Power management of PHEV using quadratic programming

Transcription

1 46 It. J. Electric ad Hybrid Vehicles, Vol. 3, No. 3, 011 Power maagemet of PHEV usig quadratic programmig Zhiguag Zhou College of Mechaical ad Vehicle Egieerig, Hua Uiversity, Yuelu District, Chagsha City, Hua Provice, 41008, Chia ad Departmet of Electrical ad Computer Egieerig, Uiversity of Michiga-Dearbor, 4901 Evergree Road, Dearbor, MI 4818, USA Chris Mi* Departmet of Electrical ad Computer Egieerig, Uiversity of Michiga-Dearbor, 4901 Evergree Road, Dearbor, MI 4818, USA *Correspodig author Abstract: This paper studies the power maagemet of a plug-i hybrid electric vehicle (PHEV) usig quadratic programmig. The proposed quadratic programmig ca obtai the global optimal solutio of the power distributio betwee battery/motor ad egie while maitaiig vehicle performace. Computatio time ca be sigificatly saved compared with dyamic programmig. Therefore, it ca be used i real-time realisatio. Two typical drivig cycles, amely, UDDS ad HWFET drivig cycles are used to test the effectiveess of optimisatio strategy. The simulatio results idicate that sigificat amout of fuel ca be saved with the proposed method. Keywords: power maagemet; optimisatio; rule-based strategy; quadratic programmig; QP; plug-i hybrid electric vehicle; PHEV; electric ad hybrid vehicles. Referece to this paper should be made as follows: Zhou, Z. ad Mi, C. (011) Power maagemet of PHEV usig quadratic programmig, It. J. Electric ad Hybrid Vehicles, Vol. 3, No. 3, pp Biographical otes: Zhiguag Zhou received his BS i Electroic Iformatio Egieerig from Xiagta Uiversity, Chia, i 004, ad his MS i Electrical Egieerig from Hua Uiversity, Chia, i 007. He is a Doctoral studet at the Hua Uiversity, Chia. He is curretly a visitig scholar i the Uiversity of Michiga-Dearbor. His research iterests focus o the desig, modellig, ad cotrol of hybrid electric vehicles ad plug-i hybrid electric vehicles. Copyright 011 Idersciece Eterprises Ltd.

