeeds5001000rpm).78Table5.7AcomparisonofLDAresultstodetectthefaulttypeforthedistributedwindingmachinebetweenexperimentsandFEAusingthefulltrainingmatrix......................79ixTable5.8AcomparisonofLDAresultstodetecttheseverityofeccentricityfaultforthedistributedwindingmachinebetweenexper-imentsandFEAusingthefulltrainingmatrix.............80Table5.9AcomparisonofLDAresultsforthedistributedwindingmachinefortSNRlevels.Eachclass10containssamplescorrespondtospeeds5501000rpm)..................81Table5.10LDAresultsforfaultdetectionusingFEAresults.Eachclasscontains11samplescorrespondtospeeds10002000rpm)...82Table6.1SimulationandtheexperimentalresultsforVdandVqfortheFSCWmachineundertfaults.....................95Table6.2ComparisonforthesimulationresultsforVdandVqfortheFSCWmachineundertfaultsandoperatingtemperatures.....102Table6.3resultsfortheconcentratedwindingmachine.....108Table6.4resultsfortheFSCWmachine.............108Table6.5Theaverageresultsforallthetestedmachines....109xLISTOFFIGURESFigure1.1ComparisonofthecurrentspectrumofPMSMunderhealthyandtfaultsforfullloadoperation.................4Figure1.2RadialforcespectraofthehealthyandfaultyPMSMunderstaticeccentricityfault.............................6Figure1.3DetectingbrokenmagnetsandeccentricityinPMSM[1].......8Figure1.4DetectingmultifaultsinPMSMusingsearchcoils[2]........9Figure1.5Spectrumofvibrationsignalunderhealthyandtfaults[3].10Figure1.6Proposedalgorithmforfaultdetectionandseparation.........12Figure2.1ComparisonbetweenthetofPMSMbasedonthemagnetplacement..........................15Figure2.2TheequivalentcircuitmodelofPMSMinthedqframeofreference.18Figure2.3modelforPMSMtransformation..............19Figure2.4AcomparisonofthedensitybetweenFEAsimulationandana-lyticalcalculationfortheconcentratedwindingmachine.......21Figure2.5Comparisonbetweenhealthyandeccentricitymachine........23Figure2.6Analyticalapproachtocalculateeccentricity.............23Figure2.7Airgapunderhealthyandeccentricityfault..............24Figure2.8FluxvsMMFunderhealthyandeccentricmachine.........26Figure2.9Comparisonofthemagneticdensitybetweenahealthymachineandtwoseveritiesofeccentricityfault.................27Figure2.10Comparisonofthemagneticunderhealthyanddemagnetizationfault...................................29Figure2.11ComparisonbetweenFEAsimulationandAnalyticalcalculationsorhealthy,onemagnetdemagnetizedand66%eccentricity.......30xiFigure2.12Serieswindingwithshortedturns....................31Figure3.1Geometrycrosssectionforthetestedmachines............35Figure3.2ImplementingshortcircuitfaultinFEAforthedistributedwindingmachine.................................37Figure3.3ImplementingshortcircuitfaultinFEAfortheFCSWmachine..38Figure3.4BlockdiagramoftheFieldOrientedControllerforPMSMs.....39Figure3.5ImplementingeccentricityfaultexperimentallyforthedistributedwindingmachineandtheFSCWmachine...............42Figure3.6Turn-to-turnshortcircuitfaultexperimentally............43Figure3.7Implementingdemagnetizationfaultexperimentally..........44Figure4.1Incrementalinductancecurve......................46Figure4.2onfaultsontheincrementalinductancecurve........48Figure4.3ofrotorposition.........................50Figure4.4Comparisonbetweenthetwomethodstogeneratetheincrementalinductancemethod(FEAsimulation).................51Figure4.5oftheACcurrentamplitude..................52Figure4.6Incrementalinductancecomparisonbetweentheslowrotationmethodandtheconstantspeedmethod.....................54Figure4.7Incrementalinductancevariationundertfaults........54Figure4.8Comparisonbetweensimulationandexperimentalincrementalinduc-tanceresults...............................55Figure4.9ComparisonbetweensimulationandexperimentalresultsfortheFSCWmachine.................................56Figure4.10ThechangeinIdsatunderstaticeccentricityfault..........57Figure4.11Blockdiagramfortheincrementalinductanceapproach.......58Figure4.12featureextractionforkNN..................59xiiFigure4.13incrementalinductanceundertmisaligningangle.......65Figure4.14variationoftheoperatingtemperature.................66Figure5.1BlockdiagramfortheMC/VSAapproach...............70Figure5.2Experimentalresultsforthestatorcurrentharmonicsundererentfaults...................................71Figure5.3ComparisonbetweenthecurrentspectrumfromphaseA,BandCunder12%shortcircuitfault......................72Figure5.4Comparisonbetweenthecurrentspectrumunderhealthyand25%shortcircuitfault............................73Figure5.5Fulltrainingmatrixforhealthycaseandtwofaults(25%eccentricityand12%turnsofphaseAshorted)...................79Figure5.6Trainingmatrixforhealthycaseonly..................80Figure6.1Comparisonofthemagneticdensitybetweenahealthymachineandamachinewith80%eccentricity..................85Figure6.2Comparisonofthelinesbetweenhealthymachineandamachinewithonemagnetfullydemagnetized..................86Figure6.3ShortcircuitcurrentfortheFSCWmachinefortseveritiesofshortcircuitfault.............................87Figure6.4Comparisonofthedensitybetweenahealthymachineandamachinewith20%oftheturnsinphaseAconductorsareshorted..88Figure6.5Theshiftinthecommandedvoltagesunderthetestedfaults....89Figure6.6SimulationresultsforthecharacterizationoftheFSCWmachineun-dertoperatingloadsataspeedof300rpm..........89Figure6.7dandqforhealthyandtseveritiesofeccentricityfaultatI=5Aand=120..........................90Figure6.8SimulationandexperimentalresultsforthechangeinVdandVqforhealthyandtseveritiesofstaticeccentricityfaultatI=5Aand=120...............................91xiiiFigure6.9SimulationsandexperimentalresultsfordandqfortheFSCWmachineunderhealthyand3levelsofdemagnetizationfault(1,2and3magnets)atI=10Aand=120...............92Figure6.10SimulationandexperimentalresultsforthechangeinVdandVqforhealthyand3levelsofdemagnetizationfaultatI=10Aand=12093Figure6.11Simulationsandexperimentalresultsfordandqunderhealthyand2levelsofturn-to-turnshortcircuitfaultatI=10Aand=12094Figure6.12SimulationandexperimentalresultsforthechangeinVdandVqforhealthyand2levelsofshortcircuitfaultatI=10Aand=120.95Figure6.13SimulationandexperimentalresultsforthechangeinVdandVqforhealthyanddtfaultsforI=5A,=120andI=10A,=12096Figure6.14SimulationresultsforthechangeinVdandVqforhealthyandthethreetestedfaultsfortheconcentratedwindingmachineforI=75Aand=120...............................97Figure6.15Singlepolemagnetrotationoftheconcentratedwindingmachine..97Figure6.16Momagnetsfortheconcentratedwindingmachine.......98Figure6.17Comparisonofthelinesfor00and150magnetrotationangleunderdemagnetizationfaut.......................98Figure6.18TheofthemagnetrotationonVdandVqfortheconcentratedmachineunderhealthyanddemagnetizationfault..........99Figure6.19TheofthemagnetrotationonVdandVqfortheconcentratedmachineunderhealthyandeccentricityfault.............100Figure6.20SimulationresultsforthechangeofVdvsVqfortheFSCWmachineunderhealthyandthreetfaultsundertwospeeds300rpm,and500rpm(I=5A;angle=1200andtemp=200C)..........101Figure6.21SimulationresultsforthechangeofVdvsVqfortheFSCWmachineunderhealthyandthreeditfaultsunderthreetemperatures200C,1000Cand1500C(I=5A;angle=1200andspeed=300rpm)101Figure6.22Blockdiagramforfaultdetectionandseparationusingthecom-mandedvoltages.............................103xivFigure6.23Comparisonbetweenactualandestimatedcommandedvoltagesun-dertoperatingconditions...................105xvChapter1Introduction1.1MotivationPermanentMagnetSynchronousMachines(PMSMs)areplayingamajorroleinawidearrayofindustrialandautomotiveapplicationsduetotheirhigh,reliability,wideoperationrange,andtheirhightorquedensity.Theseapplicationsincludepowertractionandsteeringinelectric/hybridvehicles,robotics,householdapplications,powertools,andwindgenerators.ThegrowthofuseofPMSMsinthemarkethasdriventhesemachinestobeexposedtottypesoffaults.FaultsinPMSMscanbeintothreemaincategories:statorfaults,rotorfaultsandbearingfaults.Statorfaultsincludeturn-to-turnshortcircuit,phase-to-phaseshortcircuit,phase-to-neutralshortcircuit,andopencircuitfaults.Rotorfaultsincludeeccentricityanddemagnetizationfaults.Bearingfaultsincludeouterrace,innerrace,andballbearingfaults.Basedontheindustrialandcommercialindustriesreport[4]10%ofthetotalfaultsarerelatedtorotorfaults,37%arerelatedtostatorfaultsand41%arerelatedtobearingfaults.Themainobjectiveofconditionmonitoringinelectricmachinesistocapturethepresenceoffaultsandestimatetheseveritywhileit'sstillintheearlystages.Detectingthemachinehealthstatusandimplementthesuitablemaintenancemethod,inthecaseoffaultedcases,canhelpincreasethemotorreliability,maximizethemachineoperatinglifetime,andreducethemaintenancecost.11.2ProblemStatementFaultsdevelopinrentwaysandcausestchangestothemachineparametersandperformance.Dependingonthefaulttype,severity,andlocation,tdetectionandmitigationmethodscanbeimplemented.Thesemethodscanbecategorizedaseitherinterruptionofthemachineoperationorchangeinthecontrollerscheme.Somefaultsrequireanimmediateactionstobeperformedtothemachine,whileotherfaultsallowthemachinetooperatenormally,ifthefaultseverityislow,untilasafeshutdownisperformedtothemachine.Also,inordertoavoidcatastrophicconsequences,itisimportanttodetectthefaultwhileitisstillintheearlystages.Properearlymaintenancecanbeperformedbeforethefaultexpandsandcausesseveredamage,notonlytothemachinebutalsotohumans.Theworkinthisdissertationisfocusedondevelopinganalgorithmtodetectthemachinehealthstatus(i.e.ifthemachineishealthyorfaulted)undertoperatingconditions,determinethetypeofthefaultandestimateitsseverity.1.3LiteratureReviewSeveralapproacheshavebeenproposedintheliteratureforsinglefaultdetectioninPMSMs.Thesemethodscanbecategorizedas1)themotorcurrentorvoltagesignalanalysis[1,5{11],2)thevibrationornoisesignalsanalysis[12{15],3)modelbasedandanalyticalmethods[16{19],4)temperaturemonitoring,5)monitoring[2],and6)methods[20{22].TheMotorCurrentSignatureAnalysis(MCSA)ortheMotorVoltageSignatureAnaly-sis(MVSA)isthemostcommontechniqueforfaultdiagnosis.Inthisapproach,frequencyanalysisusingFastFourierTransform(FFT)(forsteadystateoperation),ortimefrequency2analysismethodsusingShortTimeFourierTransform(STFT),DiscreteWavelettransform(DWT),ContinuousWavelettransform(CWT),...etc(fornonstationaryoperationcondi-tion)areappliedtothestatorcurrentorvoltagesignals.Featuresusingspharmonicbandcanbeusedasafaultindicator;theamplitudeofthesesignaturesareusedtoestimatetheseverity.ThemainadvantageoftheMCSAisthatitdoesnotrequireanyadditionalhardwarecomponent,thecurrentsignalsarealwaysavailableforthecontrollertomeasure.Inaddition,thismethodisnon-invasiveandcosttive.Thestatorvoltagescanalsobeusedforfaultdetection.Itwasshownin[23]thatifthecontrollerbandwidthislargeenough,thesignatureharmonicsthatappearinthecurrentsignalswillalsoappearinthestatorphasevoltagesignals.Ebrahimietal.[5]proposedusingthespectrumofthemeasuredstatorcurrentfordetect-ingeccentricityfaultsinPMSMs.Thesidebandfrequencypatterngivenby(1.1)isproposedasaneccentricityfaultssignatures.Theappearanceofthissidebandpatterninthecurrentspectrumcanbeusedasafaultindicate,andtheamplitudeofthesidebandcomponentscanbeusedtoestimatethefaultseverity.Astheseverityofeccentricityfaultsincrease,theamplitudeofthesidebandharmonicswillalsoincrease.fecc=12K1Pfs(1.1)wherePisthenumberofpolepairs,K=1;2;3;:::,andfsisthestatorcurrentfrequency.Itwasnoticedthatinthecaseofdynamiceccentricityfault,theamplitudeofthesidebandcomponentswerehighercomparedtothecaseofstaticeccentricityfault.Thiswasproposedasanindicatortoseparatebetweenthetwotypesofeccentricityfaults.ThesameapproachwasappliedtodetectshortcircuitfaultinPMSM[7].Thesidebandcomponentsofthe3statorcurrentspectrumgivenby(1.2)wereusedasanindicatortodetectshortcircuitfault.Similartothecaseofeccentricityfaults,theamplitudeofthesidebandcomponentswasusedtoestimatetheseverity.fsho=12K+1Pfs(1.2)Fig.1.1showsacomparisonofthenormalizedstatorcurrentspectrumunderhealthyandfaultedPMSM.Fig.1.2a,andFig.1.2bshowthechangeinthecurrentspectrumunderhealthyandtseveritiesofstaticanddynamiceccentricityfaults.Fig.1.1c,andFig.1.1dshowsthechangeinthespectrumofthestatorcurrentsignalunderhealthyandtseveritiesofshortcircuitfaultunderfullloadoperation.(a)Currentspectrumforhealthyandeccentricityfaults[5](b)Currentspectrumfortseveritiesofdynamiceccentricityfault[5](c)Currentspectrumforhealthyandshortcircuitfault[7](d)Currentspectrumfortseveritiesofshortcir-cuitfault[7]Figure1.1ComparisonofthecurrentspectrumofPMSMunderhealthyandtfaultsforfullloadoperation4Theincreaseinthesidebandharmonicsgivenby(1.1)canbeobservedinthecaseofeccentricityfaultandtheincreaseintheamplitudeofthesubharmonicsgivenby(1.2)canbenotedinthecaseofshortcircuitfault.Thisindicatethatthesesubharmonciscanbeusedtodetectthefaultandestimatetheseverities.[24]isareviewpaperthatdescribesthettypesoffaultsandthefrequencysignatureseachfaultgenerateandthediagnosticsschemes.Themainchallengeofusingthecurrentspectrumisthatthefaultsignaturesdependonthemachineoperatingspeedandload;atlowerspeedsitisdtodetectthesesidebandpatterns[25].Also,itwasshownin[26]and[27],thattherelationbetweenthenumberofpolesandthestatorslotstheappearanceofthestatorcurrentsubharmonicsinthecaseofeccentricityfaults.Allthesereasonstheaccuracyofthismethodasanaccuratefaultdetectionandestimationmethod,sincethatPMSMshavettopologies,slot/polecombinations,andwillberunningattoperatingconditions.In[1,6,9{11]timefrequencyanalysistechniqueslikeWaveletTransform,WignerDistribu-tionandZhao-Atlos-MarksDistributionwereappliedfordetectingseveralfaultinPMSMs.Eventhotheyarecapableoffaultsdetectionundertransientoperation.However,thesemethodsrequireadditionalhardwarecomponentsandmorecomplexsoftware.Thiswillincreasethetotalcostandthecomputationaltime.ThenoiseandvibrationsignalsarealsowidelyusedforfaultdetectioninPMSMs.Faultscauseanincreaseinthemagneticpullforce,whichincreasesthemagneticstressactingonthestator.Themagneticstressisproportionaltothesquareofthemagneticuxdensity.There-fore,anychangeinthemagneticdensityisinthenoiseandvibrationsignalsinthemachine.ByanalysingthevibrationsignalusingFFToranyofthetime-frequencyanalysismethods,faultsignaturescanbeextractedforfaultdetectionandseparation.In[15]thesidebandcomponentsofthevibrationspectrumgivenby1.3wereproposedfordetecting5eccentricityfaultsinPMSM.fecc=1KPfs(1.3)Fig.1.2showstheradialforcespectrumforhealthyandfaultedconditionsofPMSMunderunderstaticeccentricityfault.(a)Healthymachine[15](b)30%staticeccentricityfault[15]Figure1.2RadialforcespectraofthehealthyandfaultyPMSMunderstaticeccentricityfaultTheincreaseinthesubharmonicscomponentsgivenby1.3canbeobservedinthecaseofeccentricityfault.Themaindrawbackofusingthevibrationsignalsisthatitrequirestheinstallationofanoiseandvibrationsensoronthemotorsurface,whichmightbeexpensiveandnotalwayspossiblebasedonthemachineplacement.Alsothecorrespondingnoiselevelofthemachineisbythemachineoperatingloadandspeed.Analyticalapproachesandonlineparameterestimationtechniqueshavetheadvantageofobtaininganaccuratedetectionresultswhilethemotorisoperatingattoperatingconditions.However,thesetechniquesrequireanaccuratemodelforthemotor.Thismodelshouldaccountsforthemanufacturingandtheenvironmentalvariationsofthemachine.Ontheotherhand,someparameterestimationtechniquesmayrequireaheavycomputationtime,whichincreasesthecostandmakesthesystemmorecomplex.Othermethodshave6Table1.1ComparisonoffaultdetectiontechniquesDetectionTypesoffaultDrawbacksmethodsEccentricityStatorfaultDemagnetizationCurrent/DependontheVoltagespeedandloadNoise/ExtracomponentVibrationandcostAnalytical/accuratemodelParameterest.requiredTemperatureDependontheloadandspeedFluxadditionalmonitorcomponentsStandOnlyatstillstandstillbeenproposedforfaultdetectionwhenthemotorisatstandstill[20,21].Thesemethodscanbeappliedforascheduledcheckforthemotor,andtheyrequireasptesttobeappliedtothemotor.Table.1.1summarizesthemostcommondetectionmethodsandthetypesoffaultseachmethodcandetect.Afewmethodshavebeenproposedtoseparatebetweentfaults.Rouxetal.