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Energy management of a plug-in fuel cell/battery hybrid vehicle withon-board fuel processingLaura Tribiolia, Raffaello Cozzolinoa, Daniele Chiappinia, Paolo IorabaDept. of Industrial Engineering, Universit di Roma Niccol Cusano, ItalybDept. of Mechanical and Industrial Engineering, Universit di Brescia, Italyh i g h l i g h t s?Model-based simulator for energy management of parallel fuel cell/battery vehicle.?Fuel processor optimization for on-board hydrogen production and storage.?Electrochemical model of a HT-PEMFC for performance curves determination.?Design of real time Pontryagins Minimum Principle-based adaptive controller.?Results comparison against the same vehicle with conventional and hybrid powertrain.a r t i c l ei n f oArticle history:Received 22 April 2016Received in revised form 9 September 2016Accepted 2 October 2016Available online 12 October 2016Keywords:Energy managementHT-PEMFCOn-board fuel processorPontryagins Minimum PrincipleAdaptive controllera b s t r a c tThis paper describes the energy management controller design of a mid-sized vehicle driven by a fuelcell/battery plug-in hybrid powertrain, where an experimentally validated hight temperature polymerelectrolyte membrane fuel cell model is used. The power management strategy is derived by the appli-cation of the Pontryagins Minimum Principle, where the control parameter is adapted by using feedbackinformation on the state of charge and total trip length forecast as a function of a moving average of pastinformation about the driving cycle speed. The strategy we propose aims at achieving a real time sub-optimal solution of the control problem which is cast into the minimization of the consumed fuel. Thevehicle is also equipped by an auto-thermal reformer and, in order to minimize the hydrogen buffer size,the control algorithm is subject to constraints on the maximum hydrogen buffer level. A comparativeanalysis of the proposed strategy against the optimal one is conducted and results are reported. Theobtained fuel consumptions are also compared to those obtained by the same vehicle, powered by aninternal combustion engine and by a plug-in hybrid electric powertrain.? 2016 Elsevier Ltd. All rights reserved.1. IntroductionRoad transportation and, particularly, road vehicles are nowa-days proved to be one of the main contributors to pollutant andglobal green-house gas emissions 1. This, together with the risingof fuel price, is striving the automotive sector research towardsinnovative solutions, aimed at reducing costs and emissions 2.Electric Vehicles (EVs) are still too far from being a valid solutionfor the problem, both for reduced driving range and long chargingtime. Promising solutions - already widely proposed and analyzed- are plug-in hybrid electric vehicles (PHEVs), characterized byhigh overall efficiency, short transients, long range and low road-load-dependency 3,4. The same advantages apply for fuel cellvehicles (FCVs), which generally make use of polymer electrolytemembrane fuel cells (PEMFCs), with the possibility of furtherreducing pollutant emissions, giving a satisfactory range withoutthe need of an internal combustion engine (ICE) 5. In fact, whencompared to ICE-propelled vehicles, both conventional or hybridelectric ones, FCVs are, locally, zero-emission vehicles and, in prin-ciple, if the fueling hydrogen could be derived from renewableenergy sources, these vehicles could allow for zero pollutant emis-sions also at a global level. Therefore, these vehicles can give a validcontribution to make the transportation sustainable in the longtermandgovernmentsarestronglystrivingtowardsthesesolutions 6,7. Nonetheless, even being a relatively mature tech-nology, there are still some disadvantages related to the use of fuelcells for vehicles, such as high costs, low power density, and lack of/10.1016/j.apenergy.2016.10.0150306-2619/? 2016 Elsevier Ltd. All rights reserved.Corresponding author.E-mail addresses: laura.tribioliunicusano.it (L. Tribioli), raffaello.cozzolinounicusano.it (R. Cozzolino), daniele.chiappiniunicusano.it (D. Chiappini), paolo.ioraunibs.it (P. Iora).Applied Energy 184 (2016) 140154Contents lists available at ScienceDirectApplied Energyjournal homepage: /locate/apenergyhydrogen infrastructures 6. The latter issue could be solved byusing an on-board fuel processor for on-site hydrogen productionfrom hydrocarbon fuels. This solution has been often investigatedfor the use of hydrogen-enriched fuel directly in internal combus-tion engines 8,9. Early prototypes for fuel processors to be useddirectly in vehicles were obtained by scaling down already existingindustrial technologies. In this case, gasoline, ethanol and otherautomotive fuels could be successfully processed, but the proto-types still required volume and mass not suitable for automotiveapplications. In the US, on 2004, these issues and the competitionwith more mature technologies, such as gasoline/battery hybridvehicles, have convinced the DOE On-Board Fuel ProcessingGo/NoGo Decision Team to terminate the research on on-boardfuel processing for FCVs 10. In Europe, in the early 2000s, DaimlerChrysler started testing methanol processors for the fueling of fuelcell vehicle prototypes. NeCar 5, based on the A-Class Mercedesdesign, was the last launched prototype, which used a 75-kWBallard fuel cell showing impressive performance 11. In 2004,Renault/Nuvera presented a four-year project for a fuel processorfor on-board hydrogen production small enough and powerfulenough for use on a vehicle, but also this program ended in 2008with no further developments 12. In these early projects, on-board fuel processing had been considered for fuel cells providing100% of vehicle traction power, with reformer size and systemcosts which made this solution unworthy. Afterwards, on-boardfuel processing was investigated again for coupling with fuel cellsused