2 Power maagemet of PHEV usig quadratic programmig 47 Chris Mi received his BSEE ad MSEE i Electrical Egieerig from the Northwester Polytechical Uiversity, Xi a, Chia, ad his PhD degree from the Uiversity of Toroto, Caada. He was a Electrical Egieer with Geeral Electric Caada, Ic. He is curretly a Associate Professor i the Uiversity of Michiga-Dearbor ad the Director of the DTE Power Electroics Laboratory. He has bee a Guest Editor of the Iteratioal Joural of Power Electroics, a member of the editorial board of the Iteratioal Joural of Electric ad Hybrid Vehicles ad the IET Electrical Systems i Trasportatio, ad the Associate Editor for the Joural of Circuits, Systems, ad Computers ( ). He was the Geeral Chair of the Fifth IEEE Vehicle Power ad Propulsio Coferece. He is a Associate Editor of the IEEE Trasactios o Vehicular Techology, a Associate Editor of the IEEE Power Electroics Letters ad a Seior Editor of the IEEE Vehicular Techology Magazie. 1 Itroductio It is well recogised that hybrid electric vehicle (HEV) is much more efficiet ad cleaer tha the traditioal vehicles powered by gasolie ad diesel egie aloe (Gao ad Ehsai, 010). However, HEVs rely o gasolie or diesel for propulsio power eeds. The oboard battery provides peak-shavig fuctio ad optimises the overall fuel efficiecy. Therefore, the battery state of charge (SOC) is usually maitaied at the specified level over the log term of drivig. Pure battery powered electric vehicle (EV) is cosidered as the future because it does ot rely o fossil fuel. But EVs have ot bee accepted by the market because of its short drivig rage, log battery chargig time ad high cost (Gao ad Ehsai, 010; Ehsai et al., 005). Plug-i hybrid electric vehicle (PHEV) is a kid of HEV, which is purposely desiged to use the o board battery to drive the vehicle usig electric eergy charged from the electric utility grid. Therefore, fuel ca be displaced. PHEV possesses the advatages of both pure EV ad HEV. PHEV ca work as pure EV for certai distace whe the battery SOC is high after chargig, i charge-depletig (CD) operatio. I CD mode, all the propulsio eergy comes from battery. Whe battery SOC reaches a specified low level, the egie is started ad the vehicle goes to charge-sustaiig (CS) mode as regular HEV, durig which battery SOC is maitaied aroud this specified level util the ed of trip (Goder ad Markel, 007; Simpso, 006; Markel ad Simpso, 006, 005; Markel ad Wipke, 001). Power maagemet strategy used i PHEV is more complicated tha HEV ad pure EV due to the CD ad CS mode. Several power maagemet strategies, like rule-based (RB) cotrol strategy (Gog et al., 008), dyamic programmig (DP) (Gog et al., 008, 007b) ad stochastic dyamic programmig (SDP) (Moura et al., 010b) have bee used i PHEV. RB cotrol is easy to implemet, while omittig some detailed vehicle behaviour (Gog et al., 007a). RB is based o egieerig expertise ad isight, ad uder this cotrol, the global optimal is abset for the whole trip. DP method obtais global optimisatio for the whole trip, however, the whole drivig cycle must be kow at the begiig of trip. Meawhile, the eed for huge computatio time makes it very difficult for real-time implemetatio. Nevertheless, the results from off-lie computatio usig DP method ca be used to derivatio of RB cotrol algorithms (Gao ad Ehsai, 010). For SDP method, istead of optimisig over a give drivig cycle, the power

3 48 Z. Zhou ad C. Mi maagemet strategy is optimised over a family of radom drivig cycles i a average sese (Li et al., 004). The fial resolutio largely depedets o the represetativeess of the traiig drivig cycles (Wu et al., 011). PHEVs are desiged to maximise the use of battery eergy durig CD mode to maximise the displacemet of fuel cosumptio. Typical cotrol method is to use cotrol rules that first prioritise battery eergy cosumptio util the vehicle eters a CS mode. However, durig CD operatio, if the vehicle power demad is extremely high, the overall efficiecy ca be substatially impacted due to the large power loss i the battery. Requiremet for battery power ratig ca also further icrease battery cost. I this paper, cosiderig the power maagemet optimisatio is a covex problem (Koot ad Kessels, 005; Moura et al., 010a), quadratic programmig (QP) method is used to obtai the optimal global resolutio based o kowledge of previous trip. Compared to DP method, QP method ca save computatio time, which will brig prospect to the real-time implemetatio. Simulatio results show that bleded PHEV operatio with the proposed QP method provides sigificat fuel savigs over the stadard CD-CS cotrol strategy. Powertrai architecture of the PHEV I this paper, the architecture of the PHEV studied is of a power-split type similar to the Toyota Prius as show i Figure 1 ad the parameters of the PHEV is listed i Table 1. Two clutches are used to cofigure the operatio modes of the powertrai. I this cofiguratio, the vehicle powertrai ca be cofigured as series operatio or parallel operatio. The detailed operatio modes are explaied as follows: Mode 1: motor aloe mode. I this mode, C1 is egaged ad C is ope. Motor is oly source of propulsio of propulsio to drive the vehicle by takig power from the battery. Mode : series mode. I series operatio, C1 is egaged to groud the rig gear ad C is ope. So the egie drives the carrier which i tur trasfers egie power to su gear that drives the geerator to produce electricity. The motor is the oly source of propulsio. The power flow is show i Figure (a). Mode 3: parallel mode. I parallel operatio, C1 is ope ad C is egaged. So the rig gear is coected to the fial drive. The plaetary gear trai serves as a iput split device. The egie power is therefore split betwee su gear ad rig gear. The rig gear power is used to drive the vehicle while the su gear power is supplied to the geerator to geerate electricity. The motor provide torque to drive the vehicle by takig eergy from the geerator or battery. The power flow of the PHEV i parallel operatio is show i Figure (b). Mode trasitio is cotrolled by the trasmissio cotroller based o battery SOC ad vehicle power demad. To reduce impact of mode trasitio o vehicle dyamic performace, C1 is always released before C egages. For example, whe trasitioig from motor aloe or series to parallel mode, egie is first started by MG with C1 egaged to lock the rig gear. Oce egie is started, C1 ca be ope ad the geerator is cotrolled such that the rig gear will icrease. Whe the rig gear speed reaches the motor speed, C is egaged.

