Eco-effcency optmzaton of Hybrd Electrc Vehcle based on response surface method and genetc algorthm J. Nzsabra, P. Duysnx, Y. Louvgny LTAS - Automotve Engneerng, Unversty of Lege, B52, Chemns des Chevreuls, B52, 4000 Lège (Belgum) Emal: J.Nzsabra@student.ulg.ac.be, P.Duysnx@ulg.ac.be, Yannck.louvgny@ulg.ac.be EET-2008 European Ele-Drve Conference Internatonal Advanced Moblty Forum Geneva, Swtzerland, March 3, 2008 Abstract The electrc vehcles (EV) and sometmes the hybrd electrc vehcle (HEV) technologes are envronmentally very effcent but can not succeed on the market because of a smaller ablty to satsfy customer s requrements. Comparson of clean technologes n automotve and transportaton systems has been measured usng dfferent analyss tools such as LCA (lfe cycle analyss). However, these nstruments never account for the user s satsfacton whch partly explans the market acceptance problems. The Eco effcency s a global ndex whch accounts for both envronment mpacts and user satsfacton. The man objectve of vehcle powertran hybrdzaton s to mprove the fuel consumpton and envronment pollutants mpact (Eco-score) wthout decreasng the vehcle performances and other user satsfacton crtera. The objectve of ths study s to mnmze the Eco-score ndcator of HEV wth respect to the user satsfacton crtera. The approach s formulated as a multdscplnary optmzaton problem. At frst the EV or HEV are modeled and smulated usng ADVISOR (advanced vehcle smulator) wth respect to several drvng stuatons. Then emssons can be determned and the Ecoscore ndcator can be calculated. User Satsfacton can be evaluated based on performance crtera extracted from ADVISOR smulaton and on smple evaluaton tools relyng on the state-of-the art of technologcal nformaton for safety, relablty and daly cost. In ths study the desgn problem s stated as follows: select mechancal and electrc components (lke engne, motor and battery szes) to mnmze the Ecoscore ndcator and to mze user satsfacton crtera subject to catalogue constrants on the choce of the components. The approach s llustrated on applcatons dealng wth parallel hybrd electrc vehcles. Keywords: Ecoeffcency, MDO (multdscplnary optmzaton), response surface model, mult objectve optmzaton, mult objectve genetc algorthm. Introducton Hybrd Electrc Vehcle (HEV) s expected to be one of key technologes for future cleaner and fuel effcent vehcles. Typcally, the archtecture of these vehcles ncludes an nternal combuston engne (ICE) assocated wth an electrc motor and ts energy storage system (Battery). A success HEV desgn requres optmal szng of ts key mechancal and electrcal components. In addton, for more HEV effcency, an optmal management of energy flow (control strategy) s requred. Therefore, n the desgn process of a HEV, there s a large varety of desgn varable choces ncludng HEV confguraton, key mechancal and electrcal components szes and control parameters. Moreover engneers are faced wth several conflctng desgn constrants and objectves amng at ncreasng performances and comfort whle mnmzng envronmental mpact. Conversely to the mportance of ths practcal ssue, lterature revew provdes a rather lmted number of works dealng wth the applcaton of ratonale tools such as structural and multdscplnary optmzaton appled to HEV desgn (see for nstance Ref. [-7]).