as auxiliary power units (APUs). In fact, when a fuel cell isused as APU, its power is reduced, the system can be more compactand hydrogen storage unit is not required. Technological featuresand challenges of on-board reforming of heavy hydrocarbon fuelsto feed solid oxide fuel cells (SOFCs) as APUs have been summa-rized by 13, underlining the benefits of autothermal reforming(ATR) over partial oxidation (POX) and steam reforming (SR). ATRhas been again coupled to SOFCs by 14, who evaluated the effectof off-gas recycle on overall system efficiency. Albeit the lower effi-ciency and poorer fuel quality 15, ATR is recognized to be the bestsolution for transportation applications. In fact, reactions are con-sidered to be thermally self-sustaining, and therefore, they donot produce or consume external thermal energy, unlike POX or SR.In the automotive sector, though, polymer electrolyte mem-brane fuel cells are preferred to SOFCs being more reliable and hav-ing faster transients. On-board fuel processing for an APU based onalow temperature polymer electrolyte membranefuelcell(LT-PEMFC) has been investigated by 16. However, these devicesare affected by CO poisoning 15,1719 and require high-purityhydrogen, which can ask for more than one water gas shift unitsand for a preferential oxidation reactor or separation membranes.Such a complex and space consuming system is rather unsuitablefor applications like small or medium-size cars. Instead, high tem-perature PEM fuel cells (HT-PEMFCs) are more tolerant to carbonmonoxide and may cope with an increased CO level in the syngas20, avoiding the need of water gas shift units and preferentialoxidation reactor. HT-PEMFCs can also be operated without exter-nal gas humidification - further simplifying system complexity andmanagement - and have the advantage of a more efficient heat dis-sipation and of a better integration in the system thermal manage-ment 21. Moreover, the increased electrode kinetics resultingfrom the higher operating temperatures allow using alternativecatalysts for the electrodes, thus reducing costs 22. The result isa significant reduction in system complexity, size and cost. Anextensive review of HT-PEMFC-based auxiliary power units hasbeen proposed by 22 for diesel-powered road vehicles, showingtheir great potential.Beside these applications, recent developments in autothermalreactors are justifying the comeback to the use of on-board proces-sors in vehicles where the fuel cell is used for traction purposes23,24. In particular, as mentioned above, early projects failedbecause they focused on the on-board fuel processing for fuel cellsproviding 100% of vehicle traction power. Nevertheless, the coop-eration with an energy storage system, such as a battery, canreduce the fuel cell size and, consequently, the reformer size. Fuelcell size can be further reduced by employing a plug-in solution,which gives the possibility of charging the battery by means ofan external source, extending its operating range. However, thereal benefits of such a solution can only be emphasized with aproper energy management of all the in-vehicle power sources25.Several energy management control strategies have beenalready proposed for fuel cell vehicle, such as heuristic strategies2628, equivalent consumption minimization strategy (ECMS)29,30 and strategies based on optimal control theory 3135.Nonetheless, these analyses are all applied to fuel cell vehicles withhydrogen produced offline and stored on board, while the energymanagement of vehicles with on-board fuel processing is usuallybased on operation of the fuel cell at constant power, derived fromthe stand-alone optimization of the ATR/FC system efficiency. Asystem efficiency of 25.1% has been evaluated for a methanol basedon-board reformer for PEM fuel cell by 23, while 36 obtained asystem efficiency up to 41%, for a fuel cell system with auto-thermal ethanol reformer. Even claiming the possibility of usingthe system on-vehicle, those results were obtained with a stand-alone system. Also in 24, a stand-alone hydrogen production unitfrom reforming of ethanol for LT-PEMFC is simulated for on-boardpurposes. There is no evidence of studies on the energy manage-ment of fuel cell vehicles with an on-board processor and variablefuel cell load. Constraints derived from the hydrogen availabilitymust be considered in the energy management in this case.In this paper, the design of a controller for the energy manage-ment of a parallel fuel cell/battery vehicle with an on-board fuelprocessor is proposed. The application is a vehicle equipped byan autothermal reformer producing a syngas from isooctane, con-sidered as gasoline surrogate. Aspen PlusTMhas been used for thefuel processor modeling, in order to find the operating point whichmaximizes the conversion efficiency and properly evaluates thesyngas composition. The fuel cell is a HT-PEMFC, whose perfor-mance as a function of the syngas composition have been carefullyevaluated by means of a self-made semi-empirical code, realizedby the authors and presented in 37,38. As the fuel cell load canvary, the fuel processor can not satisfy the hydrogen demand inreal time and, therefore, a syngas buffer is placed between the fuelprocessor and the fuel cell.The strategy derives from the application of the framework pro-posed in 39 to fuel cell vehicles and considers the dynamic of thesyngas buffer and the constraints derived from the hydrogen avail-ability. Moreover, the adaptation law proposed in the previousalgorithm has also been improved by using the information onthe driving cycle average speed, averaged on past driving condi-tions, for pattern typology recognition.In order to demonstrate the effectiveness of the proposed algo-rithm, a comparative analysis of the algorithm against the optimalone is conducted and main results are reported. The model hasbeen validated by comparing the results to the fuel consumptionof the