IDEAS home Printed from https://ideas.repec.org/a/eee/energy/v322y2025ics0360544225011405.html
   My bibliography  Save this article

Concurrent estimation of lithium-ion battery charge and energy states by fractional-order model and multi-innovation adaptive cubature Kalman filter

Author

Listed:
  • Wang, Chao
  • Wang, Xin
  • Yang, Mingjian
  • Li, Jiale
  • Qian, Feng
  • Zhang, Zunhua
  • Zhou, Mengni
  • Guo, Xiaofeng
  • Wang, Kai

Abstract

To address the difficulties of the joint SOC and SOE estimation methods in achieving high accuracy and low complexity, a fractional-order multi-innovation adaptive square root cubature Kalman filter (FMASR-CKF) is proposed for the first time in this study. Firstly, a second-order fractional-order model (FOM) is established, and an improved dynamic genetic particle swarm optimization (DGPSO) algorithm is proposed for parameter identification. Then, the theory of multiple innovations is introduced into CKF to realize multi-step prediction based on historical data, thus enhancing the accuracy and robustness of the algorithm. At the same time, a joint estimation framework is established to correct and accurately estimate the SOE in real time through a simple relational equation. Validation under a variety of complex operating conditions shows that the mean absolute error (MAE) of the FMASR-CKF estimates of SOC and SOE is less than 0.5 % and 0.7 %, respectively. At 25 °C Federal Urban Driving Schedule (FUDS), the root mean square error (RMSE) for the SOC and SOE are 0.35 % and 0.62 %, respectively. Therefore, the proposed method exhibits high accuracy and robustness under a variety of real-world conditions with low complexity, providing an effective reference for the practical application of BMS.

