Advanced energy management strategies for vehicle power nets

Transcription

1 Advanced enegy management tategie fo vehicle powe net E.H.J.A. Nuijten, M.W.T. Koot, J.T.B.A. Keel, Bam de Jage, W..M.H. Heemel, W.H.A. Hendix,..J. van den Boch Abtact In the nea futue a ignificant inceae in electic powe conumption in vehicle i to be expected. To limit the aociated inceae in fuel conumption (and CO emiion), mat tategie fo the geneation, toage/etieval, ditibution and conumption of the electic powe can be ued. Thi pape peent a peliminay cae tudy baed on a Model edictive Contol-baed tategy that ue a pediction of the futue diving patten and load equet in ode to minimize fuel ue by geneating only at the mot efficient moment. The tategy i teted in a imulation envionment, howing a deceae in fuel conumption compaed to a baeline tategy. Index Tem electic powe management, model pedictive contol. E I. INTRODUCTION vey yea, the electic powe conumption in automobile inceae ignificantly. Ove the yea, thi ha led to eveal modification of the vehicle powe net, in ode to keep up with moe tingent electic powe demand. A majo tuning point occued aound the yea 955 when ca manufactue tated to eplace the exiting 6V powe net by a new V ytem with 4V egulation. Thi ytem ha become the tandad in today paenge ca. Ove the lat two decade, the electic powe conumption in vehicle inceaed even moe (appoximately fou pecent evey yea) and in the nea futue, eeache expect again much highe powe demand due to eveal apect: Electical device eplace taditionally mechanical and hydaulic component. A good example fo thi tend i the dive-by-wie concept. The maket expect moe pefomance, comfot and afety fom new vehicle. Hee, one hould think of function like electic active upenion but alo of video entetainment at the backeat. Today, the aveage electic powe conumption of a egula vehicle i between 75W and kw with peak load up to kw, depending on the vehicle and it acceoie []. Taking into account that a belt diven 4V altenato typically Coeponding Autho: Techniche Univeiteit Eindhoven, Dept. of Mechanical Engineeing, WH.43,.O. Box 53, 56 MB Eindhoven, The Netheland. hone: , Fax: , m.w.t.koot@tue.nl upplie.kw, powe limitation will become an impotant iue within the next yea. Aleady in the mid-99, eveal automobile manufactue ealized thi poblem and tated conideing new topologie of the vehicle powe net. Unde the name 4V owenet they popoed a cla of ytem that eem to meet tomoow powe equiement. All thee ytem have in common that they hae a powe net with a nominal voltage of 4V. It can be eaily een that the intoduction of a powe net opeating at a highe voltage level, lead to bette efficiencie when upplying powe to the electic load []. Howeve, in the field of contol tategie eveal uncetaintie exit about how the altenato (including the voltage egulato) hould opeate in ode to obtain maximum enegy efficiency within the vehicle. Thi pape peent a peliminay tudy on one poible contol tategy baed on model pedictive contol (MC) and dicue the benefit of uch an advanced enegy management tategy with epect to the fuel economy of the total vehicle. II. CONTROL STRATEGY eent vehicle ae equipped with an altenato in combination with a 4V egulato, to maintain a contant voltage at the powe net when the engine i unning. In thi way, the altenato upplie continuouly powe to all electic load a well a the V battey. Conveely, the battey povide enegy to the load only duing peak-powe demand o when the engine i tuned off. Regulating the voltage at 4V mean that the battey i alway opeated at almot % tate of chage, whee enegy i lot due to gaing eaction. Thi i one diadvantage of the conventional contol tategy. The vehicle conideed in thi pape i a conventional eiepoduction vehicle that wa equipped with a 4V powe net fo eeach pupoe. An advanced altenato (belt diven) eplace the conventional altenato and a 36V lead-acid battey take the place of the V battey. Figue how a chematic diagam of thi new powe net. One can ee that the altenato (A) and the battey ae diectly coupled to the powe net. Uing an advanced altenato, it i poible to contol powe flow. Finally, the 4V load (cuently implemented in the vehicle by mean of a pogammable load box) ae connected to the powe net by mean of fue and witche.