original conventional vehicle, namely the Chevrolet Malibu,and to a plug-in hybrid electric powertrain implemented on thesame vehicle chassis in a past work 40.2. Vehicle modelThe simulator used for the study is a quasi-static forward-looking simulator, developed in Matlab Simulink and derived froma past study 40. The driver model is based on a PID controller,L. Tribioli et al./Applied Energy 184 (2016) 140154141that compares the actual velocity of the vehicle (which is a conse-quence of the equilibrium between the torque delivered by thepowertrain to the wheels and the resistances to the vehiclemotion) with the desired velocity. The controller outputs the accel-erator or the brake pedal position, with the simulator choosing thefirst or the second if the torque at the wheels is positive or nega-tive. The actual vehicle speed is computed by solving the longitu-dinalvehicledynamics,whichtakesintoaccountalltheresistances to the vehicle motion, such as rolling resistance at tires,aerodynamic resistance and road slope. The main parameters usedfor the vehicle dynamics calculations are given in Table 1. Anequivalent vehicle mass is involved to take into account the rota-tional inertia of all the components of the driveline and is approx-imatively estimated in an increase of 10% of the overall vehiclemass, evaluated from the main components masses and the carshell and frame.The FCV powertrain, sketched in Fig. 1, consists of a HT-PEMFC,a DC/DC converter and a Li-Ion 105S 2P battery pack, linkedtogether to an electric motor by means of a DC/AC inverter. Thanksto the specific efficiency map, the motor can be directly linked tothe front wheels without any transmission ratio. The FC suppliespower directly to the electric motor or to the battery and, ifrequired, the battery and the FC can provide power to the frontmotor, together. The front motor is a GVM210-150 permanentmagnet electric machine and has been modeled by means of itsefficiency map, depicted in Fig. 2, and other performance dataavailable from the manufacturer 41.The powertrain specifications are listed in Table 2.Unlike 40, where the fuel cell was a LT-PEMFC, now the stackis composed by 325 cells in series, each of an effective area of120 cm2. A storage buffer is placed between the ATR and FC stack,where the hydrogen produced by the ATR is stored to be used bythe fuel cell when it is required. This way, the ATR can work at afixed optimized operating point. The ATR has been properly mod-eled in order to evaluate the isooctane-derived syngas compositionand the model is described in Section 2.1. Afterwards, a zero-dimensional electrochemical model of a HT-PEMFC, proposed in37,38 and briefly described in Section 2.2, makes use of theobtained syngas composition for the determination of the FC stackefficiency and the voltage-current density curve for a single cell.2.1. ATR modelThe aim of this section is to define the operating conditions thatmaximize the efficiency of ATR-based fuel processor fed by isooc-tane. Aspen PlusTMhas been used for the fuel processor modeling,in order to find the operating point which maximizes the conver-sion efficiency.The general reforming reaction mechanism can be written as:C8H18aH2O cO2 3:77cN2! Products1whereaandcare the stoichiometric coefficients of water and airrespectively. The only products considered in the global reaction(1) are H2;CO;CO2;CH4;Cs and H2O. In order to obtain maximumhydrogen production, the reforming reaction has to be carried outin two steps:? High-temperature step (reforming reaction), in which isooctaneis converted into a gaseous mixture of H2;CO;CO2;CH4;Cs andunreacted H2O;? Low temperature step (water gas shift reaction), in which CO isreacted with H2O towards H2and CO2.The main components of the process, represented in Fig. 3, are:? Autothermal Reactor (ATR): reforming reactor in which theisooctane is converted into a gaseous mixture of H2;CO;CO2,and H2O. The ATR is fed by isooctane, steam and oxygen andit is maintained under adiabatic conditions.? Water Gas Shift Reactor (WGSR): water gas shift reactor (lowtemperature water shift reactor WGSR) in which CO reacts withH2O;H2and CO2are the products considered.? Heat Recovery Line: since the thermal efficiency of the fuel pro-cessor unit depends strongly on reactants preheating tempera-tures, as reported in 42, a heat recovery line is defined bycooling the syngas stream temperature in two heat exchangers.In particular, the water and isooctane required by the steamreforming reaction are pre-heated in HEX2by cooling the syngasstream, and then heated in the HEX1; the oxygen sent to theautothermal reactor is already heated up to 351 ?C as the mem-brane separation process requires compressed air at 10 bar, andthe compression heats the oxygen.? Separation Unit (SEP1): membrane separation unit where thepure oxygen is produced. Here the air is compressed up by C1to 10 bar and then through the membrane the oxygen is sepa-rated from nitrogen with a 95% removal efficiency 43.? Inter-Refrigerated Compression Line (IRCL): last stage of thesyngas production line. This is equipped with three compres-sors and two heat exchangers and it is needed in order toincrease the syngas pressure up to the hydrogen buffer pres-sure, i.e. 250 bar, represented as IC Compression section in Fig. 3.Table 1Main parameters for vehicle dynamics calculations.Curb weightFrontal areaDrag coefficientRolling resistance coefficientWheel radius1500 kg2 m20.350.0130.2 mFig. 1. Vehicle powertrain schematic.142L. Tribioli et al./Applied Energy 184 (2016) 140154Due to the complexity of the reaction system, the thermody-namicequilibriumanalysisisdeterminedbythenon-stoichiometric approach 15. In this approach the equilibriumcomposition of the system is found by the direct minimization ofthe Gibbs free energy for a given set of species without any speci-fication of the possible reactions that might take place in the sys-tem. Thus, it is assumed that the carbon in the fuel is reformedonly to CH4;CO or CO2and C(s). The equilibrium compositionshave been calculated for a given operating condition and, in orderto determine the chemical efficiency, the mass and energy balancesare solved for each configuration. The chemical efficiency of theATR system can be written as:gchem;ATRnH2? LHVH2nC8H18? LHVC8H182where nH2mol/s is the number of moles of hydrogen produced,nC8H18mol/s the number of moles of isooctane consumed, LHVH2J/mol and LHVC8H18J/mol the lower heating values of hydrogenand isooctane, respectively.010002000300040005000600070008000250200150100500501001502002500.350.350.450.50.650.650.60.750.750.70.850.850.80.90.950.95Electric Motor Speed rpm Electric Motor Torque NmEfficiencyMax/Min TorqueFig. 