[1]proposedamethodtoseparatebetweeneccentricityfaults(staticanddynamiceccentricity)andbrokenmagnetsinPMSMs.Itwasshownthatdynamiceccentricitycanbedetectedusingtheamplitudeofthecurrentsidebandharmonicsgivenby(KPfs),andstaticeccentricitycanbedetectedusingthechangeintheamplitudeofthe5thand7thharmonicsofthenegativesequencecurrentintheabcframeofreference.Brokenmagnetscanbedetectedbycomparingtheestimatedmagneticlinkageandtheactualmagneticlinkage.Themagneticlinkagewasestimatedusingtheoperatingspeed,themeasuredvoltagesandcurrentsasfollows:edpm=vqrsiq!rLdid(1.4)7wherevqistheq-axisvoltage,rsisthestatorresistance,iqistheq-axis!ristheelectricalspeed,Ldisthed-axisinductance,andidisthed-axiscurrent.Fig.1.3ashowsthecurrentfaultfrequencycomponents(0:5=1PharmoniccomponentswherePisthenumberofpolepair)ofaPMSMunderhealthy,brokenmagnetsandeccentricityfaultatdtoperatingconditions.Fig.1.3bshowsacomparisonofthe7thharmonicofthestatorcurrentbetweenhealthyandstaticeccentricityfaultattoperatingconditions.Fig.1.3cshowsacomparisonbetweentheestimatedmagneticlinkagesforhealthyandtfaultsundertoperatingconditions.(a)Dynamiceccentricitydetection(b)Staticeccentricitydetection(c)BrokenmagnetsdetectionFigure1.3DetectingbrokenmagnetsandeccentricityinPMSM[1]Forthismethod,abaselinemeasurementforthemachineneedtobeconductedDuringnormaloperationofthemachine,themachinestatorcurrents,phasevoltages,andspeedneedtobemonitoredonlinecontinuouslyandtheestimatedxiscomparedwiththebaselinemeasurements.Atchangeinthefaultharmonicsofthestatorcurrentoradecreaseintheestimatedmagneticlinkagecanbeusedasafaultindicatortodetectthefaulttype.Thestatorcurrentspectrumwasalsousedtoseparatebetweeneccentricityandbrokenmagnetsin[28].Itwasshownthattheincreaseinthe0:75th(i.e.11=P)harmonicwasmoreobservedinthecaseofeccentricityfault,whiletheincreaseinthe0:5th8andthe0:25th(i.e.12=P,and13=P)weremoredominantinthecaseofbrokenmagnets.Themaindrawbackofthismethodisthatitrequirestindicatorsforfaultdetection,alsothedetectionisbasedontheharmonicsamplitudes.Theseharmonicsarenotalwayspossibletonotice,astheyvarywiththemachinegeometryandtheoperatingconditions.In[2]theinducedvoltagesthroughsearchcoilsareusedformonitoringthehealthstatusofPMSM,andformultifaultsdetection.Asearchcoilwaswoundaroundeacharmaturetooth,andtheinducedvoltagesweremonitoredduringnormaloperations.Thefundamentalfrequencycomponentofthemeasuredvoltageswereextractedfromeachcoilandwereusedforfaultdetectionandseparation.Fig.1.4showsacomparisonofthecomponentofthemeasuredvoltagesfromeachsearchcoilunderhealthyandthreetfaults(staticeccentricity,shortcircuit,anddemagnetizationfaults).(a)Fieldcomponentunderstaticeccentricity(b)Fieldcomponentundershortcircuitfault(c)Fieldcomponentunderdemagne-tizationFigure1.4DetectingmultifaultsinPMSMusingsearchcoils[2]Achangeintheinducedvoltagescanbeusedasafaultindicatorinthemachine.Basedonthechange,thefaulttypecanbedetectedandtheseveritycanbeestimated.Themethodwasabletoseparatebetweentfaults,alsoitwascapableofdetectingthedirectionofeccentricityfaultandthelocationofinter-turnshortcircuitfault.Themaindrawbackforthismethodistheneedforaddingasearchcoilateverystatortoothduring9themanufacturingofthemachine,whichmaybeexpensiveandnotalwayspossible.Theworkin[13]presentsastudyofdttimeandfrequencyindicators,extractedfromvibrationsignals,fordetectingeccentricityanddemagnetizationfaultsinPMSM.Itwasshownthatthecombinationoftheskewnessandthemedianfrequencyofthevibrationsignal,canbeetodecidewhateverthemachineishealthyorfaulted,andtoidentifythetypeofthefaultifexisting.[3]studiedvibrationaccelerationtodetectandseparatedemagnetizationfrominter-turnshortcircuitfaultsusingbothmodeshapeandvibrationfrequencyinformation.ByanalyzingthevibrationsignalusingFFT,thechangeinthespectrumwasusedtodetectandseparatethetwofaults.Fig.1.5showsacomparisonofthevibrationspectrumforPMSMunderhealthy,partialdemagnetization,andinter-turnshortcircuitfault.(a)Healthymachine(b)Partialdemagnetizationfault(c)Inter-turnshortcircuitfaultFigure1.5Spectrumofvibrationsignalunderhealthyandtfaults[3]Inthecaseofdemagnetizationfault,vibrationaccelerationappearsatlowfrequencyregionasshowninFig.1.5b.Inthecaseofshortcircuitfault,thevibrationaccelerationspectrumisspreadoverthefrequencyrangeasnoticedinFig.1.5c.ThischangeinthespectrumcanbeusedasanindicatortodetectthepresenceandthetypeofthefaultinPMSM.Themaindrawbackofthisapproachisthatusingthevibrationsensorsiscostly.Also,theoperatingconditionandtheplacementofthemotorthevibrationsignal,whichmighttheclarityofthedetectionapproach.10Hongetal.[20]proposedanmethodtoseparateeccentricityfromdemagnetizationfaultsinPMSMs.Thismethodisbasedonthechangeinthemachinesaturation,whichisintheincrementalinductancecurve.Thismethodhastheadvantageofusingtheinvertersignalsforfaultseparation,whichremovethenecessityofaddinganewhardwarecomponents.Thismethodwillbediscussedinmoredetailsinchapter4.There,itisalsoimplementedtodetectinter-turnshortcircuitfault,besidedemagnetizationandeccentricityfaults.Aalgorithmisproposedtoestimatethefaultseverityafterdeterminingthefaulttype.ThetmethodsforhealthmonitoringinPMSMs,andthetfaultdiagnosisandprognosismethodsarereviewedin[29].Sofar,thereisnosingleeapproachtoseparatebetweendtfaults.Mostofthemethodsintheliteratureareonlyapplicableunderspoperatingconditions,orcanbeappliedtoasptypeandtopologyofPMSMs.1.4ProposedMethodsThisworkproposesanalgorithmforfaultdetectionandideninPMSMsbasedonthemachineoperatingcondition.ThebasicwchartoftheproposedalgorithmissummarizedinFig.1.6Theproposedalgorithmisbasedonthemachineoperatingstatus.Ifthemachineisatstandstill,theincrementalinductancemethodisproposed.Inthismethod,thechangeoftheincrementalinductancecurve,duetothechangeinthemachinesaturation,isusedasafaultindicator.Thedirectionoftheshiftintheincrementalinductancecurvepeaksandthechangeofthepeaksamplitudeisusedtodetectthefaulttypeandestimatetheseverity.11StartStandstill?HighI?IncrementalinductanceMCSA/LDAVdandVqnoyesyesnoFigure1.6Proposedalgorithmforfaultdetectionandseparation.Thismethodcanalsobeappliedasalaststepinamanufacturinglinetocheckthemachinehealthstatus.Ifthemotorisoperatingatsteadystate(i.e.constantspeedandload),thechangeinthecommandedvoltagescanbeusedforfaultdetection.Theshiftdirectionofthecommandedvoltagesisusedtodetectthefaulttype,andtheamountoftheshiftisusedtoestimatethefaultseverity.However,ifthemachineisoperatingathightorque,itistodetecteccentricityfaultsusingthecommandedvoltagesapproach.Here,theMotorCurrentorVoltageSignatureAnalysis(MCSAorMVCA)methodwiththeLinearDiscriminantAnalysis(LDA)isproposedforfaultdetectionandseparation.Thismethodisbasedonthevariationintheamplitudeofthestatorcurrentorvoltagespectrumtogeneratethefaultsignatures.Themaingoaloftheproposedalgorithmistoavoidtheneedofanyadditionalhardwarecomponents.Thesamesignalsthatareusedforthecontrollerwillbeusedfordetectingthefaulttypeandestimatingitsseverity.121.5OrganizationChapter2presentsthetheoreticalbackgroundandmodelingforPMSMunderhealthyandfaultedconditions.Themodelforthedqmathematicalmodelforthemachinewillbeusedasthebasicmodelfortheproposeddetectionandestimationmethods.Ananalyticalapproachisalsodiscussedtocalculatethemagneticdistributionforbothhealthyandfaultedconditions.Chapter3showsthegeometrymodelandtheparametersforthetestedmachines.ItalsoshowshoweachfaultwasimplementedinFEAandexperimentally.Chapter4-6arethecorechaptersforthiswork.Theydiscussthethreeproposedap-proachesforfaultdetectionandestimation.Chapter4discussestheincrementalinductanceapproach;howtheincrementalinductancecurveisgenerated,theofeachfaultontheincrementalinductancecurve,andtheproposedalgorithmthatusesitforfaultdetection.Chapter5talksabouttheMCSAandtheMVSAusingtheLDAasamethod.Chapter6discussestheshiftinthecommandedvoltagesapproach.Itshowshowtousethecommandedvoltagesasaneasyandewaytodetectthemachinehealthstatusandestimatethefaulttypeandseverity.FinallyChapter7bringstheconclusionsofthisthesis.13Chapter2TheoreticalBackground2.1HealthyPMSMModelAPMSMisamotorthatusespermanentmagnets,insertedintherotor,toproducetheairgapmagneticxdensity.Thisgivesthesemachinestheadvantagesofhavingahightorquedensityandawideoperatingrangeusingtheweakening.PMSMscanbebasedonthedirectionoftheintotwomaincategories[30];ifthedirectionisalongtheradiusofthemachine,themotoriscalledradialPMSM.Ifthedirectionisparalleltotherotorshaft,themotoriscalledaxialPMSM.PMSMscanalsobecategorizedbasedontheplacementofthemagnetsintherotor.Ifthemagnetsarepositionedonthesurfaceoftherotoroutersurface,themotoriscalledSurfaceMountedPMSM(SPMSM).Ifthemagnetsarepositionedinthegroovesoftheouteredgeoftherotor,themotoriscalledSurfaceInsetPMSM(SIPMSM).Ifthemagnetsarepositionedinthecenteroftherotorlaminations,themotoriscalledInteriorPMSM(IPMSM).Fig.2.1showsthethreetofPMSMbasedonthemagnetplacement.ForSPMSMs,allthemagnetsareindirectcontactwiththeairgap,allowingthemtohavethemaximumairgapdensity.However,thispositionforthemagnethaslowerstructurerobustness,whichmakesthesemachinessuitableonlyforlowspeedoperation.InthecaseofSIPMSMsthemagnetsareinsertedinsidetherotorallowingmoremechanicallyrobuststructure,whichmakesthesemachinesmoresuitableforhighspeedoperation.IPMSMs14havethemostmechanicallyrobuststructure,thatiswhythesemachinesareusedforveryhighspeedapplications,buttheyarehardertobemanufactured.GenerallyinPMSM,twoaxesareintherotor:adirectaxis(d-axis)andaquadratureaxis(q-axis).Thed-axisistherotormagnetaxisandthepathfortheisthroughthemagnet.Theq-axisis90electricaldegreesfromthed-axis,thepathoftheisthroughtheironlaminationsonly(elect:deg:=mech:degP).Fig.2.1alsoshowstherotord-axisandtheq-axisforeachrotortype.(a)SurfaceMountedPMSM(b)SurfaceInsetPMSM(c)InteriorPMSMFigure2.1ComparisonbetweenthetnsofPMSMbasedonthemagnetplacementThisworkisfocusonabalancedthreephaseIPMSMswithwyeconnectedstatorwinding,thisisoneofthemostcommonforPMSMs.ForabalancedthreephasePMSM,thestatorvoltages,inthestatorframeofreference(alsoknownastheabcframeofreference),isgivenby(2.1)-(2.3):va=Raia+Laddtia+Mabddtib+Macddtic+!ea(2.1)vb=Rbib+Labddtib+Mbaddtia+Mbcddtic+!eb(2.2)vc=Rcic+Lcddtic+Mcaddtia+Mcbddtib+!ec(2.3)15whereva,vb,andvcarethethreephasestatorvoltages,Riisthestatorresistanceforphasei,Liistheselfinductanceforphasei,Mijisthemutualinductancebetweenphaseiandphasej,ia,ib,andicarethethreephasestatorcurrents,!eistheelectricalspeed,a,b,andcrepresentthestatorlinkagesgeneratedbytherotormagnets.Forabalancedthreephasesinusoidala=pmsin(),b=pmsin(1200),andc=pmsin(+1200).Tosimplifythemachinemathematicalmodel,Park'stransformationisusedtotransformthemachinemodelfromthestatorthreephaseabcquantitiestotherotortwophasedqquan-tities.Thistransformationisappliedintwostages,thestatorthreephasequantitiesgivenby(2.1)-(2.3)istransformedtotheequivalentstatorspacevector(;)componentsusingClark'stransformation.Second,the(;)componentsarerotatedtotobealignedwiththerotordqaxes.Park'stransformationcombinedbothclack'stransformationandtherotationmatrix.Thetransformationisappliedasfollow:xdq0=Pa:xabc(2.4)wherexisthevariabletobetransformed,andPaisPark'stransformationmatrixwhichisgivenby:Pa=2666664cos()cos(2ˇ3)cos(+2ˇ3)sin()sin(2ˇ3)sin(+2ˇ3)1212123777775(2.5)where()istherotorposition.Itisimportanttonotethatthetransformationisinvertible,theinverseofPark'stransformationmatrixcanbeusedtotransformbackthemachinemodel16fromthedqframeofreferencetotheabcframeofreferenceasfollow:xabc=P1a:xdq0(2.6)whereP1aistheinverseofPark'stransformationmatrixatitisgivenas:P1a=232666664cos()sin()1cos(2ˇ3)sin(2ˇ3)1cos(+2ˇ3)sin(+2ˇ3)13777775(2.7)Byapplyingthetransformationmatrix(2.5)to(2.1)-(2.3),thePMSMmodelinthedqframeofreferenceisgivenby(2.11)-(2.10).Therotorpositionangle()iseitherobtainedusingarotorpositionsensororitcanbeestimated.Whenthemotorisrotatingatasynchronousspeed,thedqquantitiesbecomeDCquantitiesintherotorframeofreference.TheequivalentcircuitmodelisshowninFig.2.2.vd=rsid+Lddiddt!eLqiq=rsid+ddt!eq(2.8)vq=rsiq+Lqdiqdt+!eLdid+!epm=rsiq+qdt+!ed(2.9)d=Ldid+pm(2.10)wherevdandvqarethedirectandquadratureaxisvoltages,idandiqarethedirectandquadratureaxiscurrents,rsisthestatorresistance,dandqarethedirectandquadraturelinkageLdandLqarethedirectandquadratureinductances,andpmisthemagnet17+vdidRsLd+!ed(a)d-axisequivalentcircuit+vqiqRsLq+!ed(b)q-axisequivalentcircuitFigure2.2TheequivalentcircuitmodelofPMSMinthedqframeofreferencelinkage.Understeadystateoperation(themotorisrotatingataconstantspeedandtorque),thedqquantitiesbecomeDCquantities.Inthiscasethetimevaryingcomponentsdiddtanddiqdtwillbeequaltozero.InthiscasethemathematicalmodelforPMSMinthedqframeofreferenceatsteadystateoperationisasfollows:vd=rsid!eLqiq(2.11)vq=rsiq+!ed(2.12)Thetorqueisproducedfromtheinteractionbetweenthelinkagesandandthecurrentineachaxisasfollow:T=3P2(diqqid)=3P2(pmiq+(LdLq)idiq)(2.13)AbetterrepresentationofthemachinemodeltransformationisshowninFig.2.3.Inthisorientation,thelinkageduetothemagnets(pm)isalignedwiththedaxis.Theqaxisis90electricaldegreecounterclockwisefromthedaxis.Thetorqueisproducedmainlybytheqaxiscurrent,sincethatitisperpendiculartothemagnet(pm),whileidisusedtocontroltheamountoftheBycontrollingthecurrentmagnitude(Is)andthecurrent18angle(),thegeneratedtorquecanbecontrolled.