4 Power maagemet of PHEV usig quadratic programmig 49 Whe trasitioig from parallel to series operatio, egie power is reduced ad C is released. At the same time, the geerator is cotrolled such that the rig gear speed will decrease. Whe the rig gear speed approaches zero, C1 is egaged. I traditioal PHEV cotrol, the vehicle will operate i the CD mode first by usig the battery eergy util the SOC drops below a preset threshold ad at that time, the vehicle eters ito CS mode. This mode is called CDCS mode. I this paper, the CD mode is defied slightly differet: the egie may be started if vehicle power demad exceeds certai limit. This is due to the fact that operate the vehicle usig the batter/motor oly at high power demad will become very iefficiet due to large losses associated with the motor ad battery impedace. The modified CD mode is also called bleded PHEV mode. This paper is to optimise the power distributio betwee the battery ad egie i bleded PHEV mode to miimise eergy cosumptio (Fuel + Battery eergy) for a give drivig distace. Figure 1 Architecture of PHEV Figure Power flow i the proposed of PHEV, (a) power flow i series operatio (b) power flow i parallel operatio P e P g P b P gm P m P d P r (a) P e Pd Pr P e _ t P g P m P b (b)

5 50 Z. Zhou ad C. Mi Table 1 Parameters of PHEV Compoet Cotets Ratig Vehicle Type SUV Gross weight 3,98 kg Egie Type Gasolie 5.7 L Peak power 57 5,300 RPM Motor Type Permaet maget AC Peak power 65 4,00 RPM Geerator Type Permaet maget AC Peak power 65 4,00 RPM Battery pack Type Lithium-io battery Rated capacity 10 kwh Rated voltage 300 V Total weight 76 kg 3 Power flow aalysis From Figure (b), i parallel mode, the total egie power P e_t is composed of two portios. Oe portio is P g that is used to drive the geerator to produce electricity, which ca be stored i the battery (P gb ) or used to drive electric motor (P gm ) directly; aother portio is P e which is directly used to propel the vehicle, either idepedetly, or together with power from electric motor (P m ) (Ha et al., 004). Both power from battery (P b ) ad geerator (P gm ) ca be used to drive electric motor, depedig o cotrol strategy. The total egie output power ca be obtaied: P = P + P (1) e_ t e g Total power from egie has the relatioship with fuel cosumptio: P et _ ( f) = f m () For the geerator, its out power is shared betwee the motor ad the battery, i.e., P + P = η P (3) gb gm g g where η g is efficiecy of the geerator. For the battery: ( η _ ) P = η P + P (4) b b_ D b C gb bs where η b_d is discharge efficiecy of battery, η b_c is charge efficiecy of battery ad P bs is the power cosumed from battery. For the motor: ( ) P = η P + P (5) m m b gm