2 4V owe net Beide efficiencie, the contol tategy ha to take into account that the component in the ytem will opeate afely only within cetain opeating limit. + A Battey - Figue : Topology 4V powe net Switche & Fue 4V Load A geneal contol technique to find the optimal olution but till atifying all the bounday condition a mentioned above, i called model pedictive contol (MC). A will be explained late, thi technique ue a model of the ytem to calculate the mot optimal contol action, given the peent tate of the ytem and ome pediction of the ytem in futue. Thi contol technique ha been applied in thi eeach, following the conideation of Tate and Boyd [3]. Still the quetion emain what type of contol hould be elected to obtain the mot optimal et point fo the altenato? Ultimately, it i the intenal combution engine that delive all neceay powe equeted by the electic load. Fo that eaon, the contol tategy fo the altenato will be called optimal, if it etablihe minimal fuel conumption ove a given dive cycle, with no hotcoming on the dive equet. It i common knowledge that the efficiency of a combution engine depend on it opeating point, i.e. the engine peed and toque at the cankhaft [4]. Taking into account thi efficiency and the fact that the mechanical diveline (and indiectly the dive) enfoce a et-point fo the engine, it hould be poible to inceae the total efficiency of the engine by activating the altenato at the ight moment (ee Figue ). On aveage, the engine will un in a moe efficient opeating point and hence, accomplih fuel eduction. III. VEHICLE MODEL A baic neceity fo contolle deign i a good model of the ytem. Since thi model hould epeent a complete vehicle, a fundamental appoach i uggeted. All pat of inteet ae placed in epaate (powe-baed) input/output block (ee Figue 3). The inteconnection of thee block will be done accoding to the powe flow in a eal vehicle, tating with fuel that goe into the combution engine. The mechanical powe that come out of the engine plit up into two diection: one pat goe to the mechanical diveline fo vehicle populion, wheea the othe pat goe to the altenato. Next, the altenato povide electic powe fo the electic load but alo take cae of chaging the battey. Contay to the othe block, the powe flow though the battey can be poitive a well a negative. In the end, the ueful enegy come available fo vehicle populion and fo activating electic device connected to the powe net. fuel Intenal Combution Engine m d g Mechanical Diveline Advanced Altenato Figue 3: Block diagam of vehicle' powe flow e l Electic Load b Battey E Efficiency Battey toage IV. MODEL REDICTIVE CONTROL Figue : Nomalized efficiency map of the engine Conideing the efficiency of the combution engine olely will not be enough to find the optimal contol tategy fo the altenato. The efficiency of the altenato tongly depend on it opeating point a well and alo the battey ha a timevaying efficiency that cannot be neglected. A poible contol tategy ha to take all thee efficiencie into account becaue the peed of the engine, altenato and the vehicle itelf ae diectly elated to each othe. Infomation about the vehicle peed (but alo the electic load eque in the nea futue will help to impove the pefomance of the contol tategy. Intoduction MC ha become quite popula in the poce induty due to it ability to contol plant within tight time-vaying containt and meeting deied optimal opeating condition. In indutial envionment MC pediction infomation can often be obtained by uing meauement infomation fom ealie tage in the manufactuing line. Due to inceaing computational capabilitie of micopoceo it i now even poible to apply imple MC technique online in evobaed application. New technological development uch a GS, navigation ytem and infomation exchange between vehicle and taffic contol ytem inceae the poibilitie of uing MC in automotive application.