(a)SpacevectordiagramforPMSM(b)ThreephasewindingtransformationFigure2.3SimplmodelforPMSMtransformationItisimportanttonotethatthismodelassumesthatthestatorresistance,andselfinductanceforallthreephasesarethesame(i:e:Ra=Rb=Rc=rs,La=Lb=Lc).Thismodelalsodoesnotaccountforironlosses,norfortheselfandcrosssaturationbetweenthestatorthreephases.However,itstillrepresentsthemachinebasiccharacteristicsandperformanceaccurately.ItisimportanttonotethattheproposedmethodsarealsoapplicableforallthettypesofPMSM.Therefore,thismodelwillbeusedasthereferencemachinemodelforthiswork.Toprovideabetterunderstandingofthemachinemodel,andthechangeinthemachineparametersundertfaultscomparedtothehealthycase,ananalyticalapproachforcalculatingthemotormagneticdensityisrequired.Zhuetal.in[31{34]proposedananalyticalapproachtocalculatetheairgapmagneticuxdensity,forasurfacemountBrushlessPermanentMagnetDCmotors.Basedontheiranalysis,thetotalmagneticdensitycanbecalculatedbyaddingthemagneticdensityfromthemagnets(Brm(r;))[31]tothemagneticdensitygeneratedfromthewinding(Brw(r;))[32],takingthe19slotting(~(r;))[33]intoaccountasfollow:Br(r;)=(Brm(r;)+Brw(r;)):~(r;)(2.14)Onlytheairgapmagneticdensityduetothemagnetsisofinterestforthiswork,sincethatitisdirectlyrelatedtothemotorgeometryanditwillbedirectlybythepresenceoffaultsinthemachine.Theradialcomponentofthemagnetsdensityatthestatorinnersurface(r=Rs)(withouttakingintoaccounttheslotsopeningorthemagneticdensityfromthestatorwinding)isgivenby(2.15)whennp=1Brm()=1Xn=1;3;5;:::2:0Mnr:np(np)21RsRmnp1:24(np1)R2npm+2Rnp+1rRnp1m(np+1)R2nprr+1r[R2npsR2npm]r1r[R2npmR2nps(RrRm)2np]35:cos()(2.15)Fornp6=1theradialcomponentofthemagneticdensityisgivenby(2.16)Brm()=0M1r:2664RmRs2RrRs2+RrRs2lnRmRr2r+1r1RrRs2r1rRmRs2RrRm23775:cos()(2.16)where0isthepermeabilityoffreespace(0=4ˇ107),ristherelativecoilpermeability,Rr=Rsghm,Rm=Rsg,Rsistheinnerstatorradius,gistheairgaplength,hm20isthethicknessofthemagnet,andMnisgivenby:Mn=2r0psinnˇp2nˇp2(2.17)whereristhemagnetremanence,andpisthepolearctopolepitchratio.Theairgapmagneticforeachphasecanbecalculatedbyintegratingnumericallythetotalmagneticdensityovertheentireareaas:=Z2ˇ0Zr0Br(r;)rdr(2.18)Fig.2.4showsacomparisonofthemagneticdensitycalculatedanalytically(withouttakingtheslottingintoaccount)andusingFiniteElementAnalysis(FEA)forathreephaseconcentratedwindingIPMSM.Figure2.4AcomparisonofthedensitybetweenFEAsimulationandanalyticalcalcu-lationfortheconcentratedwindingmachineThebetweenanalyticalcalculationsandFEAisduetothefactthatthean-alyticalcalculationsproposedin[31]wereapplicabletoasurfacemountPMBrushlessDCmachine,whilethetestedmachineisanIPMSM.212.2PMSMUnderEccentricityFaultsEccentricityisaconditionofanunevenairgapbetweenthestatorandtherotor.Thisleadstoanasymmetricairgapdistribution,whichcreatesanunbalancedmagneticpullcausingvibrations,noise,andpossiblywearofthebearings.Bytimetheunbalancedmagneticforcemayfurtherincreaseandcausetherotorandthestatortorub.Eccentricityfaultscanbeintothreemaintypes:staticeccentricity,dynamiceccentricity,andmixedeccentricity.Inthecaseofstaticeccentricity,thecenterofthestatorgeometricaxisistthanthatoftherotorandtherotationaxis.Thiscouldbecausedbyanincorrectrotorstatoraligningduringtheassemblyofthemachineorduetothetmechanicalandelectricalstressesappliedtothemachine.Inthecaseofdynamiceccentricity,thecenteroftherotorgeometricaxisistthanthatofthestatorandtherotationaxis.Themainreasonsfordynamiceccentricityinclude:abendinthemachineshaft,bearingwear,mechanicalandthermalstressesappliedtotheshaft,andmechanicalresonanceatcriticalspeed.Inthecaseofmixedeccentricity,therotationaxisistthanthestatorandtherotorgeometricaxes.Thistypecombinesbothstaticanddynamiceccentricities.Fig.2.5showsacomparisonofthecrosssectiongeometrybetweenhealthymachineandthethreettypesofeccentricityfaults.Onlystaticeccentricityisdiscussedandtestedforthisworkbecauseitisthemostcommontypeofeccentricity.Inthecaseofstaticeccentricity,theairgaplength(g)in(2.15)and(2.16)willnolongerbesymmetric,itdependsontherotorposition.BasedonFig.2.6andfollowing[35],ageneralformulafortheairgap,inthecaseofstaticeccentricity,canbederivedasfollows:Rs:cos(0)="cos(˚)+(Rm+gecc)cos()(2.19)22(a)Healthymachine(b)Staticeccentricity(c)Dynamiceccentricity(d)MixedeccentricityFigure2.5ComparisonbetweenhealthyandeccentricitymachineFigure2.6Analyticalapproachtocalculateeccentricity23Rs:sin(0)="sin(˚)+(Rm+gecc)sin()(2.20)Takingthesquareof(2.19)and(2.20),andaddingthemtogetherisgivenas:R2s="2+(Rm+gecc)2+2"(Rm+gecc)cos(˚)(2.21))gecc="cos(˚)qR2s"2sin(˚)2Rm(2.22)SinceRs˛",theairgapincaseofstaticeccentricityisgivenby:gecc=(RsRm)"cos(˚)=g"cos(˚)(2.23)Fig.2.7showsacomparisonoftheairgapbetweenhealthymachineandamachinewitheccentricityfault.Figure2.7Airgapunderhealthyandeccentricityfault24Theseverityofeccentricityfaultisexpressedasfollowing:ECC=g100%(2.24)Thechangeintheanalyticalcalculationforthemagneticdensityundereccentricityfaultcanbestudiedbyreplacingtheairgapin(2.15)&(2.16)thenewairgapgecc.Itisimportanttodetecteccentricityfaultswhileitisstillintheearlystage.Withtime,theunbalancedmagneticforcebetweentherotorandthestatormayfurtherincreasecausingtherotorandthestatortorub,whichwillcauseaseveredamagetothemachine.[36]studiedtheofrotoreccentricityontheUnbalancedMagneticPull(UMP)forlargeSynchronousMachineswithPermanentMagnetsSynchronousMachinesandWindingFieldsSynchronousMachines.Accordingto[37],anyeccentricitylessthan10%canbeneglected,andanyeccentricityhigherthan60%requiresimmediaterepairtopreventanyrubbingbetweenthestatorandtherotor,whichwilldamagethemachine.Staticeccentricityfaultcausesachangeintheairgaplength,whichcasesachangeinthereluctance.Changingthereluctancecausesachangeinthetotallinkagesaroundtheairgapcausingachangeinthemachinesaturationlevel.Themachinelinkagesandtheairgaplengtharerelatedbythemachinereluctanceasfollows:R=g0Ag(2.25)˚=FR(2.26)whereAgistheairgaparea,Risthereluctance,Fisthemagnetomotiveforce,and˚isthemagneticTheareawithlowerairgapwillhavelowerreluctanceandthereforehigher25concentration.Thiscauseshighersaturationinthatregion.Ontheotherhand,theareawithhigherairgaplengthwillhavehigherreluctanceandthereforelowerconcentration.Thiscauseslowersaturationinthehigherairapregion.Inthecaseofidealmachine,theamountoftheincreaseinthelinkageswillbeequaltotheamountofthedecreaseinlinkage,whichaveragethetotallinkagesinthemachine.However,duetothenonlinearityandthesaturationinthemachine,theincreaseinthemagneticatthesmallestairgapregionwillbehigherthanthedecreaseofthemagneticinthelargestairgapregion.Thisincreasesthetotalmagneticcausingthemachinetosaturatefasterinthecaseofeccentricityfaultcomparedtothehealthycase.ThiscanbeexplainedusingthevsMagnetomotiveForce(MMF)curveofthemachine.Fig.2.8showsthevsMMFcurveunderhealthycaseandeccentricityfault.Figure2.8FluxvsMMFunderhealthyandeccentricmachineTheareawiththelowerairgapregionwillcauseanincreaseintheslopeofthecurve,whiletheareawithhigherairgapwilldecreasetheslopeofthecurve.Duetothesaturationandthenonlinearityinthemachine,theaverageofthetwocurveswillbehighercomparedtothehealthymachinecurve.Therefore,themachineundereccentricityfaultsaturatesfaster,andatanyoperatingpoint,thetotallinkagesinthemachinewillbehighercompared26tothehealthycase.Fig.2.9bshowstheFEAsimulationresultsforthemaximumofthemagneticdensitymeasuredatthecenterofeachpolepairfortheFSCWmachine(themachineparametersisinTable3.1)underhealthyandtwoseveritylevelsofstaticeccentricityfault(40%and80%).Fig.2.9cshowsthevectorsummationofthexandycomponentofthemagneticforallthepolepairsunderhealthyandfourseveritiesofeccentricityfault.(a)Testedmachine(b)Maximumofthemagnetic(c)AverageoftheXandYcompo-nentsFigure2.9ComparisonofthemagneticxdensitybetweenahealthymachineandtwoseveritiesofeccentricityfaultItcanbenotedthatforhealthymachine,thevectorsummationinthexandycomponentsequaltozero.Thisisexpectedsincethatthemachineishealthyandthedistributionoftheairgaplengthandthemagneticisuniformaroundthemachine.However,foreccentricmachine,thesumwillnolongerbeequaltozero.Itwillbehighercomparedtothehealthymachine,andtheamountoftheincreaseisproportionaltotheseverityofthefault.Asthefaultseverityincreases,thetotalsummationwillincreasecausingmorelinkages.Itcanalsobenoticedthatthemainincreaseisinthexaxisbecausetheshiftoftherotorandtherotationaxiswasinthepositivexdirection.272.3PMSMUnderDemagnetizationFaultsDemagnetizationisalsoacommonrotorfaultinPMmachines.Thedemagnetizedmag-netswillcauseasymmetricdistributionofthedensity,whichcausesareductioninthetotalpermeanceinthemachine.Thisreducestheaveragetorque,increasethetorquerippleandreducethemotor.Themainfactorthatcausedemagnetizationfaultsisturn-to-turnshortcircuitfault,astheseverityofshortcircuitfaultincreases,ahighercurrentwillwintheshortedturns,thiscurrentwillweakenthemagnetsandbytimewillleadtodemagnetizingtherotormagnets.Otherfactorsthatmightcausedemagnetizationfaultinclude:theagingofthemagnet,hightemperature,andoperationunderstrongweakening.Demagnetizationfaultscanbeintotwomaintypes:uniformdemagnetizationandpartialdemagnetization.Inthecaseofuniformdemagnetization,allthemagnetsintherotoraredemagnetized.Inthecaseofpartialdemagnetization,onlyaspnumberofmagnetsaredemagnetized.Inthecaseofpartialdemagnetizationfault,anonuniformmagneticdensitygeneratesintheairgap,whichcausesadisturbancetothemagneticinthemotorandreductioninthetotalmagneticdensity.Theofdemagnetizationcanbenotedwheneverthedemagnetizedmagnetsinteractwiththestatorslots.Thiscanbeclearlyobservedinthecaseofsinglelayerfractionalslotsconcentratedwindingmachines.Fig.2.10showsacomparisonofthemagneticlinkagesofphaseAoveronemechanicalcycle,underhealthyanddemagnetizationfault(Mag1oftheFSCWmachinewasfullydemagnetized).Demagnetizationfaultsthesaturationofthemachine,butinanoppositewaycomparedtoeccentricityfaults.Thedemagnetizedmagnetswillcauseareductioninthe28Figure2.10Comparisonofthemagneticunderhealthyanddemagnetizationfaulttotalmagneticlinkages,whichreducesthetotalsaturationofthemachine.Inthiscase,themachinerequiresmorecurrentsinordertohavethesamesaturationasthehealthymachine.Foranalyticalcalculations,thesameanalyticalapproachthatwasusedforhealthymacinecanalsobeusedtoanalyzetheofdemagnetizationfaults.Inthecaseofdemagnetiza-tionfault,theremanencedensity(r)ofthedemagnetizedmagnetsin(2.17)willchangeaccordingtotheseverityandthepositionofthedemagnetizedmagnetsaredeterminedusingthefollowingequation:rdem=r(1rdemag)(2.27)whererdemagisthepercentageofdemagnetization.Fig.2.11showsthedensitydistri-butionforhealthy,66%eccentricityandonemagnetdemagnetized,usingFEAsimulationcomparedtotheanalyticalcalculations.Thechangeinthemagneticdensityundereccentricityanddemagnetizationfaultscanbeobservedusingboththeanalyticalcalcula-tionsandusingFEAsimulations.Inthecaseofeccentricityfault,thedecreaseintheairgaplengthwillcauseanlocalincreaseinthemagneticdensityandtherefore,increasethetotalofthemachine.Fordemagnetizationfault,thedemagnetizedmagnetswillcause29areductioninthemagneticdensitywhichwillreducethetotalgenerated(a)FEAsimulation(b)AnalyticalcalculationsFigure2.11ComparisonbetweenFEAsimulationandAnalyticalcalculationsorhealthy,onemagnetdemagnetizedand66%eccentricity2.4PMSMUnderTurn-to-TurnShortCircuitFaultOfthemanypossibletypesofstatorwindingfaults,turn-to-turnshortcircuitfaultconsideroneofthemostcommon.Thisfaultcanbecausedduetomechanical,electricalandthermalstressappliedtothestatorwinding.Thesestressesmayleadtoaninsulationbreakdownofthecoilconductor,whichleadstoshortingsomeoftheturns.Inthecaseofturn-to-turnshortcircuitfault,theshortedturnscreateanextrahighcurrentpaththatismagneticallyandelectricallycoupledwiththewindingcurrentandthepath.Thiscurrentwillheattheshortedturns,causingfurtherinsulationdamageandmayexpandtoshortthenearbywindings.Therefore,detectingturn-to-turnfaultatanearlystageisimportanttoprotectthemachineandthewindingfromanyfurtherdamage.Fig.2.12showsaseriesconnectedthreephasewindingwithturn-to-turnshortcircuitfaultinphaseA.ThefaultismodeledbyasmallresistanceRfconnectedinparallelacrosstheshortedturns.Twofactors30theseverityofturn-to-turnshortcircuitfault:thenumberofshortedturns,andtheshortedresistance.vaa1a2iaifRfb1b2vbibc1c2icvcFigure2.12Serieswindingwithshortedturns.Following[38],inthecaseofturn-to-turnshortcircuitfault,ahighshortcircuitcurrentwillwintheshortedturnsaddinganewinducedvoltagerelatedtotheshortcircuitfault.Themathematicalmodelforamachineunderturn-to-turnshortcircuitfaultcanbedescribedasfollows:26666666664vahvafvbvc37777777775=26666666664rah0000rf0000rs0000rs3777777777526666666664iaiaifibic37777777775+26666666664eaheafebec37777777775+26666666664LahMahafMahbMahcMahafLafMafbMafcMahbMafbLbMbcMahcMafcMbcLc37777777775ddt26666666664iaiaifibic37777777775(2.28)wherevahandvafarethevoltagesacrossthehealthyandfaultycoilsrespectively,rahandrafaretheresistanceforhealthyandfaultysectionofthecoil,ifistheshortcircuitcurrent,eahandefaretheinducedemfvoltagesacrossthehealthyandfaultedcoils,ebandecaretheinducedemfvoltagesofphaseBandphaseCrespectively.Park'stransformationcanalsobeusedtotransformthemodelofaPMSMmachineunderturn-to-turnshortcircuit31faultfromtheabcframeofreferencetothedqframeofreference.Forconcentratedwindingmachines,themutualinductancebetweentheshortedturnsandtheothertwophasescanbeneglected,onlythemutualinductancebetweentheshortedturnsandthehealthyturnsinthesamephaseneedtobeconsidered.Inthiscase,themodelforPMSMmachineunderturn-to-turnshortcircuitfaultinthedqframeofreferenceisgivenby(2.29)-(2.34)vdsh=vd+vdf(2.29)vqsh=vq+vqf(2.30)wherevd=idrs+Lddiddt!eLqiq(2.31)vdf=23rfcos()if+(Mahaf+Laf)cos()difdt!e(Mahaf+Laf)ifsin()(2.32)vq=iqrs+Lqdiqdt+!e(Ldid+pm)(2.33)vqf=23rfsin()if+(Mahaf+Laf)sin()difdt+!e(Mahaf+Laf)ifcos()(2.34)Itcanbenotedthatthemachinemodelundershortcircuitfaultcontainstwomaincomponents.Thecomponentissimilartothehealthymodel,thesecondcomponentisrelatedtotheshortcircuitfault.Thefaultrelatedcomponentdependsontheseverityoftheshortcircuitfault(i.e.numberofshortedturnsandtheshortedresistance)andthemachineoperatingcondition(i.e.operatingtorqueandspeed).Similartothehealthymachine,atsteadystateoperation,thetimevaryingcomponentsin(2.29)-(2.34)willbeequaltozero.32Inthiscase,thecomponentrelatedtoshortcircuitfaultwillbegivenby:vdf=23rfcos()if!e(Mahaf+Laf)ifsin()(2.35)vqf=23rfsin()if+!e(Mahaf+Laf)ifcos()(2.36)33Chapter3ExperimentalandSimulationSetup3.1AugmentedFiniteElementAnalysisSimulationsFiniteElementAnalysis(FEA)isapowerfulandtechniqueforsolvingordinaryandpartialtialequationusingnumericalmethods.Inthecaseofelectromagneticanalysis,FEAisusedtocalculatethemagneticinelectricalmachinebysolvingMaxwelltialequations.Thebehaviourofthemachineisdeterminedbythedistributionofthemagneticandcurrentdensity,whichiscoupledwithanexternalcircuitthatisusedtocontrolthestatorcurrents.InFEAsimulations,thegeometryisdividingintoanumberofsmallsectionscalledelements,whichmakesagridcalledmesh.Theaccuracyofthesolutiondependsontheelementtopology,thewaytheywereassigned,andonthesizeofeachelement.Theelementsareassignedtothegeometryaccordingtothevariationofthemagneticpotential;suchthatanareawithahighvariationinthemagneticvectorpotential,needahighernumberofelements(i.e.mesh)comparedtoanareawithalittleornomagneticvectorpotentialvariation.Theresultisasystemofanonlinearequations,whichissolvediterativelytillitconvergestoauniquesolution.FEAsimulationisusedformachineanalysisanddesign;itisusedtoanalyzetmachinetopologieswithanymaterials,windingsdistribution,andslot/polecombinations.ThemainadvantageofFEAistheabilitytocalculatethemotorinductances,linkages,forcesandtheelectromagnetictorqueforthemachineaccuratelywithouttheneedtoan34analyticalapproach.FEAcanalsobeusedtostudytheoffaultsonelectricalmachinesandshowshowthemachineparametersandperformancechangesaccordingtoeachfault.Therefore,forthisworkFEAsimulationswereperformedinordertounderstandtheofeachfault,andthenexperimentaltestswerecarriedouttovalidatethesimulationresults.Inthiswork,threePMSMsweretestedunderhealthyandfaultedconditions.Allthetestedmachineswerea3phaseY-connected,withtslot/polecombinations,windingdistributionandtinputandoutputpower.Thetestedmotorswereasfollows:a12-poledistributedwindingmachine,a16-poleconcentratedwindingmachineanda10-poleFractionalSlotConcentratedWinding(FSCW)machine.Fig.3.1showsthecrosssectionsforthetestedmachines,andTable3.1showstheirparameters.(a)Concentratedwindingmachine(b)Distributedwindingmachine(c)FSCWmachineFigure3.1Geometrycrosssectionforthetestedmachines35Table3.1ParametersforthetestedmachinesConcentratedwindingDistributionwinding2=5SPPFSCWmachinemachinemachineNumberofphases3phase3phase3phaseMaximumcurrent300A300A25AMaximumtorque310N.m315N.m50N.mNumberofslots244812Numberofpoles161210Turnsperphase4681503.2FaultsImplementationinFEA3.2.1ImplementingEccentricityFaultToapplystaticeccentricityfaultsinFEA,theaxisofthestatorgeometryshouldbeentthantherotorgeometryandtherotationalaxiscenter.Therefore,aseparatecoordinatesystemwasassignedtothestatorgeometrythatisdtthantherotorandtherota-tionalcoordinatesystem;bychangingthecenterofstatorcoordinatesystem,onlythestatorgeometryshiftswhiletherotorandtherotationaxisstaythesame.Thisallowscontrollingthedirectionandthedegreeofeccentricityfault,andtheseverityofthefaultwasvariedbasedonthemachineairgapaccordingto(2:24).3.2.2ImplementingDemagnetizationFaultToapplypartialdemagnetization,thematerialofthechosendemagnetizedmagnetswasreplacedwithamaterialthathasthesameelectricalandmechanicalcharacteristicsbutwithtpermeancedensitycomparedtothehealthymagnets.Thepermeanceischangingbasedonthepercentageofdemagnetizationfault(2.27).Forademagnetizationfaultwitha100%demagnetization,themagnetremanencewaschangedto0T.For36thisworkapartialdemagnetizationwithapercentageof100%wastested.Tochangetheseverityofthefault,thenumberofthedemagnetizedmagnetswasvaried.3.2.3ImplementingTurn-to-turnShortCircuitFaultThewayturn-to-turnshortcircuitfaultwasappliedinFEAsimulationsdependsonthemachinestatorwindingtopology.Forthedistributedwindingmachine,twoendturnswereshortedthroughasmallresistance.Basedonthemachinewindingdiagram,thecorrespond-ingcoilswereassignedtoafaultedcoil(Cf),whichwasshortedthrougharesistance(Rf)inthecontrolcircuit,whilethehealthycoilswereassignedtothehealthycoil(Ca)asshowninFig.3.2.Tovarytheseverityofshortcircuitfaultanothertwoendturnswereshorted.Theshortresistanceforeachcasewasvariedaswelltostudytheoftheshortresistanceonthebehaviourofshortcircuitfault.