6 Power maagemet of PHEV usig quadratic programmig 51 where η m is the efficiecy of motor. Output power to drive trai is: ( ) P = η P + P (6) d p m e where η p is the efficiecy of gear. The vehicle power demad is: P = η P (7) r d d where η d is the efficiecy of drive trai. From equatios (1) to (7), we ca obtai: ( ) P = ηη ηη η P + η P + P + ηηηη P (8) r d p m b_ D b_ C gb m gm e d p m b_ D bs I equatio (8), the first item is the power produced by the cosumptio of fuel, the secod item is power stored i battery, so we ca rewrite (8) as: ( ) P = g m + η P (9) r f bs where η = η d η p η m η b_d. From equatio (9), we ca see that with the previous kowledge of drivig cycle, the required power is kow at every time momet. So oly fuel cosumptio ad power from battery are variables, ad we ca use the followig fuctio to describe the relatioship betwee fuel cosumptio ad power from battery (Koot ad Kessels, 005; Moura et al., 010a): ( ) m P = α P + α P + α (10) f bs bs 1 bs 0 where α > 0 ad α 0 > 0. 4 Power maagemet usig QP 4.1 Solvig the quadratic equatio From Sectio 3, we ca see that power maagemet problem ca be described with quadratic polyomial, so the optimal solutio ca be obtaied usig QP method. Before usig QP, the total time of drivig cycle is discretised to time poits with the time iterval Δt: t =, (11) Δt So the relatioship betwee fuel cosumptio ad power from battery ca be described i discrete time domai: f = α bs + α1 bs + α0 m ( k) ( k) P ( k) ( k) P ( k) ( k) (1) where α( k) > 0, α0( k) > 0 ad k = 0,1,...,.

7 5 Z. Zhou ad C. Mi At every time poit k, let P bs (k) chage from: 0 Pet _ ( k) Pr( k) Pr( k) Pe_max t Pe_ t( k) < Pr( k) (13) to Pr( k) Pbsmax Pr( k) Pbs max Pbs max < Pr ( k) (14) The correspodig fuel cosumptio m f ( k) ca be obtaied at each time poit. Usig least square method, coefficiets α (k), α 1 (k) ad α 0 (k) ca be acquired. The optimisatio objective of power maagemet is to miimise fuel cosumptio, so the cost fuctio ca be described as: J = m ( k) = α( kp ) bs ( k) + α1( kp ) bs ( k) + α0( k) f (15) The target of power maagemet is to miimise the fuel cosumptio uder the precoditio of satisfyig the requiremet from the driver, so it ca be described as: mi J = mi mf ( k) = mi α( kp ) bs ( k) + α1( kp ) bs ( k) + α0( k) (16) The QP problem ca be solved aalytically by itroducig the Lagrage fuctio: ( ) L P ( k), λ = α ( k) P ( k) + α ( k) P ( k) + α ( k) bs bs 1 bs 0 λ bs P ( k) E bs (17) where E bs is the maximum usable eergy supplied by battery aloe durig the whole trip. The optimal solutio ca be obtaied by solvig: ad ( ( k), λ ) L P P bs bs ( k) = 0 (18)

8 Power maagemet of PHEV usig quadratic programmig 53 ( ( ), ) L Pbs k λ = 0 λ The solutio is: where P bs_ opt (19) λ α1( k) ( k) = (0) α ( k) λ = α1( k) + E α ( k) 1 α ( k) bs (1) From equatio (1), we ca see that λ has the relatioship with the whole drivig cycle, it is to say that before usig QP method, the drivig cycle must be kow beforehad. 4. Costraits of QP I order to maitai all the compoets operate i the reasoable rage, uder the coditio of drivig mode, the followig costraits are desiged: ωe_mi ωe( k) ωe_max Te_mi Te( k) Te_max ωm_mi ωm( k) ω m_max Tm_mi Tm( k) T m_max ωg_mi ωg( k) ωg_max Tg_mi Tg( k) Tg_max Pbs_mi Pbs ( k) P bs_max Ebs_mi Ebs ( k) E bs_max SOC SOC k SOC mi ( ) max () where ω e_mi, ω e_max, ω m_mi, ω m_max, ω g_mi ad ω g_max are the miimum ad maximum speed of egie, electrical motor ad geerator respectively; T e_mi, T e_max, T m_mi, T m_max, T g_mi ad T g_max are the miimal ad maximum torque of egie, electrical motor ad geerator uder curret speed respectively; P bs_mi, P bs_max, E bs_mi ad E bs_max are the miimal ad maximum power ad eergy from battery at the curret time; ad SOC mi ad SOC max are miimal ad maximum SOC of battery. The eergy of battery at the curret time ca be calculated from: E ( k) = E (0) P ( k) (3) bs bs bs