3 3 Cloed-loop output y Cloed-loop input u Cloed-loop input u at Figue 4: MC pinciple t t + δ Futue contol hoizon pediction hoizon Model edictive Contol Concept continuou mpc dicete mpc t + T c efeence tajectoy pedicted output y open-loop input u open-loop input equence { u k } t + Tp In geneal, the Model edictive Contol poblem can be fomulated a olving on-line a finite hoizon open-loop optimal contol poblem ubject to ytem dynamic and containt involving tate and contol. Figue 4 how the baic pinciple. Baed on meauement obtained at time t, the contolle pedict the futue dynamic behavio of the ytem ove a pediction hoizon T p and detemine the input u uch that a pedetemined open-loop pefomance objective function i optimized. If thee wee no ditubance and no model mimatche and if it would be poible to optimize ove an infinite hoizon, then one could apply the optimal contol equence found at t = t to the ytem fo all time t > t. In geneal thi i not the cae and theefoe feedback method need to be ued. An MC ytem implement the obtained open-loop input function at time t until new meauement infomation become available at time t + δ. At evey inteval of length δ a new pediction and optimization i pefomed uing updated model. Thi contol algoithm i fequently efeed to a the eceding hoizon pinciple. To obtain numeical olution on the open loop optimization poblem it i often neceay to paameteize the input u in an appopiate way. Thi can fo example be done uing a finite et of bai function. A fequently ued method i appoximation of inteval of length δ by a piecewie contant value. Thi way a dicete time Model edictive Contolle can be intoduced. Figue 4 how both a continuou and dicete tajectoy of input u fo an MC cot function penalizing diffeence between and y. A wa mentioned ealie, calculation of the contol input can be ubject to containt put on tate, input and output of the pedicted ytem a well a ubject to the optimization of a given cot function. In geneal, the pedicted ytem behavio will diffe fom the cloed-loop one. Thi implie that pecaution mut be taken to achieve cloed loop tability. Vaiou method exit fo thi pupoe. They include implementing contol hoizon limiting the egion in which contol action ae allowed along the pediction hoizon, endpoint containt demanding tate o output value to each a given value at the end of the pediction hoizon, ate limit o pecial deign method fo tabilizing cot function. A implified famewok fo implementation of cot-function, containt and ytem dynamic i hown in Figue 5. Hee e( i conideed to be an unknown ditubance known only at time t which i often conideed to be zeo mean white noie and ω (τ ) model known ditubance. The vaiable v (τ ) define the input of the ytem which can be eithe u (τ ) o u& (τ ) and x (τ ) epeent the ytem tate. All expeion containing a ba on top ae dependent of the optimization poce. Sytem tate ae paed though the equality containt x ( =. Sytem dynamic ae implemented by intoducing equality containt epeenting the ytem behavio. find min J(, v( ); Tp ) v( ) t T with J(, v( ); Tp ) : = + t ubject to x& ( τ ) = f ( τ ), e(, ω( τ ), v( τ ), τ ), g( τ ), e(, ω( τ ), v( τ ), τ ) =, h( τ ), e(, ω( τ ), v( τ ), τ ) Ψ( τ ), = Figue 5: MC famewok p F( τ ), v( τ )) dτ τ [ t, t + Tp ] τ [ t, t + Tp ] τ [ t, t + Tp ] The eade who i inteeted in moe detail on MC, i efeed to [5]. V. ALICATION ON THE FUEL REDUCTION ROBLEM MC ha one big diadvantage. Solving an optimization poblem might equie a pohibitive amount of computation time with thi technique. Theefoe a model tuctue i equied, that i accuate enough to model all deied popetie and fat enough fo eal-time calculation. Figue 3 decibe the tuctue of the ued vehicle in the following examination of an MC-baed optimization. The geneato i connected to the engine with a gea atio : N g. The diveline block contain all diveline component including clutch and gea. Thi i a typical tuctue fo a conventional vehicle. The taget i to apply an MC cheme in uch a way that divability emain unaffected. Stated othewie, the dive

