IDEAS home Printed from https://ideas.repec.org/a/eee/appene/v377y2025ipas030626192401818x.html
   My bibliography  Save this article

State of charge estimation for LiFePO4 batteries joint by PID observer and improved EKF in various OCV ranges

Author

Listed:
  • Peng, Simin
  • Zhang, Daohan
  • Dai, Guohong
  • Wang, Lin
  • Jiang, Yuxia
  • Zhou, Feng

Abstract

LiFePO4 batteries are increasingly utilized in electric vehicles due to their superior safety. Accurate state estimation is the basis for the safe and reliable application of LiFePO4 batteries. However, the flat voltage characteristics of LiFePO4 batteries lead to state estimation closed-loop correction as its inherent contradiction. To address this challenge, a model-based SOC estimation method combining proportional-integral-differential (PID) observer and improved extended Kalman filter (EKF) is developed according to different open-circuit-voltage (OCV) ranges, specific processes include: First, an exponentially weighted moving average algorithm with a temperature compensation factor is presented to compensate for the errors in the identified OCV. Secondly, the combination of the PID observer and EKF is chosen adaptively to update SOC within distinct OCV ranges, differentiated by the identified OCV. To achieve optimization of the PID parameters and temperature compensation factors across varying temperatures, an enhanced whale optimization algorithm is developed. To validate the developed method, a series of experiments are performed across a range of temperatures and with multiple driving profiles. The results show that the developed method not only guarantees maximum absolute error of <3 %, but also can converge quickly in the early stage.