9 54 Z. Zhou ad C. Mi 5 Optimisatio results ad discussio I order to verify the optimisatio results, QP method is implemeted i ADVISOR. Two typical drivig cycles UDDS ad HWFET are selected to test CDCS cotrol strategy ad QP method. The SOC with eight UDDS drivig cycles is show i Figure 3. It ca be see that that usig CDCS method the SOC decreases quickly to the specific level 0.3 ad at this time the distace is 18.6 km. O the cotrary, the SOC chages slowly to the specific level of 0.3 uder the cotrol of QP, as the dashed lie idicated. The simulatio results uder the cotrol of CDCS ad QP with differet cycles of UDDS ad HWFET drivig cycles are show i Figure 4 ad Figure 5 respectively. I both figures, the x-axis is distace ad y-axis is MPG. From Figure 4, we ca see that at differet distace QP method icreases MPG from 3.71% to 3.97% compared to CDCS method. Followig the icrease of distace, MPG uder both QP method ad CDCS method are decreasig, but the chagig rate is smaller ad smaller. From Figure 5, we ca see the same chagig tred as Figure 4, ad the same result ca be obtaied that usig QP method has higher MPG tha CDCS method, the icrease is from 3.4% to 3.69%. It ca also be see that i HWFET drivig cycle the MPG is higher tha i UDDS drivig cycle for the same distace drive. Figure 3 SOC over the drivig rage for DP ad CDCS (see olie versio for colours) CDCS QP SOC Distace(km) Figure 4 Fuel ecoomy of PHEV with UDDS (see olie versio for colours) RBS QP MPG UDDS drivig cycle(miles)

10 Power maagemet of PHEV usig quadratic programmig 55 Figure 5 Fuel ecoomy of PHEV with HWFET (see olie versio for colours) RBS QP MPG HWFET drivig cycle(miles) The efficiecy of motor ad egie uder the cotrol of CDCS method ad QP method i UDDS drivig cycle is show i Figure 6 to Figure 9 respectively. From Figure 6 ad Figure 7, we ca see that CDCS method caot achieve the global optimisatio i the whole drivig cycle, but usig QP method, the global optimisatio ca be arrived ad the motor operates i higher efficiecy area compared with CDCS method. From Figure 8 ad Figure 9, it ca also be see that by usig QP method the egie operates i higher efficiecy area compared with CDCS method. Motor ad egie operatig i high efficiecy area will lead to the decrease of fuel cosumptio. Figure 6 Efficiecy of motor with CDCS method (see olie versio for colours) actual operatig poits max motor torque max geerator torque Torque (Nm) Speed (rpm)

11 56 Z. Zhou ad C. Mi Figure Efficiecy of motor with QP method (see olie versio for colours) actual operatig poits max motor torque max geerator torque Torque (Nm) Speed (rpm) Figure 8 Torque (Nm) Efficiecy of egie with CDCS method (see olie versio for colours) actual operatig poits max egie torque Speed (rpm)

