A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 3 Issue 3
Jul.  2016

IEEE/CAA Journal of Automatica Sinica

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Article Contents
Yan Ma, Xiuwen Zhou, Bingsi Li and Hong Chen, "Fractional Modeling and SOC Estimation of Lithium-ion Battery," IEEE/CAA J. of Autom. Sinica, vol. 3, no. 3, pp. 281-287, 2016.
Citation: Yan Ma, Xiuwen Zhou, Bingsi Li and Hong Chen, "Fractional Modeling and SOC Estimation of Lithium-ion Battery," IEEE/CAA J. of Autom. Sinica, vol. 3, no. 3, pp. 281-287, 2016.

Fractional Modeling and SOC Estimation of Lithium-ion Battery


This work was supported by National Natural Science Foundation of China (615 20106008, U1564207, 61503149), High Technology Research and Development Program of Jilin (20130204021GX), Specialized Research Fund for Graduate Course Identification System Program (Jilin University) of China (450060523183), and Graduate Innovation Fund of Jilin University (20151 48).

  • This paper proposes a state of charge (SOC) estimator of Lithium-ion battery based on a fractional order impedance spectra model. Firstly, a battery fractional order impedance model is derived on the grounds of the characteristics of Warburg element and constant phase element (CPE) over a wide range of frequency domain. Secondly, a frequency fitting method and parameter identification algorithm based on output error are presented to identify parameters of the fractional order model of Lithium-ion battery. Finally, the fractional order Kalman filter approach is introduced to estimate the SOC of the lithium-ion battery based on the fractional order model. The simulation results show that the fractional-order model can ensure an acceptable accuracy of the SOC estimation, and the error of estimation reaches maximally up to 0.5% SOC.


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  • [1]
    Wang Y, Zhang C, Chen Z. A method for joint estimation of stateof-charge and available energy of LiFePO 4 batteries. Applied Energy, 2014, 135: 81-87
    Kim D, Koo K, Jeong J J, Goh T, Sang W K. Second-order discretetime sliding mode observer for state of charge determination based on a dynamic resistance Li-ion battery model. Energies, 2013, 6(10): 5538-5551
    Chen X, Shen W X, Cao Z, Kapoor A. Sliding mode observer for state of charge estimation based on battery equivalent circuit in electric vehicles. Australian Journal of Electrical and Electronics Engineering, 2012, 9(3): 225-234
    Li D, Ouyang J, Li H, Wan J F. State of charge estimation for LiMn 2O 4 power battery based on strong tracking sigma point Kalman filter. Journal of Power Sources, 2015, 279: 439-449
    He Ling-Na, Wang Yun-Hong. SOC estimation based on improved sampling point Kalman filter for mine-used battery. Journal of Mechanical and Electrical Engineering, 2014, 31(9): 1213-1217 (in Chinese)
    Wang Y J, Zhang C B, Chen Z H. A method for state-of-charge estimation of LiFePO 4 batteries at dynamic currents and temperatures using particle filter. Journal of Power Sources, 2015, 279: 306-311
    Li J H, Barillas J K, Guenther C, Danzer M A. Multicell state estimation using variation based sequential Monte Carlo filter for automotive battery packs. Journal of Power Sources, 2015, 277: 95-103
    Lu L G, Han X B, Li J Q, Hua J F, Ouyang M G. A review on the key issues for Lithium-ion battery management in electric vehicles. Journal of Power Sources, 2013, 226: 272-288
    Deng Li-Wei, Song Shen-Min. Synchronization of fractional order hyperchaotic systems based on output feedback sliding mode control. Acta Automatica Sinica, 2014, 40(11): 2420-2427 (in Chinese)
    Sadli I, Urbain M, Hinaje M, Martin J P, Ra¨el S, Davat B. Contributions of fractional differentiation to the modelling of electric double layer capacitance. Energy Conversion and Management, 2010, 51(12): 2993-2999
    Fairweather A J, Foster M P, Stone D A. Battery parameter identification with pseudo random binary sequence excitation (PRBS). Journal of Power Sources, 2011, 196(22): 9398-9406
    Sabatier J, Cugnet M, Laruelle S, Grugeon S, Sahut B, Oustaloup A, Tarascon J M. A fractional order model for lead-acid battery crankability estimation. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(5): 1308-1317
    Sabatier J, Aoun M, Oustaloup A, Grégoire G, Ragot F, Roy P. Fractional system identification for lead acid battery state of charge estimation. Signal Processing, 2006, 86(10): 2645-2657
    Wu H J, Yuan S F, Yin C L. A Lithium-Ion battery fractional order state space model and its time domain system identification. In: Proceedings of the 2012 FISITA World Automotive Congress. Berlin Heidelberg: Springer, 2013, 192: 795-805
    Luo Y F, Gong C S A, Chang L X, Liu Y H. AC impedance technique for dynamic and static state of charge analysis for Li-ion battery. In: Proceedings of the 17th IEEE International Symposium on Consumer Electronics (ISCE). Hsinchu, China: IEEE, 2013: 9-10
    Eddahech A, Briat O, Bertrand N, Delétage J Y, Vinassa J M. Behavior and state-of-health monitoring of Li-ion batteries using impedance spectroscopy and recurrent neural networks. International Journal of Electrical Power and Energy Systems, 2012, 42(1): 487-494
    Barsoukov E, Macdonald J R. Impedance Spectroscopy: Theory, Experiment, and Applications (2nd edition). Hoboken, NJ: Wiley-Interscience, 2005.
    Guermah S, Djennoune S, Bettayeb M. Discrete-time fractional-order systems: modeling and stability issues. Advances in Discrete Time Systems. INTECH Open Access Publisher, 2012.
    Guermah S, Djennoune S, Bettayeb M. Controllability and observability of linear discrete-time fractional-order systems. International Journal of Applied Mathematics and Computer Science, 2008, 18(2): 213-222
    Victor S, Malti R, Garnier H, Oustaloup A. Parameter and differentiation order estimation in fractional models. Automatica, 2013, 49(4): 926-935
    Sierociuk D, Dzieliński A. Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation. International Journal of Applied Mathematics and Computer Science, 2006, 16(1): 129-140


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