2. Electric motor efficiency map 41.Table 2Powertrain components specifications.Electric motorBattery packFuel cellH2bufferRated power75 kWEnergy capacity13 kW hRated power21 kWVolume80 LPeak torque270 Nm30004200 rpmNom. voltage340 VCells no.325H2stored mass1 kgRated torque130 Nm05000Max current180 AActive area120 cm2H2pressure250 barMin current?60 AFig. 3. ATR system layout.L. Tribioli et al./Applied Energy 184 (2016) 140154143In order to identify the thermodynamically favorable operatingconditions of the ATR system for the maximum conversion effi-ciency, a sensitivity analysis has been carried out by varying:? the steam to carbon ratio S/C at the autothermal reactor,defined as the ratio between the mole flow rate of the steamfeeding the reactor and the carbon mole flow rate of the feedingisooctane, in the range 0.23.6;? the oxygen to carbon ratio O/C at the autothermal reactor,defined as the ratio between the mole flow rate of the oxygenfeeding the reactor and the carbon mole flow rate of the feedingisooctane, in the range 1.31.7;? the pre-heat temperature of isooctane and water feeding theautothermal reactor, recovering the heat internally in theprocess.For each simulation a C8H18mass flow equal to 8:94 ? 10?4kg=shas been imposed as a constraint, in order to have an ATR systeminput power equal to 40 kW, while the other operating parametersare presented in Fig. 3.Referring to the carbon deposition in the ATR reactor, which ishighly undesirable because it deactivates the catalyst and reducesprocess efficiency, the analysis carried out to predict the thermo-dynamically carbon-free region of reforming operations 15 hasindicated that the presence of solid carbon strongly depends onthe S/C value and on reforming temperature. As a result of thisanalysis the S/C molar ratio considered here, for every reformingtemperature, are those at which carbon deposition is avoided. S/C and O/C molar ratios are important parameters for the process.These parameters should be chosen with the aim of avoiding theformation of carbonaceous deposits and maximum hydrogen pro-duction efficiency.Fig. 4 shows the ATR efficiency calculated with respect to differ-ent S/C and O/C ratios. It can be highlighted that the maximum effi-ciency value (about 80:0%) is obtained for a S/C and O/C ratio equalto 1.2 and 1.6 respectively. At this condition the preheat tempera-ture for isooctane and water feeding the reactor is equal to 261 ?C,while the operating reactor temperature is equal to 713 ?C. Thesyngas composition leaving the reactor at this condition after thedehumidification section (SEP2) is reported in the followingTable 3.The ATR model has been validated by comparing the resultswith the model proposed by 44 and reproduces a commercialdevice suitable for automotive applications 45.2.2. HT-PEMFC modelIn this section the fundamental relations used for HT-PEMFCmodeling are presented. A more detailed overview of the modelis presented by the authors in 37,38.The HT-PEMFC is basically ruled by the oxidation reactionswhich allow converting part of the fuel sent to the anode side,which is hydrogen, pure or diluted. On the other hand, the oxidantflow, generally air, is sent to the cathode side 46. The oxygen cir-culation from cathode to anode will assure the electrons motionwhich causes current circulation. In this application, the used fuelis the product of the ATR system previously presented, thus, it is inthe form of diluted hydrogen with different compositions as afunction of the starting fuel used.The reactions involved at anode and cathode sides are respec-tively the ones reported in Eq. (3):H2! 2H 2e?12O2 2H 2e?! H2O3Synthetically, the overall reaction of a HT-PEMFC may be writ-ten as follows:H212O2! H2O4The effective cell potential, VFC, starting from the Nerst poten-tial defined below, may be written as follows:VFC VNerst?gOhm?gact f i 5where,gOhmandgactare the ohmic and activation losses, while i isthe current density. According to previous works 18,47, concen-tration/diffusion losses have been neglected due to the fact thatthe standard operating conditions are far from the polarizationcurve area where this kind of losses becomes significant. In Eq.(5), it may be easily observed how the effective cell potential is onlya part of the ideal Nerst potential, VNerst, which, for a HT-PEMFC,may be written as follows:VNerst Voc;FCRunivT2Fln pH2p0:5O2?6where Voc;FC 1:229 ? 8:5 ? 10?4T ? 