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Long-term stochastic model predictive control for the energy management of hybrid electric vehicles using Pontryagin’s minimum principle and scenario-based optimization

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  • Ritter, Andreas
  • Widmer, Fabio
  • Duhr, Pol
  • Onder, Christopher H.

Abstract

This paper presents a new approach to efficiently integrate long prediction horizons subject to uncertainty into a stochastic model predictive control (MPC) framework for the energy management of hybrid electric vehicles. By exploiting Pontryagin’s minimum principle, we show that the energy supply required to obtain a certain change in the state of charge (SOC) of the battery can be approximated using a quadratic equation. The parameters of these mappings depend on the power request imposed by the driving mission and thus allow to compress the time-resolved power profile into only three scalar variables. Having a driving mission divided into several segments of arbitrary length, the corresponding sequence of quadratic approximations allows to reformulate the original energy management problem as a quadratic program, which offers an efficient way to include a large number of future scenarios. The resulting scenario-based stochastic MPC approach prevents SOC boundary violations with a certain probability, which can be controlled by the number of scenarios considered. To validate the quadratic approximation, we study two numerical examples using two different vehicles, a series hybrid electric passenger car and a battery-assisted trolley bus. Finally, a case study based on the operation of the latter is provided, which demonstrates the expected behavior and the real-time capability of the stochastic MPC approach. While the SOC is maintained in predefined boundaries with high probability, the required energy supply is only increased by 1.41% compared to the non-causal optimum.

Suggested Citation

  • Ritter, Andreas & Widmer, Fabio & Duhr, Pol & Onder, Christopher H., 2022. "Long-term stochastic model predictive control for the energy management of hybrid electric vehicles using Pontryagin’s minimum principle and scenario-based optimization," Applied Energy, Elsevier, vol. 322(C).
  • Handle: RePEc:eee:appene:v:322:y:2022:i:c:s0306261922005608
    DOI: 10.1016/j.apenergy.2022.119192
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    References listed on IDEAS

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    1. Xie, Shaobo & Hu, Xiaosong & Xin, Zongke & Brighton, James, 2019. "Pontryagin’s Minimum Principle based model predictive control of energy management for a plug-in hybrid electric bus," Applied Energy, Elsevier, vol. 236(C), pages 893-905.
    2. Algo Carè & Simone Garatti & Marco C. Campi, 2019. "The wait-and-judge scenario approach applied to antenna array design," Computational Management Science, Springer, vol. 16(3), pages 481-499, July.
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    Cited by:

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    2. Jia, Chunchun & Zhou, Jiaming & He, Hongwen & Li, Jianwei & Wei, Zhongbao & Li, Kunang & Shi, Man, 2023. "A novel energy management strategy for hybrid electric bus with fuel cell health and battery thermal- and health-constrained awareness," Energy, Elsevier, vol. 271(C).
    3. Yang, Chao & Du, Xuelong & Wang, Weida & Yuan, Lijuan & Yang, Liuquan, 2024. "Variable optimization domain-based cooperative energy management strategy for connected plug-in hybrid electric vehicles," Energy, Elsevier, vol. 290(C).
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    5. Benaitier, Alexis & Krainer, Ferdinand & Jakubek, Stefan & Hametner, Christoph, 2023. "Optimal energy management of hybrid electric vehicles considering pollutant emissions during transient operations," Applied Energy, Elsevier, vol. 344(C).
    6. Carvalho, Diego B. & Bortoni, Edson da C., 2024. "Proposed model with weighted parameters for microgrid management: Incorporating diverse load profiles, assorted tariff policies, and energy storage devices," Energy, Elsevier, vol. 296(C).

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