FullΒ ElectricalΒ Β VehiclesΒ (FEVs)Β andΒ Β Hybrid ElectricalΒ Β VehiclesΒ (HEVs)Β areΒ vehiclesΒ Β withΒ Β many electricΒ Β componentsΒ comparedΒ toΒ Β conventionalΒ ones.Β Β Β Β InΒ factΒ Β theΒ Β powerΒ trainΒ Β consistsΒ Β of electricalΒ Β machines,Β powerΒ Β electronicsΒ andΒ Β electricΒ Β energyΒ storageΒ systemΒ Β (battery,Β super capacitors)Β connectedΒ toΒ Β mechanicalΒ componentsΒ (transmissions,Β gearΒ Β boxesΒ Β andΒ Β wheels) and,Β Β forΒ Β HEV,Β Β toΒ anΒ Β InternalΒ CombustionΒ EngineΒ Β (ICE).Β Β Β TheΒ Β approachΒ forΒ Β aΒ newΒ Β vehicle designΒ hasΒ Β toΒ beΒ multidisciplinaryΒ inΒ orderΒ Β toΒ takeΒ Β intoΒ Β accountΒ theΒ Β dynamicΒ interaction amongΒ allΒ theΒ Β componentsΒ ofΒ theΒ Β vehicleΒ Β andΒ Β theΒ Β powerΒ trainΒ Β itself.Β Β TheΒ vehicleΒ Β designers inΒ orderΒ Β toΒ ο¬ndΒ Β theΒ correctΒ Β sizingΒ Β ofΒ components,Β theΒ bestΒ Β energyΒ controlΒ Β strategyΒ andΒ Β to minimize theΒ vehicleΒ Β energyΒ consumptionΒ needΒ Β modelingΒ andΒ Β simulation sinceΒ prototyping andΒ Β testingΒ Β areΒ Β expensiveΒ andΒ Β complexΒ Β operations.Β Β DevelopingΒ aΒ simulationΒ modelΒ Β with aΒ Β sufο¬cientΒ levelΒ Β ofΒ Β accuracyΒ forΒ Β allΒ Β theΒ Β differentΒ componentsΒ basedΒ Β onΒ Β differentΒ physic domainsΒ (electric,Β Β mechanical,Β thermal,Β powerΒ electronic,Β Β electrochemicalΒ andΒ Β control)Β Β isΒ a challenge.Β DifferentΒ commercialΒ simulationΒ toolsΒ haveΒ Β beenΒ Β proposedΒ inΒ literatureΒ andΒ Β they areΒ usedΒ Β byΒ theΒ automotiveΒ designerΒ [1].Β TheyΒ haveΒ differentΒ levelΒ ofΒ detailΒ Β andΒ Β areΒ basedΒ Β on differentΒ mathematicalΒ approaches.Β InΒ paragraphΒ 2Β aΒ generalΒ overviewΒ onΒ differentΒ modeling approachesΒ willΒ beΒ presented.Β InΒ theΒ followingΒ paragraphsΒ theΒ authorΒ approach,Β focusedΒ on theΒ modelingΒ ofΒ eachΒ Β componentΒ constitutingΒ aΒ FEVΒ orΒ HEVΒ willΒ beΒ detailed.Β TheΒ authors approachΒ isΒ generalΒ andΒ Β isΒ notΒ Β basedΒ Β onΒ Β vehicleΒ Β orientedΒ simulationΒ tools.Β Β Β ItΒ representsΒ a goodΒ Β compromise amongΒ modelΒ Β simplicity,Β ο¬exibility,Β Β computationalΒ loadΒ Β andΒ Β components detailΒ Β representation.Β TheΒ chapterΒ isΒ organizedΒ asΒ follows:
β’Β paragraphΒ Β 2Β Β describesΒ Β theΒ Β differentΒ Β approachesΒ Β thatΒ Β Β canΒ Β beΒ Β ο¬ndΒ Β Β inΒ Β literatureΒ and introducedΒ theΒ proposedΒ one;
β’Β paragraphsΒ 3Β toΒ 10Β describeΒ allΒ theΒ componentsΒ modelingΒ detailsΒ Β inΒ thisΒ Β order:Β Β Β battery, inverter,Β electricΒ motor,Β Β vehicleΒ Β mechanics,Β auxiliaryΒ load,Β Β ICE,Β thermalΒ modeling;
β’Β paragraphΒ 11Β presentsΒ differentΒ casesΒ Β ofΒ studyΒ withΒ Β simulationΒ resultsΒ whereΒ allΒ Β the numericalΒ modelsΒ hasΒ Β beenΒ Β validatedΒ byΒ meansΒ Β ofΒ experimentalΒ testΒ Β performedΒ byΒ the authors.