4 4 hould not expeience diffeent vehicle behavio when uing the MC appoach. Thi aumption geatly educe the poblem complexity. It implie that the diveline toque and peed emain unaffected and theefoe it i poible to ue them a pediction infomation. A a conequence, the engine will have to compenate all geneato action and vice vea. Thi equie both fuel injection and geneated powe to be contolled by the MC. g e The emaining dynamic component include the engine, geneato and battey. Uing dicete time MC with a ampling inteval of econd o lage, the engine and geneato dynamic can be excluded. Alo the battey dynamic ae neglected. A nonlinea tatic map can be ued to epeent the Intenal Combution Engine (ICE). Thi map decibe the elation between fuel conumption and engine peed and engine toque. Note that the engine toque can be deived fom the engine powe if the engine peed i known. A fuel conumption map can be ued a diplayed in Figue 6. Figue 7: Geneato owe Map When the electical load l ae pedicted, Equation 4-6 can be ued to model the electical cicuit. Hee b epeent the powe enteing o leaving the battey teminal, and E epeent the enegy toed in the battey. e = l + b (4) b = + lo(,e,t) (5) E & = (6) Function lo epeent the battey loe. Figue 8 how a typical chage/dichage powe tanfe cuve fo a contant tate of chage. Dichaging b Figue 6: Nomalized Fuel Ue Fo now thi map will be epeented by the following equation: Figue 8: Battey owe Map Chaging fuelate = f ω, ) () ( m m Uing a imila appoximation, the geneato model educe to a tatic nonlinea map (Equation ). Again the peed infomation can be ued to decibe the peed dependent behavio of the device. g = g ω, ) () + ( g e m = d g (3) Fo the altenato ued in the imulation, g how mooth and almot linea behavio within the aea of inteet. Fo a contant value of ω g a cuve fo thi function i hown in Figue 7. Uing a the optimization vaiable, the efficiencie of all component can be included into a cot function baed on fuel ue: t + T p min (7) t J = fuel( ) = min fuelate( ) dt To get a ueful contol tategy, containt have to be added. Fo example, daining the battey could educe fuel ue, but uch a olution would be unacceptable in a vehicle. In addition, containt need to be applied to et bound on allowable value fo the battey tate of chage. Exta containt pohibit the optimization to each invalid o unwanted opeating condition uch a ovechaging o allowing the SOC (State of Chage) to dop dangeouly low.

5 5 Containt ae et on engine toque T m (by containing the engine powe fo known engine peed), electical powe e, battey powe thoughput b and enegy toed in the battey E. Fo the ake of bevity thoe containt ae witten out late on. The vaiable optimized in Equation 7 i diffeent to the one ued to contol the vehicle. To deive the coect contol vaiable, the tuctue peented in Figue 9 i ued. Thee ignal will not be ued diectly but will be fed though lowlevel contolle capable of tabilizing the dynamic behavio between engine and geneato. ω, l, d Fuel Injection Requeted geneato powe MC contolle E MC Open-Loop Optimization Fuel Map m g Battey Efficiency Map d l Geneato Efficiency Map Figue 9: MC contolle implementation, uing pediction infomation of ω, l and d. Fo eal-time implementation of thi MC contolle futhe implification ae neceay, the optimization decibed by Equation 7 mut be caied out uing nonlinea (in geneal non-convex) poblem olve. Optimizing nonlinea poblem i vey time conuming and othe method need to be conideed. In the next ection implification will be intoduced to achieve a quadatic poblem tuctue, which ha a geat computational