298:15 is the ideal voltage forhydrogen oxidation at ambient pressure, as a function of tempera-ture T 47, Runivis the universal constant of ideal gases, F is theFaraday constant and pH2and pO2are the partial pressures of hydro-gen and oxygen respectively. The ohmic and activation losses maybe written in a general form as follows:gOhm ROhm? i7gactgact;angact;ca8where ROhmis the total ohmic resistance, whilegact;anandgact;caarethe anodic and cathodic activation overpotentials, calculated as dis-cussed later in this section.In a common approach, the local ohmic resistance, R, of thegeneric cell layer , may be evaluated starting from the local con-ductivity,j, (different for each fuel cell layer - e.g. gas diffusionlayer (GDL), catalyst layer (CL), electrodes, membrane, etc. - asalready proposed in 48):Fig. 4. ATR chemical efficiency as a function of S/C and O/C ratios.144L. Tribioli et al./Applied Energy 184 (2016) 140154Rdj9where dis the local thickness of the generic cell layer. The detailsabout ohmic losses for this fuel cell may be found in 37,38.Once all the conductivities are evaluated, the total ohmic resis-tance is given by:ROhmdMemjMemdGDLjGDLdEljEl10The two contributions of activation losses have to be evaluatedin two different manners. More specifically the anode ones areevaluated by means of a chemical model based on Arrhenius equa-tion, while the cathode ones are evaluated via a semi-empiric rela-tionship starting from available experimental data.2.2.1. Anode activation overpotentialAs proposed by 37,38,18,49,17, the complete set of reactionswhich takes place at anode side is considered, as shown in the fol-lowing table: M represents a platinum catalyst site where the reac-tion takes place, and the factors krrepresent the reaction rate of thegeneric reaction r, listed in Table 4. This model reconstructs a non-linear system of equations solved numerically in the implementedmodel. For a more detailed analysis, reader can refer to 37,. Cathode activation overpotentialAs stated before, in order to model the cathode activation lossesa semi-empirical model is used, as proposed by 18:gact;ca b1 b2T b3T ln cO2? b4T ln i 11where cO2represents the oxygen concentration at cathode mem-brane/gas interface, which may be evaluated by means of Henryslaw:cO2pO22:5 ? 108exp ?1700T?mol=cm3?12In order to evaluate the empirical coefficients bz, with z 2 1;4?,a set of experimental data is needed. The unknown coefficientsmay be derived by means of a multiple regression starting fromthe experimental polarization curves. In this work the ATR groupis fed by standard isooctane, thus, the composition of the fuel sentto the fuel cell is the one previously reported in Table 3. As it maybe observed in this table, the CO concentration is about 1:907%,then, starting from the results proposed in 37,38, the bzvaluesmay be evaluated from a set of known values. For the above men-tionedfuelcompositiontheresultsaresummarizedinTable Table 5.With these parameters, assuming a fixed working cell tempera-ture about 160?C, the following curves are obtained, Fig. 5. Thefirst one is the polarization curve and it represents the cell voltageas a function of the density current, while the second one is theefficiency curve, where the HT-PEMFC efficiency is reported as afunction of the output power.2.3. Battery modelThe electric storage system is a battery pack of Li-Ion cells man-ufactured by A123. The battery has been modeled by means of azero-th order equivalent circuit. This model has been demon-strated to be adequate enough to predict battery losses, but beingas fast as needed in an energy-based simulator 50,51. In thisapproach, the battery is modeled by its open circuit voltage, Voc;B,in series with its internal resistance, R0. For the equivalent resis-tance one value in charging and another in discharging are used.Moreover, all the battery parameters vary with the SoC. The varia-tion of the open circuit voltage with respect to temperature hasbeen neglected as explained in 39, while the internal resistanceis also a function of battery temperature. The battery operatingtemperature is evaluated by means of a simple thermal modelbased on the heat released due to internal thermal losses. Theseparameters, shown in Fig. 6, have been evaluated in a past projectby conducting a set of experiments.Thus, applying the well-known Kirchhoff law, the battery loadvoltage, VB, is obtained as:VB Voc;BSoC ? I ? R0SoC13where I is the current flowing through the battery terminals (posi-tive during discharge). The battery power can be thus expressed as:PB VB? I Voc;BSoC ? I ? I2? R0SoC143. Optimization problem formulationThe proposed FCV is a plug-in vehicle and thus the optimalenergy management strategy results in being the one which min-imizes fuel consumption,_mf, by performing a blended battery dis-charge operation. In particular, the optimization problem lies infinding the optimal trajectory u?t, which minimizes an integralcost function, J, defined on the entire optimization horizon t0;tf?,which corresponds to the length of the driving cycle:minuJ Ztft0_mft;ut;xtdt15subject to the dynamic constraints:_x gt;ut;xt16The control vector ut ut 2 U #Rr, where U is a set ofadmissible controls in Rrand is composed by a number of controlvariables depending on the degrees of freedom of the energy paths.Table 4Reactions and preferential directions on anode side.ReactionForwardBackwardH2 2M $ 2 M ? Hkfhkbh2 M ? H ! 2H 2e? 2MkehM CO $ M ? COkfckbcM ? CO H2O ! CO2 2H 2e? MkCO2CO2 2 M ? H ! M ? CO H2O MkrwgsTable 5Values of bzcoefficients for the used syngas.b1b2b3b4?1:13681:0745 ? 10?24:4410 ? 10?45:8125 ? 10?5Table 3Syngas composition at ATR outlet section in terms of molar fractions.H2COCO2CH4N20.677230.019070.287220.009840.00664L. Tribioli et al./Applied Energy 184 (2016) 140154145In this problem, the system is characterized by only one degree offreedom and the control function can be seen as the powerdelivered by the fuel cell stack, PFCt, directly related to the powersplit between the FC and the battery, such as: ut PFCt PMt ? PBt, being PMthe power of the front motor - negative inrecuperating and positive in motoring - and PBthe battery power- negative in recuperating and positive in motoring. Being thehydrogen consumption minimization the only optimization target,then the system can be threated as quasi-static and the state vari-ables are the state of charge, SoC, namely x1t SoCt and thehydrogen buffer level - hereafter referred to as State of Tank (SoT)by analogy - x2t SoTt. Both the state variables can be properlyrelated to the fuel cell power request, so that x1t f1u andx2t f2u. The choice of SoC and SoT as the only state variablesis due to the fact that the other components dynamics are muchfaster and it has been demonstrated in 52 that, for the purposeof fuel economy estimation, they can be neglected.The variation of the battery SoC is defined as:_SoC ?gc?IQnom17withgcthe coulombic efficiency 53 and Qnomthe battery nominalcapacity. Solving the algebraic Eq. (14) for the current, we obtain:I Voc;BSoC ?ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVoc;BSoC2? 4 ? PBR0SoCq2R0SoC18and recalling that PB PM? PFC, we can finally write:_SoC ?gcVoc;BSoC ?ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVoc;BSoC2? 4 ? PM? PFC ? R0SoCq2R0SoCQnom g1SoCt;PFCt19The SoT evaluates the tank level dynamics as the differencebetween the incoming and outcoming hydrogen flows, i.e. the fuelconsumption_mfand the hydrogen produced by the ATR_mH2;ATR,01020304050607080901003.43.5SoC %Cell Open Circuit Voltage V010203040506070809000.0020.0040.0060.0080.010.012SoC %Internal Resistance R0 (Charge), 5CR0 (Charge), 5CR0 (Charge), 15CR0 (Charge), 25CR0 (Charge), 35CR0 (Charge), 45CR0 (Charge), 55CR0 (Discharge), 5CR0 (Discharge), 5CR0 (Discharge), 15CR0 (Discharge), 25CR0 (Discharge), 35CR0 (Discharge), 45CR0 (Discharge), 55CFig. 6. Open-circuit voltage as a function of SoC and battery charge and discharge internal resistances as a function of SoC for different temperatures.Fig. 5. Polarization and power/efficiency curves of the HT-PEMFC.146L. Tribioli et al./Applied Energy 184 (2016) 140154respectively, referred to the maximum buffer capacity, mH2;max. Thehydrogen consumption can be related to the fuel cell power asfollows:_mfPFCLHVH2?gFCPFC20with LHVH2lower heating value of the hydrogen andgFCPFC effi-ciency of the fuel cell. Since the reformer works at a fixed point,_mH2;ATR const, and the rate of change in the tank level is a functionof the only control variable:_SoT ?_mf?_mH2;ATRmH2;max ?1mH2;max?PFCtLHVH2?gFCPFCt?_mH2;ATR? g2PFCt21The global constraints on the state variable x1t concern withinitial and final values of SoC over the optimization horizon.Namely, x1t t0 SoC0and x1t tf SoCf, with SoC0 0:95as the battery state of charge is considered to be fully restored atthe beginning of each driving mission and SoCf 0:3 as a 30%SoC threshold is selected to prevent battery wear, by limiting itsactivity at low state of charge. For the state variable x2t, the initialcondition is the initial buffer level x1t t0 SoT0, set equal to80% - which means 0.8 kg of hydrogen and 8.9 kg of syngas - whilethe terminal condition is free. At every instant of time, also localconstraints due to the physical limits of each component, as wellas the drivability constraint, must be satisfied.3.1. Pontryagins Minimum PrincipleThe problem has been solved by applying the Pontryagins Min-imum Principle. This algorithm is well-suited for implementationin forward-looking simulators 54 and has been demonstrated tobe able to minimize the hydrogen consumption in fuel cell vehicles55. The application of the PMP requires the definition of anHamiltonian function, H, so that:Ht;ut;xt;kt k0_mft;ut;xt ktgt;ut;xt22where k0is a constant (with k0 0 or k0 1), kt k1t;k2t? aretheco-statevariableswhichvarywithtime,sothatkt 08t 2 t0;tf?andgt;ut;xt g1t;ut;x1t;g2t;ut;x2t? represent the states dynamics. Eq. (22), and therefore theco-states and the state variables, must satisfy the followingdynamic equations 56:_kj ?Hu;x;kxj;j 1;223_xjHu;x;kkj;j 1;224In this study, considering Eqs. (19)(21), the Hamiltonian hasbeen formulated as follows (note that the dependence on timehas been dropped for the sake of fluency):Hu;x;k k0uLHVH2gFCu? k1gc?Voc;B?ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2oc;B? 4 ? PM? u ? R0q2R0Qnom? k2?1mH2;max?uLHVH2?gFCu?_mH2;ATR?25It is immediate to note that (23) applied to j = 2 leads to:_k2 ?Hu;x;kx2 026as the system equation g2u is not a function of x2, but only of thecontrol variable u. On the other hand, the co-state k1variation withrespect to time is in principle different from zero, being the systemdynamic equation g1x1;u a function of x1, given that the open-circuit voltage and the internal resistance of the battery dependon the SoC. Nonetheless, as demonstrated in 57 and also foundin 58,59, the variation of k1with respect to time can be neglectedwhen the battery efficiency is almost constant, as in this applica-tion. Hence:_k1 ?Hu;x;kx1 027BymanipulatingEq.(25),wecanobtainthefollowingformulation:Hu;x;k k0?k2mH2;max !uLHVH2?gFCu k2_mH2;ATRmH2;max? k1gc?Voc;B?ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2oc;B? 4 ? PM? u ? R0q2R0Qnom28where both the termsk0?k2mH2;max?andk2mH2;max_mH2;ATR?are con-stants. Therefore, if we set k0 0, Eq. (28) can be normalized bydividing each element byk2mH2;max, leading to:Hu;x;k ?uLHVH2?gFCu_mH2;ATR? kugc?Voc;B?ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2oc;B? 4 ? PM? u ? R0q2R0Qnom29with kuk1k2mH2;max. Finally, the optimal control variable, for eachtime step, must satisfy the following condition:Hu;x;k P Hu;x?;k?30The system defined by Eqs. (29) and (30) is a two-point bound-ary value problem which can be solved only numerically by usingthe shooting method 60, which implies the initial-guess of the co-state, namely kut t0, to reduce it to a conventional initial-condition problem. The initial-guess of the co-state is crucial toensureoptimality61.Ask1t k1t08t 2 t0;tf?andk2t k2t08t 2 t0;tf? - see Eqs. (26) - determining the value ofkut0 k1t0k2t0mH2;maxthat solves the optimization problem will guar-antee optimality.In order to ensure the global constraints on SoC and SoT to bemet in a real time application, in practical implementation, penaltyfunctions need to be used in the Hamiltonian 52,56. In the pre-sent work, a piecewise functionljxj, is added to the co-states,when the SoC or the SoT reach the boundary limits.l1SoC K1if SoC SoCmax0else8:andl2SoT K2if SoT SoTmax0else8:where K1and K2are design parameters selected in simulations.L. Tribioli et al./Applied Energy 184 (2016) 140154147The Hamiltonian function eventually becomes:Hu;x1;ku ?uLHVH2?gFC_mH2;ATR?1 l2? ku1 l1?mH2;maxgc?Voc;B?ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiV2oc;B? 4 ? PM? u ? R0q2R0Qnom314. Supervisory control strategyAs already mentioned above, the Pontryagins Minimum Princi-ple is implementable online, but ensures optimality only given thatthe driving cycle is known a priori. In particular, the optimal solu-tion strictly depends on speed trace and total traveled distance61, which can not be known in advance.Fig. 7 shows the speed profile of an extra urban path, namelythe Artemis Extraurban standard cycle, and the SoC trajectoriesrelated to different values of the co-state ku. One can note that,as for the PHEVs, the optimal trajectory - i.e. the trajectory withthe lower fuel consumption - results in a blended discharge ofthe battery, which assumes a quasi-linear decreasing trend withrespect to the total traveled distance, confirming what has beenalready shown in 40,32. Fig. 8 shows a portion of a real drivingcycle, derived from data collected by a GPS in the city of Aachen.For this cycle, also the optimal power sharing among the fuel celland the battery is shown. As one can note, the optimizer makesthe fuel cell operate at a nearly constant power, around 8 kW,which correspond to a stack efficiency of around 60% (see Fig. 5).Therefore, the battery is used for transients and load following,while the fuel cell is used for traction when needed (e.g. kilometersfrom 16 to 25) or to charge the battery. Obviously, this behavior ofthe controller has the additional benefit of avoiding rapid varia-tions of the fuel cell load, thus preventing the device wear. Fig. 9shows the state of charge and state of tank variations for the entirelength of the same cycle. The black curve in the bottom plot ofFig. 8 represents the optimal state of charge, which correspondsto black curve in the upper plot of Fig. 9. A 1200 s warm up timeis imposed for the ATR, which means that for the first 20 minhydrogen can not be produced, thus explaining the initial decreaseof the SoT.Even if this cycle has different typological characteristics, also inthis case the optimal trajectory of the SoC is the one that realizes ablended discharge. For this cycle, it is interesting to note that thetrend of the trajectories corresponding to kufrom 12 kg to12.5 kg are affected by the penalty functions, while for kufrom9.25 kg to 9.75 kg the vehicle is not able to accomplish the entiredriving mission, as both the battery and the buffer are completelyemptied at the end of the driving cycle, Fig. 9, due to an inefficientvehicle operation. In particular, this happens because the battery isdischarged too fast at the very beginning of the driving cycle, fall-ing in the charge sustaining operation, which is very far from theoptimal solution. Moreover, Fig. 9 shows that also the hydrogenstored in the buffer should be used gradually, i.e. with a semi-blended discharge of the buffer. In fact, a heavy use of the fuel cell,thus discharging the buffer very fast, corresponds to a light use ofthe battery, which is not used or even recharged by the fuel cell,thus diverging from the blended trajectory. Similarly, a light useof the fuel cell, thus allowing the buffer to be recharged, could cor-respond to a heavy use of the battery, which is discharged quickly,event which may cause a charge sustaining mode of operation. Infact, Fig. 9 shows the interdependence of the two state variables,further justifying the decision of using a unique co-state ku.In 59 it has been found that, for PHEVs, the optimal value of theco-state is strongly dependent on the driving cycles and, in particu-lar, it can be related to cycle average velocity and trip length 61. In54 it has also been shown that for high-demanding driving cycles,i.e. characterized by high average velocities, higher values of the co-state are required to ensure an optimal trajectory of the state ofcharge. This still holds also for FCVs. As one can note, the selectionof the optimal (and unique) value of kuvaries from cycle to cycle -e.g. 11.15 kg for the Artemis Extra Urban against 10.5 kg for theAachencycle.LookingatFigs.7and9,onecannotethatthefirstdriv-ingpattern,characterizedbyahigheraveragespeed(60.34 km/h),inorder to perform the optimal trajectory, requires a value of theco-state greater than the one needed by the second driving pattern,characterized by a lower average speed (41.97 km/h). Figs. 10portrays the Aachen driving cycle for a total length equal to thelength of the Artemis Extra Urban driving cycle (around 160 km),in order to evaluate the effect of the only average speed on the opti-mal co-state value. For the same traveled distance, the differencebetween the optimal values of the co-state is more evident, being10 kgfortheAachencycleagainst11 kgfortheArtemisExtraUrban.Therefore, even if the Aachen cycle requires more energy to beaccomplished (higher fuel consumption), because of the frequentvelocity variations, having a smaller average velocity its optimalityis guaranteed by a lower value of the co-state.Unfortunately,thecyclecharacteristicsareunknownatthe beginning of the driving mission and hence the on-line0204060801001201401600.81SoC u=9.5 kg, mf=1.7588 kgH2u=9.75 kg, mf=1.7126 kgH2u=10 kg, mf=1.6629 kgH2u=10.25 kg, mf=1.6169 kgH2u=10.5 kg, mf=1.5749 kgH2u=10.75 kg, mf=1.5307 kgH2u=11 kg, mf=1.4846 kgH2u=11.15 kg, mf=1.44643 kgH2u=11.25 kg, mf=1.509 kgH2u=11.5 kg, mf=1.6367 kgH2020406080100120140160050100150Distance kmSpeed km/hFig. 7. Influence of kuon the SoC trajectory and hydrogen mass consumption mfkgH2 - Artemis Extraurban (standard) driving cycle.148L. Tribioli et al./Applied Energy 184 (2016) 140154implementationofthePMPcannotguaranteeoptimality.Nonetheless, a co-state adaptation algorithm can make the energymanagement strategy based on PMP implementable in real time. Inthis paper, an algorithm adaptive to varying driving conditions isproposed, inspired by the adaptation law proposed in 62,39. Inparticular, the controller only makes use of feedback informationabout the state of charge and about the average cycle speed, calcu-lated from past information on the on-going driving mission.The feedback information about the state of charge is used, as in39, to update the co-state (ku) in order to ensure the actual SoCtracking a linear reference SoC profile, SoCref. Being the SoC optimalprofile linear in space - rather than in time - the co-state is updated0510152025303540050100150Speed km/h051015202530354050050100Distance kmElectrical Power kWSoC %Battery SoCBattery PowerEM PowerHTPEMFC PowerFig. 