In these works most of them focus on one sngle objectve functon and emssons are restrcted to fuel emssons. In ths study, HEV desgn problem s consdered as a mult objectve and multdscplnary optmzaton problem. In addton one of the man goals s the smultaneous mnmzaton of the vehcle envronmental mpacts (Ecoscore) whle also mzng User satsfacton crtera (US). Satsfacton of needs or user satsfacton (US) s formulated as an aggregaton of several crtera whch reflects several aspects of vehcle characterstcs for users.e daly cost, relablty, safety, performances, etc. In order to assess more clearly the trade-off between these antagonstc crtera, the authors have developed n past works, the concept of an Ecoeffcency ndex to provde a global ndex whch accounts for both envronmental mpacts and user satsfacton crtera. Ths Ecoeffcency ndex s based on one hand on the Ecoscore [8,9] for the envronmental mpact and on the other hand on a User Satsfacton composte ndex to assess the ablty of the vehcle to meet customer s expectatons about hs transport needs. Our work on eco effcency showed clearly the dffculty to defne aggregate ndces for US & Ecoscore and the senstvty of the results n the weghtng of the two crtera on the result. Therefore ths paper proposes a novel desgn approach of HEV and EV based on multdscplnary optmzaton usng genetc algorthms and response surface methods. The multobjectve approach that s developed naturally crcumvents the problem of consderng conflctng crtera of dfferent natures. The approach s formulated as a multdscplnary optmzaton problem based on dfferent coupled analyss problems. At frst the EV or HEV model s smulated usng ADVISOR (advanced vehcle smulator) [0,]. Then emssons can be determned for several drvng scenaros and the Ecoscore ndcator can be calculated. The User Satsfacton can be evaluated based on performances crtera evaluated from ADVISOR smulatons and from smple safety, relablty and daly cost scores, whch are computed from smple evaluaton tools and data bases relyng on state-of-the-art of technologcal nformaton. In ths study the desgn problem s stated as follows: select mechancal and electrc components (lke engne, motor and battery szes) to mnmze the Ecoscore ndcator and mze the user satsfacton crtera subject to dscrete valued szes of components chosen from catalogues. Because of the large number of HEV parameters, tral-and-error-based desgn approaches of a HEV s generally mpossble and cumbersome to handle by human ntuton. On the contrary, a ratonale and effcent desgn procedure s based on dgtal smulaton and optmzaton algorthms. As response functons may be nosy and/or dscontnuous, dervatve-free algorthms are preferred to gradent-based optmzaton algorthms, such as Sequental Quadratc Programmng (SQP) to solve the problems. Moreover multobjectve versons of Genetc Algorthms are avalable to handle the eco-effcency desgn problem. Fnally snce response functons are mplct functons of desgn varables and ther evaluaton requres every tme a smulaton run, the numerous drect calls to the smulaton code are replaced by surrogate models or metamodels n order to carry out the optmzaton work wth a moderate computatonal cost. In ths study we have selected the software tool Boss Quattro from Samtech [2] to carry out the optmzaton and the task management tasks of the chan of coupled smulaton tools. The followng soluton flowchart s used: Use a parametrc study n BOSS QUATTRO to construct some response surface approxmatons (polynomal) of US and Ecoscore from ADVISOR smulaton models. Formulate a mult objectve optmsaton problem to mnmze the Ecoscore and mze the US. Solve the eco effcency desgn optmzaton problem usng a mult objectve genetc algorthm (MOGA) avalable n BOSSQUATTRO. The approach s llustrated on eco-effcency desgn problems of parallel HEV, seres HEV and an HEV bus. 2 Modelng and Smulaton 2. HEV Confguratons The basc two archtectures of HEV powertrans are the seres and parallel confguratons. However, multmode and complex types are also consdered to combne the features of both seres and parallel hybrds (.e. Toyota Prus) as stressed by Ref []. As shown n Fgure, the seres HEV confguraton ncludes a fuel converter (ICE), a generator, a battery and an electrc motor. In ths case, the engne does not drve the vehcle shaft drectly, but the