Suggested Citation

  • Peng, Simin & Zhang, Daohan & Dai, Guohong & Wang, Lin & Jiang, Yuxia & Zhou, Feng, 2025. "State of charge estimation for LiFePO4 batteries joint by PID observer and improved EKF in various OCV ranges," Applied Energy, Elsevier, vol. 377(PA).
    • Handle: RePEc:eee:appene:v:377:y:2025:i:pa:s030626192401818x
    DOI: 10.1016/j.apenergy.2024.124435
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030626192401818X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.apenergy.2024.124435?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. Zheng, Linfeng & Zhu, Jianguo & Wang, Guoxiu & Lu, Dylan Dah-Chuan & He, Tingting, 2018. "Differential voltage analysis based state of charge estimation methods for lithium-ion batteries using extended Kalman filter and particle filter," Energy, Elsevier, vol. 158(C), pages 1028-1037.
    2. Peng, Simin & Miao, Yifan & Xiong, Rui & Bai, Jiawei & Cheng, Mengzeng & Pecht, Michael, 2024. "State of charge estimation for a parallel battery pack jointly by fuzzy-PI model regulator and adaptive unscented Kalman filter," Applied Energy, Elsevier, vol. 360(C).
    3. Peng, Simin & Sun, Yunxiang & Liu, Dandan & Yu, Quanqing & Kan, Jiarong & Pecht, Michael, 2023. "State of health estimation of lithium-ion batteries based on multi-health features extraction and improved long short-term memory neural network," Energy, Elsevier, vol. 282(C).
    4. Sun, Daoming & Yu, Xiaoli & Wang, Chongming & Zhang, Cheng & Huang, Rui & Zhou, Quan & Amietszajew, Taz & Bhagat, Rohit, 2021. "State of charge estimation for lithium-ion battery based on an Intelligent Adaptive Extended Kalman Filter with improved noise estimator," Energy, Elsevier, vol. 214(C).
    5. Ma, Wentao & Guo, Peng & Wang, Xiaofei & Zhang, Zhiyu & Peng, Siyuan & Chen, Badong, 2022. "Robust state of charge estimation for Li-ion batteries based on cubature kalman filter with generalized maximum correntropy criterion," Energy, Elsevier, vol. 260(C).
    6. 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).
    7. Xiong, Rui & Yu, Quanqing & Wang, Le Yi & Lin, Cheng, 2017. "A novel method to obtain the open circuit voltage for the state of charge of lithium ion batteries in electric vehicles by using H infinity filter," Applied Energy, Elsevier, vol. 207(C), pages 346-353.
    8. Tian, Yong & Huang, Zhijia & Tian, Jindong & Li, Xiaoyu, 2022. "State of charge estimation of lithium-ion batteries based on cubature Kalman filters with different matrix decomposition strategies," Energy, Elsevier, vol. 238(PC).
    9. Peng, Simin & Zhu, Junchao & Wu, Tiezhou & Yuan, Caichenran & Cang, Junjie & Zhang, Kai & Pecht, Michael, 2024. "Prediction of wind and PV power by fusing the multi-stage feature extraction and a PSO-BiLSTM model," Energy, Elsevier, vol. 298(C).
    10. Hu, Lin & Hu, Xiaosong & Che, Yunhong & Feng, Fei & Lin, Xianke & Zhang, Zhiyong, 2020. "Reliable state of charge estimation of battery packs using fuzzy adaptive federated filtering," Applied Energy, Elsevier, vol. 262(C).
    11. Yang, Xiaolong & Chen, Yongji & Li, Bin & Luo, Dong, 2020. "Battery states online estimation based on exponential decay particle swarm optimization and proportional-integral observer with a hybrid battery model," Energy, Elsevier, vol. 191(C).
    12. Xiong, Rui & Duan, Yanzhou & Zhang, Kaixuan & Lin, Da & Tian, Jinpeng & Chen, Cheng, 2023. "State-of-charge estimation for onboard LiFePO4 batteries with adaptive state update in specific open-circuit-voltage ranges," Applied Energy, Elsevier, vol. 349(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sun, Jing & Wang, Haitao, 2025. "State of health estimation for lithium-ion batteries based on optimal feature subset algorithm," Energy, Elsevier, vol. 322(C).
    2. Tao, Junjie & Wang, Shunli & Cao, Wen & Cui, Yixiu & Fernandez, Carlos & Guerrero, Josep M., 2024. "Innovative multiscale fusion – Antinoise extended long short-term memory neural network modeling for high precision state of health estimation of lithium-ion batteries," Energy, Elsevier, vol. 312(C).
    3. Peng, Simin & Chen, Shengdong & Liu, Yong & Yu, Quanqing & Kan, Jiarong & Li, Rui, 2025. "State of power prediction joint fisher optimal segmentation and PO-BP neural network for a parallel battery pack considering cell inconsistency," Applied Energy, Elsevier, vol. 381(C).
    4. Li, Yang & Gao, Guoqiang & Chen, Kui & He, Shuhang & Liu, Kai & Xin, Dongli & Luo, Yang & Long, Zhou & Wu, Guangning, 2025. "State-of-health prediction of lithium-ion batteries using feature fusion and a hybrid neural network model," Energy, Elsevier, vol. 319(C).
    5. Meng-Xiang Yan & Zhi-Hui Deng & Lianfeng Lai & Yong-Hong Xu & Liang Tong & Hong-Guang Zhang & Yi-Yang Li & Ming-Hui Gong & Guo-Ju Liu, 2025. "A Sustainable SOH Prediction Model for Lithium-Ion Batteries Based on CPO-ELM-ABKDE with Uncertainty Quantification," Sustainability, MDPI, vol. 17(11), pages 1-28, June.
    6. Mu, Guixiang & Wei, Qingguo & Xu, Yonghong & Li, Jian & Zhang, Hongguang & Yang, Fubin & Zhang, Jian & Li, Qi, 2025. "State of health estimation of lithium-ion batteries based on feature optimization and data-driven models," Energy, Elsevier, vol. 316(C).
    7. Ni, Yulong & Song, Kai & Pei, Lei & Li, Xiaoyu & Wang, Tiansi & Zhang, He & Zhu, Chunbo & Xu, Jianing, 2025. "State-of-health estimation and knee point identification of lithium-ion battery based on data-driven and mechanism model," Applied Energy, Elsevier, vol. 385(C).
    8. Zhao, Haichuan & Meng, Jinhao & Peng, Qiao, 2025. "Early perception of Lithium-ion battery degradation trajectory with graphical features and deep learning," Applied Energy, Elsevier, vol. 381(C).
    9. Tao, Junjie & Wang, Shunli & Cao, Wen & Fernandez, Carlos & Blaabjerg, Frede & Cheng, Liangwei, 2025. "An innovative multitask learning - Long short-term memory neural network for the online anti-aging state of charge estimation of lithium-ion batteries adaptive to varying temperature and current condi," Energy, Elsevier, vol. 314(C).
    10. Wang, Zhenxi & Ma, Yan & Gao, Jinwu & Chen, Hong, 2025. "Remaining useful life prediction for solid-state lithium batteries based on spatial–temporal relations and neuronal ODE-assisted KAN," Reliability Engineering and System Safety, Elsevier, vol. 260(C).
    11. Peng, Simin & Wang, Yujian & Tang, Aihua & Jiang, Yuxia & Kan, Jiarong & Pecht, Michael, 2025. "State of health estimation joint improved grey wolf optimization algorithm and LSTM using partial discharging health features for lithium-ion batteries," Energy, Elsevier, vol. 315(C).