FEV and HEV modeling
AsΒ Β shownΒ Β inΒ Β FigureΒ Β Β 1,Β Β theΒ Β wholeΒ Β Β vehicleΒ Β Β power-trainΒ Β modelΒ Β Β isΒ Β composedΒ Β byΒ Β many subsystems,Β connectedΒ inΒ according toΒ theΒ energy andΒ informationΒ physicalΒ exchanges.Β TheyΒ represent theΒ driver (pilot),Β theΒ vehicleΒ Β controlΒ Β system,Β theΒ battery,Β theΒ inverter,Β theΒ Electrical MotorΒ Β (EM),Β theΒ Β mechanicalΒ transmissionΒ system,Β theΒ Β auxiliaryΒ onΒ Β boardΒ electricalΒ Β loads, theΒ vehicleΒ Β dynamical modelΒ Β andΒ Β for,Β HEVsΒ andΒ Β Plug-inΒ Β Hybrid ElectricalΒ Β VehiclesΒ (PHEVs), alsoΒ anΒ ICEΒ andΒ Β aΒ fuelΒ tankΒ areΒ considered.Β ToΒ correctlyΒ Β describe them,Β Β aΒ multidisciplinary methodologyΒ analysisΒ isΒ required.Β FurthermoreΒ theΒ design ofΒ aΒ vehicleΒ Β requiresΒ aΒ complete systemΒ Β analysisΒ includingΒ theΒ controlΒ Β ofΒ theΒ energyΒ givenΒ Β fromΒ Β theΒ on-boardΒ source,Β Β the optimizationΒ ofΒ theΒ Β electricΒ Β andΒ Β electronicΒ Β devicesΒ Β installedΒ onΒ Β theΒ Β vehicleΒ Β andΒ Β theΒ Β design ofΒ allΒ theΒ mechanicalΒ connectionΒ betweenΒ theΒ differentΒ powerΒ sourcesΒ Β toΒ reachΒ Β theΒ Β required performances.Β Β So,Β theΒ completeΒ simulationΒ modelΒ Β hasΒ toΒ describeΒ theΒ interactionsΒ between theΒ Β systemΒ Β components,Β correctlyΒ Β representingΒ theΒ Β powerΒ fluxΒ exchanges,Β inΒ orderΒ Β toΒ help theΒ Β designersΒ duringΒ theΒ Β study.Β Β ForΒ Β modelingΒ eachΒ Β component,Β twoΒ Β differentΒ approaches canΒ Β beΒ used:Β Β Β anΒ Β βequation-basedβΒ orΒ aΒ βmap-basedβΒ modeΒ Β [1].Β Β InΒ theΒ Β firstΒ Β method,Β each subcomponentΒ isΒ definedΒ byΒ meansΒ Β ofΒ itsΒ quasi-staticΒ characteristicΒ equationsΒ thatΒ Β haveΒ Β to beΒ solvedΒ Β inΒ orderΒ Β toΒ obtainΒ Β theΒ Β outputΒ responsesΒ toΒ theΒ Β inputs.Β Β TheΒ Β mainΒ Β drawbackΒ isΒ representedΒ byΒ theΒ computationalΒ effortΒ Β neededΒ toΒ resolveΒ Β theΒ modelΒ Β equations.Β ViceΒ versa usingΒ Β aΒ βmap-basedβ approachΒ eachΒ sub-model isΒ representedΒ byΒ meansΒ Β ofΒ aΒ setΒ ofΒ look-up tablesΒ Β toΒ numericallyΒ representsΒ theΒ setΒ ofΒ workingΒ conditions.Β TheΒ mapΒ Β hasΒ toΒ beΒ definedΒ by meansΒ Β ofΒ βoff-lineβΒ Β calculation algorithmΒ basedΒ Β onΒ componentΒ modelΒ Β equationΒ orΒ collected experimentalΒ data.