Skip to main content
Log in

State of charge estimation by square root cubature particle filter approach with fractional order model of lithium-ion battery

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

In this paper, a square root cubature particle filter approach was designed to estimate the state of charge of lithium-ion battery, which not only enhanced the numerical stability and guaranteed positive definiteness of the state covariance, but also increased accuracy and decreased computation quantity. Due to the fractional characteristics of the battery capacitance, a fractional order model was used to formulate the lithium-ion battery. Considering the high accuracy and easy convergence, a particle swarm optimization algorithm was utilized to identify the model parameters. The above-mentioned approach was modelled and translated into C code, which was downloaded into battery control unit of battery management system for experimental validation. Two kinds of dynamic cycles were utilized to validate the proposed approach at different temperatures, where both unscent Kalman filter and cubature Kalman filter were compared with the proposed approach. Experimental results indicate that the proposed approach has better accuracy and robustness, and fractional order model is more accurate than integer order model. Therefore, the square root cubature particle filter with fractional order model of lithium-ion battery is a good candidate to estimate the state of charge.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Wang H W, Zhang X B, Ouyang M G. Energy and environmental life-cycle assessment of passenger car electrification based on Beijing driving patterns. Sci China Tech Sci, 2015, 58: 659–668

    Article  Google Scholar 

  2. Zhang X, Liang Y, Yu E, et al. Review of electric vehicle policies in China: Content summary and effect analysis. Renew Sustain Energy Rev, 2017, 70: 698–714

    Article  Google Scholar 

  3. He L, Hu M K, Wei Y J, et al. State of charge estimation by finite difference extended Kalman filter with HPPC parameters identification. Sci China Tech Sci, 2020, 63: 410–421

    Article  Google Scholar 

  4. Xiong R, Cao J, Yu Q, et al. Critical review on the battery state of charge estimation methods for electric vehicles. IEEE Access, 2017, 6: 1832–1843

    Article  Google Scholar 

  5. Hannan M A, Lipu M S H, Hussain A, et al. A review of lithium-ion battery state of charge estimation and management system in electric vehicle applications: Challenges and recommendations. Renew Sustain Energy Rev, 2017, 78: 834–854

    Article  Google Scholar 

  6. Peng S, Zhu X, Xing Y, et al. An adaptive state of charge estimation approach for lithium-ion series-connected battery system. J Power Sources, 2018, 392: 48–59

    Article  Google Scholar 

  7. Gao Y, Zhu C, Zhang X, et al. Implementation and evaluation of a practical electrochemical-thermal model of lithium-ion batteries for EV battery management system. Energy, 2021, 221: 119688

    Article  Google Scholar 

  8. Lipu M H, Hannan M A, Karim T F, et al. Intelligent algorithms and control strategies for battery management system in electric vehicles: Progress, challenges and future outlook. J Cleaner Prod, 2021, 292: 126044

    Article  Google Scholar 

  9. Cheng K W E, Divakar B P, Wu H, et al. Battery-management system (BMS) and SOC development for electrical vehicles. IEEE Trans Veh Technol, 2010, 60: 76–88

    Article  Google Scholar 

  10. Lee S, Kim J, Lee J, et al. State-of-charge and capacity estimation of lithium-ion battery using a new open-circuit voltage versus state-of-charge. J Power Sources, 2008, 185: 1367–1373

    Article  Google Scholar 

  11. Yang N, Zhang X, Li G. State of charge estimation for pulse discharge of a LiFePO4 battery by a revised Ah counting. Electrochim Acta, 2015, 151: 63–71

    Article  Google Scholar 

  12. Hossain Lipu M S, Hannan M A, Hussain A, et al. Data-driven state of charge estimation of lithium-ion batteries: Algorithms, implementation factors, limitations and future trends. J Cleaner Production, 2020, 277: 124110

    Article  Google Scholar 

  13. Zhu R, Duan B, Zhang J, et al. Co-estimation of model parameters and state-of-charge for lithium-ion batteries with recursive restricted total least squares and unscented Kalman filter. Appl Energy, 2020, 277: 115494

    Article  Google Scholar 

  14. Xia B, Cui D, Sun Z, et al. State of charge estimation of lithium-ion batteries using optimized Levenberg-Marquardt wavelet neural network. Energy, 2018, 153: 694–705

    Article  Google Scholar 

  15. Alvarez Anton J C, Garcia Nieto P J, Blanco Viejo C, et al. Support vector machines used to estimate the battery state of charge. IEEE Trans Power Electron, 2013, 28: 5919–5926

    Article  Google Scholar 

  16. Deng Z, Hu X, Lin X, et al. Data-driven state of charge estimation for lithium-ion battery packs based on Gaussian process regression. Energy, 2020, 205: 118000

    Article  Google Scholar 

  17. Tian J, Xiong R, Shen W. State-of-health estimation based on differential temperature for lithium ion batteries. IEEE Trans Power Electron, 2020, 35: 10363–10373

    Article  Google Scholar 

  18. Tian J, Xiong R, Shen W, et al. State-of-charge estimation of LiFePO4 batteries in electric vehicles: A deep-learning enabled approach. Appl Energy, 2021, 291: 116812

