428 28,,,, 1. 1 Fig. 1 Scheme of a series HEV 2, P ft (t) t /, P bat (t) t, P el (t) t,, P req (t) t.,,,,.,, P ft (t) + P bat (t) = P req (t) + P el (

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1 : (2011) Control Theory & Applications Vol. 28 No. 3 Mar. 2011, (, ) :,,., PSATv6.1.,, ;, 28.47%. : ; ; : U463 : A Control strategy of series hybrid electric vehicle based on improved dynamic programming SHEN Cai-ying, XIA Chao-ying (School of Electrical Engineering and Automation Tianjin University, Tianjin , China) Abstract: Hybrid electric vehicles(hev) are usually powered by two different energy sources. Typically, those are equipped with an internal combustion engine and a bank of batteries. In a given driving cycle, it is important to minimize the total fuel consumption by properly sharing the instantaneous power between the two energy sources. This problem is solved by using the improved dynamic programming(idp) algorithm. Simulation results from PSATv6.1 indicate that this algorithm helps saving fuel consumption more than the Thermostat approach. In the operation, this algorithm requires smaller memory capacity and reduces the operation time to 28.47% of the unimproved dynamic programming algorithm. Key words: control strategy; dynamic programming; series hybrid electric vehicle 1 (Introduction),, : 1) ; 2) ; 3),,,. 4,,,,,. [1 6],,, ;,,. [7] ; [8] ; [9, 10],, ; [11],,, ;,, ; [12, 13].,,,,,. 2 (Statement of problem) 2.1 (Abstract model) 1. : ; :

2 428 28,,,, 1. 1 Fig. 1 Scheme of a series HEV 2, P ft (t) t /, P bat (t) t, P el (t) t,, P req (t) t.,,,,.,, P ft (t) + P bat (t) = P req (t) + P el (t), (1).,, (T m, ω), (e-line), f e-line (P ft ) = f(t m, ω) e-line = min f(p ft ω ). (2) (T m,ω) Ω(P ft ) : Ω(P ft ) = (T m, ω) P ft = T m ω }, f, f e-line (P ft ) P ft,, f(p ft ω ) ω, P ft. 3,, PSAT, (2).,, PI,,,., ( 3)., Fig. 3 Characteristic fuel map of an engine 2 Fig. 2 Abstract scheme for a series HEV system,,,,,,. 2.2 (Engine and generator),,. 2.3 (Battery) 4, : K I, SOC,. 4 Fig. 4 Model of battery SOC, (3) : SOC(t) = Q(t) = Q max t SOC init Q max I s(τ)dτ 0, (3) Q max

3 3 : 429 : SOC(t) t, Q(t) t, Q max, SOC init.,, (4), I b, I s, I s (t) = K I (I b )I b (t). (4),, 5,,, P bat (t) = UI b (t)n. (5) : P bat, n, U. SOC 0 = SOC T. (11) P ft (6), (7), SOC, (8) (11). 3 (Improved dynamic programming),,. 3.1 (Dynamic programming algorithm), 6. [0 T ] N, t, [SOC min SOC max ] M, SOC. M = 4, N = 6, (7) SOC(k+1, j) SOC(k, i) = I s(k, i, j), t 3600Q max (12) k 0, 1,, N 1}, i, j 0, 1,, M}. 5 I s I b Fig. 5 Relationship between I s and I b of battery 2.4 (Problem formulation),., min V (P ft ) = min P ft T 0 f e-line(p ft (s))ds. (6),,,, SOC, (3): dsoc(t) dt = I s(t) 3600Q max. (7), I s min I s (t) I s max, t, (8) P ft min P ft (t) P ft max, t. (9) : I s min < 0,, I s max > 0,,,, SOC min SOC(t) SOC max, t. (10),, 6 Fig. 6 Network in DP algorithm SOC(k, i)k, i SOC, I s (k, i, j) k, SOC ij, (12) SOC SOC(k, i) I s (k, i, j) t, SOC SOC (k + 1, j). (11) SOC0 = SOC N, (13) k 0, N}, (1)(4)(5) P ft (k) + P bat (k) = P req (k) + P el (k),. (14) I s (k) = K I (I b )I b (k). (15) P bat (k) = UnI b (k). (16) (6)

4 V d (P ft ) = N 1 k=0 Is min I s (k) I s max, f e line (P ft (k)) t. (17) k 0, 1,, N}, Pft min P ft (k) P ft max, k 0, 1,, N}, SOCmin SOC(k) SOC max, k 0, 1,, N}. (18) (19) (20) SOC SOC(k + 1, j), SOC y, p = j e 1, q = j e 2,, (k + 1, j), p, q, k p q. (12) : x = I s min t, y = I s max t, 3600Q max 3600Q max e 1 = x SOC, e 2 = y SOC., k = 0, 1,, N 1, P ft (k)(17), (12), (13) (16)(18) (20). : k = 0, 1,, N 1; j = 0, 1,, M; i = 0, 1,, M. (12)I s (k, i, j), I s (k, i, j) (18), (14) (16)P ft (k, i, j), P ft (k, i, j) (19), j, j S k+1, a(k, i, j) : V d (k + 1, j) = min i S k a(k, i, j) + V d (k, i)}. (21) : P ft (k, i, j) SOC SOC(k, i) SOC(k + 1, j),, a(k, i, j), V d (k + 1, j) (k + 1, j). : indice(k, i ) = arg min i S k a(k, i, j) + V d (k, i)}. (22) : arg min i S k a(k, i, j) + V d (k, i)} a(k, i, j)+v d (k, i), (22) (k + 1, j) (k, i ), j, j / S k (Improved dynamic programming),,,,. 7, SOC SOC(k, p), I s min, t, SOC SOC(k + 1, j), SOC x;, SOC SOC(k, q), I s max, t, 7 Fig. 7 Network in IDP algorithm 8 Fig. 8 Flow chart of IDP