advantage. Quadatic ogamming VI. IMLEMENTATION It i pefeable to tuctue the optimization a a Quadatic ogamming poblem becaue doing o, a global minimum i guaanteed and hot computation time can be achieved. A Q poblem i given by a quadatic cot citeion ubject to linea containt. T T min J ( x) = x H x + f x + f, A x b (8) x Cot citeion Becaue the main goal i to educe fuel conumption, a cot function i choen that expee the fuel ue ove the hoizon a function of the battey toage powe. Thi way, loe in the ICE, the altenato and the battey will all be included in the cot function. Othe cot citeia could be implemented b e hee a well. To obtain a quadatic cot function, the nonlinea component model ae appoximated a quadatic elation between incoming and outgoing powe and then combined to a ingle expeion. Engine The fuel map of the engine i appoximated by a quadatic fit. The paamete α i depend on the engine peed fo which a lookup table can be ued. fuelate = f(ω, ) m α (ω) m + α (ω) m + α(ω) whee m = d + g Altenato The altenato map i alo appoximated by a quadatic fit whee the paamete γ i depend on the engine peed. g = g( ω, ) e γ (ω) e + γ( ω) e + γ(ω) whee e = l + b (9) () Battey The loe in the battey ae poitive fo both chaging and dichaging and dependent on the SOC and the tempeatue. Thi can be obtained by making the loe quadatic with the toage powe: b = + lo(,e,t) + β(e,t) () Thi model can be extended uing piecewie linea tem fo chaging and dichaging to obtain cloe appoximation to a eal battey. Thi concept can till be handled within a Q famewok [6]. Fo implicity diffeence in loe ae hee aumed to aveage out. Cot function Combining the quadatic elation fo the engine, the altenato and the battey eult in an 8 th ode elation decibing the fuel ue a function of. Becaue the cot function can only be quadatic, the highe ode tem ae omitted. The expeion fo the fuel ue then become: + λ λ fuelate λ + () In Equation, the paamete λ i depend on the following paamete: λ λ (α (ω),γ (ω,β (E,T),, ) (3) i i j j ) j d l

6 6 The vaiable ued in equation epeent the deign vaiable, wheea the actual contolled input i e. Becaue the elation between and e i taightfowad, e can be computed eaily fo each optimization tep uing the tuctue decibed in Figue 9. The cot function i the fuel ue integated ove the pediction hoizon. By dicetization one may obtain: J = fuel( N p ) = N k= fuelate( k) t Containt The component ae ubject to the following limitation: m,min e,min b,min E,min ( ω) ( ω) b E e m E b,max e,max,max m,max ( ω) ( ω) (4) (5) Uing the quadatic elation fo the component, the containt on m, e and b can be ewitten a linea containt on. Combining them lead to one lowe and uppe bound fo at each time intant., min ( d l, max d l ω,, ) ( ω,, ) (6) The lowe and uppe bound of E, which epeent the tate of chage, can alo be witten a linea containt of, by uing the following dicetization: E = k ( k) ( q) t + E () (7) q= End-point containt A chage-utaining vehicle equie ome kind of endpoint penalty in ode to guaantee that the tate of chage emain in a neighbohood aound a deied value. The value may be choen with an eye on maximizing battey efficiency o expectation of battey life. Hee an endpoint containt i implemented equiing the tate of chage at the end of the hoizon to be the ame a o lage than at the beginning. A dawback of thi method i that it will limit the vaiation in and thu the pefomance when uing hot pediction hoizon. An advantage i that fo all imulation the SOC at the end i equal, o thee i no need fo SOC compenation in the calculation of the fuel ue. Thi equality containt fo E (N p ) can alo be witten a a linea function of, by uing the following elation: E ( N N i= N i= ) = ( i) t + E () = E () ( i) = VII. SIMULATION MODEL (8) Simulation ae done fo a conventional vehicle equipped with a