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State of Charge Estimation for Lithium-Ion Battery Based on Improved Cubature Kalman Filter Algorithm

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Abstract

An improved cubature Kalman filter (CKF) algorithm for estimating the state of charge of lithium-ion batteries is proposed. This improved algorithm implements the diagonalization decomposition of the covariance matrix and a strong tracking filter. First, a first-order RC equivalent circuit model is first established and verified, whose voltage estimation error is within 1.5%; this confirms that the model can be used to describe the characteristics of a battery. Then the calculation processes of the traditional and proposed CKF algorithms are compared. Subsequently, the improved CKF algorithm is applied to the state of charge estimation under the constant-current discharge and dynamic stress test conditions. The average errors for these two conditions are 0.76% and 1.2%, respectively, and the maximum absolute error is only 3.25%. The results indicate that the proposed method has higher filter stability and estimation accuracy than the extended Kalman filter (EKF), unscented Kalman filter (UKF) and traditional CKF algorithms. Finally, the convergence rates of the above four algorithms are compared, among which the proposed algorithm track the referenced values at the highest speed.

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Abbreviations

CKF:

Cubature Kalman filter

DST:

Dynamic stress test

EKF:

Extended Kalman filter

HPPC:

Hybrid pulse power characteristic

KF:

Kalman filter

LSTM:

Long short-term memory

OCV:

Open-circuit voltage

STF:

Strong tracking filter

SOC:

State of charge

UKF:

Unscented Kalman filter

UT:

Unscented transformation

References

  1. Yu, C., Ji, G., Zhang, C., et al.: Cost-efficient thermal management for a 48v li-ion battery in a mild hybrid electric vehicle. Automot. Innov. 1(4), 320–330 (2018)

    Article  Google Scholar 

  2. Lu, L., Han, X., Li, J.: A review on the key issues for lithium-ion battery management in electric vehicles. J. Power Sources 226, 272–288 (2013)

    Article  Google Scholar 

  3. Ng, K.S., Moo, C.S., Chen, Y.P., et al.: Enhanced coulomb counting method for estimating state-of-charge and state-of-health of lithium-ion batteries. Appl. Energy 86(9), 1506–1511 (2009)

    Article  Google Scholar 

  4. Xing, Y., He, W., Pecht, M., et al.: State of charge estimation of lithium-ion batteries using the open-circuit voltage at various ambient temperatures. Appl. Energy 113, 106–115 (2014)

    Article  Google Scholar 

  5. Snihir, I., Rey, W., Verbitskiy, E., Belfadhel-Ayeb, A., Notten, P.H.L.: Battery open-circuit voltage estimation by a method of statistical analysis. J. Power Sources 159, 1484–1487 (2006)

    Article  Google Scholar 

  6. Liu, F., Liu, T., Fu, Y.: An improved SOC estimation algorithm based on artificial neural network. In: 2015 8th International Symposium on Computational Intelligence and Design (ISCID), pp. 152–155. IEEE (2015).

  7. Singh, P., Vinjamuri, R., Wang, X., Reisner, D.: Design and implementation of a fuzzy logic-based state-of-charge meter for Li-ion batteries used in portable defibrillators. J. Power Source 162, 829–836 (2006)

    Article  Google Scholar 

  8. Ma, Y., Duan, P., Sun, Y., Chen, H.: Equalization of lithium-ion battery pack based on fuzzy logic control in electric vehicle. IEEE Trans. Ind. Electron. 65, 6762–6771 (2018)

    Article  Google Scholar 

  9. Sheng, H., Xiao, J.: Electric vehicle state of charge estimations: nonlinear correlation and fuzzy support vector machine. J. Power Sources 281, 131–137 (2015)

    Article  Google Scholar 

  10. Wang, Y.J., Chen, Z.H.: A framework for state-of-charge and remaining discharge time prediction using unscented particle filter. Appl. Energy. 26, 114324 (2020)

    Article  Google Scholar 

  11. Cao, W., Ming, Z., Wang, X., Cai, S.: Improved bidirectional extreme learning machine based on enhanced random search. Memetic Comput. 11, 19–26 (2019)

    Article  Google Scholar 

  12. Plett, G.L.: LiPB dynamic cell models for Kalman-filter SOC estimation. Paper presented at the 19th electric vehicle symposium (EVS19), Busan, Korea (2002).

  13. Ting, T.O., Man K.L., Lim E.G., Leach M.: Tuning of Kalman filter parameters via genetic algorithm for state-of-charge estimation in battery management system. Sci. World J. 2014, 176052 (2014)

  14. Sturm, J., Ennifar, H., Erhard, S.V., et al.: State estimation of lithium-ion cells using a physicochemical model based extended Kalman filter. Appl. Energy 223, 103–123 (2018)

    Article  Google Scholar 

  15. Sepasi, S., Ghorbani, R., Liaw, B.Y.: Improved extended Kalman filter for state of charge estimation of battery pack. J. Power Sources 255, 368–376 (2014)

    Article  Google Scholar 

  16. He, H.W., Xiong, R., Peng, J.K.: Real-time estimation of battery state-of-charge with unscented Kalman filter and RTOS μCOS-II platform. Appl. Energy 162, 1410–1418 (2016)

    Article  Google Scholar 

  17. Xiao, M., Zhang, Y., Fu, H.: Three-stage unscented Kalman filter for state and fault estimation of nonlinear system with unknown input. J. Franklin Inst. 354(18), 8421–8443 (2017)