mechancal power s converted nto the electrcal energy usng a generator. Then, the torque requred to drve the vehcle can be suppled by the electrc motor. Sometmes, electrc energy s also saved n the energy storage system (.e. battery). However, n parallel HEV, both electrc motor and IC engne can delver power to wheels as shown n Fgure 2. The electrc motor can also be used as a generator to charge the battery by ether the regeneratve brakng or by absorbng the excess power produced by the engne when ts output s greater than that requred to drve the wheels. In the combned seresparallel hybrd, the confguraton nvolves an addtonal mechancal lnk compared wth the parallel hybrd and also an addtonal generator compared wth the seres hybrd, whch makes the seres-parallel HEV a relatvely more complcated and costly verson. Fgure : Seres HEV Confguraton Fgure 2: Parallel HEV confguraton
2.2 Smulaton Smulaton tool: ADVISOR (advanced vehcle smulator) s used for smulatng the fuel consumpton, the emssons and the performances of the vehcles. ADVISOR was ntally developed by the Natonal Renewable Energy Laboratory [0,] from 994 to 2002. ADVISOR combnes forward /backward facng approach for the vehcle performances smulaton (see Ref. [0]). In addton, t offers graphcal user nterface to select the component modules requred to construct the vehcle system. Among several components of a HEV, the IC engne, electrc motor and energy storage system are consdered as the most crtcal components. Proper selecton of these components manly affects the vehcle characterstcs and performance. Desgn model parameterzaton n ADVISOR: To consder the effect of component szes n the optmsaton of HEV desgn, ADVISOR approach s to consder a baselne confguraton components. The baselne confguraton can then scaled up durng the desgn process. For nstance for the energy storage system, a battery pack s selected and then the number of battery modules s modfed. The baselne scalng factor wll later be naturally consdered as our desgn varables durng optmzaton process. For example the baselne confguraton of the hybrd vehcle n the frst numercal applcatons s summarsed n Table. Table : Baselne confguraton of a passenger car Component Fuel Converter Motor Battery Baselne Geo.0 ltre SI 4 kw engne, peak effcency: 0.34 75 kw Westnghouse AC nducton motor/nverter valve-regulated lead-acd (VRLA) battery, 25 modules of 25 Ah and 2 V each representatve of an urban cycle (ECE5 drve cycle) and lasts about 800s, the mum speed beng 50km/h, whereas the second part smulates an extra urban cycle (EUDC drve cycle) and lasts about 400s wth a mum speed of 20km/h. 3 User satsfacton crtera The choce of a clean technology whch respects both envronment packagng, engneerng constrants and user needs s a mult objectve problem. Satsfacton of needs s based on several crtera.e securty, daly cost, relablty, performances, etc. Some crtera lke performances are easly quantfable but others lke comfort are qualtatve so that they can only be estmated by fuzzy descrpton. In ths study we wll consder only quanttatve crtera: cost, performances and securty. Performances: performances nclude mal vehcle velocty, acceleraton performances and gradeablty. They can be evaluated by smulaton n ADVISOR by followng standard approaches descrbed n classcal vehcle theory (see ref [7,8] for nstance). Maxmum speed s evaluated when solvng equlbrum equaton between propulson power and dsspated power by resstance forces (rollng resstance, aerodynamc resstance ) ηppropulson ( ω ) = Press tan ce ( v) = c0v+ cv ² + c2v³ () Whereω s engne speed whle v s the vehcle ground speed, η s the transmsson effcency, c 0, c, c 2 coeffcents of a general expresson of the drvng resstance forces. Acceleraton tme (from V to V 2 kph) can be evaluated by solvng ntegraton of equaton of moton of the vehcle v 2 dv t = meff (2) F net( V ) v Where meff s the equvalent or effectve mass and F net, the net force between propulson force and drvng resstance forces. Gradeablty: s estmated by solvng the equaton lmtng the propulson force that can be transmtted to the ground whle takng care of mass transfer durng clmbng n steady sate moton F = F W (3) µ propulson ress tan ce f / r Wf andw r are respectvely the front and rear weght under front or rear wheels. Fgure 3: CYC_ECE_EUDC drve cycle Drve