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Comparison of PMP and DP in fuel cell hybrid vehicles

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Abstract

Pontryagin’s Minimum Principle (PMP) and Dynamic Programming (DP) are both from the optimal control theory and can both achieve optimal trajectories when they are applied to power management strategies of hybrid vehicles. However they have totally different control concepts. In order to select the superior one, the PMP-based and the DP-based power management strategies are introduced and compared for a fuel cell hybrid vehicle (FCHV) in this paper. The two power management strategies are applied to the FCHV in a computer simulation environment, and the simulation results from the two strategies are compared when the control variable for the PMP is fuel cell system (FCS) net power and for the DP is battery power. As a result, the superiority of the PMP-based power management strategy is proved.

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Abbreviations

V :

open circuit voltage (V)

R :

internal resistance (Ohm)

Q bat :

battery capacity (C)

P bat :

battery power at terminals (W)

P fcs :

FCS net power (W)

J :

performance measure (g)

\(\dot m_{h_2 }\) :

fuel consumption rate (g/s)

t 0 :

initial time (s)

t f :

final time (s)

p :

costate (g)

H :

Hamiltonian (g/s)

x :

state variable

u :

control variable

N :

the number of time steps

J * N−k,N :

optimal performance measure from N-k time step to the final time step

J * N−(k−1),N :

optimal performance measure from N-(k-1) time step to the final time step

PMP:

Pontryagin’s Minimum Principle

DP:

Dynamic Programming

FCHV:

fuel cell hybrid vehicle

FCS:

fuel cell system

OCV:

open circuit voltage

SOC:

state of charge

References

  • Bernard, J., Delprat, S., Buechi, F. and Guerra, T. M. (2006). Global optimization in the power management of a fuel cell hybrid vehicle (FCHV). Proc. IEEE Veh. Power Propuls. Conf., 1–6.

    Google Scholar 

  • Bernard, J., Delprat, S., Buechi, F. and Guerra, T. M. (2009). Fuel-cell hybrid powertrain: toward minimization of hydrogen consumption. IEEE Trans. Veh. Technol., 58, 3168–3176.

    Article  Google Scholar 

  • Bernard, J., Delprat, S., Guerra, T. M. and Buechi, F. (2010). Fuel efficient power management strategy for fuel cell hybrid powertrains. Control Eng. Practice, 18, 408–417.

    Article  Google Scholar 

  • Ehsani, M., Gao, Y. M. and Emadi, A. (2010). Modern Electric, Hybrid Electric, and Fuel Cell Vehicles. 2nd edn. CRC Press. Boca Raton. 459–469.

    Google Scholar 

  • Kim, M. J. and Peng, H. (2007). Power management and design optimization of fuel cell/battery hybrid vehicles. J. Power Sources, 165, 819–832.

    Article  Google Scholar 

  • Kim, N. W. (2009). Energy Management Strategy for Hybrid Electric Vehicles based on Pontryagin’s Minimum Principle. Ph. D. Dissertation. Seoul National University. Seoul. Korea.

    Google Scholar 

  • Kirk, D. E. (1970). Optimal Control Theory. Prentice-hall. New York. 184–209.

    Google Scholar 

  • Liu, X., Diallo, D. and Marchand, C. (2011). Design methodology of hybrid electric vehicle energy source: Application to fuel cell vehicles. Int. J. Automotive Technology 12,3, 433–441.

    Article  Google Scholar 

  • Pukrushpan, J. T., Peng, H. and Stefanopoulou, A. G. (2004). Control-oriented modeling and analysis for automotive fuel cell systems. Trans. ASME, 126, 14–25.

    Google Scholar 

  • Xu, L. F., Li, J. Q., Hua, J. F., Li, X. J. and Ouyang, M. G. (2009). Optimal vehicle control strategy of a fuel cell/battery hybrid city bus. Int. J. Hydrogen Energy, 34, 7323–7333.

    Article  Google Scholar 

  • Zheng, C. H., Kim, N. W. and Cha, S. W. (2012). Optimal control in the power management of fuel cell hybrid vehicles. Int. J. Hydrogen Energy, 37, 655–663.

    Article  Google Scholar 

  • Zheng, C. H., Oh, C. E., Park, Y. I. and Cha, S. W. (2012). Fuel economy evaluation of fuel cell hybrid vehicls based on equivalent fuel consumption. Int. J. Hydrogen Energy, 37, 1790–1796.

    Article  Google Scholar 

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Authors and Affiliations

  1. Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, China

    C. H. Zheng & G. Q. Xu

  2. Department of Mechanical and Automotive Engineering, The Chinese University of Hong Kong, Hong Kong, China

    C. H. Zheng & G. Q. Xu

  3. Department of Mechanical System Design Engineering, Seoul National University of Science and Technology, Seoul, 139-743, Korea

    Y. I. Park

  4. Department of Mechanical and Automotive Engineering, Seoul National University of Science and Technology, Seoul, 139-743, Korea

    W. S. Lim

  5. School of Mechanical and Aerospace Engineering/SNU-IAMD, Seoul National University, Seoul, 151-742, Korea

    S. W. Cha

Authors
  1. C. H. Zheng
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  2. G. Q. Xu
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  3. Y. I. Park
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  4. W. S. Lim
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  5. S. W. Cha
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Correspondence to S. W. Cha.

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Zheng, C.H., Xu, G.Q., Park, Y.I. et al. Comparison of PMP and DP in fuel cell hybrid vehicles. Int.J Automot. Technol. 15, 117–123 (2014). https://doi.org/10.1007/s12239-014-0013-y

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  • DOI: https://doi.org/10.1007/s12239-014-0013-y

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