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Improved multi-scale cosine control whale optimization–error feedforward double Kalman filtering for the online state of charge and state of health co-estimation of lithium-ion batteries

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Abstract

Lithium-ion batteries play a pivotal role in diverse applications, necessitating the precise estimation of their parameters for safe and efficient energy utilization. In the context of ternary lithium-ion battery research, this study introduces the cosine control whale optimization (CCWO) method to real-time optimization of the forgetting factor. Concurrently, an innovative multi-scale error feedforward extended double Kalman filter (EFDKF) algorithm, featuring model error feedforward, is presented for dynamic optimization of the state noise covariance matrix. This approach diminishes reliance on the model while jointly estimating the state of charge (SOC) and state of health (SOH). The algorithm’s feasibility is validated under varied operational conditions, encompassing both normal and low temperatures. The maximum absolute errors of SOC and SOH estimation are 1.09% and 3.16% at normal temperature, and 3.46% and 4.96% at low temperature, respectively. The results affirm the algorithm’s enhanced precision in joint SOC and SOH estimation, heightened robustness, and superior convergence. This contribution introduces a novel methodology for lithium-ion battery state estimation.

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Data availability

The datasets used or analyzed during the current study are available from the corresponding author upon reasonable request.

References

  1. Zhang R, Xia B, Li B, Cao L, Lai Y, Zheng W et al (2018) State of the art of lithium-ion battery SOC estimation for electrical vehicles. Energies 11:1820. https://doi.org/10.3390/en11071820

    Article  CAS  Google Scholar 

  2. Worku BE, Zheng S, Wang B (2022) Review of low-temperature lithium-ion battery progress: new battery system design imperative. Int J Energy Res 46:14609–14626. https://doi.org/10.1002/er.8194

    Article  CAS  Google Scholar 

  3. Divakaran AM, Minakshi M, Bahri PA, Paul S, Kumari P, Divakaran AM et al (2021) Rational design on materials for developing next generation lithium-ion secondary battery. Prog Solid State Chem 62:100298. https://doi.org/10.1016/j.progsolidstchem.2020.100298

    Article  CAS  Google Scholar 

  4. Li J, Zhao M, Dai C, Wang Z, Pecht M (2021) A mathematical method for open-circuit potential curve acquisition for lithium-ion batteries. J Electroanal Chem 895:115488. https://doi.org/10.1016/j.jelechem.2021.115488

    Article  CAS  Google Scholar 

  5. Chen C, Xiong R, Yang R, Li H (2022) A novel data-driven method for mining battery open-circuit voltage characterization. Green Energy Intell Transp 1:100001. https://doi.org/10.1016/j.geits.2022.100001

    Article  Google Scholar 

  6. Xiong X, Wang SL, Fernandez C, Yu CM, Zou CY, Jiang C (2020) A novel practical state of charge estimation method: an adaptive improved ampere-hour method based on composite correction factor. Int J Energy Res 44:11385–11404. https://doi.org/10.1002/er.5758

    Article  Google Scholar 

  7. Liu D, Wang S, Fan Y, Xia L, Qiu J (2022) A novel fuzzy-extended Kalman filter-ampere-hour (F-EKF-Ah) algorithm based on improved second-order PNGV model to estimate state of charge of lithium-ion batteries. Int J Circuit Theory Appl 50:3811–3826. https://doi.org/10.1002/cta.3386

    Article  Google Scholar 

  8. Zhang X, Hou J, Wang Z, Jiang Y (2022) Study of SOC estimation by the Ampere-hour integral method with capacity correction based on LSTM. Batteries 8:170. https://doi.org/10.3390/batteries8100170

    Article  CAS  Google Scholar 

  9. Gu T, Sheng J, Fan Q, Wang D (2022) The modified multi-innovation adaptive EKF algorithm for identifying battery SOC. Ionics 28:3877–3891. https://doi.org/10.1007/s11581-022-04603-6

    Article  CAS  Google Scholar 

  10. Zhang M, Wang S, Yang X, Xie Y, Liu K, Zhang C (2023) Improved backward smoothing—square root cubature kalman filtering and variable forgetting factor—recursive least square modeling methods for the high-precision state of charge estimation of lithium-ion batteries. J Electrochem Soc 170:030511. https://doi.org/10.1149/1945-7111/acb10b

    Article  CAS  Google Scholar 

  11. Feng L, Ding J, Han Y (2020) Improved sliding mode based EKF for the SOC estimation of lithium-ion batteries. Ionics 26:2875–2882. https://doi.org/10.1007/s11581-019-03368-9

    Article  CAS  Google Scholar 

  12. Hong J, Wang Z, Chen W, Wang L-Y, Qu C (2020) Online joint-prediction of multi-forward-step battery SOC using LSTM neural networks and multiple linear regression for real-world electric vehicles. J Energy Storage 30:101459. https://doi.org/10.1016/j.est.2020.101459