Suggested Citation

  • Wang, Chao & Wang, Xin & Yang, Mingjian & Li, Jiale & Qian, Feng & Zhang, Zunhua & Zhou, Mengni & Guo, Xiaofeng & Wang, Kai, 2025. "Concurrent estimation of lithium-ion battery charge and energy states by fractional-order model and multi-innovation adaptive cubature Kalman filter," Energy, Elsevier, vol. 322(C).
    • Handle: RePEc:eee:energy:v:322:y:2025:i:c:s0360544225011405
    DOI: 10.1016/j.energy.2025.135498
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0360544225011405
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.energy.2025.135498?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Zhenhua Cui & Jiyong Dai & Jianrui Sun & Dezhi Li & Licheng Wang & Kai Wang & A. M. Bastos Pereira, 2022. "Hybrid Methods Using Neural Network and Kalman Filter for the State of Charge Estimation of Lithium-Ion Battery," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-11, May.
    2. Chen, Liping & Wu, Xiaobo & Lopes, António M. & Yin, Lisheng & Li, Penghua, 2022. "Adaptive state-of-charge estimation of lithium-ion batteries based on square-root unscented Kalman filter," Energy, Elsevier, vol. 252(C).
    3. Zhang, Xinghui & Li, Zhao & Luo, Lingai & Fan, Yilin & Du, Zhengyu, 2022. "A review on thermal management of lithium-ion batteries for electric vehicles," Energy, Elsevier, vol. 238(PA).
    4. Shrivastava, Prashant & Soon, Tey Kok & Idris, Mohd Yamani Idna Bin & Mekhilef, Saad, 2019. "Overview of model-based online state-of-charge estimation using Kalman filter family for lithium-ion batteries," Renewable and Sustainable Energy Reviews, Elsevier, vol. 113(C), pages 1-1.
    5. Bizhong Xia & Zizhou Lao & Ruifeng Zhang & Yong Tian & Guanghao Chen & Zhen Sun & Wei Wang & Wei Sun & Yongzhi Lai & Mingwang Wang & Huawen Wang, 2017. "Online Parameter Identification and State of Charge Estimation of Lithium-Ion Batteries Based on Forgetting Factor Recursive Least Squares and Nonlinear Kalman Filter," Energies, MDPI, vol. 11(1), pages 1-23, December.
    6. Zhu, Qiao & Xu, Mengen & Liu, Weiqun & Zheng, Mengqian, 2019. "A state of charge estimation method for lithium-ion batteries based on fractional order adaptive extended kalman filter," Energy, Elsevier, vol. 187(C).
    7. Zheng, Linfeng & Zhu, Jianguo & Wang, Guoxiu & He, Tingting & Wei, Yiying, 2016. "Novel methods for estimating lithium-ion battery state of energy and maximum available energy," Applied Energy, Elsevier, vol. 178(C), pages 1-8.
    8. Bizhong Xia & Haiqing Wang & Mingwang Wang & Wei Sun & Zhihui Xu & Yongzhi Lai, 2015. "A New Method for State of Charge Estimation of Lithium-Ion Battery Based on Strong Tracking Cubature Kalman Filter," Energies, MDPI, vol. 8(12), pages 1-15, November.
    9. Peng, Jiankun & Luo, Jiayi & He, Hongwen & Lu, Bing, 2019. "An improved state of charge estimation method based on cubature Kalman filter for lithium-ion batteries," Applied Energy, Elsevier, vol. 253(C), pages 1-1.
    10. Zhang, Jie & Xiao, Bo & Niu, Geng & Xie, Xuanzhi & Wu, Saixiang, 2024. "Joint estimation of state-of-charge and state-of-power for hybrid supercapacitors using fractional-order adaptive unscented Kalman filter," Energy, Elsevier, vol. 294(C).
    11. Hu, Minghui & Li, Yunxiao & Li, Shuxian & Fu, Chunyun & Qin, Datong & Li, Zonghua, 2018. "Lithium-ion battery modeling and parameter identification based on fractional theory," Energy, Elsevier, vol. 165(PB), pages 153-163.
    12. Bizhong Xia & Haiqing Wang & Yong Tian & Mingwang Wang & Wei Sun & Zhihui Xu, 2015. "State of Charge Estimation of Lithium-Ion Batteries Using an Adaptive Cubature Kalman Filter," Energies, MDPI, vol. 8(6), pages 1-21, June.
    13. Xia, Bizhong & Chen, Chaoren & Tian, Yong & Wang, Mingwang & Sun, Wei & Xu, Zhihui, 2015. "State of charge estimation of lithium-ion batteries based on an improved parameter identification method," Energy, Elsevier, vol. 90(P2), pages 1426-1434.
    14. Chen, Lin & Yu, Wentao & Cheng, Guoyang & Wang, Jierui, 2023. "State-of-charge estimation of lithium-ion batteries based on fractional-order modeling and adaptive square-root cubature Kalman filter," Energy, Elsevier, vol. 271(C).
    15. Chen, Lei & Wang, Shunli & Jiang, Hong & Fernandez, Carlos, 2024. "A multi-time-scale framework for state of energy and maximum available energy of lithium-ion battery under a wide operating temperature range," Applied Energy, Elsevier, vol. 355(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Maheshwari, A. & Nageswari, S., 2022. "Real-time state of charge estimation for electric vehicle power batteries using optimized filter," Energy, Elsevier, vol. 254(PB).
    2. Wang, Yujie & Tian, Jiaqiang & Sun, Zhendong & Wang, Li & Xu, Ruilong & Li, Mince & Chen, Zonghai, 2020. "A comprehensive review of battery modeling and state estimation approaches for advanced battery management systems," Renewable and Sustainable Energy Reviews, Elsevier, vol. 131(C).