cycles: In ths study the New European Drve Cycle (NEDC) s selected for passengers vehcle smulaton (see fgure 3) because t s the legal reference n Europe. Ths drve cycle has two parts, the frst one s Securty: It s the capablty of the vehcle to ensure both the passengers and other road users safety. Safety can be based on several crtera lke securty equpment avalable on the vehcle, crash test results (e.g. Euro NCAP [5]), statc stablty factor estmatng rollover resstance [3], etc. But the vehcle mass s the man factor for road securty, especally for securty of collson partners. Based upon the FARS (Fatal Analyss Reportng System) database, Joksch et al. [6] have estmated the
relatonshp between the mass rato of collson partners, and the fatalty rato of collson partners to be: 4 F 2 m = (4) F m2 where m and m 2 are the mass of vehcle and 2, F and F 2 are the fataltes n vehcle and 2. As an example, for a mass rato of 2:, the formula (4) predcts a fatalty rato of 6: between the lghter car and the heaver one. Ths mean that for vehcle-to-vehcle collsons n whch one vehcle weghs twce more than ts collson partner, for every fatalty unt n the heaver car there would be sxteen n the lghter car. Because of ths we decded to focus on the securty crtera to evaluate securty solely by formula (4) of the mass rato between the consdered vehcle and a reference one. In ADVISOR, the vehcle mass s a functon of selected vehcle components. Cost: A smple cost model s ntroduced to estmate the total vehcle cost wtch s devsed nto two costs: an operatng cost, C operatng and an nvestment cost, C nv C = c P + c P + c N + C (5) nv engne engne elec elec bat bat fxed where c engne, c elec are respectvely the cost per kw of the IC engne and the electrcal components and P engne, P elec are the mum rated power output n kw. In order to account for parallel hybrd desgns that have no generator (snce the electrc machne works reversbly as a motor or a generator), the P elec s defned as: P elec = P motor + P generator (6) c bat s the module battery cost and N bat the modules number. The c fxed s taken to nclude the bodywork and all the accessory components, and s assumed to be fxed and s the same for a hybrd or a conventonal vehcle. In realty t s clear that ths s a greatly smplfed costng, snce as engne power vares so does the cost of many assocated components such as brakng systems, suspenson systems and tres. Operatng cost s calculated as: C = c M + c (7) op fuel fuel mant enance Where c fuel s the cost per ltre of fuel and M fuel s the volume of fuel used over the assumed lfe of the vehcle. In ths study we have assumed a lfe of 5 years wth 00,000 km whch s rather small. The mantenance costs have been neglected because we assume that the mantenance cost s more or less smlar for the hybrd and conventonal vehcles, whch s agan a rough approxmaton. Aggregated performance crtera: When workng wth several metaheurstc algorthms such as Genetc Algorthms, one major ssue s concerned wth consderng desgn constrants. Therefore one strategy to crcumvent the problem conssts n defnng aggregate objectve functons or constrants. In order to ntroduce the performance crtera nto the multobjectve approach later, we defne here global performance crtera embeddng prevously defned performance crtera (vehcle mum velocty, gradeablty and the acceleraton performance). User satsfacton can therefore be estmated usng a lnear combnaton of dfferent crtera weghted by approprate targets values related to a reference vehcle. SB V 2 p 200 40000 t m C = + + + + 40 acc 6 (8) Where: V s the estmated mum vehcle mum speed (to be mzed) t acc s the estmated acceleraton tme (from 0 to 00 kph) (to be mnmzed) p s the estmated gradeablty (to be mzed) m s the vehcle mass (to mnmzed) C s the total cost estmate (to be mnmzed) Makng use of reference car target crtera also ensures the consstency of metrc unts n the aggregated functon. For mum accuracy, t s a standard procedure n multdscplnary optmzaton to estmate each crtera usng response surface approxmatons and then, n a second step, to calculate the user satsfacton from the lnear combnaton of the values comng from the surrogate models. 