(a)Distributedwindingmachinewith12%shortcircuitfault(b)ControlcircuitwithshortcircuitfaultFigure3.2ImplementingshortcircuitfaultinFEAforthedistributedwindingmachineForconcentratedwindingsmachines,anewfaultedregionsrelatedtotheshortedturnsneedstobeaddedinthefaultedslots.Thenumberofshortedturnsneedtobeassignedto37thenewregionsandsubtractedfromthehealthyone.Forthecontrolcircuit,theshortedturnswereassignedtoafaultedcoil(Cf),andasmallresistancewasconnectedinparalleltotheshortedcoiltorepresentshortcircuitfault.Fig.3.3showsthemocrosssectionandthecontrolcircuitoftheconcentratedwindingmachinewithturn-to-turnshortcircuitfault.Tovarytheseverityofthefault,thenumberofshortedturnswerevariedandalsotheshortresistancewasvariedaswell.(a)Mocrosssectionareaforthetestedmachinewithashortcircuitfault(b)MocontrolcircuitwithextracoiltorepresentashortcircuitfaultFigure3.3ImplementingshortcircuitfaultinFEAfortheFCSWmachine3.3ExperimentalSetupExperimentaltestswereperformedonthethreetestedmachinestovalidatethesimulationresults.NationalInstrument(NI)RealTimeLab-VIEW(RTLV),wasusedtooperateandcontrolthetestedmachines.Thisreal-timesystemconsistsoftwodesktopcomputers:oneisusedashostandtheotherasthetarget.Thecontrollerwasdevelopedinthehostcomputerthendeployedtothetargetwhereitisrunbythetargetcomputersprocessor.38Thehostcomputerwasusedtomonitorthefeedbackdatafromthetargetandappliesthechangestothecontrollerparameters.TheFieldOrientedControl(FOC)wasusedasacontrolschemetooperatethetestedmachines.Themainobjectiveofthiscontrolleristocontrolthedirectandquadraturecurrents(IdandIq)usingtherotorposition()toachievethedesiredtorque.Idisusedtocontroltheamountofthelinkage,whileIqisthemaintorqueproducingcomponent.Fig.3.4showsthebasicblockdiagramfortheFOC.Inthiscontroller,thethreephasestatorcurrentsaremeasured.ThesemeasuredcurrentsarefedintoPark'stransformationthatoutputthecurrentinthedqframeofreference.Themeasureddqcurrentsarecontrastedwiththecommandeddqcurrents.TheoutputofthePIcontrollersarethecommandedvoltages(vdandvq).ThesevoltagesareappliedtotheinverseParktransformationtogeneratethethreephasemachinevoltagesintheabcframeofreference.ThethreephasevoltagesarefedtotheSpaceVectorPulseWidthModulationthatcontroltheinvertersignals,thatusedtocontrolthetestedmachine.Figure3.4BlockdiagramoftheFieldOrientedControllerforPMSMsThemainadvantagesofusingtheFOCincludefastdynamicresponse,high,andtheabilitytocontrolthetorqueoverawideoperatingspeedusingweakening.Forthistypeofcontroller,themeasuredcurrentsandthecommandedvoltagesarealways39available.Therefore,signaturesgeneratedfromthesesignalswillbeusedforfaultdetectionandestimation.Inordertoobtainamodelthatisarealisticrepresentationoftheactualmachine,themainmachineparametersneedtobecalculatedaccurately.Themachineparameterscanbedeterminedusingaprocessknownasmotorcharacterization.ThemainparametersthatneedtobeestimatedinPMSMsarethelinkages.Inthisprocessthemachineterminalvoltages,currentsandtherotorpositionareusedtocalculatethemachineparametersfortoperatingconditions.Usingthemethodproposedin[39,40]thecharacterizationmethodcanbesummarizedasfollows:Theopencircuitvoltagesareusedtoaligntherotorpositionsensorwiththerotordandqaxis.Whilethemachineisrotatingataconstantspeed(usuallylowerthanthebasespeed),thestatorcurrentIsisvariedfrom0tothebasecurrent(Ismax),andforeverycurrentstepthecurrentangleisvariedfrom90to180degrees.ThecommandedcurrentmagnitudeIsandthecurrentanglecontroltheamountoftheandtorqueinthemachine.Park'stransformation,withtherotorposition,isappliedtothemeasuredthreephasecurrentsandthecommandedthreephasevoltagestocalculatethecorrespondingdqaxescurrentsandvoltagesforeverydatapoint.Based(2:11)and(2:12),themachinelinkagesarecalculatedandusing(2:13)thegeneratedtorquecanbeestimated.ForSPMSMthemaximumtorqueisarchivedatacurrentangleof(=900)since40thatLd=Lq,inthiscasethetorqueisgivenby3.1.However,forIPMSM,Ld6=Lqthecurrentangleneedstobeestimatedfromthedqusing3.2tothepointwherethemotorwillbeoperatingatmaximumtorque.TSPMSM=3P2pmiq(3.1)TIPMSM=3P2(pmiq+(LdLq)idiq)(3.2)3.4FaultImplementationExperimentally3.4.1ImplementingEccentricityFaultForthedistributedandtheconcentratedwindingmachine,shimsof25%thicknessoftheairgapweremountedbelowthemachinebearingtolifttherotorandtherotationaxis.Thisshiftstherotorgeometryandtherotationaxistothepositiveydirectionwithoutthestatorgeometryaxis,asshowninFig.3.5a.Itwouldmakenoiftheshiftwasinanyotherdirectionoratatangle.Toapplythesecondseverity;additional4shimswereaddedonthetopofthe4shimstofurthershifttherotorandtherotationaxiscausingfurtherreductionintheairgaplengthinthepositiveydirectionandmoreairgaplengthinthenegativeydirection.Twoseveritiesweretested25%and50%.FortheFSCWmachine,amobrassringsweremountedbetweentheshaftbearingandtheendring.Theringsweremodisuchthatthecenteroftheseringsisshifted.Thiscausedashiftinthemachinerotorgeometryandtherotationaxiswithoutchangingthestatorgeometry,asshowninFig.3.5b.Thecenterforthemoringswasshiftedbasedonthedesiredseverityofeccentricityfault.Threeringswereusedtorepresentthree41severitiesofeccentricityfault(40%,60%,and80%).(a)Implementingeccentricityfaultforthedistributedwindingmachine(b)MoringfortheFSCWmachineFigure3.5Implementingeccentricityfaultexperimentallyforthedistributedwindingma-chineandtheFSCWmachine3.4.2ImplementingTurn-to-turnShortCircuitFaultTurn-to-turnshortcircuitfaultwasappliedexperimentallytothedistributedwindingma-chineandtheFSCWmachine.Forthedistributedwindingmachine,twooftheendturnswereweldedtoacopperwireandshortedusingashortresistanceequalto200%ofthestatorphaseresistance,asshowninFig.6.4.Theshortedresistancewaschosentobe200%ofthephaseresistancebecauseitwasthelowestavailableresistancethatcanhandlethehighwingcurrentundershortcircuitfaultfault.Torepresentthesecondseverity,anothertwoadjacentendturnswereshortedtoashortresistanceusingcopperwires.Shortingoneendturnisequivalenttoshorting12:5%ofthetotalconductorsofphaseA,andshortingthesecondendturnisequivalenttoshorting25%ofthetotalconductorsofphaseA.FortheFSCWmachine,apercentageoftheturnsofphaseAwereshortedthrougharesistance.Thenumberofshortedturnsrepresentsthefaultseverity,twoseveritiesweretested,10%(15outof150turnswereshorted)and20%(30outof150turnswereshorted).42Figure3.6Turn-to-turnshortcircuitfaultexperimentallyForeachfaultseverity,twoshortedresistanceswereused0:and0:whichisequivalentto25%and12:5%ofthestatorwindingresistance.3.4.3ImplementingDemagnetizationFaultDemagnetizationfaultwasappliedexperimentallyonlytotheFSCWmachine.Anon-magneticmaterial,wasusedtoreplacedthehealthymagnet.Onlypartialdemagnetizationwith100%demagnetizationwasapplied.Threeseveritiesofdemagnetizationfaultweretestedbychangingone,twoandthreemagnets.ThecorrespondingdemagnetizedmagnetsisshowninFig.6.2NeodymiumIronBoron(NdFeB)Magnetswithpermeance(r=1:2T)andrelativeper-meabilityof(r=1:05)waschosenasthematerialforthemagnets.Stainlesssteelmaterialwasusedtoreplacethedemagnetizedmagnets.Thismaterialhavethesameconductivityandrelativepermeabilityasthemagnetsmaterial,butwithzeromagnetpermeance.43Figure3.7Implementingdemagnetizationfaultexperimentally.44Chapter4TheIncrementalInductanceApproachOfthetchangesfaultsmightcausetothemachine,changingthesaturationlevelisoneofthesemainchanges.Faultswillcauseadisturbanceinthemagneticdistribution,whichthelocalizedandthetotallinkagesinthemachinecausingachangeinthemachinesaturation.Thischangeisreintheincrementalinductancecurveasachangeinthepeakamplitudeand/orashiftsofthepositionofthepeaks.Basedontheshiftdirectionandtheamplitudeofthecurvepeaks,thetypeofthefaultcanbedetectedanditsseveritycanbeestimated.Thischaptershowshowtousetheincrementalinductancecurveasafaultdetectionandseparationtechnique.Thisapproachcanbeperformedwhenthemotorisatstandstill,itcanalsobeusedasatestingstageattheendofamanufacturinglinetocheckthemachinehealthstatus.4.1ofIncrementalInductanceFig.4.1showsthesaturationcurveforPMSM.Thiscurverepresentstherelationbetweenthedaxis(d)andthedaxiscurrent(Id).Thesaturationcurvecanbedividedintothreeregions:thelinearregion,thekneeregionandthesaturationregion.Inthelinear45regiontherelationbetweendandIdislinearandcanbegivenby:d=LdId+m(4.1)Thekneeregion,istheregionwherethemachinestartstosaturate.There,therelationbetweendandIdstartstochangefromlineartononlinear.ThesaturationregionistheregionwhentherelationbetweendandIdisnonlinear.Itisimportanttonotethatthesaturationcurvedependsonthemachinegeometryandthematerialscharacteristicsofthestator,therotor,andthemagnets.TheincrementalinductanceisastherateofchangeofdoverIdasfollow:^Ld=dId(4.2)Thekneeregionwillappearasapeakintheincrementalinductancecurve.Thispeakcanbeusedasanindicatortoshowwhenthemachinestartstosaturate.Fig.4.1showsthesaturationcurveandthecorrespondingincrementalinductance.(a)dvsIdcurve.(b)IncrementalinductancevsIdcurve.Figure4.1Incrementalinductancecurve464.2ofFaultsontheIncrementalInductanceCurveItwasshowninChapter2thatinthecaseofeccentricityfaultthetotallinkagesinthemachinewillbehighercomparedtohealthymachine.Thiswillcauseanearlysaturationinthemachine.Thisearlysaturationmeansthatthemachinerequirelesscurrenttosaturate,whichcanbeobservedintheincrementalinductanceasashiftofthekneeregionpeaktotheleft,andachangeinthepeak'samplitude.Theamountoftheshiftdependsontheseverityofeccentricityfault;astheseverityofeccentricityfaultincreases,themachinesaturatessooner,causingthepeaktoshiftmoretotheleft.Inthecaseofturn-to-turnshortcircuitfault,theshortedturnswillcauseareductioninthetotalarmatureinthemachine,whichcausesashiftdownintheincrementalinductancecurve.Thisshiftcausesareductioninthepeaksamplitude,butitwontcauseashiftinpositionofthesaturationcurvepeaks.Thedecreaseisproportionaltotheseverityoftheshortcircuitfault.Asthenumberofshortedturnsincreasesorasthevalueoftheshortedresistancedecreases,theincrementalinductancecurvewillshiftdownmore.Forpartialdemagnetizationfault,theregionwithdemagnetizedmagnetswillhaveasimilarcharacteristicsofanairregion.Thiswillcausetwointheincrementalin-ductancecurve.Thetotalmagneticwillbelower.Therefore,themotorrequiresmorecurrenttosaturate,whichmeanthatthepeakoftheincrementalinductancewillhaveahigheramplitude.Anotherincludesanearlysaturationduetotheconcentratedinthedemagnetizedmagnetarea.Theregionofthedemagnetizedmagnetswillforcemoretoconcentratecausinganearlysaturationinthatregion,whichcausesasanincreaseinthecurvepeakatId=Id0.Fig.4.2summarizestheofeachfaultontheincremental47inductancecurveandhowitcanbeusedtodetectthetypeofthefault.Figure4.2sonfaultsontheincrementalinductancecurve4.3MethodstoGeneratetheIncrementalInductanceCurvetmethodscanbeusedtogeneratetheincrementalinductancecurve.Hongetal.[20]proposedamethodusingtheinvertersignalstogeneratetheincrementalinductancecurve.ThemethodisbasedonapplyingasmallACcurrentwithttothepositived-axisofthemachinewhilethemotorisatstandstill.ThemeasuredthreephasecurrentsandthecommandedthreephasevoltagesarefedintoPark'stransformationtocalculatetheequivalentcurrentsandvoltagesspacevectorusing4.3and4.4.vd=cos()va+cos(2ˇ3)vb+cos(+2ˇ3)vc(4.3)48id=cos()ia+cos(2ˇ3)ib+cos(+2ˇ3)ic(4.4)Fromthecommandedvoltagesandthemeasuredcurrentsspacevectorsthemotorimpen-dencecanbecalculated,andfromthemachineimpedance,theincrementalinductancecanbeextractedusing4.5Zd=~Vd~Id=rd+|!^Ld(4.5)where~Vd,and~Idarethefundamentalcomponentsofthevoltageandcurrentspacevector.Anothermethodtogeneratetheincrementalinductancecurveisbyrotatingthemachineataconstantspeedandcommandingacurrenttothepositivedaxisofthemachine.Asthecommandeddaxiscurrentincreases,thelinkageswillincreasecausingthemachinetosaturate.Fromthemeasuredthreephasecurrentsandthecommandedthreephasevoltages,thedandqaxisvoltagesandcurrentcanbecalculatedusing(2.11)and(2.12).Atsteadystateoperation,thetimevaryingcomponentsin(2.11)and(2.12)areequaltozero,sothedandqaxiscanbecalculatedasfollows:d=VqRs:Iq!e(4.6)q=VdRs:Id!e(4.7)Thecommandedcurrentisappliedtothepositivedaxisofthemachine,sotheqaxiscur-rentwillbeequaltozero.Therefore,(4.6)isgivenby(4.8),andtheincrementalinductancecurvecanbegeneratedusing(4.2).d=Vq!e(4.8)49ThisapproachistthanthetypicalcontrolforPMSMs.Duringnormalcontrol,thecurrentisappliedtotheqaxisofthemachineinordertoproducetorque.However,inthiscase,thecurrentisappliedtothepositivedaxis(Iq=0A)tocontroltheinthemachine,inthiscasenotorqueisproduced.Themainobjectiveistoincreasethesaturationinthemachinebyincreasingthetotal4.4ComparisonBetweentheIncrementalInductanceApproachesUsinganyofthetwomethodsshouldmakenoinordertogeneratetheincrementalinductancecurve.However,usingthestandstillapproachmightproducesomeFirst,thestandstillmethodisbytherotorposition.Fig.4.3showstheFEAsimu-lationresultsforthechangeintheincrementalinductancecurvefortheFSCWmachinebychangingtherotorpositioninstepsof2mechanicaldegrees.Figure4.3ofrotorpositionItcanbenotedthattherotorpositiontheshapeandthepeakpositionofthegeneratedincrementalinductancecurve.Thiscanecttheaccuracyoffaultdetectionif50themotoristestedattpositions.Thechangeintheincrementalinductanceduetotherotorpositionisbasedonthethemotorgeometryandtherelationbetweenthenumberofpolesandslots.Fig.4.4showsacomparisonoftheincrementalinductancecurveforboththeconcentratedandthedistributedwindingmachinescalculatedusingthetwomethods.