12 Power maagemet of PHEV usig quadratic programmig 57 Figure Efficiecy of egie with QP method (see olie versio for colours) actual operatig poits max egie torque Torque (Nm) Speed (rpm) 6 Coclusios I this paper, QP approach for the optimisatio of PHEV power maagemet is preseted. This optimisatio problem is formulated based o QP method. The variables i PHEV power maagemet iclude the egie, geerator, electric motor ad eergy storage system. The objective fuctio is defied to miimise the fuel cosumptio. The satisfactio of vehicle performace requiremets is the precoditio of the optimisatio problem ad usable power rage of egie ad battery are selected as the costraits. The optimisatio is performed i two kids of drivig cycles. The results show that i both UDDS ad HWFET drivig cycles, the MPG uder the cotrol of QP is higher tha uder the cotrol of CDCS, it is meas that QP method ca decrease the fuel cosumptio while maitaiig the vehicle performace. Furthermore, the simulatio results reveal that the icrease of MPG is less with the icreasig of distace. The coclusio also ca be draw that with the same cotrol method, vehicle i the HWFET drivig cycle has higher MPG tha i the UDDS drivig cycle. Refereces Ehsai, M., Gao, Y. ad Gays, S.E. (005) Moder Electric, Hybrid Electric, ad Fuel Cell Vehicle: Fudametals, Theory, ad Desig, CRC, Boca Rato. Gao, Y. ad Ehsai, M. (010) Desig ad cotrol methodology of plug-i hybrid electric vehicles, IEEE Trasactios o Idustrial Electroics, Vol. 57, No., pp Goder, J. ad Markel, T. (007) Eergy maagemet strategies for plug-i hybrid electric vehicles, 007 World Cogress, Detroit, Michiga.

13 58 Z. Zhou ad C. Mi Gog, Q., Li, Y. ad Peg, Z-R. (007a) Optimal power maagemet of plug-i HEV with itelliget trasportatio system, 007 IEEE/ASME Iteratioal Coferece o Advaced Itelliget Mechatroics, pp.1 6. Gog, Q., Li, Y. ad Peg, Z-R. (007b) Trip based power maagemet of plug-i hybrid electric vehicle with two-scale dyamic programmig, IEEE Vehicle Power ad Propulsio Coferece, pp Gog, Q., Li, Y. ad Peg, Z-R. (008) Trip-based optimal power maagemet of plug-i hybrid electric vehicles, IEEE Trasactios o Vehicular Techology, Vol. 57, No. 6, pp Ha, Z., Yua, Z. ad Guagyu, T. (004) Optimal eergy maagemet strategy for hybrid electric vehicles, 004 SAE World Cogress, Detroit, Michiga. Koot, M. ad Kessels, J.T.B.A. (005) Eergy maagemet strategies for vehicular electric power systems, IEEE Trasactios o Vehicular Techology, Vol. 54, No. 3, pp Li, C-C., Peg, H. ad Grizzle, J.W. (004) A stochastic cotrol strategy for hybrid electric vehicles, Proceedigs of the 004 America Cotrol Coferece, 30 Jue to July, pp Markel, T. ad Simpso, A. (005) Eergy storage systems cosideratios for grid-charged hybrid electric vehicles, SAE Future Trasportatio Techology ad IEEE Vehicle Power ad Propulsio Joit Cofereces, Chicago, Illiois. Markel, T. ad Simpso, A. (006) Plug-i hybrid electric vehicle eergy storage system desig, Advaced Automotive Battery Coferece, Baltimore, Marylad. Markel, T. ad Wipke, K. (001) Modelig grid-coected hybrid electric vehicle usig ADVISOR, 16th Aual Battery Coferece o Applicatios ad Advaces, Log Beach, Califoria, 9 1 Jauary, pp.3 9. Moura, S.J., Callawayb, D.S. ad Fathya, H.K. (010a) Tradeoffs betwee battery eergy capacity ad stochastic optimal power maagemet i plug-i hybrid electric vehicles, Joural of Power Sources, Vol. 195, No. 9, pp Moura, S.J., Fathy, H.K. ad Callaway, D.S. (010b) A stochastic optimal cotrol approach for power maagemet i plug-i hybrid electric vehicles, IEEE Trasactios o Cotrol Systems Techology, Vol. 19, No. 3, pp Simpso, A. (006) Cost-beefit aalysis of plug-i hybrid electric vehicle techology, d Iteratioal Battery, Hybrid ad Fuel Cell Electric Vehicle Symposium ad Exhibitio (EVS-), Yokohama, Japa, pp Wu, X., Cao, B. ad Li, X. (011) Compoet sizig optimizatio of plug-i hybrid electric vehicles, Applied Eergy, Vol. 88, No. 3, pp