Page - 299 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 997 Figure17.Thepotentialoptimalhyper-rectangleofeach iteration. Formultidimensional spaceoptimizationproblems, theDIRECTalgorithmtakessimilarsteps to select thebestpotentialoptimalhyper-rectangle. 5.2.OptimizationofKeyParameters forLogicThresholdEnergyManagementStrategyUsingDIRECT AlgorithmBasedonFuelEconomy Basedonthediscussions in the thirdsection, thekeyparametersof the logic thresholdenergy managementstrategyfor theHEVarepresented inTable3. In this research, thepurposeof theenergy management strategy is toachieve thebest fuel economyforagivendrivingcycle. Therefore, the target function is FC=minf(x), (16) where f(x) is theequivalentfuelconsumptionper100km,whichincludestheenginefuelconsumption andequivalent fuel consumptionof theelectricenergyfromthepowerbattery. Theunit isL/100km. Thecalculationfor f(x) is shownasbelow. f(x)=100 ∫ k1UIdt q ρ ∫ vdt +100 ∫ k2 fr(Te,ωe)Teωe9550dt ρ ∫ vdt ne (17) whereρ is thegasolinedensity ing/L; fr(Te,ωe) is thecurrentenginefuelconsumptionrate,which isa lookupfunctionof theengine torqueandspeed,with theunitg/kWh;Te andωe are thecurrent enginetorqueandspeed,withtheunitsN ·mandrpm,respectively;k1 andk2 are thegasoline–electric conversionconstantcoefficients;Uand I are thepresentbatteryvoltageandcurrent,with theunitsV andA,respectively;q refers to thegasolinecalorificvalue in J/kg;v is thecurrentspeedinkm/h. Theengine torqueandspeed,batteryvoltageandcurrent,andaveragespeedarerelatedto the sevenparameters tobeoptimizedasshowninTable3. Therefore, the optimization of key parameters for theHEV energymanagement strategy is convertedto theoptimizationofsevendimensionalparameters. TheDIRECTalgorithmisselected tosolve thisproblem.Theprocess isshowninFigure18. First,wenormalizedn-dimensionalspace into n-dimensional unit hyper-cube and calculate the equivalent fuel consumptionper 100 kmat thecenterpointas the initialminimumfuel consumption. Thehyper-cube is thepotentialoptimal hyper-rectanglewheniterationstarts. Then,wechooseapotentialoptimalhyper-rectangleanddivide it.Afterwards,wecalculate theequivalent fuelconsumptionper100kmat thecenterpointofeach rectangle. After that,we compare itwith theminimal value collected in the last iteration. If this value is smaller thanthepreviousminimumfuel consumption,weupdateandstore theminimum fuelconsumption. Inaddition,weupdate thepotentialoptimalhyper-rectangle. Theoptimizationof DIRECTalgorithmwill stopuntil thedefinedmaximumnumberof iterationsor thepotentialoptimal hyper-rectangle isempty. 299