    Article  Google Scholar 

  19. He L, Wang Y, Wei Y, et al. An adaptive central difference Kalman filter approach for state of charge estimation by fractional order model of lithium-ion battery. Energy, 2022, 244: 122627

    Article  Google Scholar 

  20. Xu Y, Hu M, Zhou A, et al. State of charge estimation for lithium-ion batteries based on adaptive dual Kalman filter. Appl Math Model, 2020, 77: 1255–1272

    Article  MathSciNet  Google Scholar 

  21. Wang Y, Chen Z. A framework for state-of-charge and remaining discharge time prediction using unscented particle filter. Appl Energy, 2020, 260: 114324

    Article  Google Scholar 

  22. Zhong Q, Zhong F, Cheng J, et al. State of charge estimation of lithium-ion batteries using fractional order sliding mode observer. ISA Trans, 2017, 66: 448–459

    Article  Google Scholar 

  23. Xu J, Mi C C, Cao B G, et al. The state of charge estimation of lithium-ion batteries based on a proportional-integral observer. IEEE Trans Veh Technol, 2013, 63: 1614–1621

    Google Scholar 

  24. Sandoval-Chileño M A, Castañeda L A, Luviano-Juárez A, et al. Robust state of charge estimation for Li-ion batteries based on extended state observers. J Energy Storage, 2020, 31: 101718

    Article  Google Scholar 

  25. Jiang Z, Shi Q, Wei Y, et al. An immune genetic extended Kalman particle filter approach on state of charge estimation for lithium-ion battery. Energy, 2021, 230: 120805

    Article  Google Scholar 

  26. Peng S, Chen C, Shi H, et al. State of charge estimation of battery energy storage systems based on adaptive unscented Kalman filter with a noise statistics estimator. IEEE Access, 2017, 5: 13202–13212

    Article  Google Scholar 

  27. Yang H, Sun X, An Y, et al. Online parameters identification and state of charge estimation for lithium-ion capacitor based on improved Cubature Kalman filter. J Energy Storage, 2019, 24: 100810

    Article  Google Scholar 

  28. Li S, Li Y, Zhao D, et al. Adaptive state of charge estimation for lithium-ion batteries based on implementable fractional-order technology. J Energy Storage, 2020, 32: 101838

    Article  Google Scholar 

  29. Chen Z, Sun H, Dong G, et al. Particle filter-based state-of-charge estimation and remaining-dischargeable-time prediction method for lithium-ion batteries. J Power Sources, 2019, 414: 158–166

    Article  Google Scholar 

  30. Liu Z, Dang X, Jing B, et al. A novel model-based state of charge estimation for lithium-ion battery using adaptive robust iterative cubature Kalman filter. Electric Power Syst Res, 2019, 177: 105951

    Article  Google Scholar 

  31. Shi E, Xia F, Peng D, et al. State-of-health estimation for lithium battery in electric vehicles based on improved unscented particle filter. J Renew Sustain Energy, 2019, 11: 024101

    Article  Google Scholar 

  32. Liu M, He M, Qiao S, et al. A high-order state-of-charge estimation model by cubature particle filter. Measurement, 2019, 146: 35–42

    Article  Google Scholar 

  33. Li X, Fan G, Pan K, et al. A physics-based fractional order model and state of energy estimation for lithium ion batteries. Part I: Model development and observability analysis. J Power Sources, 2017, 367: 187–201

    Article  Google Scholar 

  34. Zhang Q, Shang Y, Li Y, et al. A novel fractional variable-order equivalent circuit model and parameter identification of electric vehicle Li-ion batteries. ISA Trans, 2020, 97: 448–457

    Article  Google Scholar 

  35. Xiong R, Tian J, Shen W, et al. A novel fractional order model for state of charge estimation in lithium ion batteries. IEEE Trans Veh Technol, 2018, 68: 4130–4139

    Article  Google Scholar 

  36. Hu M H, Li Y X, Li S X, et al. Lithium-ion battery modeling and parameter identification based on fractional theory. Energy, 2018, 165: 153–163

    Article  Google Scholar 

  37. Deng Z, Zhang Z, Lai Y, et al. Electrochemical impedance spectroscopy study of a lithium/sulfur battery: modeling and analysis of capacity fading. J Electrochem Soc, 2013, 160: A553–A558

    Article  Google Scholar 

  38. Zou C, Zhang L, Hu X, et al. A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and super-capacitors. J Power Sources, 2018, 390: 286–296

    Article  Google Scholar 

  39. Wang B, Li S E, Peng H, et al. Fractional-order modeling and parameter identification for lithium-ion batteries. J Power Sources, 2015, 293: 151–161

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lin He.

Additional information

This work was supported by the National Key Research and Development Program of China (Grant No. 2017YFB0103104), the Key Research and Development Program of Jiangsu Province (Grant No. BE2021006-2), the Innovation Project of New Energy Vehicle and Intelligent Connected Vehicle of Anhui Province, and the Foundation of State Key Laboratory of Automotive Simulation and Control (Grant No. 20201107).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Y., Shi, Q., Wei, Y. et al. State of charge estimation by square root cubature particle filter approach with fractional order model of lithium-ion battery. Sci. China Technol. Sci. 65, 1760–1771 (2022). https://doi.org/10.1007/s11431-021-2029-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-021-2029-y

Keywords

Navigation