4 Eco-score model Eco-score [,2] s a sngle envronmental ndcator whch ntegrates dfferent aspects of the envronmental mpacts of the road vehcles such as global warmng, ar qualty, energy depleton and nose polluton. The emssons pollutants consdered by Eco-score are related to the drect and ndrect emssons. Drect emssons are lnked to the use of the vehcle tself (tank-to-wheel) whereas ndrect emssons are those related to the extracton and transportaton of the raw materals for the fuel producton, together wth the emssons lnked to refnng and dstrbutng the carburant (well-to-tank). In ths study the drect emssons are obtaned by the vehcle smulaton n ADVISOR and the ndrect emssons are based on the fuel consumpton and the ndrect emssons factors. The ar pollutants cause varous damages dvded nto dfferent categores lke global warmng, human health mparng effects, harmful effects on ecosystems and buldng drtness. The partal damage of each pollutant s calculated as: d = β E (9) j j j, totales Where dj s the partal damage of pollutant j to category I, βj s the mpact factor of pollutant j to the category E j, totales s the total contrbutng emssons of pollutant j to the category The damages are explaned n common unts by category so the total damage of each damage category can be obtaned summng up the partal damages for the dfferent damage categores: D = d (0) j, j In order to quantfy the relatve severty of the evaluated damages of each damage category, a normalsaton step
based on a specfc reference value s performed. The damage assocated to the emssons norms EURO IV (drectve 98/69/EC) s taken as the reference pont. Q D = () D ref, Where: Q s the normalsed damage on category D s the total damage of the assessed vehcle on category ; Dref, s the total damage of the reference vehcle on category The dfferent damages are weghted before beng aggregated to obtan the global damage. E = WQ (2) Where: W s the weght of damage. 5 Response Surface method Because of the larger number of functon evaluaton that can be necessary to carry out optmzaton process, especally when usng meta heurstc algorthms, a standard approach n structural and multdscplnary optmzaton conssts n resortng to global or local approxmaton models (see for nstance [7,8,9]) Approxmatons wll replace drect smulaton runs durng optmzaton teratons and wll be updated durng a lmted number of step ([20]). They provde explct relatons that enable a fast and small cost evaluaton of the consdered response functons. Ths approach wll avod dramatc ncrease of smulaton tme related to teratve soluton procedure. The basc dea of global approxmaton used here s to construct an approxmate model usng functon values (from smulaton runs or mathematcal model computatons) at some samplng ponts, whch are typcally determned usng expermental desgn methods such as factoral desgn, central composte desgn, or Taguch orthogonal array. Model ftness s subsequently checked usng varous statstcal methods. In ths secton, we gve a bref overvew of the response surface methodology. Desgn of Experments (DoE): Desgn of Experments addresses the problem of dstrbutng the expermental ponts n the desgn space. The dffculty les n mnmzng the number of ponts, and, at the same tme, n obtanng an approxmaton wth good qualty,.e. that mnmzes errors. The defnton of the locaton of sampled ponts can nfluence the precson of the model because a correct choce of evaluaton ponts can reduce the uncertanty of the approxmated model. The samplng ponts are typcally determned usng expermental desgn methods such as a factoral desgn, a central composte desgn, or a Taguch orthogonal array. In a DoE each varable or factor, s assgned wthn a range, defned wth mnmum (low bound: LB) and mum (upper bound: UB) values. For the problem of the hybrd powertran that wll be consdered n the applcaton one can see at Table 2 the dfferent desgn varables and ther bounds. The DoE table then defnes the ponts that should be used to create the response surface. Table 2: Desgn Varables and assgned bounds baselne Desgn Descrpton LB UB Varable P ICE (kw) P motor (kw) N bat Fuel converter mum power Motor mum power Battery number of modules 4 20 65 75 20 60 25 20 80 Modellng approach: There are varous response surface approxmaton methods avalable n the lterature [9,20]. The polynomal-based approxmatons are the most popular. In ths study, we typcally use frst or secondorder models and ther nverse n the form of lnear or quadratc polynomal