kw. lite SI engine and a manual tanmiion with 5 gea. A 4V 5kW altenato and a 4V 3Ah lead-acid battey make up the geneato and toage component of the 4V powe net. The opeating ange of the battey i limited between 6% and 8% SOC, becaue the efficiencie fo both chaging and dichaging in thi ange ae acceptable. The paamete β (E,T) i choen to be independent of E and T and ha a contant value of 5-5 (Equation ). The battey i paameteized to povide an efficiency of 95% at W and 9% at W. When the peed pofile and the elected gea ae known befoehand, the coeponding engine peed and toque needed fo populion can be calculated uing the following fomula: τ d ( = µ d w f ( m v& ( + g ( ρ Cd Αd v( f ω ( = g ( v( w + m g C ) (9) The paamete value fo the imulation model ae given in Table. Ma m kg Fontal aea A d m Ai fiction coefficient C d.3 Rolling eitance C.5 Ai denity ρ. kg/m 3 Wheel adiu w.3 m Final dive atio f 4. Gea atio g Diveline efficiency µ d.9 Table : aamete value fo the imulation model When the vehicle i tanding till, the diveline toque i zeo

7 7 and the engine un at an idle peed of 7 pm (73 ad/). When the diveline toque i negative, it i patly deliveed by the ICE (which ha a negative dag toque duing vehicle deceleation), the altenato and by the bake. Becaue egeneative baking delive electical powe with no exta fuel ue, it i ued a much a poible. The bake ae only ued when the deied deceleation toque i geate than the maximum negative toque that could be deliveed by the engine and the altenato: τ < τ τ. d m, min g, max Diving cycle Simulation ae done fo the NEDC cycle, which conit of an uban and an exta-uban pat. The vehicle peed of thi cycle and the coeponding engine peed and diveline toque and gea numbe, ae given in Figue. The electic powe equet i a contant load of W. Vehicle Speed [km/h] Engine Speed [pm] Toque [Nm] 5 5 NEDC Gea [-] Time [] Figue : Applied vehicle peed, engine peed, engine toque and gea hifting duing imulation VIII. RELIMINARY RESULTS The following tategie ae implemented on imulation level and thei eult will be compaed: Optimal: hoizon with limited length. Thi tategy calculate the Q poblem once fo the complete cycle. The eulting contol ignal i implemented aftewad. Thi hould give the lowet fuel conumption. The MC contolle i ued with pediction hoizon of, 3, and 3. Towad the end of the imulation, the pediction hoizon i limited to the end of the cycle. An ideal integato on the ignal i ued to accomplih the feedback of E in the imulation model, a hown in Figue 9. Fo the optimal tategy, the eulting equence of the battey SOC i hown in Figue. A can be een, the optimization eem to anticipate on egeneation phae and geneate between them a little a poible. The vaiation in SOC i vey low, becaue of the lage capacity of the battey. Thi jutifie that fo thi imulation, the battey efficiency i choen independently of E. Battey owe [W] Battey SOC [%] 3 - Reult of the optimal tategy Time [] Figue : Simulation eult optimal tategy The fuel ue ove the entie cycle i computed aftewad uing thee method: Uing the quadatic cot function Uing the 8 th ode expeion Uing the meaued fuel map, and altenato map and the quadatic battey model Baeline : Baeline : MC: No electic load. Thi indicate how much fuel i needed fo populion only. The powe povided by the altenato i equal to the equeted load. Thi indicate how much fuel i needed in the nomal ituation. Thi tategy doe not include egeneative baking. Optimization at evey time tep ove a eceding By compaing thee value, the influence of the model eduction can be tudied. The nomalized fuel ue i peented in Table. The diffeence between the 8 th ode and the quadatic fit ae maginal, which jutifie the omiion of the highe ode tem in the cot function. Both how a diffeence of ca. % compaed to the fuel ue computed with the meaued data.

