Closed-form solution to the dynamic programming for a heavy-duty parallel hybrid vehicle energy management

Abstract

Dynamic programming (DP) is frequently used to obtain the optimal solution to the hybrid electric vehicle (HEV) energy management. The trade-off between the accuracy and the computational effort is the biggest problem for the DP method. The closed-form solution to the DP is proposed to solve this problem. Firstly, the affine linear model of the engine fuel rate is obtained based on engine test data. The piecewise linear approximation of the motor power demand is obtained considering the different energy flows in the charging and discharging stages of the battery. Then, the second-order Taylor expansion for the cost matrix at each time and state grid point is introduced to get the closed-form solution of the optimal torque split. The results show that this method can greatly reduce the computing burden by 93% while ensuring near-optimal fuel economy compared with the conventional DP method.

KEYWORDS:

• Dynamic programming
• energy management
• closed-form solutions
• fuel economy
• hybrid electric vehicles

Acknowledgments

The authors would like to thank the National Key Laboratory for Vessel Integrated Power System Technology, Naval University of Engineering, China. This research was funded by the National Natural Science Foundation of China (NSFC) under Project Number 52077217.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China: [Grant Number 52077217].

Notes on contributors

Tao Zhang

Tao Zhang received a B.S. degree in Mechatronics Engineering from Army Engineering University, Nanjing, in 2019. He is studying for a Ph.D. degree at the National Key Laboratory for Vessel Integrated Power System Technology, Naval University of Engineering. His current research interest is the energy management of hybrid power systems.

Zhongjun Yu

Zhongjun Yu acquired a master's degree and Ph.D. degrees in power engineering and engineering thermophysics from the BeiHang University, Beijing, in 2005 and 2010, respectively. He is a Professor and doctoral advisor at the Naval University of Engineering. His current research orientation involves electric propulsion and the advanced cooling technology of the electric machine.

Huangda Lin

Huangda Lin acquired his master's degree and Ph.D. degrees in the National Key Laboratory for Vessel Integrated Power System Technology from Naval University of Engineering in 2011 and 2016, respectively. He is a lecturer at the Naval University of Engineering now. His research orientation is motor and driving systems.