    Article  Google Scholar 

  13. Ren X, Liu S, Yu X, Dong X (2021) A method for state-of-charge estimation of lithium-ion batteries based on PSO-LSTM. Energy 234:121236. https://doi.org/10.1016/j.energy.2021.121236

    Article  Google Scholar 

  14. Wang S, Fan Y, Jin S, Takyi-Aninakwa P, Fernandez C (2023) Improved anti-noise adaptive long short-term memory neural network modeling for the robust remaining useful life prediction of lithium-ion batteries. Reliab Eng Syst Saf 230:108920. https://doi.org/10.1016/j.ress.2022.108920

    Article  Google Scholar 

  15. Xi C, Kaoru H, Dai Yaping JZ (2020) Estimation of SOC Based on LSTM-RNN and design of intelligent equalization charging system. J Adv Comput Intell Intell Inform 24:855–863. https://doi.org/10.20965/jaciii.2020.p0855

    Article  Google Scholar 

  16. Kaur K, Garg A, Cui X, Singh S, Panigrahi BK (2021) Deep learning networks for capacity estimation for monitoring SOH of Li-ion batteries for electric vehicles. Int J Energy Res 45:3113–3128

    Article  CAS  Google Scholar 

  17. Lee G, Kwon D, Lee C (2023) A convolutional neural network model for SOH estimation of Li-ion batteries with physical interpretability. Mech Syst Signal Process 188:110004

    Article  Google Scholar 

  18. Chen L, Lü Z, Lin W, Li J, Pan H (2018) A new state-of-health estimation method for lithium-ion batteries through the intrinsic relationship between ohmic internal resistance and capacity. Measurement 116:586–595

    Article  Google Scholar 

  19. Kong X, Zhang X, Lu N, Ma Y, Li Y (2021) Online smart meter measurement error estimation based on EKF and LMRLS method. IEEE Trans Smart Grid 12:4269–4279

    Article  Google Scholar 

  20. Dawei Q, Zixuan L, Fan Y, Luyan F, Mingyue Z, Haoxuan L (2022) State of charge estimation for the Vanadium Redox Flow Battery based on Extended Kalman filter using modified parameter identification. Energy Sources, Part A: Recovery, Utilization, Environ Eff 44:9747–9763

    Article  Google Scholar 

  21. Wang C, Wang S, Zhou J, Qiao J (2022) A novel BCRLS-BP-EKF method for the state of charge estimation of lithium-ion batteries. Int J Electrochem Sci 17:220431

    Article  CAS  Google Scholar 

  22. Chikkalkar SG, Kumar MN, Chidanandappa R (2022) Online State of Charge (SOC) estimation of Lithium-Ion battery using Improved Extended Kalman Filter. 2022 IEEE 2nd Mysore Sub Section International Conference (MysuruCon). IEEE, pp 1–7

    Google Scholar 

  23. Sun H, Wen X, Liu W, Wang Z, Liao Q (2022) State-of-health estimation of retired lithium-ion battery module aged at 1C-rate. J Energy Storage 50:104618. https://doi.org/10.1016/j.est.2022.104618

    Article  Google Scholar 

  24. Yang N, Song Z, Hofmann H, Sun J (2022) Robust State of Health estimation of lithium-ion batteries using convolutional neural network and random forest. J Energy Storage 48:103857. https://doi.org/10.1016/j.est.2021.103857

    Article  Google Scholar 

  25. Lin Z, Hu H, Liu W, Zhang Z, Zhang Y, Geng N et al (2023) State of health estimation of lithium-ion batteries based on remaining area capacity. J Energy Storage 63:107078. https://doi.org/10.1016/j.est.2023.107078

    Article  Google Scholar 

  26. Zhang S, Zhang X (2021) Joint estimation method for maximum available energy and state-of-energy of lithium-ion battery under various temperatures. J Power Sources 506:230132. https://doi.org/10.1016/j.jpowsour.2021.230132

    Article  CAS  Google Scholar 

  27. Lai X, Huang Y, Han X, Gu H, Zheng Y (2021) A novel method for state of energy estimation of lithium-ion batteries using particle filter and extended Kalman filter. J Energy Storage 43:103269. https://doi.org/10.1016/j.est.2021.103269

    Article  Google Scholar 

  28. Zhang S, Zhang X (2022) A novel low-complexity state-of-energy estimation method for series-connected lithium-ion battery pack based on “representative cell” selection and operating mode division. J Power Sources 518:230732. https://doi.org/10.1016/j.jpowsour.2021.230732