Β Β Β ThisΒ approachΒ impliesΒ Β aΒ lighterΒ Β computationΒ loadΒ Β butΒ Β isΒ notΒ parametric andΒ Β requiresΒ anΒ βoff-lineβΒ Β mapΒ Β manipulationΒ ifΒ aΒ componentΒ parameterΒ hasΒ Β toΒ beΒ changed. ForΒ theΒ Β modelΒ Β developingΒ process,Β Β anΒ Β object-orientedΒ causalΒ Β approachΒ canΒ Β beΒ adopted.Β Β In factΒ theΒ completeΒ modelΒ Β canΒ beΒ splitΒ intoΒ differentΒ subsystems.Β EachΒ subsystemΒ representsΒ a componentΒ ofΒ theΒ vehicleΒ Β andΒ Β containsΒ theΒ equationsΒ orΒ theΒ look-upΒ tableΒ Β usefulΒ Β toΒ describe itsΒ behavior.Β Β ConsequentlyΒ eachΒ Β objectΒ Β canΒ Β beΒ connectedΒ toΒ theΒ Β otherΒ Β objectsΒ Β byΒ meansΒ Β of inputΒ andΒ Β outputΒ variables.Β InΒ thisΒ Β way,Β Β theΒ Β equationsΒ describingΒ eachΒ Β subsystemΒ areΒ not dependentΒ byΒ theΒ Β externalΒ configuration,Β soΒ everyΒ Β objectΒ isΒ independentΒ byΒ theΒ Β othersΒ Β and canΒ beΒ verified,Β Β modified,Β replacedΒ withoutΒ modifyΒ theΒ equationsΒ ofΒ theΒ restΒ ofΒ theΒ model.Β Β At theΒ sameΒ Β time,Β Β itΒ isΒ possibleΒ Β toΒ defineΒ Β aΒ βpowerΒ fluxβΒ amongΒ theΒ subsystems:Β everyΒ Β outputΒ variableΒ ofΒ anΒ objectΒ connectedΒ toΒ anΒ inputΒ signalΒ Β ofΒ anotherΒ createsΒ Β aΒ powerΒ fluxΒ fromΒ Β the firstΒ Β toΒ Β theΒ Β secondΒ Β subsystemΒ (βcausalityΒ approachβ).Β Β ThisΒ Β methodΒ hasΒ Β theΒ Β advantageΒ toΒ realizeΒ Β aΒ modularΒ approach thatΒ Β allowsΒ Β toΒ obtainΒ Β differentΒ andΒ Β complexΒ Β configurationΒ onlyΒ rearrangingΒ theΒ objectΒ connection.
AΒ Β completeΒ Β modelΒ Β Β canΒ Β beΒ Β composedΒ Β connectingΒ Β theΒ Β Β objectsΒ Β Β accordingΒ Β twoΒ Β Β different approaches:Β theΒ βreverseΒ approachβΒ (alsoΒ calledΒ Β βquasi-static approachβΒ –Β seeΒ FigureΒ Β 2)Β and theΒ Β βforwardΒ approachβΒ (alsoΒ Β calledΒ Β βdynamicΒ approachβΒ –Β seeΒ FigureΒ Β 3).Β Β FigureΒ Β 2Β andΒ Β 3 showΒ Β simplifiedΒ modelsΒ ofΒ aΒ HEV,Β whereΒ VΒ isΒ theΒ Β vehicleΒ Β model,Β Β GBΒ theΒ Β gearΒ Β box,Β Β PCΒ the powerΒ converter,Β BΒ theΒ Β batteryΒ pack,Β Β FTΒ theΒ Β fuelΒ Β tank,Β Β ALΒ isΒ theΒ Β auxiliaryΒ loadsΒ Β block,Β Β v andΒ Β aΒ areΒ Β respectivelyΒ theΒ Β vehicleβsΒ Β speedΒ Β andΒ Β acceleration,Β Β fΒ Β isΒ theΒ Β vehicleΒ Β tractionΒ force, Ω isΒ theΒ Β EMΒ angularΒ speed,Β TICEΒ Β andΒ Β TEΒ MΒ Β areΒ Β respectivelyΒ theΒ Β ICEΒ andΒ Β theΒ Β EMΒ torques,Β Ξ©ICEΒ Β isΒ theΒ ICEΒ angularΒ speed,Β fcΒ Β isΒ theΒ fuelΒ consumption,Β IΒ andΒ Β VsΒ areΒ theΒ electricalΒ Β motor currentΒ andΒ Β voltage,Β ibattΒ Β andΒ Β VbattΒ Β areΒ theΒ Β batteryΒ currentΒ andΒ Β voltage,Β PIΒ nΒ MotΒ Β isΒ theΒ Β powerΒ requestedΒ byΒ theΒ Β EMΒ toΒ theΒ Β powerΒ converter,Β PBΒ Β isΒ theΒ Β totalΒ Β powerΒ requestedΒ toΒ theΒ Β battery thatΒ Β isΒ obtainedΒ asΒ Β aΒ sumΒ Β ofΒ theΒ Β powerΒ requestedΒ byΒ Β theΒ Β powerΒ converterΒ PIΒ nΒ IΒ nvΒ Β andΒ Β the