    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. Xiong, Rui & Duan, Yanzhou & Zhang, Kaixuan & Lin, Da & Tian, Jinpeng & Chen, Cheng, 2023. "State-of-charge estimation for onboard LiFePO4 batteries with adaptive state update in specific open-circuit-voltage ranges," Applied Energy, Elsevier, vol. 349(C).
    2. Peng, Simin & Wang, Yujian & Tang, Aihua & Jiang, Yuxia & Kan, Jiarong & Pecht, Michael, 2025. "State of health estimation joint improved grey wolf optimization algorithm and LSTM using partial discharging health features for lithium-ion batteries," Energy, Elsevier, vol. 315(C).
    3. Wang, Ya-Xiong & Chen, Zhenhang & Zhang, Wei, 2022. "Lithium-ion battery state-of-charge estimation for small target sample sets using the improved GRU-based transfer learning," Energy, Elsevier, vol. 244(PB).
    4. Shu, Xiong & Li, Yongjing & Wei, Kexiang & Yang, Wenxian & Yang, Bowen & Zhang, Ming, 2025. "Research on the output characteristics and SOC estimation method of lithium-ion batteries over a wide range of operating temperature conditions," Energy, Elsevier, vol. 317(C).
    5. Zhu, Yunlong & Dong, Zhe & Cheng, Zhonghua & Huang, Xiaojin & Dong, Yujie & Zhang, Zuoyi, 2023. "Neural network extended state-observer for energy system monitoring," Energy, Elsevier, vol. 263(PA).
    6. Chen, Yuan & Duan, Wenxian & Huang, Xiaohe & Wang, Shunli, 2024. "Multi-output fusion SOC and SOE estimation algorithm based on deep network migration," Energy, Elsevier, vol. 308(C).
    7. 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).
    8. Mu, Guixiang & Wei, Qingguo & Xu, Yonghong & Li, Jian & Zhang, Hongguang & Yang, Fubin & Zhang, Jian & Li, Qi, 2025. "State of health estimation of lithium-ion batteries based on feature optimization and data-driven models," Energy, Elsevier, vol. 316(C).
    9. 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).
    10. Xiong, Wei & Xie, Fang & Xu, Gang & Li, Yumei & Li, Ben & Mo, Yimin & Ma, Fei & Wei, Keke, 2023. "Co-estimation of the model parameter and state of charge for retired lithium-ion batteries over a wide temperature range and battery degradation scope," Renewable Energy, Elsevier, vol. 218(C).
    11. Enguang Hou & Heyan Song & Zhen Wang & Jingshu Zhu & Jiarui Tang & Gang Shen & Jiangang Wang, 2024. "State of energy estimation of lithium-ion battery based on long short-term memory optimization Adaptive Cubature Kalman filter," PLOS ONE, Public Library of Science, vol. 19(7), pages 1-19, July.
    12. Liu, Zheng & Zhao, Zhenhua & Qiu, Yuan & Jing, Benqin & Yang, Chunshan & Wu, Huifeng, 2023. "Enhanced state of charge estimation for Li-ion batteries through adaptive maximum correntropy Kalman filter with open circuit voltage correction," Energy, Elsevier, vol. 283(C).
    13. Tang, Zhongyi & Zhang, Zhirong & Shen, Xianxian & Zhong, Anjie & Nazir, Muhammad Shahzad & Peng, Tian & Zhang, Chu, 2024. "Evolutionary hybrid deep learning based on feature engineering and deep projection encoded echo-state network for lithium batteries state of health estimation," Energy, Elsevier, vol. 313(C).
    14. Simone Barcellona & Lorenzo Codecasa & Silvia Colnago & Luigi Piegari, 2023. "Calendar Aging Effect on the Open Circuit Voltage of Lithium-Ion Battery," Energies, MDPI, vol. 16(13), pages 1-16, June.
    15. Chu, Yunkun & Cui, Naxin & Liu, Kailong, 2025. "Nonlinear modeling and SOC estimation of lithium-ion batteries based on block-oriented structures," Energy, Elsevier, vol. 315(C).
    16. Xin Lai & Ming Yuan & Xiaopeng Tang & Yi Yao & Jiahui Weng & Furong Gao & Weiguo Ma & Yuejiu Zheng, 2022. "Co-Estimation of State-of-Charge and State-of-Health for Lithium-Ion Batteries Considering Temperature and Ageing," Energies, MDPI, vol. 15(19), pages 1-20, October.
    17. Peng, Simin & Zhu, Junchao & Wu, Tiezhou & Yuan, Caichenran & Cang, Junjie & Zhang, Kai & Pecht, Michael, 2024. "Prediction of wind and PV power by fusing the multi-stage feature extraction and a PSO-BiLSTM model," Energy, Elsevier, vol. 298(C).
    18. Fan, Kesen & Wan, Yiming & Wang, Zhuo & Jiang, Kai, 2023. "Time-efficient identification of lithium-ion battery temperature-dependent OCV-SOC curve using multi-output Gaussian process," Energy, Elsevier, vol. 268(C).
    19. Li, Kangqun & Zhou, Fei & Chen, Xing & Yang, Wen & Shen, Junjie & Song, Zebin, 2023. "State-of-charge estimation combination algorithm for lithium-ion batteries with Frobenius-norm-based QR decomposition modified adaptive cubature Kalman filter and H-infinity filter based on electro-th," Energy, Elsevier, vol. 263(PC).
    20. Yang, Mao & Li, Xiangyu & Fan, Fulin & Wang, Bo & Su, Xin & Ma, Chenglian, 2024. "Two-stage day-ahead multi-step prediction of wind power considering time-series information interaction," Energy, Elsevier, vol. 312(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    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:appene:v:377:y:2025:i:pa:s030626192401818x. 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.elsevier.com/wps/find/journaldescription.cws_home/405891/description#description .

    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.