Page - 283 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 997 thedefinedtypicaldrivingcycle. Inaddition, thismethodcannotensureoptimalglobalparameters. Therefore, it isnecessary toadoptanoptimizationmethodthatcanautomaticallysearchtheglobally optimizedthresholdparameters for theenergymanagementstrategy. The optimization of key parameters for logic threshold energymanagement strategies is a mathematicalnonlinearproblemwithmanyvariableconstraints. Thegeneticalgorithmwasapplied inoptimizingvariousgoverningparametersofhybridelectricvehicles (HEVs)andthe fueleconomy was improved significantly [3–6]. Themulti-objectivegenetic algorithmwasadopted tooptimize thecontrolparametersof theHEVfor improvingthefueleconomyandemissionperformance[7,8]. Lietal.utilizedamodifiednon-dominatedsortinggeneticalgorithm-II toeffectivelyoptimizethelogic thresholdcontrol strategyparametersof theHEVtominimize theequivalent fuel consumption[9]. Lietal. appliedahybridgeneticalgorithm(HGA),whichcombinesanenhancedgeneticalgorithm with simulatedannealing, inoptimizing thepowertrainandcontrolparameters ofplug-inhybrid electric bus simultaneously. Simulation results show that HGAhas a better convergence speed andglobal searchingability [10]. Theparticle swarmoptimization (PSO)algorithmwasapplied to search theoptimalvalueof thepower systemandcontrolparameters ofHEVto improve the fuel economy[11–13]. Inorder toachieveabetter fuel economyandemissionperformance,Dengetal. presentedanoptimizationmethodfor logic thresholdcontrol strategyparametersofaparallelHEV using thesimulatedannealingparticle swarmoptimization [14].Wangetal. utilizedevolutionary algorithm in conjunctionwithan instantaneousoptimal energymanagement strategy tooptimize thepropulsion systemparameters aswell as the energy control parameters for plug-inHEV [15]. Zhangetal. used differential evolution algorithm to globally optimize the plug-in HEV control parameters [16]. Long et al. optimized the key component and control parameters by using the beesalgorithm[17]. Chrisetal. showedthat theDIvidedRECTangle (DIRECT)algorithmhasabetter optimaleffectcomparedwiththegeneticalgorithm,simulatedannealing,PSOandotheralgorithmsby test,becauseitcancovertheglobalspaceforparameteroptimizationwithoutmissinganyoptimization value [18]. TheDIRECTalgorithm[19]doesnot requireaclearexpressionof theobjective functionequation aswellasderivative information,butdecidesonthenextsearchingareabasedontheestimatedvalue of the functionat thesamplingpointsofeach iterationandthedivisionofahyper-rectangle. Thus, it is ideal forsimulationof theblack-boxfunctionoptimization[20].However, it requiresa largenumber ofsamples in theregiontoensure thefinalglobaloptimum.Besides, thenumberofestimatedfunction is relatively larger than that of the gradient-basedoptimizationmethod. Inpractical engineering optimization, themeta-modeloptimization isoftenverycomplexandthesimulationtimeis relatively long[21]. Insteadof thecomplexmeta-model, anapproximatemodelbuiltby thesamplingpointsof eachDIRECTalgorithmiteration isutilized, therebyreducingthenumberofsimulations, improving theconvergencespeed, shorteningtheoptimizationtime,andsavingcomputingresources. Asmentionedabove, theadvantageofDIRECTalgorithmis toobtain theglobaloptimization result comparedwithotheroptimizationalgorithm.Besides, italsohas lowcomputationalburden, rapidconvergence. So it ismeaningful toutilize theDIRECTalgorithmtoacquire theglobaloptimized valueof theparametersofHEVenergymanagementstrategy.However,a fewworkshavebeenfound tooptimize thecontrol strategyparametersofhybridelectricvehicleutilizing theDIRECTalgorithm. Rousseauet al. andHeet al. establishedapowercomponentparameteroptimizationmodel for a HEVtominimize the fuel consumption. Theconstraintsare thedynamicdesignspecificationsand variables, namely the enginepower, batterypower, battery capacity, batterybusvoltage, etc. The DIRECTalgorithm is utilized to optimize these parameters. Whereas, the logic threshold control strategyparametershavenotbeenanalyzedandoptimized [22,23]. Pandayetal. utilizedDIRECT algorithmtooptimizepartialparametersofHEVcontrol strategy, suchasstateofcharge in thebattery, engine idlespeed,engineondurationandpowerdemand[24]. Thegeneral comparisonofdifferentalgorithms ispresented inTable1. Theresearchworkswhich optimizetheparametersofHEVenergymanagementstrategyutilizingGA,PSO,etc.mayleadto local 283