auxiliaryΒ loadsΒ Β PauxΒ Β (PBΒ Β =Β PIΒ nΒ IΒ nvΒ +Β PauxΒ )Β andΒ Β finallyΒ Β iauxΒ Β isΒ theΒ amountΒ ofΒ currentΒ requested toΒ theΒ Β batteryΒ forΒ auxiliaryΒ electricalΒ Β loads.Β Β Β Quasi-staticΒ methodΒ useΒ Β asΒ inputΒ variablesΒ the desiredΒ speedΒ Β andΒ Β accelerationΒ ofΒ theΒ Β vehicle,Β Β henceΒ Β theΒ Β equationsΒ areΒ solvedΒ Β startingΒ from theΒ VΒ modelΒ Β andΒ Β goingΒ Β back,Β blockΒ byΒ block,Β toΒ theΒ B model.Β Β InΒ theΒ dynamicΒ approachΒ each subcomponentΒ hasΒ interconnectionΒ variablesΒ withΒ Β theΒ previousΒ andΒ Β theΒ nextΒ Β blocks.Β Β InΒ thisΒ wayΒ Β eachΒ Β sub-modelΒ isΒ stronglyΒ interleavedΒ withΒ Β theΒ Β othersΒ Β andΒ Β itsΒ behaviorΒ hasΒ Β influence onΒ theΒ totalΒ Β system.Β TheΒ secondΒ Β methodΒ requiresΒ aΒ higherΒ computationalΒ effortΒ butΒ Β isΒ more accurateΒ andΒ Β hasΒ Β beenΒ Β appliedΒ byΒ theΒ Β authorsΒ inΒ severalΒ Β casesΒ [2β4].Β Β InΒ fact,Β usingΒ Β theΒ Β first method,Β theΒ informationΒ fluxΒ isΒ unidirectionalΒ andΒ theΒ equationΒ setΒ isΒ moreΒ simplerΒ oftenΒ only algebraic.Β ThisΒ approachΒ doΒ notΒ takeΒ Β intoΒ accountΒ theΒ realΒ responseΒ andΒ Β constrainΒ ofΒ power trainΒ Β component.Β OnΒ theΒ contraryΒ theΒ dynamicΒ approachΒ producesΒ alsoΒ aΒ responseΒ thatΒ Β runs
forwardΒ theΒ Β completeΒ model,Β Β influencingΒ theΒ Β outputΒ ofΒ theΒ Β followingΒ sub-models.Β Β InΒ thisΒ way,Β itΒ isΒ possibleΒ Β toΒ studyΒ theΒ totalΒ behaviorΒ includingΒ theΒ physicalΒ limitsΒ ofΒ eachΒ component and,Β Β so,Β theΒ Β simulationΒ modelΒ Β isΒ ableΒ Β toΒ describeΒ correctlyΒ Β bothΒ Β theΒ Β singleΒ Β componentΒ and theΒ Β overallΒ Β performancesΒ ofΒ theΒ Β system.Β Β ForΒ thisΒ Β methodΒ moreΒ Β complexΒ Β equationsΒ (aΒ few numberΒ ofΒ differentialΒ equation)Β orΒ mapsΒ Β areΒ Β needed.Β Β TheΒ Β followingΒ paragraphsΒ Β describe componentΒ byΒ componentΒ theΒ Β proposedΒ methodΒ whichΒ Β isΒ basedΒ Β onΒ Β aΒ simplifiedΒ dynamic forwardΒ approachΒ thatΒ Β couldΒ Β beΒ implementedΒ usingΒ Β bothΒ Β equationsΒ orΒ Β off-lineΒ Β computed look-upΒ tables.