5 3 : 431 : k = 0, 1, N 1; j = 0, 1, M; p = max(j e 1, 0), q = min(j e 2, M). p i q i S k, I s (k, i, j), P ft (k, i, j), P ft (k, i, j)(19), j S k+1, a(k, i, j), V d (k + 1, j) (k, i ). P ft (k, i, j) (19), j / S k (Simulation results and conclusion) PSATv6.1,, 1, SOC 57%, 63%, SOC 60%, 0.016%, 505, 2 s. SOC 0.59, 9.84 L/100 km; SOC 0.6, 8.33 L/100 km, h, h %. 10, 10(b),,,, 10(c),, 11(b),, 11(c),,,. 1 Table 1 Parameter of SHEV / kg 2000 / kw 60 /% / kw 60 /% 92 / kw 70 /% 94 /Ah 40 /V 240 / kw , 10, 10(a), 10(b), 10(c). 11, 11(a), 11(b), 11(c). 12 SOC. : thermostat, IDP. (a) (b) (c) 10 Fig. 10 Simulation results under thermostat Fig driving cycle (a)

6 (b) (c) 11 Fig. 11 Simulation result under IDP 12 SOC Fig. 12 SOC profile under IDP and thermostat,, 28.47%. (References): [1] SCIARRETTA A, BACK M. GUZZELLA L. Optimal control of parallel hybrid electric vehicles[j]. IEEE Transactions on Control Systems Technology, 2004, 12(3): [2] ANDERSON C, PETTIT E. The effects of APU characteristics on the design of hybrid control strategies for hybrid electric vehicles, SAE Paper, [R]. USA: Society of Automotive Engineers, 1995: [3] HOCHGRAT C, RYAN M, WIEGMAN H. Engine control strategy for a series hybrid electric vehicle incorporating load-leveling and computer controlled energy management, SAE Paper, [R]. USA: Society of Automotive Engineers, 1996: [4] STEFANO B. Techniques to control the electricity generation in a series hybrid electric vehicle[j]. IEEE Transactions on Energy conversion, 2002, 17(2): [5] BARGAR H, LI JINGBO, GOERING D J, et al. Modeling and verification of hybrid electric HMMWV performance[c] //Proceedings of the 29th Annual Conference of the IEEE Industrial Electronics Society. New York: IEEE, 2003: [6] AOYAGI SATOSHI, YUSUKE HASEGAWA, TAKAHIRO YONE KURA, et al. Energy efficiency improvement of series hybrid vehicle[j]. JSAE Review, 2001, 22(3): [7] JALIL N, AKHEIR N, SALMAN M. A rule-based energy managenment strategy for a series hybrid vehicle[c] //Proceedings of the 1997 American Control Conference. Albuquerque, NM, USA: IEEE, 1997: [8] BARSALI S, MIULLI C, POSSENTI A. A control strategy to minimize fuel consumption of series hybrid electric vehicles[j]. IEEE Transaction on Energy Conversion, 2004, 19(1): [9] KLEIMAIER A, SCHRODER D. An approach for the online optimized control of a hybrid powertrain[c] //International Workshop on Advanced Motion Control. Maribor, Slovenia: Institute of Electrical and Electronics Engineers Inc, 2002: [10] MUSARDO C, RIZZONI G, STACCIA B. A-ECMS: an adaptive algorithm for hybrid electric vehicle energy management[j]. European Journal of Control, 2005, 11(4/5): [11] PEREZ L, ELVIO A. Optimal power split in hybrid electric vehicle using direct transcription of an optimal control problem[j]. Mathematics and Computers in Simulation, 2009, 79(6): [12] PEREZ L, ELVIO A. Optimization of power management in an hybrid electric vehicle using dynamic programming[j]. Mathematics and Computers in Simulation, 2006, 73(1): [13],. [J]., 2008, 25(6): (ZHANG Ju, WANG Wanliang. Dynamic-programming-based multiparametric programming method for constrained optimal control problem and its applications[j]. Control Theory & Applications, 2008, 25(6): ) : (1981 ),,,, shencaiying@163.com; (1958 ),,,, xiachaoying@126. com.

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602 31,,.,,,,. HEV,.,, HEV,,,.,,. 2 (Basic assumptions) HEV, : 1) P ice (t), (continuously variable transmission, CVT) ω ice (t), T ice (t), 10 ; 2) ( 31 5 2014 5 DOI: 10.7641/CTA.2014.30642 Control Theory & Applications Vol. 31 No. 5 May 2014, (, 300072) :.,. 5,,. : ; ; : U463 : A Real-time optimization control for hybrid electric vehicles based on