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Energy-efficientoperationofrailvehiclesRongfang(Rachel)Liua,*,IakovM.Golovitcherb,1aDepartmentofCivilandEnvironmentalEngineering,NewJerseyInstituteofTechnology,UniversityHeights,Newark,NJ07102,USAbParsonsRailandTransitSystems,15thFloor,469SeventhAve,NewYork,NY,USAReceived5April2002;receivedinrevisedform27March2003;accepted7July2003AbstractThispaperdescribesananalyticalprocessthatcomputestheoptimaloperatingsuccessionsofarailvehicletominimizeenergyconsumption.Risingenergypricesandenvironmentalconcernshavemadeenergyconservationahighpriorityfortransportationoperations.ThecostofenergyconsumptionmakesupalargeportionoftheOperationandMaintenance(O&M)costsoftransitespeciallyrailtransitsystems.Energyconservationorreductioninenergycostmaybeoneoftheeffectivewaystoreducetransitoperatingcost,thereforeimprovetheefficiencyoftransitoperations.Fromatheoreticalpointofview,theproblemofenergyefficienttraincontrolcanbeformulatedasoneofthefunctionsofOptimalControlTheory.However,theclassicnumericaloptimizationmethodssuchasdiscretemethodofoptimumprogrammingaretooslowtobeusedinanon-boardcomputerevenwiththemuchimprovedcomputationpower,today.Thecontributionofthisparticularresearchistheanalyticalsolutionthatgivesthesequenceofoptimalcontrolsandequationstofindthecontrolchangepoints.Asaresult,acalculationalgorithmandacomputerprogramforenergyefficienttraincontrolhasbeendevel-oped.Thisprogramisalsocapableofdevelopingenergyefficientoperatingschedulesbyoptimizingdis-tributionsofrunningtimeforanentirerouteoranypartofrailsystems.WeseethemajorapplicationoftheproposedalgorithmsinfullyorpartiallyautomatedTrainControlSystems.Themoderntraincontrolsystems,oftenreferredas‘‘positive’’traincontrol(PTC),havecollectedalargeamountofinformationtoensuresafetyoftrainoperations.Thesamedatacanbeutilizedtocomputetheoptimumcontrolson-boardtominimizeenergyconsumptionbasedonthealgorithmspro-posedinthispaper.Mostoftheinputdata,suchastrackplan,trackprofile,tractionandbrakingchar-acteristics,speedlimitsandrequiredtriptimearelocatedinanon-boarddatabaseand/ortheycanbetransmittedviaradiolinktobeprocessedbytheproposedalgorithmandprogram.2003ElsevierLtd.Allrightsreserved.*Correspondingauthor.Tel.:+1-973-596-5884;fax:+1-973-596-5790.E-mailaddresses:rliu@adm.njit.edu(R.R.Liu),iakov.golovitcher@parsons.com(I.M.Golovitcher).1Tel.:+1-212-643-2139;fax:+1-212-695-2483.0965-8564/$-seefrontmatter2003ElsevierLtd.Allrightsreserved.doi:10.1016/j.tra.2003.07.001TransportationResearchPartA37(2003)917–932:Automatedtrainoperation;Energyconsumption;Optimalcontrol1.IntroductionAtthepresenttime,themainapproachtoenergysavingsforrailroadsandrailtransitsystemsisthroughenergy-efficientdesignoflocomotivesandmotorunits,effectivereductionofresistancetothetrainmovement,andpropermaintenanceofrollingstockandtracks.Meantime,risingenergypricesandenvironmentalconcernsmakeotherenergysavingapproachesdesirable,suchasenergyefficienttraincontrolforrailroadsandtransitagenciesand,inthenearfuture,forautomatedtrainoperationsystems.AccordingtotheTransportationEnergyDataBook:Edition20-2000(Davis,2000),trans-portationshareofUSenergyconsumptionis28%,andtheenergyconsumptionforUSrailmodealoneamountsto586trillionBTUin1998.Althoughthemodesharesofrailtransportationissmallwhencomparedtooverallothermodes,suchasautomobile,intermsofbothpassengerandgoodsmovedandenergyconsumed,thecostsfor586trillionBTUstillamountstobillionsofdollars.Moreover,theenergycostusuallymakesupatleast15–20%oftheannualoperationandmaintenancecostsofrailtransitproperties(DiRenzoandPeskin,Undated)intheUnitedStates.Theshareforenergycostmaygetevenhigherfortherestofworld,especiallyinthedevelopingcountrieswherelaborcostsarerelativelylow.Inaddition,thereareotherelementsofoperatingcosts,whichareproportionaltoenergyconsumption,suchascostsofmaintenanceoftractionsystems,etc.Therefore,transitoperators,especiallythosewhooperatealargefleetofrailvehiclesareverymotivatedtoreducetheenergyconsumption,which,inturnmayleadssignificantre-ductioninoperationefficiency.Ontheotherhand,moderntraincontrolsystems,oftenreferredtoas‘‘positive’’traincontrol(PTC)will,eventually,replaceconventionalsignalsystems.ThePTCsystemhascollectedmostoftheinformationneededforcomputingtheoptimalcontrolson-boardbecausethesamedataarerequiredtomonitoroperationsafety.Theinformation,suchastrackplan,trackprofile,civilspeed,tractionandbrakingcharacteristicsmaybelocatedinanon-boarddatabase.Temporaryspeedlimitsandrequiredtriptimecanbetransmittedviaradiolinks.Allitneeds,foranautomatedtrainoperationsystem,isappropriatealgorithmforanon-boardcomputerthatiscapableofprovidingoperatingguidancetoimproveenergyefficiencyduringtheoperationprocess.Theobjectiveofthispaperistopresentananalyticalsolutiontothefollowingoptimizationproblem:calculateoptimumcontrolparameters(i.e.tractionandbrakingforces)whichmoveatrainfromonegivenpointtoanotherinrequiredtimewithminimumenergyconsumed.Thissolutionshalltakeintoaccountthefollowing:•Constraintsontractionandbrakingforces(i.e.maximumtractionandbrakingforces),whicharefunction