functons to develop an approxmate model that provdes an explct relatonshp between desgn varables and the response of nterest. The unknown coeffcents n the model are determned wth a least squares method. Statstcal analyss technques such as ANOVA (analyse of varance) are used to check the ftness of the response surface model. An approprate order polynomal s ftted to a set of data ponts, such that the adjusted root mean square error s mnmzed. The adjusted root mean square error σ a s defned as followng: Lets Np be the number of data ponts and Nc be the number of coeffcents and error e at any desgn pont beng defned as: e = y yˆ (3) where y s the actual value of the functon at the desgn ponts and y ˆ s the predcted value. Hence on gets: σ ( ) (4) N p 2 a = e Np Nc = If Nt s the number of addtonal test data that are used to test the qualty of the approxmaton, the root mean square error σ a s gven as: N t 2 a e Nt = σ = (5) Predcton capablty of the response surface s gven by the coeffcent of multple determnaton R adj ² defned as: Wth N p 2 2 2 adj = σ a ( p ) ( ) = R N y y (6) N p y = ( y N ) (7) = For a good ft, R adj ² should be close to. In ths study, the response surface method s employed to generate smulaton-based surrogate models of performance crtera. Table 3 ndcates the multple determnaton coeffcents for sx response functon and ther meta models. As shown n the table 4, the quadratc polynomal model s effcent for three functons (Eco- p
score, m and C) and second order nverse polynomal s effcent for also three functons (v, p, t acc ) Table 3: Ecoscore v t acc p m C 2 R adj for dfferent models st order polynom al Quadratc polynomal st order nverse 2 nd order nverse 0.973 0.98826 0.8758 0.98634 0.63539 0.90885 0.6938 0.93896 0.60948 0.92955 0.64 0.9604 0.73877 0.96565 0.784 0.9876 0.8937 0.99292 0.99873 0.8989 0.99870 Fgure 4 shows two of those responses: the acceleraton tme (from 0 to 00 kph) and the vehcle mum velocty. Remnd also the reader that meta models are bult for sngle performance crtera and then the aggregate user satsfacton functon s calculated, leadng to a better precson. 6 Optmzaton 6. Mult-objectve optmzaton Mult-objectve optmzaton problem conssts n fndng a vector of desgn varables whch smultaneously satsfes the constrants and mnmzes / mzes a vector of objectve functons. These functons are usually antagonstc and conflctng wth each other. Formally, mult-objectve optmzaton problem s formulated as: Mnmze F( X ), Where F = { f} : j =, M; X = x : =, N Subject to: CX ( ) 0, where C = { C } : p =, P (8) ( ) 0 H X =, where = { } : =, p H h k K All objectve functons can not be smultaneously optmzed. In others words, there s not a sngle soluton whch smultaneously provdes the optmal value for all objectves. Ths ntroduces the Pareto optmalty or the non-domnated solutons set concept. 6.2 Pareto-Optmalty When two desgn ponts are compared, they are nondomnated wth respect to each other f no desgn domnates the other. In other words, a desgn X Є D (D s the set of all feasble desgns) s non-domnated wth respect to a set A D, f a A: a< X. In addton, any desgn X s Pareto optmal f X s non-domnated wth respect to D.e there s no feasble desgn whch would mprove any objectve functon wthout worsenng at least an other one. All non-domnated desgn ponts n set D sweep the Pareto optmal set. The objectve functons representaton of the Pareto optmal set s the Pareto optmal front (POF). Fgures 5 represents the Pareto optmal set for a two objectves problem. k Fgure 4: Response surfaces of Parallel HEV Once the surrogate models are avalable, any optmzaton method can be used to solve mult-objectve optmzaton problems wth a reduced computatonal effort. Fgure 5: Pareto-optmal front Generally t s not easy to fnd an analytcal expresson of the Pareto optmal front. Therefore, the mult-objectve problem solutons consst n a dscretzaton of the Pareto front and the algorthm ams at fndng several nondomnated solutons by applyng approprate technques. There are many methods to solve mult-objectve optmzaton problems. They can be dvded nto two categores. In the frst category, the user specfes hs/her