8 8 Nomalized Fuel Ue Quadatic 8 th ode Meaued map Baeline.7 Baeline.. 4. MC N p = MC N p = MC N p = MC N p = Optimal Table : Influence of model eduction on pefomance In Table 3, the fuel aving with epect to the Baeline tategy ae given. A can be een, the aving baed on the meaued data ae even highe then fo the educed model that i ued in the optimization. The maximum aving baed on meaued data i.9 %. Thi can aleady be achieved with a pediction hoizon of, while.37 % i aleady obtained with a pediction hoizon of only. Saving [%] Quadatic 8 th ode Meaued map Baeline Baeline MC N p = MC N p = MC N p = MC N p = Optimal.5..9 Table 3: Fuel aving with epect to baeline tategy Evaluation The imulation how that the concept i woking, although the fuel aving ae athe mall. Thee ae eveal explanation fo thi. Although the efficiency of the fuel convete vaie datically ove the diving cycle, thi i meely caued by the off-et (zeo toque coepond with poitive fuel ue, while zeo fuel ue coepond with negative toque), wheea the tategy peented hee only benefit fom diffeence in (the incement of) the fuel ate at vaiou opeating point. Fo moden engine, thi change in lope i athe low, becaue of electonic ignition, fuel injection, and advanced moto management. Although thi impove the efficiency of the engine in geneal, it limit the exta impovement that can be made with thi tategy. Futhemoe, ignificant loe occu duing chaging and dichaging of the battey. Thi i diadvantageou compaed to the baeline tategy, whee the battey i not ued. A an altenative fo the battey, an ulta capacito can be ued, which ha a lowe capacity but on the othe hand it ha a highe efficiency. The lowe capacity will not be a limitation ince the vaiation in SOC ae vey mall. Anothe eaon fo the mall impovement i that the NEDC i a athe conevative cycle. Fo the tet vehicle ue hee, the NEDC cycle equie an aveage powe of kw and peak of 4 kw, while the engine i capable of deliveing kw. When uing a diving cycle that cove the whole opeation ange of the engine, moe pofit i likely to be made. Futhemoe it hould be mentioned, that fo thi peliminay cae tudy, the eult baed on meaued map tuned out to be bette than with the educed model, but in geneal thi will not be the cae. IX. CONCLUSIONS An MC-baed enegy management tategy fo the electical powe net i peented, that ue futue knowledge of the diving patten to minimize the fuel conumption ove a diving cycle. The initial imulation how that the concept i woking, although fuel aving ae lowe than expected. Howeve, a a peliminay tudy thi look quite pomiing. A futhe in depth invetigation hould eveal the eal potential of thi appoach. X. FURTHER RESEARCH A next tep befoe implementing the tategy in a eal vehicle would be implementation on a hadwae-in-the-loop tet etup coniting of a oftwae emulation of the dive tain and eal electical component. Anothe inteeting topic i to adapt the concept behind the tategy fo othe powe net o dive tain configuation. The tategy can be extended to a vehicle with a dual voltage powe net (4V and 4V) with one o two geneato, two electical powe toage device (batteie and/o upe capacito) and a DC/DC-convete. The tategy can eaily be adapted to be ued fo paallel hybid electic vehicle, whee the altenato can alo be ued a a moto. Thi way, the opeating ange of the altenato i much lage, o moe pofit can be made. Othe diection fo extenion lie in the diection of eie hybid electic vehicle, vehicle that ue a flywheel fo tempoay enegy toage and vehicle with a CVT, whee vaiation in both engine toque and peed i poible. Futhemoe, the tategy can be expanded with pioity contol. Thi i a powe cheduling ytem that can potpone o quicken the electic powe equet. REFERENCES [] J. G. Kaakian, J. M. Mille, and N. Taub, Automotive electonic powe up, IEEE pectum, pp , May.

9 9 []. Nicati, and H. Huang, 4V powenet: oviding the vehicle electical powe fo the t centuy, SAE, Futue Tanpotation Technology Confeence and Expoition, Cota Mea, Aug. -3,. [3] E. D. Tate, and S.. Boyd, Finding ultimate limit of pefomance fo hybid electic vehicle, SAE, Futue Tanpotation Technology Confeence and Expoition, Cota Mea, Aug. -3,. [4] V. H. Johnon, K. B. Wipke, and D. J. Rauen, HEV contol tategy fo eal-time optimization of fuel economy and emiion, SAE, Futue Ca Conge, Alington, Viginia, USA, Feb. -6,. [5] E. F. Camacho, and C. Bodon, Model pedictive contol, Spinge- Velag, London, 999. [6] Bam de Jage, edictive toage contol fo a cla of powe conveion ytem, ubmitted to the ECC 3 confeence, Cambidge, UK. The autho ae woking at eithe the Depatment of Mechanical Engineeing o the Depatment of Electical Engineeing at the Techniche Univeiteit Eindhoven in the Netheland.