8. Aachen (real) driving cycle speed trace.Fig. 9. Influence of kuand penalty function on the SoC and SoT trajectories and hydrogen mass consumption mfkgH2 - Aachen (real) driving cycle.0204060801001201401600.81mf = 1.6142 kgH2u = 10 kgDistance kmSoC SoT Fig. 10. Optimal SoC and SoT trajectories for a traveled distance of around 160 km - Aachen (real) driving cycle.L. Tribioli et al./Applied Energy 184 (2016) 140154149based on the traveled distance according to an auto-regressivemoving-average (ARMA) filter:kus f kus kus ? f2 KpSoCrefs ? SoCs32with s the current covered distance, f the sampling distance and Kpa proportional gain. The SoCrefis a linear function of the current dri-ven distance, that reproduces a SoC profile able to guarantee com-plete battery discharge, i.e. over the total trip length, Dtot.SoCrefs a b ? d33wherea SoCfb SoC0? SoCfd Dtot?sDtot;8:34Since Dtotis not known, an average cycle speedvavg, which canbe related to the mission typology, is calculated as a moving aver-age of vehicle speedvvehdata collected during the driving cycle, inorder to estimate the possible travel length:vavgs vavgs ? 1 vvehs235This way, a speed thresholdvthrcan be fixed in order to recog-nize the driving cycle typology and select a corresponding possiblevalue of Dtot:DtotD1ifvavgvthrD2ifvavgPvthr?with D1 D2, since a value ofvavg D2)14 kg150L. Tribioli et al./Applied Energy 184 (2016) 1401546. ConclusionsIn the proposed study a sub-optimal energy management strat-egy for a fuel cell/battery hybrid vehicle with an on-board proces-sor has been presented. The vehicle is equipped by a HT-PEM,which has been modeled by means of a self-made semi-empiricalcode and an autothermal reformer, also modeled in order to opti-mize its operation and estimate a meaningful value of its conver-sion efficiency. The ATR is fed by isooctane and is able toproduce a syngas to be used by the HT-PEM during the drivingcycle, after a 20-min start up period. The controller, based on thePontryagins Minimum Principle, solves the on-line energy man-Table 7Adaptive control strategy performance.Length kmvavgkm/hPavgkWConsumption H2kgConsumption C8H18litersAdaptive vs PMP %FUDS + FHDS14248.19.770.8804.253+3.49Artemis Urban4517.57.810.3081.491+0.40Aachen26742.011.923.21915.55+8.46Aachen (Short)16542.011.921.8288.832+13.24Arco Merano22548.811.061.9919.620+10.33Artemis Extra Urban16460.312.811.6037.747+13.050510152025303540450204060Speed km/h05101520253035404500.51SoC AdaptiveSoCrefPMP0510152025303540450.511.5Distance kmSoT AdaptivePMPFig. 11. SoC and SoT trajectories - Artemis Urban (standard) driving cycle.020406080100120140160050100Speed km/h02040608010012014016000.51SoC AdaptiveSoCrefPMP0204060801001201401601Distance kmTank Level kgAdaptivePMPFig. 12. SoC and SoT trajectories - FUDS + FHDS (standard) driving cycle.L. Tribioli et al./Applied Energy 184 (2016) 140154151agement problem by adapting itself to changes in driving condi-tions. The adaptation law makes use of feedback information aboutthe state of charge and recognizes the driving pattern by elaborat-ing driving past data. A comparative analysis of this adaptive algo-rithm with the optimal solution has been presented. Results havealso been compared to a conventional vehicle and a PHEV operat-ing with a CD/CS strategy. Results have shown that the algorithm isable to reach close-to-the optimum fuel consumptions in all theproposed missions and it performs always better than the originalconventional vehicle. At the same time, the comparison against aPHEV has shown the limits of having an on-board reformer whichhas a warm-up time not comparable to the driving cycle dynamics.As the ATR can be switched-off for no more than 10 min, some-times the fuel cell must be used to charge the battery with anundesired consumption of hydrogen. This way, the controller cansometimes provide results quite worse than the PHEV, althoughstill performing better than the ICE-powered vehicle. Future stud-ies could be addressed at improving this aspect. In particular,future studies can investigate the effects of the optimization ofthe system thermal management, in order to recover thermalenergy to keep the ATR warm during switch-off periods and allowfor the use of the reformer only when really needed. Moreover,future investigations would also consider the influence of temper-ature, pressure, relative humidity on the ATR and HT-PEMFC per-formance and compare the control strategy effectiveness in caseof different fuels usage.050100150200250300050100150Speed km/h0501001502002503000.81SoC -AdaptiveSoCrefPMP (Aachen Short)PMP (Aachen)050100150200250300Distance km00.51Tank Level kgAdaptivePMP (Aachen Short)PMP (Aachen)Fig. 13. SoC and SoT trajectories - Comparison Aachen vs Aachen Short.050100150200250050100150Speed km/h05010015020025000.51SoC AdaptiveSoCrefPMP0501001502002501Distance kmSoT AdaptivePMPFig. 14. SoC and SoT trajectories - Arco Merano (real) driving cycle.152L. Tribioli et al./Applied Energy 184 (2016) 140154References1 European Commission, EU transport in figures: statistical pocketbook, 2016.2 Roskilly AP, Palacin R, Yan J. Novel technologies and strategies for cleantransport systems. Appl Energy 2015;157:5636.3 Chan CC. 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