    3. Chen, Lin & Yu, Wentao & Cheng, Guoyang & Wang, Jierui, 2023. "State-of-charge estimation of lithium-ion batteries based on fractional-order modeling and adaptive square-root cubature Kalman filter," Energy, Elsevier, vol. 271(C).
    4. 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.
    5. Guanghai Zhu & Jianbin Lin & Qingwu Liu & Hongwen He, 2019. "Research on the Energy-Saving Strategy of Path Planning for Electric Vehicles Considering Traffic Information," Energies, MDPI, vol. 12(19), pages 1-14, September.
    6. Luc Vivien Assiene Mouodo & Petros J. Axaopoulos, 2025. "Optimization and Estimation of the State of Charge of Lithium-Ion Batteries for Electric Vehicles," Energies, MDPI, vol. 18(13), pages 1-25, June.
    7. Chen, Liping & Wu, Xiaobo & Lopes, António M. & Yin, Lisheng & Li, Penghua, 2022. "Adaptive state-of-charge estimation of lithium-ion batteries based on square-root unscented Kalman filter," Energy, Elsevier, vol. 252(C).
    8. Chen, Zheng & Zhao, Hongqian & Shu, Xing & Zhang, Yuanjian & Shen, Jiangwei & Liu, Yonggang, 2021. "Synthetic state of charge estimation for lithium-ion batteries based on long short-term memory network modeling and adaptive H-Infinity filter," Energy, Elsevier, vol. 228(C).
    9. Wan, Sicheng & Yang, Haojing & Lin, Jinwen & Li, Junhui & Wang, Yibo & Chen, Xinman, 2024. "Improved whale optimization algorithm towards precise state-of-charge estimation of lithium-ion batteries via optimizing LSTM," Energy, Elsevier, vol. 310(C).
    10. Bizhong Xia & Zhen Sun & Ruifeng Zhang & Deyu Cui & Zizhou Lao & Wei Wang & Wei Sun & Yongzhi Lai & Mingwang Wang, 2017. "A Comparative Study of Three Improved Algorithms Based on Particle Filter Algorithms in SOC Estimation of Lithium Ion Batteries," Energies, MDPI, vol. 10(8), pages 1-14, August.
    11. Xia, Bizhong & Cui, Deyu & Sun, Zhen & Lao, Zizhou & Zhang, Ruifeng & Wang, Wei & Sun, Wei & Lai, Yongzhi & Wang, Mingwang, 2018. "State of charge estimation of lithium-ion batteries using optimized Levenberg-Marquardt wavelet neural network," Energy, Elsevier, vol. 153(C), pages 694-705.
    12. Bizhong Xia & Zhen Sun & Ruifeng Zhang & Zizhou Lao, 2017. "A Cubature Particle Filter Algorithm to Estimate the State of the Charge of Lithium-Ion Batteries Based on a Second-Order Equivalent Circuit Model," Energies, MDPI, vol. 10(4), pages 1-15, April.
    13. Tian, Yong & Lai, Rucong & Li, Xiaoyu & Xiang, Lijuan & Tian, Jindong, 2020. "A combined method for state-of-charge estimation for lithium-ion batteries using a long short-term memory network and an adaptive cubature Kalman filter," Applied Energy, Elsevier, vol. 265(C).
    14. Lai, Xin & Huang, Yunfeng & Gu, Huanghui & Han, Xuebing & Feng, Xuning & Dai, Haifeng & Zheng, Yuejiu & Ouyang, Minggao, 2022. "Remaining discharge energy estimation for lithium-ion batteries based on future load prediction considering temperature and ageing effects," Energy, Elsevier, vol. 238(PA).
    15. He, Lin & Wang, Yangyang & Wei, Yujiang & Wang, Mingwei & Hu, Xiaosong & Shi, Qin, 2022. "An adaptive central difference Kalman filter approach for state of charge estimation by fractional order model of lithium-ion battery," Energy, Elsevier, vol. 244(PA).
    16. Qian, Wei & Li, Wan & Guo, Xiangwei & Wang, Haoyu, 2024. "A switching gain adaptive sliding mode observer for SoC estimation of lithium-ion battery," Energy, Elsevier, vol. 292(C).
    17. Zhao, Xinze & Sun, Bingxiang & Zhang, Weige & He, Xitian & Ma, Shichang & Zhang, Junwei & Liu, Xiaopeng, 2024. "Error theory study on EKF-based SOC and effective error estimation strategy for Li-ion batteries," Applied Energy, Elsevier, vol. 353(PA).
    18. Bizhong Xia & Rui Huang & Zizhou Lao & Ruifeng Zhang & Yongzhi Lai & Weiwei Zheng & Huawen Wang & Wei Wang & Mingwang Wang, 2018. "Online Parameter Identification of Lithium-Ion Batteries Using a Novel Multiple Forgetting Factor Recursive Least Square Algorithm," Energies, MDPI, vol. 11(11), pages 1-19, November.
    19. Li, Yanwen & Wang, Chao & Gong, Jinfeng, 2016. "A combination Kalman filter approach for State of Charge estimation of lithium-ion battery considering model uncertainty," Energy, Elsevier, vol. 109(C), pages 933-946.
    20. Fan Zhang & Lele Yin & Jianqiang Kang, 2021. "Enhancing Stability and Robustness of State-of-Charge Estimation for Lithium-Ion Batteries by Using Improved Adaptive Kalman Filter Algorithms," Energies, MDPI, vol. 14(19), pages 1-18, October.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:energy:v:322:y:2025:i:c:s0360544225011405. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/energy .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.