(a)ConcentratedwindingmachineStandstillmethod(b)DistributedwindingmachineStandstillmethod(c)ConcentratedwindingmachineRotationmethod(d)DistributedwindingmachineRotationmethodFigure4.4Comparisonbetweenthetwomethodstogeneratetheincrementalinductancemethod(FEAsimulation)Itcanbenoticedthatforthedistributedwindingmachine,bothmethodsgeneratesimilarcurves,inwhichitiscleartodetectthepositionandtheamplitudeoftheincrementalinductancepeaksusingbothmethods.However,fortheconcentratedwindingmachine,itisnotpossibletodetectthepeakusingthestandstillmethod.Thisisduethethemotorgeometryandtheslot/polecombination:forthedistributedwindingmachine,atanyrotor51position,thed-axesarealignedtobothatoothandaslotwhichaveragethetotalFortheconcentratedwindingmachine,alltherotord-axesarealignedwitheitheratoothoraslotatanyinstantoftime,causinganunbalanceinthemagneticlinkagesbasedontherotorposition.Fortherotatingmethod,sincethatthemotorisrotatingataconstantspeed,thed-axiswillfacebothaslotandatooth,whichaveragethetotalairgapTheofthemachinegeometrycanbesolvedbyrotatingthemotorataverylowspeedwhileapplyingtheACcurrentsignal.Thisallowsthed-axistopassbyaslotandatooth,whichaveragethetotalandsincethatthemotorisrotatingataverylowspeed,thentheoftheBackemfvoltageisneglected.AnotherfactorthatneedstobeconsideredwhileusingthestandstillapproachistheamplitudeoftheACcurrent;applyingalargeACamplitudewilltheamplitudeofthegeneratedincrementalinductancecurvepeak.Insomecasesiftheamplitudeoftheincrementalinductancecurveistoohighitmightmasktheappearanceofthepeakifthekneeregionistoosmall.Fig.4.5showsthesimulationresultsforthechangesintheincrementalinductancecurveusingthestandstilltestwithtamplitudesoftheACsignalfortheFSCWmachineunderhealthyconditions.Figure4.5tsoftheACcurrentamplitude52ItcanbenotedthatastheamplitudeoftheACsignalincreases,itbecomeshardertodetectthepeakoftheincrementalinductancecurve.Therefore,itispreferredfortheACsignaltobeaslowaspossible.however,theamplitudeoftheACsignalischosenbasedonthemachineparametersandthecontrolresolution.Toovercomethedrawbacksofthestandstillmethod,themotorcanberotatingataverylowspeedwhileapplyingtheACsignaltothed-axis.Themotorisrotateaveryslowspeedtoallowthed-axistopassbyatoothandaslot,whichaveragethetotalandneglecttheofthepositiondependent.Themotorneedstobeoperatingataverylowspeedtoneglecttheoftheinducedbackemfduetotherotationoftherotor.Forthisworktheincrementalinductancecurvewasgeneratedexperimentallybyrotatingthemotoratalowspeed(10rpm),andexcitingthepositived-axiswithasmallACsignalofamplitude0:5Aatafrequencyof100Hz.Fig.4.6showscomparisonoftheincrementalinductancegeneratedusingtheslowrotationmethodandthefastspeedmethodusingFEAsimulation.Itcanbenotedthatthereisnobetweenthetwomethods(slowrotationandfastrotation)intheshapeoftheincrementalinductancecurve,sincethatbothofthemaccountforthevariationintheduetotheslotsandtooth.Themaindrawbackofusingtherotatingmethodisthattheincrementalinductanceisgeneratedusingthederivativeofthewhichmayintroducenoiseespeciallyfromtheexperimentaldata.4.5SimulationandExperimentalResultsFig.4.7showsthecalculationoftheincrementalinductancecurveusingFEAsimulationsfortheconcentratedwindingmachinesunderhealthyandthethreetestedfaultswithtseverities.Theincrementalinductancecurvesweregeneratedusingtherotatingmethod,53(a)Slowrotationmethod(b)FastrotationmethodFigure4.6Incrementalinductancecomparisonbetweentheslowrotationmethodandtheconstantspeedmethodthemotorwasoperatingataspeedof500rpm,theappliedd-axiscurrentwasvariedfrom50to200Ainstepsof5A.Fourseveritiesofeccentricityfaultweretested(20%,40%,60%and80%),threeseveritiesofpartialdemagnetizationfault,byfullydemagnetizing1,2and3magnets,andthreeseveritiesofturn-to-turnshortcircuitfault.Theseveritiesofshortcircuitfaultwerevariedbyshorting12:5%,25%and62:5%oftheturnsinphaseAcoilsthrougharesistanceof0:(a)Incrementalinductancevaria-tioneccentricityfault(b)Incrementalinductancevaria-tiondemagnetizationfault(c)Incrementalinductancevari-ationturn-to-turnshortcircuitfaultFigure4.7IncrementalinductancevariationundertfaultsFig.4.8showsacomparisonbetweentheexperimentalandtheFEAsimulationresultsforthedistributedwindingmachineunderhealthy,twoseveritiesofeccentricityfault(25%54and50%)andtwoseveritiesofturn-to-turnshortcircuitfault(12%and25%).(a)Simulationresultsforeccentricityfault(b)Simulationresultsforshortcircuitfault(c)Experimentalresultsforeccentricityfault(d)ExperimentalresultsforshortcircuitfaultFigure4.8ComparisonbetweensimulationandexperimentalincrementalinductanceresultsFig.4.9showsacomparisonbetweentheexperimentalandtheFEAsimulationresultsfortheFSCWmachineunderhealthy,threeseveritiesofeccentricityfault(40%,60%and50%)andthreeseveritiesofdemagnetizationfault(1,2,and3magnetswerefullydemagnetized).Asdiscussedearlier,itcanbenotedthatinthecaseofstaticeccentricityfault,thepeakoftheincrementalinductanceisshiftedtotheleft(pointB),whilenochangeinthepeakamplitudeorpositionatId=0(pointA).Itcanalsobenotedthattheamountoftheshiftdependsontheseverityofthefault.Astheseverityofthefaultincreases,theshiftinthepeakwillalsoincreases.Fortheconcentratedwindingmachine,itstarttosaturateat55(a)Simulationresultsforeccentricityfault(b)Simulationresultsforexperimentalfault(c)Experimentalresultsfordemagnetizationfault(d)ExperimentalresultsfordemagnetizationfaultFigure4.9ComparisonbetweensimulationandexperimentalresultsfortheFSCWmachineId=150A.However,forastaticeccentricityfaultof80%,thepeakpositionwasshiftedfromId=150AtoId=45A.ForthedistributedwindingmachinethesaturationpeakwasshiftedfromIdsat=135AtoIdsat=75Aunder66%eccentricity.ThepeakshiftcanalsobenoticedfortheFSCWmachineunderstaticeccentricityfault.Fig.4.10showstherelationbetweentheseverityofeccentricityfaultvsthesaturationcurrentIdsat(pointB)fortheconcentratedandtheFSCWmachines.ItisclearthattherelationbetweentheseverityofeccentricityfaultandIdsatisalmostlinear.Basedonthiscurve,anyseverityofstaticeccentricityfaultcanbeestimatedusingthepeakposition.Inthecaseofpartialdemagnetizationfault,duetotheearlysaturationinthedemag-56(a)concentratedwindingmachine(b)FSCWmachineFigure4.10ThechangeinIdsatunderstaticeccentricityfaultnetizedmagnetsregion,achangeinthepeakamplitudeandpositioncanbenotedintheincrementalinductancecurveatId=0(pointA).However,nodetectablechangecanbenoticedinthesaturationpeak.ThechangeinthepeakamplitudeandpositionatId=0Acanbeusedasanindicatortodetecttheseverityofpartialdemagnetizationfault.Forturn-to-turnshortcircuitfault,duetothereductioninthetotalinthemotor,thein-crementalinductancecurveisshifteddowncomparedtothehealthycase.Theamountoftheshiftdependsontheseverityofthefault.Asthenumberofshortedturnsincreasesortheshortedresistanceincrease,thereductionintheincrementalinductancewillincrease.4.6FaultDetectionandSeparationAlgorithmThechangeinthepeaksamplitudeandpositionoftheincrementalinductancecurvecanbeusedasanindicatorstodetectthefaulttypeandestimateitsseverity.However,theslope,thepositionofthepeak,andthepeakamplitudevariesbetweenmotors,dependingonthemachinegeometryandthematerialused.Toautomatethedetectionmethod,thealgorithminFig.4.11isproposed.57StartIncrementalInductancecurveWavelettransformEnvelopdetectionfaulted?FaulttypeHealthyEccentricityDemagnetizationShortcircuitnoyesFigure4.11Blockdiagramfortheincrementalinductanceapproach[1]Usinganyoftheproposedmethodsdiscussedearlier,theincrementalinductanceforthetestedmachineisgenerated.Fortheconcentratedandthedistributedwindingmachine50pointswereusedtogenerateincrementalinductancecurvebyvaryingthed-axiscurrentfrom0Ato250Ainstepsof5A.FortheFSCWmachine31pointswereusedtogenerateincrementalinductancecurvebyvaryingthed-axiscurrentfrom5Ato10Ainstepsof0:5A[2]Wavelettransformisappliedtotheincrementalinductancecurvetodetectthecurvepeaks.Forthiswork,a4levelHaarwaveletdecompositionisapplied.Inordertohaveabetterresolutionforthewavelettransform,interpolationwasappliedtotheincrementalinductancecurvetoincreasethecurveresolution.58[3]Usinganenvelopedetectionalgorithm,thepeaksandthecorrespondingd-axiscurrentcanbedetected(pointsAadB)asshowninFig.4.12[4]Thed-axiscurrentandthevalueoftheincrementalinductanceatthed-axiscurrentcanbeusedasthefeatures.Theoutputofthethemachinehealthstatus,detectsthefaulttype,andestimatesitsseverity.(a)Incrementalinductancehealthycase(b)Haarwavelettransformation(c)EnvelopecurvedetectionFigure4.12featureextractionforkNNThreeapproacheswereappliedtovalidatethedetectionandestimationmethod:k-NearestNeighbor,LinearDiscriminantAnalysis,andQuadratureDiscriminantAnalysis.Thesamefeatureswereselectedforeach4.6.1k-NearestNeighbork-NN[41]isacommonnon-parametricmethod.Inthisforaknowntrainingvector,thesamplespaceisdividedintoanumberofclustersbasedonadistancefunction.Atestedsampleisassignedtoaspclusterwiththenearestksamples.Forthisworkkischosentobe1,whichmeansthatthetestedsampleisassignedtoitsclosestsampleinthesamplespace.ThedistancefunctionischosentobeEuclideandistance.ForajntrainingmatrixYandalntestingmatrixX,theEuclideandistanceisgivenas:59dXY=vuutnXi=1(xmiypi)2(4.9)whereX=[xm1;:::;xmn]isthetestedmatrix,Y=[yp1;:::;ypn]isthetrainingmatrix,m=1;:::;jisthenumberoftestedsamplesandp=1;:::;listhenumberoftestingsamples.Theamplitudeandthepositionofthepeaksareusedasfeaturesfork-NN4.6.2DiscriminantAnalysisDiscriminantAnalysisisusedtomaximizetheratiobetweenthevariancefortclassesandthevariancewithinthesameclasstoachievemaximumseparationbetweenthefeaturesetsineachclass.ForthisthesamplespaceisdividedintoKclasses,whereeachclassconsistsofaspnumberofsamplescorrespondingtothesamestate.Theseclassesareassociatedwithweightingcoets,andeachclasshasitsowncotsthatareusedtocalculatethecorrespondingdiscriminantfunctionforthatclass.Thediscriminantfunctionforclasskisgivenby(4.10)Ck(X)=1kx1+2kx2++NkxN+N+1k(4.10)whereX=[x1;x2;:::;xN]istheNdimensionalsamplevectorand[1k;2k:::N+1k]isthecotmatrixforthekthclass.Theweightingcotmatrixisdeterminedusinganiterativeprocess,thetrainingphase.Duringthisphase,sinceweknowtheproperforeachsample,theweightingmatrixwillkeepchanginguntileachsampleisintoitscorrectclass.Toclassifyanunknownsample,themeasuredcotsfromthetrainingphaseareusedin(4.10)tocalculatethediscriminantfunctionsforthissample.Asamplevectorbelongstoa60particularclassifthelineardiscriminantfunctionforthatsampleisgreaterthananyotherlineardiscernmentfunction.Forexample,asamplevectoribelongstoaclassjif,Cj(Xi)Ck(Xi)8j6=k(4.11)4.6.3MethodologyandResultsFEAsimulationsandexperimentaltestswereperformedtogeneratetheincrementalinduc-tancecurveunderhealthyandfaultedconditions.Fortheconcentratedwindingmachine,11casesweregeneratedusingFEA.Onecasecorrespondstothehealthyconditions,fourcasescorrespondtostaticeccentricityfault,generatedbyvaryingtheseverityfrom20%to80%instepsof20%oftheairgaplength,threecasescorrespondstodemagnetizationfault,bydemagnetized1,2and3consecutivemagnets,andthreecasesrepresentturn-to-turnshortcircuitfault(12:5%and25%and62:5%ofthetotalphaseAconductorsareshorted).Forthedistributedwindingmachine,atotalofecasesweregenerated.TwofaultsweretestedusingbothFEAandexperimentally;acaseforhealthycondition,twoseveritiesofstaticeccentricityfault(40%and66%)andtwoseveritiesofturn-to-turnshortcircuitfault(12%and25%).FortheFSCWmachine12casesweregeneratedusingFEA,oneforhealthy,4foreccentricityfault(20%-40%instepsof20%),threecasesfordemagnetizationbydemag-netizing1,2,and3adjacentmagnets,and4casesrepresentshortcircuitfault(10%withRf=0:5,12%withRf=0:25,20%withRf=0:5,and20%withRf=0:25).Experi-mentaltestswereperformedfortheFSCWmachineunderhealthy,staticeccentricity,andpartialdemagnetizationfaults.Fourfeatureswereextractedfromeachcase:thesaturationcurrentIdsat=I(B),the61incrementalinductancepeakamplitudeatthesaturationcurrent(L(Idsat)=L(B)),thezerod-axiscurrent(Id0=I(A)),andtheincrementalinductancepeakamplitudeatthezerod-axiscurrent(L(Id0)=L(A)).100samplesweregeneratedfromeachcasebyvaryingtheselectedd-axisandthecorrespondingincrementalinductanceamplitudearoundId=I(A)andId=I(B).10currentswereselectedaroundId=I(A)andanother10currentswereselectedaroundId=I(B).Thevariationofthecurrentwaschosentobe15%oftheselectedcurrents,(i.e.ifthemachinesaturatesatId=150A,theselectedcurrentsvariesfrom142:5Ato157:5A).Atotalof100combinationsamplescanbegeneratedforallthecurrentcombinations.Thefeaturevectorforeachsampleisselectedbasedon(4.12)xij=[Iij(A)Lij(A)Iij(B)Lij(B)](4.12)whereiisthenumberofmachinehealthstatuscases,jisthenumberofsamplesineachcase,andxisthefeaturesvector.Allthesamplesforhealthyandfaultedcaseswerecom-binedtogetherinonematrix.Theleaveoneoutmethodwasusedtovalidatetheresults;onesamplefromthesamplespaceisselectedandleftout.Thecotmatrixiscalculatedfromtherestofthesamples.Theselectedsamplewasclassi-usingthesecots.Thisprocesswasthenrepeatedforeverysampleinthesamplespace.Eachtimethecotsarerecalculatedandtheleft-outsampleisusingthesecots.Theonaccuracyforeachclasswascalculatedas:CC(%)=NcorrectNtotal100%(4.13)whereNcorrectisthenumberofsamplesthatwerecorrectly,andNtotalisthetotalnumberofsamplesinthesamplespace.Table6.3comparesthetionresultsfor62theconcentratedwindingmachineusingthethreeclasers.Table4.2showsacomparisonoftheclassiresultsbetweensimulationsandexperimentaldataforthedistributedwindingmachine,andTable6.4showstheresultsforfortheFSCWmachine.Table4.1resultsfortheconcentratedwindingmachineConcentratedwindingmachineMachineStatusK-NNLDAQDAHealthy90%98%95%20%Eccentricity80%96%95%40%Eccentricity82%100%98%60%Eccentricity100%100%100%80%Eccentricity100%100%100%1Magnet82%98%95%2Magnets85%97%96%3Magnets96%98%98%12.5%Short83%92%92%25%Short90%90%90%50%Short92%90%90%Table4.2k-NNresultsfortheconcentratedwindingmachineDistributedwindingmachineFEASimulationExperimentalresultsMachineStatusK-NNLDAQDAK-NNLDAQDAHealthy80%97%95%80%92%91%40%ECC90%100%97%88%97%97%60%ECC93%100%98%89%98%98%12.5%Short88%95%95%85%90%90%25%Short85%100%97%83%92%88%Table4.4summarizesthetheaverageresultsforalltestedmachinesusingthethreeionmethods.Theresultsshowthattheproposedalgorithmwasabletodetectthefaulttypeandestimateitsseverityaccurately.Evenforthecaseswhentheseverityarenot63Table4.3k-NNresultsfortheconcentratedwindingmachineDistributedwindingmachineFEASimulationExperimentalresultsMachineStatusK-NNLDAQDAK-NNLDAQDAHealthy92%96%97%90%97%96%40%ECC82%100%95%80%92%93%60%ECC88%98%94%82%95%94%80%ECC88%100%94%90%94%94%1Magnet89%93%93%89%88%88%2Magnets84%96%95%85%88%87%3Magnets85%95%94%85%87%85%Table4.4k-NNresultsfortheconcentratedwindingmachineConcentratedwindingDistributedwindingFSCWmachineFEAFEAEXPFEAEXPKNN89.1%87.2%85%86.8%85.8%LDA96.2%98.4%93.8%96.8%91.5%QDA95.3%96.4%92.8%94.5%91%correctly,thealgorithmwasabletodetectthefaulttype.ItisalsonotedthatusingLDAclassiprovidethehighestaccuracyforfaultdetectionand4.7ofParameterVariationTotesttherobustnessofthedetectionmethod,FEAsimulationswereperformedbyvaryingthemachineoperatingandenvironmentalconditions.Twoparameterswerevaried:thealigningangleandtheoperatingtemperature.Theincrementalinductancecurvedependsonthechangeinthesaturationofthemachine.Therefore,itisimportantfortheappliedd-axiscurrenttobeaccuratelyalignedtotherotord-axis.Anymisalignmentbetweentheappliedcurrentandtherotord-axiswillthesaturationinthemachine.Toestimate64thesensitivityofthealigningangle,themotorwasmisalignedby1,6and10mechanicaldegrees.TheresultsoftheincrementalinductanceundertmisalignmentanglesfortheconcentratedwindingmachineareshowninFig.4.13(a)Incrementalinductancehealthy0degreemisaligned(b)Incrementalinductancehealthy1degreemisaligned(c)Incrementalinductancehealthy6degreemisaligned(d)Incrementalinductancehealthy10degreemisalignedFigure4.13incrementalinductanceundertmisaligningangleTovarytheoperatingtemperatureofthemachine,themotorstatorresistanceandthemagnetpermeancewerechangedinthemodelbasedonthefollowingequations:Rs(T)=Rs0[1+R(TT0)](4.14)Br(T)=Br0[1+Br(TT0)](4.15)65whereRisthetemperaturecotforthestatorresistance(R=0:00393),Bristhetemperaturecotforthemagnets(Br=0:0011),Tistheoperatingtemperature,andT0isthereferencetemperature.Threetemperaturesweretested200C,1000Cand1500C.TheresultsoftheincrementalinductancecurveundertemperaturevariationfortheconcentratedwindingmachineisshowninFig.4.14(a)IncrementalinductancehealthyatT=200C(b)IncrementalinductancehealthyatT=1000C(c)IncrementalinductancehealthyatT=1500CFigure4.14variationoftheoperatingtemperatureItcanbenotedthattheoftheoperatingtemperaturewon'ttheshapeoftheincrementalinductancecurve;thetwopeakswerestilldetectable.However,inthecaseofthealigningangle,asthemachinebecamemoremisaligned,itbecamehardertodetectthesaturationpeakandthereforeestimatethefaulttype.Table4.5showstheresultsfortheconcentratedwindingmachineundertparametervariations.Table4.5k-NNresultsunderparametersvariationResults20oC1000C1500C20oC20oC20oC0degree0degree0degree1degree6degree10degreeKNN89.1%88%85%89%84%80%LDA96.2%95%94.2%96%91%83%QDA95.3%93%92.2%95%90%81%Thewasabletodetectthefaulttypeanditsseveritywithagoodaccuracy66fortlevelsofvariationsintheoperatingtemperatures.Themainparameterthatneedstobeconsideredisthealigningangle.Inaccuratealigninganglewillmaskthefaultsignature,whichwillreducethedetectionaccuracy,only80%ofthesampleswerecorrectlyinthecaseof10degreemisalignedanglecomparedtoa96:3%withcorrectaligningusingtheKNN67Chapter5TheMC/VSAandLDAApproachMostofthedetectionmethodsintheliteratureusingtheMCSAapproachhavebeentestedforsinglefaultdetection.Theyarebasedonanalyzingthestatorcurrentsignalunderhealthyandfaultedconditions.Theamplitudeofthegeneratedsubharmonicsareusedtodetectthefaulttypeandestimateitsseverity.TheuseofthesesubharmonicspresentssomeItwasshownin[5]and[9]thatsimilarsidebandpatternswillappearforbotheccentricityandshortcircuitfaults,whichmakesthisapproachunabletoseparatebetweenthetwofaults.Also,theamplitudesofthegeneratedsubharmonicsdependontheoperatingspeedandloadconditions;atlowerspeedsitwastodetectthesesidebandpatternscomparedtohighspeedoperation[25].In[26]and[27],itwasshownthattherelationbetweenthenumberofpolesandthestatorslotstheappearanceofthestatorcurrentsubharmonicsrelatedtoeccentricityfaults.Basedonthis,usingthesubharmonicsonlyforfaultdetectionmightnotbeadequateforfaultdetectionandseparation.Ontheotherhand,therewillalwaysbeachangeintheamplitudeoftheharmonicsofthevoltageorthecurrentsignalsinfaultedcases.Thechangeintheamplitudeisrelatedtothetypeandtheseverityofthefault.Themainobjectivesofthischapterinclude1)evaluatingtheaccuracyofusingtheMCSA68andtheLDAtodetectthemachinestatus,whetheritishealthyorfaulted,separationbetweentfaults,andestimationofthefaultseverity.2)Usingeitherthemeasuredstatorcurrentsorthecommandedvoltagesforfaultdetectionandiden3)Usingtheamplitudeoftheharmonicsasfaultdetectionandfeaturesinsteadofthesubharmonics.Thisapproachcanbeusedasamethodtoseparatebetweentfaultwhenthemotorisoperatingatsteadystate.However,Sincethatonlythe15harmonicsareneededfortheonlyfewcyclesareneededwhichcanbeextractedwhenthemotorisatoperatingstandstillforashortperiodoftime.5.1AlgorithmforFaultDetectionandFig.5.1showsthegeneralwdiagramforthefaultdetectionalgorithmusingtheMC/VSAapproach.ThealgorithmcontainstwoTherstrisusedtodetectthepresenceandtypeofthefault,whilethesecondisusedtoestimatethefaultseverityoncethetypeoffaultisdetermined.Theproposedmethodisasfollows:[1]Threephasecurrentsareusedtocontrolandoperatethemachineunderbothhealthyandfaultedconditions.Thestatorphasecurrentorvoltagesignalsintheabcframeofreferenceweremeasuredforprocessing.