prortes before optmzaton (a pror methods). In ths category, the ntal mult-objectve problem s transformed nto a mono-objectve problem by aggregatng all objectves (weghted sum) or consderng one objectve as the man objectve and other ones as constrants (.e e-constrant method). The problem can then be optmzed usng a standard gradent based algorthm f dervatves are avalable or dervatve-free algorthm. The common drawback of these methods s that a sngle soluton s obtaned after optmzaton. To fnd an other soluton (for Pareto front), the user has agan to restart an optmzaton run wth an new problem formulaton by modfyng the weght coeffcents or by expressng other prortes. In addton the Pareto front s n general not homogeneous, convex or even contnuous and the non domnated solutons may be grouped n the same regon so that the desgner choce s lmted. On the contrary, the a posteror search technques work wthout prortes nformaton about the set of optmal solutons. Afterwards the desgner can choose hs/her most prefered soluton from the pareto set after optmzaton. Genetc algorthm s one of these a posteror technques, because t yelds a set of non-domnated solutons. In addton, the use of the sharng operator makes the Pareto front homogeneous. In ts basc form, GA operates on a populaton of ndvduals (potental solutons), each of them beng an encoded strng (chromosome), contanng the decson varables (genes). The structure of a GA s composed by an teratve procedure through the followng fve man steps: Creatng an ntal populaton P 0; 2 Evaluaton of the performance of each ndvdual p of the populaton, by means of a ftness functon; 3 Selecton of ndvduals and reproducton of a new populaton; 4 Applcaton of genetc operators: crossover and mutaton; 5 Iteraton of steps 2 4 untl a termnaton crteron s fulflled. To apply GA to the optmsaton of HEV, a ftness functon s requred to evaluate the performance of each soluton. In ths study, the ftness functon s the objectve functon. To account for the mult-objectve aspects, several GA have been drawn up [2] and the most popular are MOGA (Mult objectve genetc algorthm), NSGA (Nondomnated Sortng Genetc Algorthm) and NPGA (Nched-Pareto Genetc Algorthm). 6.3 Problem statement of HEV desgn The objectve s to optmze a Hybrd Electrc Vehcle component to ncrease user satsfacton and decrease the Eco-score on the bass of European normatve drvng cycle. The mathematcal problem of the multobjectve desgn problem of a HEV vehcle can be stated s as follows: Mnmze F( X) = ( f( x) = E ; f2( x) = / SB ) Wth respect to X = ( Pengne, Pmotor, Nbat ) Subject to t acc 2s v 40kph p 6% m 200kg C 40000 20 Pengne 65 20 Pmotor 60 20 N 80 MB (9) The optmzaton s ntally lmted to three desgn varables, two of them defnng the power ratngs of the fuel converter and the motor controller. The thrd varable defnes the number of battery modules. As t can be seen n formula (9), we have a two objectve functon optmzaton problem. Mult-objectve genetc algorthms, MOGA and NSGA are avalable n BOSS- QUATTRO tools [20] and the MOGA one s selected n ths study. Ths algorthm accounts for mult-objectve aspects by a selecton step based on flng: after each generaton, populaton ndvduals are classfed and each ndvdual have a value defned as: r () = + p () (20) Where p() s the number of j populaton ndvduals wth an objectve functon f(j) that domnates f(). For each ndvdual, an ntermedate ftness functon value s calculated as a functon of hs flng: f ' ( ) = f ' ( r ( )) (2) ad ad A mean value s calculated on all of the populaton and an ndvdual ftness functon value s obtaned: fad () fad () = Npop (22) N pop f () = The sharng operator s then appled on the ndvduals whch have the same flng; A roulette wheel wth stochastc sample s appled for flng step. 7 Numercal applcaton The method has been llustrated wth the example of a parallel hybrd electrc vehcle. Ths applcaton s contnued along here, optmzng at frst a parallel hybrd electrc (PHEV) powertran confguraton and later a seral hybrd electrc vehcle (SHEV). We also develop here a second numercal applcaton wth the optmzaton of the seral hybrd electrc bus wth, n ths case, a dfferent baselne confguraton (see Table 4). The selected battery packs are based on NMH modules. The relevant drve cycle that s chosen s CYC_MANHATTAN for the bus, whch s avalable n ADVISOR lbrary. ad