    Article  CAS  Google Scholar 

  29. Wang Y, Zhang C, Chen Z (2016) An adaptive remaining energy prediction approach for lithium-ion batteries in electric vehicles. J Power Sources 305:80–88. https://doi.org/10.1016/j.jpowsour.2015.11.087

    Article  CAS  Google Scholar 

  30. Wu T, Liu S, Wang Z, Huang Y (2022) SOC and SOH joint estimation of lithium-ion battery based on improved particle filter algorithm. J Electr Eng Technol 17:307–317

    Article  Google Scholar 

  31. Hu P, Tang W, Li C, Mak S-L, Li C, Lee C (2023) Joint State of Charge (SOC) and State of Health (SOH) estimation for lithium-ion batteries packs of electric vehicles based on NSSR-LSTM neural network. Energies 16:5313

    Article  CAS  Google Scholar 

  32. Wei J, Chen C (2021) A multi-timescale framework for state monitoring and lifetime prognosis of lithium-ion batteries. Energy 229:120684

    Article  CAS  Google Scholar 

  33. Guo R, Shen W (2021) A review of equivalent circuit model based online state of power estimation for lithium-ion batteries in electric vehicles. Vehicles 4:1–29. https://doi.org/10.3390/vehicles4010001

    Article  Google Scholar 

  34. Li Y, Vilathgamuwa M, Farrell T, Tran NT, Teague J (2019) A physics-based distributed-parameter equivalent circuit model for lithium-ion batteries. Electrochim Acta 299:451–469. https://doi.org/10.1016/j.electacta.2018.12.167

    Article  CAS  Google Scholar 

  35. Geng Z, Wang S, Lacey MJ, Brandell D, Thiringer T (2021) Bridging physics-based and equivalent circuit models for lithium-ion batteries. Electrochim Acta 372:137829. https://doi.org/10.1016/j.electacta.2021.137829

    Article  CAS  Google Scholar 

  36. Tran M-K, DaCosta A, Mevawalla A, Panchal S, Fowler M (2021) Comparative study of equivalent circuit models performance in four common lithium-ion batteries: LFP, NMC, LMO. NCA Batteries 7:51. https://doi.org/10.3390/batteries7030051

    Article  CAS  Google Scholar 

  37. Tran M-K, Mevawala A, Panchal S, Raahemifar K, Fowler M, Fraser R (2020) Effect of integrating the hysteresis component to the equivalent circuit model of Lithium-ion battery for dynamic and non-dynamic applications. J Energy Storage 32:101785. https://doi.org/10.1016/j.est.2020.101785

    Article  Google Scholar 

  38. Luo J, Shi B (2019) A hybrid whale optimization algorithm based on modified differential evolution for global optimization problems. Appl Intell 49:1982–2000. https://doi.org/10.1007/s10489-018-1362-4

    Article  Google Scholar 

  39. Nadimi-Shahraki MH, Zamani H, Asghari Varzaneh Z, Mirjalili S (2023) A systematic review of the whale optimization algorithm: theoretical foundation, improvements, and hybridizations. Arch Computat Methods Eng 30:4113–4159. https://doi.org/10.1007/s11831-023-09928-7

  40. Rana N, Latiff MSA, SiM A, Chiroma H (2020) Whale optimization algorithm: a systematic review of contemporary applications, modifications and developments. Neural Comput Appl 32:16245–16277. https://doi.org/10.1007/s00521-020-04849-z

    Article  Google Scholar 

  41. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008

    Article  Google Scholar 

  42. Chakraborty S, Saha AK, Sharma S, Mirjalili S, Chakraborty R (2021) A novel enhanced whale optimization algorithm for global optimization. Comput Ind Eng 153:107086. https://doi.org/10.1016/j.cie.2020.107086

    Article  Google Scholar 

  43. Ding H, Wu Z, Zhao L (2020) Whale optimization algorithm based on nonlinear convergence factor and chaotic inertial weight. Concurr Computn: Pract Experience 32:e5949. https://doi.org/10.1002/cpe.5949

    Article  Google Scholar 

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Funding

The work is supported by the National Natural Science Foundation of China (Nos. 62173281), and the Natural Science Foundation of Sichuan Province (2023NSFSC1436).

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Contributions

J.J.Tao: conceptualization, methodology, software, investigation, formal analysis, writing—original Draft; S.L.Wang: data curation; W.Cao: visualization, investigation; M.Y.Zhang: resources, supervision; C.Wang: validation.

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Correspondence to Shunli Wang.

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Tao, J., Wang, S., Cao, W. et al. Improved multi-scale cosine control whale optimization–error feedforward double Kalman filtering for the online state of charge and state of health co-estimation of lithium-ion batteries. Ionics 30, 2039–2053 (2024). https://doi.org/10.1007/s11581-024-05428-1

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