[2]FFTwasappliedtothemeasuredcurrentorvoltagesignals.TheamplitudesoftheharmonicswereselectedasfeaturesfortheInthismethod,avectoroftheamplitudeofthe15harmonicswaschosenfromphaseAspectrum,asthefeaturesforeachsample.(i.e.thefundamentalandtheharmonics2nd-15th)[3]LDAisappliedtodetectwhetherthemachineishealthyorfaulted,and69StartphasecurrentorvoltageFFTLDAfaulted?HealthyTypedemagnetizationEccentricityShortcircuitLDALDA12%Ecc25%Ecc50%Ecc12%Short25%ShortnoyesFigure5.1BlockdiagramfortheMC/VSAapproachdeterminethetypeofthefault.Thesamplespaceforthecontainssamplesfromallthestudiedfaults.Inthefaultedcase,itdetectsthetypeasoneofthefollowing:staticeccentricity,turn-to-turnshortcircuit,orpartialdemagnetization.[4]Ifthefaultisdetectedasstaticeccentricityorturn-to-turnshortcircuitfault,anotherLDAisappliedtodeterminetheseverityofthatfault.Inthisthesamplespacecontainssamplesfromthesametypeoffaultbutwithtseverities.705.2SimulationandExperimentalResultsFig.5.2ashowsthespectrumofthestatorcurrentforthedistributedwindingmachineunderhealthyandtwofaultswithtseverities(25%and50%ofeccentricityfaultand12%ofthecoilsinphaseAshorted).Fig.5.2bshowsthespectrumofthestatorcurrentoftheconcentratedwindingmachineunderhealthyandtwoseveritiesofeccentricityfaults(25%and50%).Thecurrentspectrumwascollectedexperimentallyforaloadof50Aandoperatingspeedof500rpm.Thechangeintheamplitudesofthe5thand7thharmonicswereunderfaultedcasescomparedtothehealthyone.(a)Experimentalresultsofthestatorcurrentspec-trumforthedistributedwindingmachine(b)ExperimentalresultsofthestatorcurrentspectrumfortheconcentratedwindingmachineFigure5.2ExperimentalresultsforthestatorcurrentharmonicsundererentfaultsItcanbenoticedfromFig.5.2thatfaultsintroducestchangestothecurrentspectrum,theamplitudeofsomeharmonicslikethe5thharmonicincreasesinthecaseofeccentricityfault,butitdecreasesinthecaseofturn-to-turnshortcircuitfault.Thischangedependsonthetypeandtheseverityofthatfault.Thesechangesintheharmonicsamplitudecanbeusedasfeaturestodetectthefaulttypeandestimatetheseverity.It71isimportanttomentionthattheharmonicsofthecurrentsignalfromphaseAonlywereselectedforthefeatures.Thismighttheresultsforshortcircuitfaultbutnotdemagnetizationoreccentricity.However,theshortcircuitfaultwasappliedusingahighshortresistance(Rf=0:whilethemachinephaseresistanceisaround0:Thisreducestheunbalancebetweenthethreephases.Fig.5.3acomparisonofthecurrentspectrumfromphaseA,BandCinthecaseof12%turn-to-turnshortcircuitfaultforthedistributedwindingmachine.Theharmonicsfromthethreephaseshavesimilaramplitudes.Therefore,thismethodisabletodetecttheshortcircuitfault,nomatterwhichphasetheharmonicswereselectedfrom.However,itisnotabletodetectwhichphaseistheshortedone.Figure5.3ComparisonbetweenthecurrentspectrumfromphaseA,BandCunder12%shortcircuitfaultThereasonwhyallthe15harmonicswerechosenasfeaturesfortheisthatturn-to-turnshortcircuitfaultoftengeneratesevenorderharmonics,Therefore,boththeoddandtheevenharmonicswereselectedtoimprovethedetectionaccuracyinthecaseofshortcircuitfault.Fig.5.4showsacomparisonofthecurrentspectrumbetweenhealthycaseand25%shortcircuitfault.Theincreaseintheharmonicsamplitudeat200and400Hz72(4thand8thharmonics)canbenotedinthecaseofshortcircuitfault.Figure5.4Comparisonbetweenthecurrentspectrumunderhealthyand25%shortcircuitfault5.2.1IdentifyingtheFaultTypeLDAisusedtodetectthetypeoffault.Sincethe15harmonicsareusedasfeaturesfortheclassianumberofsampleshigherthan15isrequiredinthesamplespaceforthematrixtoconverge[42].Table5.1showstheresultsoffaultdetection,fortheconcentratedanddistributedwindingmachines,usingFEAsimulationfortwotoperatingloads(30%and60%ofthefullload).LDAwasperformedseparatelyateachload.Thesamplespacecontains44samplesthatcorrespondtofourtclasses.Eachclassrepresentsaspmachinestateasfollows:class0correspondstothehealthycase,class1correspondsto12%staticeccentricity,class2correspondsto12%shortedconductors(oneshortedturnofthedistributedwindingmachine)andclass3correspondsto80%demagnetizationforonemagnet.11samplesweregeneratedforeachclassbyvaryingthespeedfrom1000rpmto2000rpminstepsof100rpm.Thesamplesfor73eachfaultwerechosenastheminimumacceptedseverity,sothat,ifthealgorithmwasabletodetectthefaultwithlowerseverity,thefaultwithahigherseveritycanalsobedetected.The15harmonicsfromthecurrentorvoltagespectrumwithasamplingfrequencyof10kHz,werechosenasfeaturesfortheTovalidatetheresultstheleave-one-outmethodwasused.FromtheresultsinTable5.1,itcanbenotedthatLDAwasabletoclassifythetypeoffaultcorrectlyanddistinguishbetweentfaultsforbothmachinesattoperatingconditions.Table5.1LDAresultsforfaultdetectionusingFEAresults.(Eachclasscon-tains11samplescorrespondtospeeds10002000rpm).ResultsConcentratedWindingDistributionWinding30%60%30%60%fullloadfullloadfullloadfullloadHealthy100%100%100%91%12%eccentricity91%91%100%91%Oneshortedturn100%100%100%100%80%demag.100%100%100%100%5.2.2DeterminingtheFaultSeverityAfterdetectingthefaultanddeterminingitstype,itisnecessarytodetectitsseverity.Inthissection,itisassumedthatthetypeoffaultiscorrectlydetected.AnotherLDAwasusedagaintoestimatetheseverityofeccentricityfaultortheturn-to-turnshortcircuitfault.Table5.2showstheresultsforeccentricityseveritiesforbothmachinesundertwodtloadsat30%and60%offullloadusingFEAsimulation.Table5.3showstheresultsfortheturn-to-turnshortcircuitfault.Forstaticeccentricitycase,74thesamplespaceconsistsof33samplesforthreetseverities:12%,25%,and45%.Eachsamplecorrespondstoaspspeedfrom1000rpmto2000rpminstepsof100rpm.Atotalof3classesassignedasfollows:class0correspondsto12%staticeccentricity,class1correspondsto25%staticeccentricityandclass2correspondsto45%staticeccentricity.Fortheturn-to-turncircuitfault,thesamplespaceconsistsof33samples,correspondingtohealthycaseandtwodegreesofshortedturns:class0correspondstohealthycase,class1correspondsto12%shortedconductors(oneturnwasshorted)andclass2correspondsto24%shortedconductors(twoturnswereshorted).Theleave-one-outmethodwasusedtovalidatetheresults.Table5.2LDAresultstodetecttheseverityofstaticeccentricityfaultusingFEAresults.Eachclasscontains11samplescorrespondtospeeds10002000rpm).ResultsConcentratedWindingDistributionWinding30%60%30%60%fullloadfullloadfullloadfullload12%eccentricity91%100%100%91%25%eccentricity91%100%100%100%45%eccentricity100%100%100%100%Table5.3LDAresultstodetecttheseverityofturntoturnshortcircuitfaultusingFEAresults.(Eachclasscontains11samplecorrespondstospeeds10002000rpm).ResultsConcentratedWindingDistributionWinding30%60%30%60%fullloadfullloadfullloadfullloadHealthy100%100%100%91%12.5%shortcircuit91%100%91%100%25%shortcircuit100%100%100%100%Fromtheresults,itisclearthatLDAcanbeusedforeither75machine,todetectthetypeoffaultandestimateitsseverity.However,someofthesamplesrelatedtothe12%staticeccentricityfaultwerenotcorrectly,eventhoughonlysimulationexperimentswereusedthatdidnothavemeasurementnoise.Thereasonforthat,becauseforlowseveritiesofeccentricityfaults,mostoftheharmonicamplitudesforthe12%eccentricitywereclosetothoseforthehealthymachine;hencetheLDAcannotdistinguishbetweenhealthyandthe12%staticeccentricityfaultforafewsamples.5.2.3ComparingFEAwithExperimentalDataTovalidatetheproposeddetectionmethod,experimentaldatawerecollectedforbothma-chinesundertfaults.Theexperimentaldataforthedistributedwindingmachinewerecarriedoutforhealthyandtwotypesoffault:staticeccentricitywithtwoseverities(25%and50%),andoneturn-to-turnshortcircuitfault.Theconcentratedwindingmachinewastestedunderhealthyandtwoseveritiesofstaticeccentricityfaults(25%and50%).TheofbothspeedandtorquewerecombinedtoevaluatetheaccuracyofLDAforfaultdetectionandidenFirst,thetrainingsamplesandthetestingsampleswerecollectedofthesametorque.LDAwasperformedseparatelyforsamplescollectedfromthreetorquelevels(20A,50Aand70A).Eachtorquecasecontainsanumberofclassesthatthemachinehealthstatus.Thesamplespaceforeachclasscontains11samplesgeneratedbyvaryingthespeedfrom500rpmto1000rpminstepsof50rpm,withasamplingfrequencyof10kHz(10000pointswererecordedforeachsample(1s)).Theleave-one-outmethodwasusedtotestandvalidatethemethod.(ResultsareshowninTables5.4and5.5forcases1,3and4).Inthesecondcase,thetrainingsamplesandthetestingsampleswerecollectedusingttorquelevels.Twotorqueswastested:30Aand100A.Inthe30Acase,thetesting76sampleswerecollectedwhilethemachineisoperatingatatorquecorrespondingto30Awhilethetrainingsampleswereinterpolatedfromsamplescollectedfromtorquesof20A,50Aand70A.Thesamplespaceforeachclasscontains11samplesgeneratedbyvaryingthespeedfrom500rpmto1000rpminstepsof50rpm.Thesameprocedurewasfollowedforthe100AcaseandtheresultsareshowninTables5.4and5.5forcases2and5).Table.5.4showsacomparisonoftheresultsforfaultdetectionbetweentheexperimentalandFEAsimulationforthedistributedwindingmachineunderhealthy,25%eccentricityfaultand12%shortcircuitfault.Table5.5showsacomparisonoftheresultsbetweentheexperimentalandFEAsimulationfortheconcentratedwindingmachineunderhealthyandtwoseveritiesofeccentricityfault(25%and50%).Table5.6showsacomparisonoftheresultsforfaultseveritydetectionbetweentheexperimentalandFEAsimulationforthedistributedwindingmachineundertwoseveritiesofeccentricityfault(25%and50%).Table5.4ComparisonofLDAresultsbetweenexperimentsandFEAtode-tectthefaulttypeforthedistributedwindingmachine.Eachclasscontains11samplescorrespondtospeeds5001000rpm).ResultsExperimentalresultsFEAresultscase#Healthy25%OneturnHealthy25%Oneturneccentricityshorteccentricityshort1-20A91%91%100%100%100%100%2-30A82%82%82%91%82%91%3-50A91%82%91%91%91%100%4-70A91%82%82%90%82%82%5-100A72%63%72%82%72%82%Theresultsshowthatthemostaccuratecanbeachievedwhenthetestingandthetrainingsampleswerecollectedfromthesameload.Aminimumof82%ofthe77Table5.5ComparisonofLDAresultsbetweenexperimentsandFEAfortheconcentratedwindingmachine.Eachclasscontains11samplescorrespondtospeeds5001000rpm).ResultsExperimentalresultsFEAresultscase#Healthy25%OneturnHealthy25%Oneturneccentricityshorteccentricityshort1-20A100%91%100%100%100%100%2-30A82%72%82%91%82%91%3-50A91%82%91%91%91%91%4-70A91%82%91%91%91%91%5-100A72%72%72%72%72%82%Table5.6ComparisonofLDAresultsbetweenexperimentsandFEAtode-tectthefaultseverityforthedistributedwindingmachine.Eachclasscontains11samplecorrespondstospeeds5001000rpm).ResultsExperimentalresultsFEAresultscase#Healthy25%50%Healthy25%50%eccentricityeccentricityeccentricityeccentricity1-20A91%91%91%100%91%100%2-30A82%82%82%91%82%91%3-50A91%82%82%91%91%91%4-70A82%82%82%91%82%82%5-100A72%62%82%82%82%82%sampleswerecorrectly.Interpolationforthetrainingsamplescanbeusedifthetestingsampleswerecollectedfromaloadclosetothetrainingsamplesload,buttheaccuracydecreasesifthetrainingsampleswerecollectedfromloadsthatweretootfromthetestingsamplesloads.Aminimumcorrectof62%inthecaseof100Awasachievedtodetecteccentricityfault.Aminimumpercentageof72%achievedinthecaseof30Aforeccentricityfaultdetection.Totestthemethodovertheoperatingrangeandnotonlyatasptorque,theentire78samplingspacewasmotocontainttorquesandspeeds.Tables5.7and5.8showacomparisonofthecorrectresultsbetweenexperimentaldataandFEAoffaultdetectionandforthedistributedwindingmachine.Thesamplespaceforeachclasscontains40samples,soatotalof120sampleswereusedtogeneratethetrainingmatrix.The40samplescorrespondto4dtcurrents,eachcasecontains10samplesthatweregeneratedbyvaryingthespeedfrom550rpmto1000rpminstepsof50rpm.Thecombinationoftheamplitudeofthe15harmonicswereusedasthefeaturesfortheLDAtheleave-one-outmethodwasusedtovalidatethe.Fig.5.5showsthefulltrainingmatrixconstructionforthehealthycaseandtwotfaults.Fig.5.6showstheconstructionofthehealthyportionofthefulltrainingmatrix.2666666666666664x11x12x13x115............x401x402x403x4015x411x412x413x4115............x801x802x803x8015x811x812x813x8115............x1201x1202x1203x1201537777777777777759>=>;H9>=>;25%ECC.9>=>;12%shortFigure5.5Fulltrainingmatrixforhealthycaseandtwofaults(25%eccentricityand12%turnsofphaseAshorted).Table5.7AcomparisonofLDAonresultstodetectthefaulttypeforthedis-tributedwindingmachinebetweenexperimentsandFEAusingthefulltrainingmatrix.ResultsExp.usingcurrentExp.usingvoltageFEADataHealthy87.5%85%95%25%eccentricity85%80%88%Oneturnshort88%85.5%92.5%79H8>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>:26666666666666666666664x11x12x13x115............x101x102x103x1015x111x112x113x1115............x201x202x203x2015x211x212x213x2115............x301x302x303x3015x311x312x313x3115............x401x402x403x4015377777777777777777777759>=>;20A9>=>;30A9>=>;40A9>=>;50AFigure5.6Trainingmatrixforhealthycaseonly.Table5.8AcomparisonofLDAresultstodetecttheseverityofeccentricityfaultforthedistributedwindingmachinebetweenexperimentsandFEAusingthefulltrainingmatrix.ResultsExp.usingcurrentExp.usingvoltageFEADataHealthy85.5%87.5%91%25%eccentricity77.5%80%87.5%50%eccentricity80%77.5%90.5%TheresultsshowthatusingtheMSCAwiththeLDAasamethodwasabletodetectthetypeofthefaultandestimatetheseverity,eitherbyusingtheharmonicsofthephasevoltagesorofthecurrentsignals.Whenthetrainingandtestingfeaturesareextractedfromsamplescollectedattoperatingloads,theresultwasnotasaccuratecomparedtothecasewhenthesamplesarecollectedfromthesameoperatingtorque.Forfaultdetection,anaverageof89:6%ofthesampleswerecorrectlyfortheFEAsamples,while81%ofthetotalsampleswerecorrectlyfromtheexperimentaldatausingtheharmonicsinthemeasuredfeedbackcurrent,and81:6%80werecorrectlybasedontheharmonicsinthevoltagesignal.Inpracticalapplications,testedmachinesmightduetothemanufacturingtoleranceandthevariationsinthematerialproperties.Toevaluatetherobustnessofthedetectionmethods,AdditiveWhiteGaussianNoise(AWGN)withtSignaltoNoiseRation(SNR)levelswasaddedtothetestedcurrentsamples.AcomparisonoftheresultsforfaultdetectionbetweenexperimentalandFEAisshowninTable5.9.Forthiscase,thesamplespacecontains30samplescorrespondingtothreeclasses:healthy,25%staticeccentricityandoneturn-to-turnshortcircuitfault.Eachclasscontains10samplesgeneratedbyvaryingthespeedfrom550rpmto1000rpminstepsof50rpm,withasamplingfrequencyof10KHzforacurrentof20A.Itisnotedthatthechangeintheharmonicsamplitudeduetothenoisethenresults,whichmakesthedetectionbasedontheharmonicsamplitudenotrobustathighnoiselevels.Table5.9AcomparisonofLDAresultsforthedistributedwindingmachinefortSNRlevels.Eachclass10containssamplescorrespondtospeeds5501000rpm).ResultsExperimentalresultsFEAresultsSNRH25%OneturnH25%Oneturn(dB)eccentricityshorteccentricityshort10090%80%90%100%100%90%9090%80%90%100%100%90%8088%83%85%95%92%88%7080%75%79%90%86%82%6070%65%71%80%70%76%5.2.4ofTemperatureThechangeintheoperatingtemperaturecausesmultiplechangestothestatorcurrentandvoltage.Theincreaseoftheoperatingtemperaturewillcauseanincreaseinthestator81phaseresistanceandadecreaseinthemagnetremanenceTheoftemperatureissimulatedbychangingthevaluesofthestatorresistanceandthemagnetremanencebasedon(4.14)and(4.15).Table6.21showsthesimulationresultsoffaultforfaultdetectionunderttemperatures.Thesamplespacecontains40samplescorrespondingto4classes:Healthy,12%staticeccentricity,12%shortcircuitfaultand80%demagnetization.Eachclassconsistsof11samplesgeneratedbyvaryingthespeedfrom1000rpmto2000rpminastepsof100rpm.Thetrainingsampleswerecollectedatanoperatingloadof20Aatatemperatureof200C,whilethetestingsampleswerecollectedatatemperaturesof200C;700Cand1500C.Table5.10LDAresultsforfaultdetectionusingFEAresults.Eachclasscontains11samplescorrespondtospeeds10002000rpm).ResultsConcentratedWindingDistributionWinding200C700C1200C200C700C1200CHealthy100%72%63%100%72%63%12%eccentricity91%72%55%91%72%63%12%short100%81%63%100%81%72%80%demag.100%63%55%91%55%55%Itcanbenoticedthatifthetrainingsampleswerecollectedfromanoperatingtemper-aturethatisclosetotheoperatingtemperatureofthetestingsamples,therwasabletodetectthefaulttype.However,ifthetestingsampleswerecollectedfromatoperatingtemperaturescomparedtothetemperatureatwhichthetrainingsampleswerecollected,theaccuracyofthereduced,especiallyfordemagnetizationfaultbecauseitismainlyrelatedtotemperature.Aminimumpercentageof63%ofthesampleswerecorrectlyforthe700Ccasewhileaminimumcorrectpercentageof8255%achievedforthe1200Ccase.83Chapter6TheCommandedVoltagesApproachtfaultsinPMSMswillcausevariousandindependentchangestothemachineperfor-manceandparameters.Thesechangeswillbeectedinthemachinelinkages,whichcanbedeterminedandmeasuredfromthemachinevoltages.Thischaptershowshowtousethecommandedvoltagesasamethodforfaultdetectionandseparation.Theshiftdirectioninthecommandedd-axisandq-axisvoltagescanbeusedtodetectthetypeofthefault,andtheamountoftheshiftcanbeusedtoestimatetheseverity.Thismethodcanbeappliedduringthenormaloperationofthemachine,whilethemotorisrunningatsteadystate.6.1VariationsofVdandVqUnderVariousFaults6.1.1VdandVqVariationsUnderEccentricityFaultItwasshowninChapter2andChapter4thatinthecaseofstaticeccentricity,themachinesaturatesearliercomparedtothehealthymachine.Thisearlysaturationisasanincreaseinthetotallinkagesinthemachine.Fig.6.1showsacomparisonofthemagneticdensityfortheFSCWmachinebetweenthehealthymachineandamachinewith80%staticeccentricityfault.Theincreaseinthemachinedensity(inthezoomedregion)canbenoticedinthecaseofeccentricmachine.Duetothenonlinearityofthemachine,theincreaseinthemagnetic84(a)Fluxdensityforhealthymachine(b)Fluxdensityforamachinewith80%eccentric-ityFigure6.1Comparisonofthemagneticdensitybetweenahealthymachineandamachinewith80%eccentricity.density,inthelowerairgapregion,willbelargerthanthedecreaseinthemagneticdensity,inthehigherairgapregion.Thiscausesanincreaseinthetotallinkagesinthemachine.Theincreaseinthetotallinkagesincreasethevalueofbothdandq.Basedon(2.11)and(2.12),increasingdandq,forthesameoperatingload,increasesVdbutdecreasesVq.Sointhecaseofaneccentricityfault,thepoint(Vd,Vq)intheVd-Vqplanewillshifttowardthetopleft,andastheseverityofeccentricityfaultincreasesthepoint(Vd,Vq)shiftsmoretothetopleftofthecurve.6.1.2VdandVqVariationsUnderDemagnetizationFaultInthecaseofpartialdemagnetizationfault,anonuniformmagneticdensitygeneratesaroundtherotor,whichcausesadisturbancetothemagneticinthemotorandreducethetotalmagneticdensitygeneratedfromthemagnets.Fig.6.2showsacomparisonofthemagneticxlinebetweenhealthyandthemachinewithMag1demagnetized.Demagnetizingoneormoreoftherotormagnetscauseadecreasinginthetotalmagneticlinkages(pm).Basedon(2.10),decreasingpmcausesareductioninthetotald-axisOtherofdemagnetizationfaultisthechangeinthemagneticinthe85(a)Fluxlinesforhealthymachine(b)Fluxlinesforamachinewithmag.1demag-netizedFigure6.2Comparisonofthelinesbetweenhealthymachineandamachinewithonemagnetfullydemagnetized.machine.Thedemagnetizedregionwillhavethesameasanairregion,forcingthetoconcentratemoreintheq-axisofthemachine.Thisincreasesthetotalqaxislinkagesinthemachine.Basedon(2.11)and(2.12),decreasingdandincreasingqimpliesadecreaseofbothVdandVqcomparedtothehealthycase.Therefore,inthecaseofdemagnetizationfaultthepoint(Vd,Vq)intheVd-Vqplanewillshifttowardthebottomleft,andasthenumberofdemagnetizedmagnetsincreasestheshiftinthepoint(Vd,Vq)willincrease.6.1.3VdandVqVariationsUnderTurn-to-turnShortCircuitFaultItwasshownin(2.29)-(2.34)thatinthecaseofturn-to-turnshortcircuitfault,theequiv-alentmodelforPMSMwillcontaintwocomponents:ahealthycomponentandavariablecomponentrelatedtotheshortcircuitfault.Thevariablecomponentisrelatedtothecircu-latingshortcircuitcurrentintheshortedturns.Thiscurrentiscanbeapproximatedasasinusoidalcurrentandcanbedescribedasif=jifjcos(+˚f),wherejifjisthemagnitudeoftheshortcircuitcurrent,and˚fisthephaseshiftoftheshortcircuitcurrent.Basedonthisassumption,thevariablecomponentcanbeexpandedtocontainaDCcomponent86andanoscillatedcomponent.TheDCcomponentofthedandqaxesundersteadystateoperationisgivenas:vdf;DC=13rfjifjsin(˚f)!e(Mahaf+Laf)jifjsin(˚f)(6.1)vqf;DC=13rfjifjcos(˚f)!e(Mahaf+Laf)jifjcos(˚f)(6.2)Theshortcircuitcurrentcanbeestimatedusingthefollowingequation:if=rfia+efrf+Rf(6.3)whererfistheequivalentresistanceoftheshortedturns,andRfisvalueoftheshortresistance.Itisnotedfrom(6.1)and(6.2)thattheDCcomponentdependsonthemagnitudeandtheangleshiftofshortcircuitcurrent,whichisdeterminedbytheseverityoftheshortcircuitfault.Fig.6.3showstheshortcircuitcurrentintheFSCWmachineundertseveritiesofturn-to-turnshortcircuitfault.Figure6.3ShortcircuitcurrentfortheFSCWmachinefortseveritiesofshortcircuitfault.Astheseverityofturn-to-turnshortcircuitfaultincreases,themagnitudeoftheshort87circuitcurrentandthereforetheDCcomponentinboththedandtheqaxeswillincreaseaswell.IncreasingtheDCcomponentscasesthevalueofthedandqvoltagestoincreasetoo.Theofshortcircuitfaultcanalsobeobservedusingthechangeinthemagneticdensityandlines.Fig.6.4showsacomparisonofthedensityandthelinesbetweenhealthymachine,andamachinewith20%oftheturnsofphaseAcoilconductorsareshorted.(a)Fluxdensityandlinesforahealthyma-chine(b)Fluxdensityandlinesfor20%shortcircuitfaultFigure6.4Comparisonofthedensitybetweenahealthymachineandamachinewith20%oftheturnsinphaseAconductorsareshorted.Underturn-to-turnshortcircuitfault,thetotalxdensitydecreasesintheshortedregion(thezoomedregion),thismeansadecreaseinthevalueofq.However,intheshortregion,morelinesareclosinginthed-axisofthemachinecausinganincreaseind.DecreasingqandincreasingdincreasesthevalueofVdandVq.Therefore,inthecaseofshortcircuitfault,thepoint(Vd,Vq)shiftstowardsthetoprightintheVd-Vqplane.Itisnoticedthatturn-to-turnshortcircuitfaultdependsonthenumberoftheshortedturnsandthevaluesoftheshortedresistance.Asthenumberofshortedturnsincreasesorthevalueoftheshortedresistancedecreases,thevaluesofVdandVqincreasesmore.Fig.6.5summarizethechangeinthecommandedvoltagesundertfaultscomparedtothehealthycase.88Figure6.5Theshiftinthecommandedvoltagesunderthetestedfaults6.2NumericalAndExperimentalResultsThetestswereappliedwhilethemotorswereoperatingatsteadystatewithratedtorque.Totheoperatingconditionswhenthemachineisoperatingatthistorque,themachineneedstobecharacterized(i.e.thevalueofthemachinedandqaxesinductancesundertoperatingconditions).Followingthecharacterizationmethoddiscussedinchapter2,thesimulationresultsforthetorque,d,andqversusthecurrentangle()attcurrentloadsfortheFSCWmachineisshowninFig.6.6(a)Torquevs(b)dvs(c)qvsFigure6.6SimulationresultsforthecharacterizationoftheFSCWmachineundertoperatingloadsataspeedof300rpmThemaximumtorquewasachievedatanoperatingangle=120.Therefore,allthe89testswillbeappliedatacontrolangleof120.6.2.1StaticEccentricityFaultResultsFig.6.7showsthesimulationresultsforthevariationindandqfortseveritiesofeccentricityfaultscomparedwiththehealthymachine.Themachinewasrunningataspeedof300rpmandtheappliedcurrentwas5Aatanangleof120(i:e:Iq=4:33A;Id=2:5A).AsdiscussedinSection6:1:1,theextrasaturationduetotheshiftinthestatorgeometrywillbringupthevaluesofdandqrelativetoahealthymachine.(a)Simulationresultsford(b)Simulationresultsforq(c)Experimentalresultsford(d)ExperimentalresultsforqFigure6.7dandqforhealthyandtseveritiesofeccentricityfaultatI=5Aand=12090Fig.6.8showsthechangeinthevaluesofVdandVqfortheFSCWmachineundertseveritiesofstaticeccentricitycomparedtothehealthycase.Itcanbenotedthatinthecaseofeccentricityfault,thevalueofVddecreases,andthevalueofVqincreases,movingthepoint(Vd,Vq)totheupperleftintheVd-Vqplane.ThechangeinVdandVqdependsontheseverityofeccentricityfault.Aseccentricitybecomesmoreseverity,thepoint(Vd,Vq)shiftsmoretotheupperleftintheVd-Vqplane.(a)SimulationresultsVdvsVq(b)ExperimentalresultsVdvsVqFigure6.8SimulationandexperimentalresultsforthechangeinVdandVqforhealthyandtseveritiesofstaticeccentricityfaultatI=5Aand=1206.2.2PartialDemagnetizationFaultResultsThreelevelsofpartialdemagnetizationfaultweretestedfortheFSCWmachineusingsim-ulationsandexperimentaltests.Fig.6.9showsacomparisonofthevariationindandqbetweensimulationsandexperimentaldata.Themachinewasoperatedataspeedof300rpmandthecurrentappliedis10Aatanangleof120.Fig.6.9showsthatbothsimulationandexperimentalresultsexhibitthesamebehavior.Thevalueofddecreases,butthevalueofqincreases.ThisdecreasesthevalueofVdandVqmovingthepoint(Vd,Vq)tothebottomleftoftheVd-Vqplane.Fig.6.10showsa91(a)Simulationresultsford(b)Simulationresultsforq(c)Experimentalresultsford(d)ExperimentalresultsforqFigure6.9SimulationsandexperimentalresultsfordandqfortheFSCWmachineunderhealthyand3levelsofdemagnetizationfault(1,2and3magnets)atI=10Aand=120comparisonbetweensimulationsandexperimentalresultsforthechangeinVdandVqunderhealthyandthreeseveritiesofpartialdemagnetizationfaults.6.2.3Turn-to-turnShortCircuitFaultResultsSimulationsandexperimentaltestswereperformedontwolevelsofturn-to-turnshortcircuitfault:10%and20%ofthetotalturnsofphaseAconductors.Tovarytheseverityofeachlevel,twotshortedresistanceswereused(0:5and0:25whichisequalto33:3%and16:6%ofthestatorresistancerespectively).Fig.6.11showsthevariationindandq92(a)SimulationresultsVdvsVq(b)ExperimentalresultsVdvsVqFigure6.10SimulationandexperimentalresultsforthechangeinVdandVqforhealthyand3levelsofdemagnetizationfaultatI=10Aand=120forthetestedturn-to-turnshortcircuitfault.Themachinewasoperatedataspeedof300rpmandthecurrentappliedwas10Aatanangleof120.Inthecaseofshortcircuitfault,thevalueofdincreases,butthevalueofqdecreases,whichcausesanincreasinginbothVdandVq;thisshiftsthe(Vd,Vq)pointintheVd-VqplanetotheupperrightasshowninFig.6.12.Basedonthepreviousresults,theshiftdirectionofthepoint(Vd,Vq)canbeusedasanindicatortodetectthetypeoffaultandalsoestimatetheseverity.Inthecaseofaneccentricityfault,thepoint(Vd,Vq)shiftstowardstheupperleftoftheplane;inthecaseofpartialdemagnetizationfault,thepoint(Vd,Vq)shiftstowardsthebottomleftoftheplane;andforturn-to-turnshortcircuitfault,thepoint(Vd,Vq)shiftstowardstheupperrightoftheplane.Fig.6.13comparestheresultsbetweensimulationsandexperimentalresultsthatsummarizethechangeinthepoint(Vd,Vq)attfaulttypesandseverities,fortwotorques(I=5AandI=10A)atanangleof=120runningataspeedof300rpm.ItcanbenotedfromFig.6.13thatasthecurrentincreases,itbecamehardertodetecteccentricityfault.Astheappliedcurrentincreases,thesaturationinthemachinefrom93(a)Simulationresultsford(b)Simulationresultsforq(c)Experimentalresultsford(d)ExperimentalresultsforqFigure6.11Simulationsandexperimentalresultsfordandqunderhealthyand2levelsofturn-to-turnshortcircuitfaultatI=10Aand=120thestatorwillmasktheoftheextrasaturationfromeccentricityfaultmakesithardertoobservetheshiftinVdandVq.However,forpartialdemagnetizationandshortcircuitfaults,theshiftinVdandVqcanstillbeobservedevenathighcurrentsusingbothsimulationsandexperimentally.Table6.1summarizethechangesinthedandqaxisvoltagesundertfaultsandseveritieswhilethemachinewasoperatingataspeedof300rpmandacurrentof5Aatanangleof1200.94(a)SimulationresultsVdvsVq(b)ExperimentalresultsVdvsVqFigure6.12SimulationandexperimentalresultsforthechangeinVdandVqforhealthyand2levelsofshortcircuitfaultatI=10Aand=120Table6.1SimulationandtheexperimentalresultsforVdandVqfortheFSCWmachineundertfaultsFEASimulationExperimentalFaultTypeVdVqVdVqHealthy-64.833.6-78.944.620%Eccentricity-6533.6--40%Eccentricity-65.333.9--60%Eccentricity-65.634.4--80%Eccentricity-66.135--1MagnetDemag.-66.330-81.6402MagnetsDemag.-67.727.9-81.931.53MagnetsDemag.-69.224.2-82.728.610%ShortRf=0.5-64.334.5-75.352.910%ShortRf=0.25-63.535.2-71.95220%ShortRf=0.5-61.835.7-70.65320%ShortRf=0.25-59.135.3-68.753.76.2.4ofMagnetAngleFig.6.14showsthesimulationresultsfortheshiftinthedandqvoltagesfortheconcentratedwindingmachineunderhealthy,andthethreetestedmachine.Thesameshiftbehaviourinthecommandedvoltagescanbeobservedinthestaticeccentricityandturn-to-turnshort95(a)VdvsVqsimulationresultsI=5A;=120(b)VdvsVqexperimentalresultsI=5A;=120(c)VdvsVqsimulationresultsI=10A;=120(d)VdvsVqexperimentalresultsI=10A;=120Figure6.13SimulationandexperimentalresultsforthechangeinVdandVqforhealthyandtfaultsforI=5A,=120andI=10A,=120circuitfaults.However,forpartialdemagnetizationtheshiftinthecommandedvoltageswasmainlyintheqaxisvoltagebutnotinthedaxis.Thebehaviourofthereductionintheq-axisvoltageissimilartothecaseoftheFSCWmachine.However,thed-axisvoltageincreasedwhichisoppositetothecaseoftheFSCWmachine.Thisisduetothemagnetsrotationangle.Inthecaseofpartialdemagnetization,thedemagnetizedmagnetwillhavepropertiessimilartotheairthatblockthelinespath.Ifthemagnetsarenotrotated(asinthecaseoftheconcentratedwindingmachine),thelineswillpassthroughthebackironoftherotorcausingadecreaseinqandtherefore96Figure6.14SimulationresultsforthechangeinVdandVqforhealthyandthethreetestedfaultsfortheconcentratedwindingmachineforI=75Aand=120increaseinVd.However,ifthemagnetsarerotated,thedemagnetizedmagnetswillblockthepathofthelinesandpushthemtowardtheq-axisofthemachine.ThiscausesanincreaseinqandthereforedecreaseinVd.Tostudytheofthemagnetrotationangle,therotorgeometryfortheconcentratedwindingmachinewasmobyrotatingthemagnetangleattdegrees.Fig.6.15showsthemointhemagnetplacementofonepoleoftherotormagnetsandFig.6.16showsthecrossgeometryfortheoriginalconcentratedwindingmachineandthemorotormagnetsfor0,10,and20rotationangles.Figure6.15SinglepolemagnetrotationoftheconcentratedwindingmachineFig.6.17showsacomparisonofthelines,fortheconcentratedwindingmachine,97(a)=00(b)=100(c)=200Figure6.16Momagnetsfortheconcentratedwindingmachinebetweenazerorotationangleand150rotationangleunderonemagnetfullydemagnetized.