Table 5: HEV Performances comparson PHEV SHEV PHEV-BUS before After before after before after Fuel consumpton (l/00km) 7.5 6 6.8 5.9 56.2 52.7 Tacc (from 0 to 00 kmph) 9 0.4 8 0 8.9 (from 0 to 60 kph) 8.8 V (km/h) 9 73 57 58 84 83.9 P at 80km/h (%) 2 6.4 6 0 3.4 (at 48 kph) 3.6 NOX (g/km) 0.324 0.3 0.64 0.426 80 59 CO (g/km) 2.755 2.34.349 5 4.5 HC (g/km) 0.46 0.253 0.482 0.259 200 03 M (kg) 350 97 648 323 606 5993 C ( ) 28475 7282 35400 25952 256490 27420 Eco score.5799.2684 2.326.6586 2.8585 2.593 SB 8.7730 8.6 6.9 6.4 6.2328 6.2390 The multobjectve optmzaton s carred out usng the MOGA approach. The ntal populaton of the GA s set to 20 ndvduals. After 50 generatons the objectve functons of the populaton spans the Pareto front as llustrated n Fgure 6. mn f 2=Eco-score 2,8,6,4,2 0,8 0,6 0,4 0,2 POF 0 0 0,02 0,04 0,06 0,08 0, 0,2 0,4 0,6 mn f=/sb Fgure 6: Eco-score and /SB functons results In Table 4, we selected some optmzed confguraton to be compared wth those before optmzaton (baselne confguraton) n table 5: PHEV SHEV PHEV- BUS Table 4: Components szes comparson component Before optmzaton After optmzaton Before optmzaton After optmzaton Before optmzaton After optmzaton P ICE (kw) Pm (kw) N bat 4 75 25 30 20 20 4 75 50 75 20 43 33 42 206 22 57 50 28 763 Pgen (kw) In some cases the engne and motor power have been sgnfcantly decreased. The performances of the hybrd Electrc Vehcle before and after the optmzaton are gven n Table 5 for comparson. The fuel consumpton of a parallel hybrd electrc vehcle has dropped from 7.5l/00km to 6l/00km However the emssons have been reduced (about 20% for PHEV) n the three cases and one can notce subsequently a sgnfcantly Ecoscore mprovement (about 20% for PHEV). In other hand, performances are slghtly deterorated because of the decrease n the fuel converter and motor szes. However the user satsfacton s not sgnfcantly affected: the deteroraton s about 2% whle the Eco-score mprovement s about 8% for PHEV. 8 Concluson We have developed a general optmzaton procedure to optmze the desgn of Hybrd Electrc Vehcle powertrans based on the conflctng objectve functons of mnmzng the envronmental mpact (ecoscore) whle mzng the performance of the vehcle. In ths study meta heurstc algorthms such as Genetc Algorthms have been selected n order to cope wth nosy and nonsmooth response functons. Performance crtera and emssons of vehcles are smulated usng the ADVISOR software tool, whle the optmzaton teratve process s carred out n Boss Quattro. In order to reduce the computatonal cost, one major contrbuton conssts n developng approxmatons of performance and envronmental crtera based on response surface methods. The approach has been llustrated on two numercal applcatons dealng wth the optmzaton of a hybrd electrc passenger car and of a seral hybrd electrc bus. In future developments, our approach should be extended to account for more parameters such as the HEV control strategy for further mprovement. In addton, precson of response surfaces strategy wll be further mproved to be more robust n cases where optmums are dffcult to determne. For nstance t wll be nterestng to couple genetc algorthms wth local search algorthms. As shown n Table 4, all component szes have been decreased except n the bus case for whch the motor power and the batteres modules numbers were ncreased.
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Authors After hs Electro-mechancal Engneerng degree at Unversty of Lege (Belgum) n 990, Perre Duysnx obtaned hs PhD n Structural optmzaton from the same Unversty n 996. He worked as an Assstant Professor at Dansh Techncal Unversty (DTU) n Copenhagen n 996 and at Unversty of Lege from 999. In 2003, he was promoted Professor at Unversty of Lege and became head of Automotve Engneerng lab. Research nterests are advanced smulaton and optmzaton methods for vehcle desgn and clean propulson technologes J.Nzsabra obtaned hs master n Engneerng Scences from the Unversty of Lège. Hs research nterests nclude hybrd electrc vehcle smulaton and optmzaton. He works now (for a graduate) on clean propulson technologes. He partcpate actvely n transportaton projects organzed by the Wallon regon Yannck Louvgny graduated as electro-mechancal engneer from the Unversty of Lege (Belgum) n 2006. Now, he s workng as a research assstant n the automotve engneerng lab of the unversty. Hs research nterests ncorporate engne dynamc, fuel cell, hybrd vehcles and clean transportaton n general.