Reliability-basedphasormeasurementunitplacementinpowersystemsconsideringtransmissionlineoutagesandchannellimitsOscarGomez1,2,MarioA.Rios1,GeorgeAnders31DepartmentofElectricalEngineeringandElectronics,SchoolofEngineering,UniversidaddelosAndes,Bogotá,Colombia2DepartmentofTechnology,SchoolofElectricalTechnology,UniversidadTecnológicadePereira,Pereira,Colombia3ElectricalEngineering,TechnicalUniversityofLodz,Lodz,PolandE-mail:o.gomez31@uniandes.edu.coAbstract:Sincephasormeasurementunit(PMU)wasinvented,therehasbeengrowinginterestindevelopingmethodologiesforfindingtheminimumnumberofPMUsforcompletesystemobservability.ThemethodsforthePMUplacementmustconsiderthefactthatthenetworktopologymaychangewhenthepowersystemisaffectedbyacontingencyevent.ThereforethePMUplacementproblemcanbestatedasfindingtheminimumnumberofPMUsforcompletesystemobservabilityconsideringthefailureprobabilityoftransmissionlines.Inthisstudy,theauthorsproposeanewreliabilitybasedmodelforthecontingencyconstrainedPMUsplacement.Initially,amethodology,thatconsiderstheprobabilityoffailureofthepowersystemcomponents,isproposed.Next,analgorithmispresentedforselectingtheminimalnumberofPMUsandtheirlocationstomonitorthesystemundernormaloperationandthemostcrediblecontingencies.Aprobabilisticindexisintroducedtoselectadesiredlevelofreliabilityforthewide-areamonitoringsystem.Finally,theavailabilityofPMUmeasuringchannelsisincorporatedinthemodel,somorerealisticandusefulresultscanbeobtained.TheproblemisformulatedandsolvedasabinaryintegerlinearprogrammingmodelandtestedontheIEEE9-bus,IEEE57-busandRTS96testsystems.1IntroductionAphasormeasurementunit(PMU)providessynchronisedphasormeasurementsofvoltagesandcurrentsfromwidelydispersedlocationsinanelectricpowergrid.SincePMUwasinvented,therehasbeengrowinginterestindevelopingmethodologiesforfindingtheminimumnumberofPMUsforcompletesystemobservability.Theproblemwasinitiallyintroducedin[1];then,severalapproaches,thatcanbecategorisedintotwogroups,themeta-heuristicoptimisationmethodsandtheconventionaldeterministictechniques,havebeenproposed.Examplesofthemeta-heuristicmethodsincludecanonicalgeneticalgorithm[2],non-dominatedsortinggeneticalgorithm[3],Tabusearch[4],simulatedannealingcombinedwithTabusearch[5],particleswarmoptimisation[6],adaptiveclonalalgorithm[7],differentialevolutionalgorithm[8]andimmunitygeneticalgorithm[9].Thedisadvantageofthesemethodsisthelongexecutiontimes,whichcanrestricttheirapplicationstolargepowersystems,andthepossibilityofobtaininganon-optimalsolution.Ontheotherhand,numerousresearchstudiesbasedondeterministicapproacheshavebeendeveloped.Forinstance,in[10],theintegerprogrammingapproachisappliedtothePMUplacementproblem.Amethod,usingintegerlinearprogrammingforpowernetworkswithandwithoutconventionalmeasurements,wasproposedin[11].Themodelpresentedin[11]wasextendedin[12]toconsiderthezero-injectioneffect,incompleteobservabilityandmeasurementredundancy.In[13],aformulationwasproposedwhichappliesintegerlinearprogramming,andincorporatestheeffectofzero-injection;inaddition,amultistageschedulingframeworkforPMUplacementinagiventimehorizonwassuggested.PMUsplacementandconventionalflowmeasurementslocationaresimultaneouslyconsideredasdecisionvariablesin[14].Theformulationisinitiallyposedasanon-linearintegerprogrammingproblemandthentransformedintoanequivalentintegerlinearprogramming.ThePMUpla...