(a)=00(b)=150Figure6.17Comparisonofthelinesfor00and150magnetrotationangleunderdemag-netizationfautFig.6.18showsacomparisonoftheshiftinVdandVqfortheconcentratedwindingmachineunderhealthyandtseveritiesofdemagnetizationfaultforthetmagnetrotationangles.ItcanbenotedthatthevalueofVqdoesnotchangeforallthecasesasexpected.TheonlychangeisinthevalueofVdwhichisduetothechangeintheconcentrationduetothemagnetrotationangle.98Figure6.18TheofthemagnetrotationonVdandVqfortheconcentratedmachineunderhealthyanddemagnetizationfaultTherotationofthemagnetanglewillalsothechangeVdandVqundereccentricityfault.Whenthemagnetsarerotated,thewillhavemoresteeltopassthrough.Thisreducesthesaturationintherotorsteelcomparedtothecasewhenthemagnetarenotrotated.Inthiscase,theextrasaturationinthemachineduetoeccentricityfaultwillbemorenoticeableandtheoftheextrasaturationcanbemorenoticablewiththerotatedmagnetscomparedtooriginalmagnetsposition.Therefore,theincreaseindandqwillbehigherinthecaseofrotatedmagnetscomparedtothenonrotatedmagnetsforeccentricmachine.TheincreaseindandqimpliesthattheincreaseinVqandthedecreaseinVdwillbemoreinthecaseofrotatingmagnets.Fig.6.19showsacomparisonoftheshiftinVdandVqfortheconcentratedwindingmachineunderhealthyandtseveritiesofeccentricityfaultforthetmagnetrotationangles,themotorwasoperatingataspeedof2000rpmandtheappliedcurrentis75A.ItcanbenotedfromFig.6.19thatthechangeinthesaturationctbothVdandVq,butitwontchangethedirectingoftheshift.Inallcases,thepoint(Vd;Vq)wasshiftedtothetopleftoftheVd-Vqplane,buttheamountoftheshiftwashigherinthecaseofrotated99Figure6.19TheofthemagnetrotationonVdandVqfortheconcentratedmachineunderhealthyandeccentricityfaultmagnetscomparedtononrotatedmagnets.6.2.5ofSpeedandTemperatureTheoperatingspeedandtemperatureofPMSMwillchangefrequently.Therefore,itisimportanttovalidatetheseparationmethodundertoperationspeedsandtemper-ature.ThreespeedsweresimulatedfortheFSCWmachineusingFEA(300rpm,500rpmand600rpm).Foreachspeedthecommandedvoltages(VdandVq)weremeasuredundertloads.Fig.6.20showsthesimulationresultsforthevariationintheFSCWmachinevoltagesVdandVqunderhealthyandthethreetestedfaults.Thechangeinthemachineoperatingtemperaturecausesachangeinthemachinevoltagesduetothechangeinthestatorresistanceandthechangeofthemagnetremanentwithtemperature.TheincreaseinthetemperaturewassimulatedinFEAbychangingthephaseresistanceandthemagnetremanenceasin(4.14)and(4.15).Fig.6.21showsthesimulationresultsfortheofthetemperatureincreaseonthedandqaxisvoltagesforhealthythethreetfaults.Table6.2summarizethechangeinthecommandedvoltagesforthe100Figure6.20SimulationresultsforthechangeofVdvsVqfortheFSCWmachineunderhealthyandthreetfaultsundertwospeeds300rpm,and500rpm(I=5A;angle=1200andtemp=200C)threefaultsundertoperatingtemperatures.Figure6.21SimulationresultsforthechangeofVdvsVqfortheFSCWmachineunderhealthyandthreetfaultsunderthreetemperatures200C,1000Cand1500C(I=5A;angle=1200andspeed=300rpm)ItcanbenotedfromFig.6.20andFig.6.21thatthechangeinthespeedandtemperatureshiftsthevalueofboththedandtheqaxisvoltages,whichmightdecreasetheaccuracyof101Table6.2ComparisonforthesimulationresultsforVdandVqfortheFSCWmachineundertfaultsandoperatingtemperatures200C1000C1500CStatusVdVqVdVqVdVqHealthy-64.933.5-67.829.8-69.527.620%eccentricity-6533.6-67.930-69.727.740%eccentricity-65.333.9-68.330.2-70.12860%eccentricity-65.934.4-68.730.7-70.628.480%eccentricity-66.135-69.331.4-71.329.21Magnetdemag.-66.330-69.326.7-71.124.72Magnetsdemag.-67.727.9-70.724.8-72.522.93Magnetsdemag.-69.224.2-71.921.4-73.619.810%shortRf=-64.334.5-67.231-6928.820%shortRf=-61.835.7-64.931.4-66.830.410%shortRf=-63.535.2-66.531.7-68.429.620%shortRf=-59.135.3-62.332.2-64.230.3thedetectionmethod;howevertheshiftofthe(Vd,Vq)pointcausedbythetfaultsshowsthesamebehaviourunderttemperatures.6.3FaultDetectionandSeparationAlgorithm6.3.1ProposedDetectionMethodTheshiftinthevoltages(VdandVq)undertfaultsisconsistentforntoperatingloads,speedsandtemperatures.Therefore,theshiftinthecommandedvoltagescanbeusedasadetectionmethodtodetectthefaulttypeandestimateitsseverity.However,themachineoperatesatrentoperatingandenvironmentalconditions.Therefore,itisimportanttoaccountforthechangesinthecommandedvoltagesusingthesefactorsintoconsideration.Fig.6.22showsablockdiagramoftheproposeddetectionandseparationmethodusingthecommandedvoltageapproach.102StartOperating/controlparametersVdandVqVedandVeqCharacterizationDataFault?FaulttypeEccentricityDemagnetizationShortcircuitnoyesTorqueSpeedTempFigure6.22BlockdiagramforfaultdetectionandseparationusingthecommandedvoltagesThefollowingdetectionmethodisproposed:ThemotorneedstobecharacterizedtogeneratethemotorlinkagesmapsasshowninFig.6.6bandFig.6.6c.Thesemapscanbeusedasalookuptabletoestimatethedandqinductancesatanytoperatingpoint.Atanyoperatingpointthevalueofthemotorcommandedvoltagescanbeestimatedasfollows:103{Theangularspeed!eeiscalculatedfromthemeasuredspeedasfollow:!ee=Speed2ˇ60P(6.4){Themotorinductances(LdandLq)areestimatedusingtheoperatingtorquefromthelookuptables.Ansplineinterpolationisusedtoestimatethevalueof(LdandLq)ifthemachineisoperatingatatorquethatisnottestedduringthemotorcharacterization.{Theoperatingtemperaturethestatorresistanceandthemagnetperme-ance.Theincreaseinthestatorresistanceandthedecreaseinthemagnetpermeancecanbeestimatedasfollows:RST=Rs0[1+R(TT0)](6.5)pmT=pm0[1Br(TT0)](6.6){Theestimatedcommandedvoltagesareestimatedusingthefollowingequations:Ved=RsT:Id LqIq!ee(6.7)Veq=RsT:Iq+pmT+LdId!ee(6.8)Themeasuredvoltagesofthemachineisrecordedandcomparingtotheestimatedvoltages.Thesevoltagescanbeusedafeatures.Theoutputthemachinehealthstatus(whetheritishealthyorfaulted),andbyusingthevoltagesshiftdirection,thefaulttypecanbedetectedandtheseveritycanbe104estimated.Inordertohaveahighclasationaccuracy,itisimportantforthevoltagestobeestimatedcorrectlytotheactualmeasuredvoltages.Fig.6.23showsacomparisonbetweentheactualandtheestimatedvoltagesfortheFSCWmachineundertoperatingcon-ditions.TheFSCWmachinewascharacterizedusing6toperatingtorques(0,2,5,10,15and20A)ataspeedof300rpm,andforanoperatingtemperatureof200C.Thees-timatedvoltageswerecalculatedattspeeds,loads,andtemperatures.Interpolationusingsplineinterpolationwasperformedtoestimatethedandqinductances.(a)3A120oCand300rpm(b)5A80oCand300rpmFigure6.23ComparisonbetweenactualandestimatedcommandedvoltagesundertoperatingconditionsTheresultsshowsthattheproposedmethodisableofestimatingthemachinevoltagescorrectlyfortoperatingload,speed,andtemperature.Itisalsoshownthattheofthespeedandtemperaturecanbeadjustedanalytically,whichreducethenum-berofvariationparameterstoonlythecurrent.However,theaccuracyoftheestimatedvoltagesdependsonthenumberofsamplesinthelookuptables,thehigherthenumberofcharacterizationtests,themoreaccuratetheestimation.1056.3.2ImplementationTohaveanaccurateresultsfordetectingthefaultthetypeandseverity,aclasscationmethodisneeded.Twofeatureswereextractedfromeachcase:thed-axisvoltageandtheq-axisvoltage.Theactualcommandedvoltagesattoperatingconditionisusedasthetestingsamples.Foreverytestingsample,thetrainingsamplesweregeneratedbycalculatingVedandVeqaroundthattestedsampleoperatingcondition.Thevariationwaschosentobe10%.Forexampleifthetestingsamplecollectedforamachineoperatingataspeedof200rpm,atorqueof10A,andatemperatureof200C,thetrainingtrainingsamplesiscalculatedforallthespeedsfrom190rpmto210rpm,foreachspeedtheloadsisvariedfrom9:5Ato10:5A,andthetemperatureisvariedfrom190Cto210C.Atotalof1000combinationsamplescanbegeneratedasatrainingsamplesforeachtestingsample.Fortheconcentratedwindingmachine,11casesweregeneratedusingFEA.Onecasecorrespondstothehealthyconditions,fourcasescorrespondtostaticeccentricityfault,generatedbyvaryingtheseverityfrom20%to80%instepsof20%oftheairgaplength,threecasescorrespondstopartialdemagnetizationfault,bydemagnetized1,2and3consecutivemagnets,andthreecasesrepresentturn-to-turnshortcircuitfault(12:5%and25%and62:5%oftheturnsinphaseAareshorted).Themachinewascharacterizedataspeedof500rpm,theoperatingtemperatureis200Candthecurrentwasvaryingfrom0Ato150Ainstepsof10A.Thecharacterizationdatacanbeusedtogeneratethelookuptablesforthelinkages.Theselookuptableswereusedtoestimatethelinkagesforthetrainingsamples.Thetestingsampleswerecollectedfromspeedsof500rpmand1000rpmatanoperatingtemperaturesof200C,1000C,and1500Cwithloadsof10A,50A,and100A.18samplesweregeneratedasatestingsamplesforeachhealthstatus(atotalof198testing106samples),andforeachtestingsamplea1000samplesweregeneratedasatrainingsamples.FortheFSCWmachine11casesweregeneratedusingFEA,oneforhealthy,3foreccen-tricityfault(40%-80%instepsof20%),threecasesfordemagnetizationbydemagnetizing1,2,and3adjacentmagnets,and4casesrepresentshortcircuitfault(10%withRf=0:5,12%withRf=0:25,20%withRf=0:5,and20%withRf=0:25).Themachinewascharacterizedataspeedof300rpm,theoperatingtemperatureis200Candthecurrentwasvariedfrom0Ato20Ainstepsof5A.Thetestingsampleswerecollectedfromspeedsof300rpmand500rpmatanoperatingtemperaturesof200C,1000C,and1500Cwithloadsof2A,3A,5A,8A,and10A.36samplesweregeneratedasatestingsamplesforeachhealthstatus(atotalof432testingsamples),andforeachtestingsamplea1000samplesweregeneratedasatrainingsamples.ExperimentaltestswereperformedfortheFSCWmachineunderhealthyandthetestedfaultswiththesameseverities.Thetestingsamplesfortheexperimentaldatawerecollectedfromspeedsof300rpmand500rpmatanoperatingtem-peraturesof200Cwithloadsof2A,3A,5A,8A,and10A.10samplesweregeneratedasatestingsamplesforeachhealthstatus(atotalof110testingsamples),andforeachtestingsamplea1000samplesweregeneratedasatrainingsamples.6.3.3ResultsTable6.3showstheresultsoffaultdetectionandseparationfortheconcen-tratedwindingmachineusingthree(KNN,LDA,andQDA).Table4.2showsacomparisonoftheresultstheresultsoffaultdetectionandseparationbetweensimulationsandexperimentaldatafortheFSCWmachineusingthecommandedvoltagesapproach.Table6.5summarizesthetheaverageresultsoffaultdetectionandsepa-107Table6.3resultsfortheconcentratedwindingmachineConcentratedwindingmachineMachineStatusK-NNLDAQDAHealthy80%83%82%20%ECC75%79%78%40%ECC80%80%82%60%ECC78%79%78%80%ECC79%81%80%1Magnet88%88%86%2Magnets89%91%90.5%3Magnets91.5%93%91.5%12.5%Short82%88%85%25%Short87%90%90%50%Short88%92%91%Table6.4resultsfortheFSCWmachineFSCWmachineFEASimulationExperimentalresultsMachineStatusK-NNLDAQDAK-NNLDAQDAHealthy98%100%99%95%97%96%40%ECC86%85%86%79%79%78%60%ECC82%82.5%83%80%78%75%80%ECC80%82.5%82.5%75%80%80%1Magnet92%95%95%90%92%88%2Magnets88%92%90%90%88%89%3Magnets90%95%94%85%89%88%10%shortRf=0:90%85%90%82%80%82%10%shortRf=0:90%90%90%84%88%87%20%shortRf=0:90%92%91%80%90%88%20%shortRf=0:92%92%90%83%91%85%rationusingthecommandedvoltagesapproachforalltestedmachines(includingthedis-tributedwindingmachine)usingthethreemethods.Theresultsshowthattheproposedalgorithmwasabletodetectthefaulttypeandestimateitsseverityaccuratelyfortoperatingandenvironmentalcondi-108Table6.5TheaverageresultsforallthetestedmachinesConcentratedwindingDistributedwindingFSCWmachineFEAFEAEXPFEAEXPKNN83.4%88.9%83.9%87.8%82.8%LDA85.8%90.1%86.5%88.8%86.2%QDA84.9%90%85.1%87.9%86.2%tions.However,athighoperatingloads,itwashardtoclassifyeccentricityfaultcorrectlysincethattheextrasaturationduetoeccentricityfaultismaskedbecausethemachineissaturatedathighoperatingtorque.109Chapter7ConclusionThisworkproposedageneralalgorithmforfaultdetectionandideninPMSMsundertoperatingconditions.Theincrementalinductanceapproachisproposedasadetectionmethodwhenthemotorisoperatingatstandstill,theMCSA/MVSAandthecommandedvoltagesapproachesareproposedwhenthemotorisoperatingatsteadystate.Themainadvantageofthemethodsisthatitdoesn'trequireanyadditionalhardwarecomponents,thesamesignalsthatareusedforthecontrollerareusedfordetectingthefaulttypeandestimatingtheseverity.Thismakestheproposedmethodscostt,easytoimplementregardingthemotorplacement,anditremovethenecessarytotakethemotoraparttodetectthehealthstatus.Theincrementalinductanceapproachisbasedonthechangeinthesaturationinthemachineunderfaultedconditioncomparedtothehealthymachine.Eccentricityandde-magnetizationfaultsdirectlythesaturationinthemachine.Therefore,usingtheincrementalinductancecanbemostsuitabletodetectthesetwofaults.Turn-to-turnshortcircuitfaultdoesn'tcauseadirectchangeinthesaturation.Therefore,usingtheincrementalinductancemethodcanbeusedasanindicatorforashortcircuitfault,buttheclasscationaccuracydecreaseswhenitcomestodetecttheseverityofthisfault.Themainadvantageforthecommandedvoltageapproachisthatitcanbeappliedduringnormaloperationofthemachine.Theresultsshowahighaccuracyindetectingdemagnetizationandshortcircuitfaults.Eccentricityshowedahighdetection110atlowertorquelevel.However,astheoperatingtorqueincreases,thedetectionaccuracydecrease.Therefore,thismethodcanbesuitablefordetectingdemagnetizationandshortcircuitfaultsregardlessoftheoperatingload.TheMCSAisthemoststraightforwardmethodforfaultdetection.Thismethodcanbeappliedfordetectingallthreefaultsduringsteadystateoperation.However,inordertohaveahighaccuracy,alargenumberofsamplesisrequiredtocoverthewholeoperatingrange.whichmightnotbepossibleandeasytoobtain.111BIBLIOGRAPHY112BIBLIOGRAPHY[1]W.leRoux,R.Harley,andT.Habetler,\Detectingrotorfaultsinlowpowerpermanentmagnetsynchronousmachines,"IEEETrans.PowerElectron.,vol.22,pp.322{328,Jan2007.[2]Y.Da,X.Shi,andM.Krishnamurthy,\Anewapproachtofaultdiagnosticsforper-manentmagnetsynchronousmachinesusingelectromagneticsignatureanalysis,"IEEETrans.PowerElectron.,vol.28,pp.4104{4112,Aug2013.[3]Z.Yang,X.Shi,andM.Krishnamurthy,\VibrationmonitoringofPMsynchronousmachinewithpartialdemagnetizationandinter-turnshortcircuitfaults,"in2014IEEETransportationEleationConferenceandExpo(ITEC),pp.1{6,June2014.[4]\Reportoflargemotorreliabilitysurveyofindustrialandcommercialinstallations,partI,"IEEETrans.Ind.App.,vol.IA-21,pp.853{864,July1985.[5]B.Ebrahimi,M.JavanRoshtkhari,J.Faiz,andS.Khatami,\Advancedeccentricityfaultrecognitioninpermanentmagnetsynchronousmotorsusingstatorcurrentsigna-tureanalysis,"IEEETrans.Ind.Electron.,vol.61,pp.2041{2052,April2014.[6]S.Rajagopalan,W.Roux,T.Habetler,andR.Harley,\Dynamiceccentricityandde-magnetizedrotormagnetdetectionintrapezoidal(brushlessDC)motorsoperatingundertloadconditions,"IEEETrans.PowerElectron.,vol.22,pp.2061{2069,Sept2007.[7]B.EbrahimiandJ.Faiz,\Featureextractionforshort-circuitfaultdetectioninpermanent-magnetsynchronousmotorsusingstator-currentmonitoring,"IEEETrans.PowerElectron.,vol.25,pp.2673{2682,Oct2010.[8]J.Rosero,L.Romeral,J.Ortega,andE.Rosero,\Short-circuitdetectionbymeansofempiricalmodedecompositionandwigner-villedistributionforPMSMrunningunderdynamiccondition,"IEEETrans.Ind.Electron.,vol.56,pp.4534{4547,Nov2009.[9]J.Rosero,J.L.Romeral,J.Cusido,J.A.Ortega,andA.Garcia,\Faultdetectionofeccentricityandbearingdamageinapmsmbymeansofwavelettransformsdecompo-sitionofthestatorcurrent,"inAppliedPowerElectronicsConferenceandExposition,2008.APEC2008.Twenty-ThirdAnnualIEEE,pp.111{116,Feb2008.113[10]S.Rajagopalan,J.A.Restrepo,J.M.Aller,T.G.Habetler,andR.G.Harley,\Nonsta-tionarymotorfaultdetectionusingrecentquadratictime-frequencyrepresentations,"IEEETransactionsonIndustryApplications,vol.44,pp.735{744,May2008.[11]S.Rajagopalan,J.M.Aller,J.A.Restrepo,T.G.Habetler,andR.G.Harley,\Detec-tionofrotorfaultsinbrushlessdcmotorsoperatingundernonstationaryconditions,"IEEETransactionsonIndustryApplications,vol.42,pp.1464{1477,Nov2006.[12]Z.Yang,X.Shi,andM.Krishnamurthy,\Vibrationmonitoringofpmsynchronousmachinewithpartialdemagnetizationandinter-turnshortcircuitfaults,"in2014IEEETran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