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Integer variable-order equivalent circuit model and switching strategy for lithium-ion power batteries for vehicles based on information criterion under dynamic and static working conditions

Author

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  • Zhu, Guangyao
  • Hu, Minghui
  • Qiu, Chengyang
  • Deng, Kejun

Abstract

Accurately description of the dynamic and static characteristics of lithium-ion batteries using a single model is difficult under complex and variable charging and discharging conditions. Based on the lithium-ion equivalent circuit model and distribution characteristics of the battery voltage platform, this study proposes an integer variable-order RC equivalent circuit model and uses the variable forgetting factor least squares method to complete the online identification of model parameters. The best system characterization model was selected according to the information criterion of different-order equivalent circuit models at each state of charge, and the switching strategy of different current directions was formulated. The particle swarm optimisation algorithm was used to explore the best parameters for the fitting degree and complexity evaluation index of the information criteria, to realise the optimal switching and accurate output of the integer variable order RC equivalent circuit model. The experimental results show that the output error of the end-voltage calculation of the integer variable-order RC equivalent circuit model based on information criterion switching can be maintained within 17.60 mV under dynamic and static conditions of various environmental temperatures, demonstrating good accuracy, robustness and potential for practical applications.

Suggested Citation

  • Zhu, Guangyao & Hu, Minghui & Qiu, Chengyang & Deng, Kejun, 2025. "Integer variable-order equivalent circuit model and switching strategy for lithium-ion power batteries for vehicles based on information criterion under dynamic and static working conditions," Energy, Elsevier, vol. 322(C).
    • Handle: RePEc:eee:energy:v:322:y:2025:i:c:s0360544225013362
    DOI: 10.1016/j.energy.2025.135694
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    1. He, Xitian & Sun, Bingxiang & Zhang, Weige & Fan, Xinyuan & Su, Xiaojia & Ruan, Haijun, 2022. "Multi-time scale variable-order equivalent circuit model for virtual battery considering initial polarization condition of lithium-ion battery," Energy, Elsevier, vol. 244(PB).
    2. Hu, Xiaosong & Feng, Fei & Liu, Kailong & Zhang, Lei & Xie, Jiale & Liu, Bo, 2019. "State estimation for advanced battery management: Key challenges and future trends," Renewable and Sustainable Energy Reviews, Elsevier, vol. 114(C), pages 1-1.
    3. Cui, Zhenhua & Kang, Le & Li, Liwei & Wang, Licheng & Wang, Kai, 2022. "A combined state-of-charge estimation method for lithium-ion battery using an improved BGRU network and UKF," Energy, Elsevier, vol. 259(C).
    4. Zafar, Muhammad Hamza & Mansoor, Majad & Abou Houran, Mohamad & Khan, Noman Mujeeb & Khan, Kamran & Raza Moosavi, Syed Kumayl & Sanfilippo, Filippo, 2023. "Hybrid deep learning model for efficient state of charge estimation of Li-ion batteries in electric vehicles," Energy, Elsevier, vol. 282(C).
    5. Guo, Ruohan & Shen, Weixiang, 2022. "Online state of charge and state of power co-estimation of lithium-ion batteries based on fractional-order calculus and model predictive control theory," Applied Energy, Elsevier, vol. 327(C).
    6. Li, Junfu & Wang, Lixin & Lyu, Chao & Pecht, Michael, 2017. "State of charge estimation based on a simplified electrochemical model for a single LiCoO2 battery and battery pack," Energy, Elsevier, vol. 133(C), pages 572-583.
    7. Ren, Xiaoqing & Liu, Shulin & Yu, Xiaodong & Dong, Xia, 2021. "A method for state-of-charge estimation of lithium-ion batteries based on PSO-LSTM," Energy, Elsevier, vol. 234(C).
    8. Zou, Songchun & Zhao, Wanzhong, 2020. "Energy optimization strategy of vehicle DCS system based on APSO algorithm," Energy, Elsevier, vol. 208(C).
    9. Li, Yanwen & Wang, Chao & Gong, Jinfeng, 2017. "A multi-model probability SOC fusion estimation approach using an improved adaptive unscented Kalman filter technique," Energy, Elsevier, vol. 141(C), pages 1402-1415.
    10. Wang, Yujie & Zhang, Chenbin & Chen, Zonghai, 2015. "A method for state-of-charge estimation of Li-ion batteries based on multi-model switching strategy," Applied Energy, Elsevier, vol. 137(C), pages 427-434.
    11. Li, Changlong & Cui, Naxin & Wang, Chunyu & Zhang, Chenghui, 2021. "Reduced-order electrochemical model for lithium-ion battery with domain decomposition and polynomial approximation methods," Energy, Elsevier, vol. 221(C).
    12. Xi, Zhimin & Wang, Rui & Fu, Yuhong & Mi, Chris, 2022. "Accurate and reliable state of charge estimation of lithium ion batteries using time-delayed recurrent neural networks through the identification of overexcited neurons," Applied Energy, Elsevier, vol. 305(C).
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