Estimating the State-of-Charge of Lithium-Ion Batteries Using an H-Infinity Observer with Consideration of the Hysteresis Characteristic

Xie, Jiale;Ma, Jiachen;Sun, Yude;Li, Zonglin

  • Received : 2015.06.12
  • Accepted : 2015.10.03
  • Published : 2016.03.20


The conventional methods used to evaluate battery state-of-charge (SOC) cannot accommodate the chemistry nonlinearities, measurement inaccuracies and parameter perturbations involved in estimation systems. In this paper, an impedance-based equivalent circuit model has been constructed with respect to a LiFePO4 battery by approximating the electrochemical impedance spectrum (EIS) with RC circuits. The efficiencies of approximating the EIS with RC networks in different series-parallel forms are first discussed. Additionally, the typical hysteresis characteristic is modeled through an empirical approach. Subsequently, a methodology incorporating an H-infinity observer designated for open-circuit voltage (OCV) observation and a hysteresis model developed for OCV-SOC mapping is proposed. Thereafter, evaluation experiments under FUDS and UDDS test cycles are undertaken with varying temperatures and different current-sense bias. Experimental comparisons, in comparison with the EKF based method, indicate that the proposed SOC estimator is more effective and robust. Moreover, test results on a group of Li-ion batteries, from different manufacturers and of different chemistries, show that the proposed method has high generalization capability for all the three types of Li-ion batteries.


H-infinity observer;Hysteresis characteristic;Impedance-based modeling;State-of-charge


  1. S. Piller, M. Perrin, and A. Jossen, “Methods for state-of-charge determination and their applications,” Journal of power sources, Vol. 96, No. 1, pp. 113-120, Jun. 2001.
  2. M. A. Roscher and D. U. Sauer, “Dynamic electric behavior and open-circuit-voltage modeling of LiFePO4-based lithium ion secondary batteries,” Journal of Power Sources, Vol. 196, No. 1, pp. 331-336, Jan. 2011.
  3. Y. He, X. T. Liu, C. B. Zhang, and Z. H. Chen, “A new model for state-of-charge(SOC) estimation for high-power Li-ion batteries,” Applied Energy, Vol. 101, pp. 808-814, Jan. 2013.
  4. K. S. Ng, C.-S. Moo, Y.-P. Chen, and Y.-C. Hsieh, “Enhanced coulomb counting method for estimating state-of-charge and state-of-health of lithium-ion batteries,” Applied energy, Vol. 86, No. 9, pp. 1506-1511, Sep. 2009.
  5. S. Lee, J. Kim, J. Lee, and B. H. Cho, “State-of-charge and capacity estimation of lithium-ion battery using a new open-circuit voltage versus state-of-charge,” Journal of power sources, Vol. 185, No. 2, pp. 1367-1373, Dec. 2008.
  6. P. Spagnol, S. Rossi, and S. M. Savaresi, "Kalman filter SOC estimation for Li-ion batteries," in IEEE International Conference on Control Applications(CCA), pp. 587-592, Sep. 2011.
  7. M. Charkhgard and M. Farrokhi, “State-of-charge estimation for lithium-ion batteries using neural networks and EKF,” IEEE Trans. Ind. Electron., Vol. 57, No. 12, pp. 4178-4187, Dec. 2010.
  8. X. Li, J. Jiang, C. Zhang, W. Zhang, and B. Sun, "Effects analysis of model parameters uncertainties on battery SOC estimation using H-infinity observer," in IEEE 23rd International Symposium on Industrial Electronics(ISIE), pp. 1647-1653, Jun. 2014.
  9. W. He, N. Williard, C. Chen, and M. Pecht, “State of charge estimation for electric vehicle batteries using unscented Kalman filtering,” Microelectronics Reliability, Vol. 53, No. 6, pp. 840-847, Jun. 2013.
  10. B. Fridholm, M. Nilsson, and T. Wik, "Robustness comparison of battery state of charge observers for automotive applications⋆," in 19th World Congress, Vol. 19, No. 1, pp. 2138-2146, Aug. 2014.
  11. X. Chen, W. Shen, Z. Cao, and A. Kapoor, "A comparative study of observer design techniques for state of charge estimation in electric vehicles,"in 7th IEEE Conference on Industrial Electronics and Applications(ICIEA), pp. 102-107, Jul. 2012.
  12. D. D. Domenico, G. Fiengo, and A. Stefanopoulou, "Lithium-ion battery state of charge estimation with a kalman filter based on a electrochemical model," in IEEE International Conference on Control Applications(CCA), pp. 702-707, Sep. 2008.
  13. H. He, R. Xiong, and J. Fan, “Evaluation of lithium-ion battery equivalent circuit models for state of charge estimation by an experimental approach,” Energies, Vol. 4, No. 4, pp. 582-598, Mar. 2011.
  14. F. Huet, “A review of impedance measurements for determination of the state-of-charge or state-of-health of secondary batteries,” Journal of power sources, Vol. 70, No. 1, pp. 59-69, Jan. 1998.
  15. M. Thele, O. Bohlen, D. U. Sauer, and E. Karden, “Development of a voltage-behavior model for NiMH batteries using an impedance-based modeling concept,” Journal of Power Sources, Vol. 175, No. 1, pp. 635-643, Jan. 2008.
  16. J. Qiu, G. Feng, and J. Yang, “A new design of delay-dependent robust H-infinity filtering for discrete-time T-S fuzzy systems with time-varying delay,” IEEE Trans. Fuzzy Syst., Vol. 17, No. 5, pp. 1044-1058, Oct. 2009.
  17. A. A. H. Hussein, N. Kutkut, and I. Batarseh, "A hysteresis model for a lithium battery cell with improved transient response," in 26th Annual IEEE Applied Power Electronics Conference and Exposition(APEC), pp. 1790-1794, Mar. 2011.
  18. V. H. Johnson, A. A. Pesaran, and T. Sack, Temperature-dependent battery models for high-power lithium-ion batteries, City of Golden: National Renewable Energy Laboratory, pp. 1-17, 2001.
  19. I. Petersen, V. A. Ugrinovskii, and A. V. Savkin, Robust Control Design Using H-∞ Methods, Springer Science & Business Media, Chap. 3, 2012.
  20. Z. He, M. Gao, C. Wang, L. Wang, and Y. Liu, “Adaptive state of charge estimation for Li-ion batteries based on an unscented Kalman filter with an enhanced battery model,” Energies, Vol. 6, No. 8, pp. 4134-4151, Aug. 2013.
  21. Dynamometer Driving Scheules Utilized at the National Vehicle and Fuel Emissions Laboratory,, Jun. 2012.
  22. G. Sarre, P. Blanchard, and M. Broussely, “Aging of lithium-ion batteries,” Journal of Power Sources, Vol. 127, No. 1-2, pp. 65-71, Mar. 2004.

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