Battery modeling
InΒ orderΒ Β toΒ correctlyΒ Β simulateΒ theΒ behaviorΒ ofΒ aΒ FEV,Β HEVΒ orΒ PHEVΒ itΒ isΒ importantΒ toΒ setΒ up aΒ batteryΒ modelΒ Β thatΒ Β evaluateΒ theΒ Β outputΒ voltageΒ consideringΒ theΒ Β StateΒ OfΒ ChargeΒ (SOC)Β of theΒ batteryΒ itself.Β SinceΒ aΒ batteryΒ packΒ isΒ obtainedΒ byΒ aΒ seriesΒ connectionΒ ofΒ manyΒ Β cellsΒ (ncellΒ ), itΒ isΒ quiteΒ Β usualΒ Β toΒ construct aΒ numerical modelΒ Β considering oneΒ singleΒ cell.Β TheΒ totalΒ batteryΒ voltageΒ VbattΒ Β isΒ obtainedΒ usingΒ Β equationΒ (1)Β assumingΒ thatΒ Β allΒ cellsΒ haveΒ Β anΒ uniformΒ behavior andΒ Β whereΒ velΒ isΒ theΒ voltageΒ ofΒ aΒ singleΒ Β cell.
Dynamical modelΒ of battery
SinceΒ Β batteriesΒ Β forΒ Β tractionΒ Β applicationΒ Β areΒ Β usedΒ Β Β underΒ heavyΒ Β Β dynamicΒ conditionΒ with suddenlyΒ variationΒ ofΒ theΒ suppliedΒ currentΒ ibattΒ ,Β theΒ staticΒ modelΒ Β canΒ notΒ beΒ adoptedΒ forΒ allΒ the casesΒ ofΒ studyΒ whereΒ dynamicΒ isΒ fundamentalΒ (forΒ exampleΒ controlΒ Β analysis).Β DifferentΒ type
ofΒ ECMΒ haveΒ beenΒ developedΒ forΒ simulatingΒ batteryΒ voltageΒ velΒ whereΒ moreΒ thatΒ oneΒ RCΒ block areΒ usedΒ Β inΒ orderΒ Β toΒ obtainΒ Β aΒ OrdinaryΒ DifferentialΒ EquationΒ (ODE)Β ofΒ orderΒ Β nΒ andΒ aΒ parasitic parallelΒ branchΒ Β isΒ addedΒ toΒ theΒ ECMΒ toΒ simulateΒ theΒ selfΒ dischargeΒ phenomenon.Β Β SinceΒ the mainΒ objectiveΒ isΒ notΒ toΒ simulateΒ allΒ theΒ batteryΒ detailsΒ Β butΒ theΒ globalΒ vehicleΒ behaviorΒ aΒ singleΒ RCΒ circuitΒ forΒ anΒ enoughΒ accurateΒ modelΒ Β canΒ beΒ adopted,Β asΒ reportedΒ inΒ FigureΒ Β 4.
InΒ orderΒ Β toΒ haveΒ Β goodΒ Β simulationΒ resultsΒ aΒ fineΒ tuningΒ ofΒ theΒ dynamicΒ ECMΒ parametersΒ has toΒ beΒ done.Β Β AΒ goodΒ Β procedureΒ forΒ parameterΒ identification,Β consideringΒ alsoΒ thermalΒ effects, isΒ reportedΒ inΒ [5].
ItΒ possibleΒ Β toΒ solveΒ Β theΒ Β circuitΒ Β consideringΒ theΒ Β cellΒ voltageΒ velΒ ,Β asΒ reportedΒ inΒ equationΒ (4)1Β ,
whereΒ theΒ Β splittingΒ ofΒ theΒ Β totalΒ Β currentΒ ibattΒ Β intoΒ Β theΒ Β capacitorΒ C andΒ Β intoΒ Β theΒ Β resistorΒ R1Β Β is consideredΒ adΒ reportedΒ inΒ equationΒ (5)Β andΒ Β theΒ noΒ loadΒ voltageΒ v0Β isΒ SOCΒ dependant
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