    Article  MathSciNet  Google Scholar 

  18. He, W., Williard, N., Chen, C.: State of charge estimation for electric vehicle batteries using unscented Kalman filtering. Microelectron. Reliab. 53, 840–847 (2013)

    Article  Google Scholar 

  19. Gadsden, S.A., AI-Shabi, M., Arasaratnam, I., et al.: Combined cubature Kalman and smooth variable structure filtering: a robust nonlinear estimation strategy. Signal Process. Part B 96, 290–299 (2014)

    Article  Google Scholar 

  20. Arasaratnam, I., Haykin, S.: Cubature Kalman filters. IEEE Trans. Autom. Control 54(6), 1254–1269 (2009)

    Article  MathSciNet  Google Scholar 

  21. Jia, B., Xin, M., Chen, Y.: Higher-degree cubature Kalman filter. Automatica 49(2), 510–518 (2013)

    Article  MathSciNet  Google Scholar 

  22. Zhou, W., Liu, L.: Adaptive cubature Kalman filter based on the expectation-maximization algorithm. IEEE Access 7, 158198–158206 (2019)

    Article  Google Scholar 

  23. Linghu, J., Kang, L., Liu, M., Luo, X., Feng, Y.B., Lu, C.S.: Estimation for state-of-charge of lithium-ion battery based on an adaptive high-degree cubature Kalman filter. Energy 189, 116204 (2019)

    Article  Google Scholar 

  24. Tian, Y., Lai, R.C., Li, X.Y., et al.: 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. Appl. Energy 265, 114789 (2020)

    Article  Google Scholar 

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

    Article  Google Scholar 

  26. Liu, Z., Dang, X.J., Jing, B.Q., Ji, J.B.: A novel model-based state of charge estimation for lithium-ion battery using adaptive robust iterative cubature Kalman filter. Electr. Power Syst. Res. 177, 105951 (2019)

    Article  Google Scholar 

  27. Zeng, Z., Tian, J., et al.: An online state of charge estimation algorithm for lithium-ion batteries using an improved adaptive cubature Kalman filter. Energies 8(6), 5916–5136 (2018)

    Google Scholar 

  28. Tang, X.P., Wang, Y.J., et al.: A novel framework for Lithium-ion battery modeling considering uncertainties of temperature and aging. Energy Convers. Manag. 180, 162–170 (2019)

    Article  Google Scholar 

  29. Tang, X.P., Gao, F.R., Zou, C.F., et al.: Load-responsive model switching estimation for state of charge of lithium-ion batteries. Appl. Energy 238, 423–434 (2019)

    Article  Google Scholar 

  30. Wang, Y.J., Gao, G.Z., Li, X.Y., et al.: A fractional-order model-based state estimation approach for lithium-ion battery and ultra-capacitor hybrid power source system considering load trajectory. J. Power Sources 449, 227543 (2020)

    Article  Google Scholar 

  31. Wang, Y.J., Zhang, C.B., Chen, Z.H.: A method for state-of-charge estimation of Li-ion batteries based on multi-model switching strategy. Appl. Energy 137, 427–434 (2015)

    Article  Google Scholar 

  32. Tian, N., Wang, Y.B., Chen, J., Fang, H.Z.: One-shot parameter identification of the Thevenin’s model for batteries: methods and validation. J. Energy Storage 29, 101282 (2020)

    Article  Google Scholar 

  33. He, H., Xiong, R., Guo, H.: Online estimation of model parameters and state-of-charge of LiFePO4 batteries in electric vehicles. Appl. Energy 89, 413–420 (2012)

    Article  Google Scholar 

  34. Zhang, A., Bao, S.D., Gao, F., Bi, W.H.: A novel strong tracking cubature Kalman filter and its application in maneuvering target tracking. Chin. J. Aeronaut. 32, 2489–2502 (2019)

    Article  Google Scholar 

  35. Yao, Y., Cheng, K., et al.: A novel method for estimating the track-soil parameters based on Kalman and improved strong tracking filters. ISA Trans. 59, 450–456 (2015)

    Article  Google Scholar 

  36. Ge, Q.B., Wen, C.L., Chen, S.D., Sun, R.Y., Li, Y.: Adaptive Cubature strong tracking information filter using variational Bayesian method. IFAC Proc. Vol. 47, 5945–5950 (2014)

    Article  Google Scholar 

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Acknowledgements

The authors acknowledge funding from the National Natural Science Foundation of China (52072155, 51707084), the Six Talent Peaks Project in Jiangsu Province (2018-XNYQC-004), the Open Research Subject of Key Laboratory of Automotive Measurement and Control and Safety (QCCK2020-009), the Natural Science Research Project of Jiangsu Higher Education Institutions (19KJB470013), the Young Talent Cultivation Project of Jiangsu University.

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Authors and Affiliations

  1. Automotive Engineering Research Institute, Jiangsu University, Zhenjiang, 212013, China

    Guochun Li, Chang Liu, Enlong Wang & Limei Wang

  2. Institute for Energy Research, Jiangsu University, Zhenjiang, 212013, China

    Guochun Li

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  1. Guochun Li
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  2. Chang Liu
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  3. Enlong Wang
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  4. Limei Wang
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Correspondence to Limei Wang.

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Li, G., Liu, C., Wang, E. et al. State of Charge Estimation for Lithium-Ion Battery Based on Improved Cubature Kalman Filter Algorithm. Automot. Innov. 4, 189–200 (2021). https://doi.org/10.1007/s42154-021-00134-4

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  • DOI: https://doi.org/10.1007/s42154-021-00134-4

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