A Lithium-Ion Battery Fractional Order State Space Model and its Time Domain System Identification

  • Hongjie Wu
  • Shifei Yuan
  • Chengliang Yin
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 192)


This paper deals with a fractional order state space model for the lithium-ion battery and its time domain system identification method. Currently the equivalent circuit models are the most popular model which was frequently used to simulate the performance of the battery. But as we know, the equivalent circuit model is based on the integer differential equations, and the accuracy is limited. And the real processes are usually of fractional order as opposed to the ideal integral order models. So here we propose a lithium-ion battery fractional order state space model, and compare it with the equivalent circuit models, to see which model fit with the experiment results best. Then the hybrid pulse power characterization (HPPC) test has been implemented in the lithium-ion battery during varied state-of-charge (SOC). Based on the Levenberg–Marquardt algorithm, the parameters for each model have been obtained using the time-domain test data. Experimental results show that the proposed lithium-ion fractional order state space model has a better fitness than the classical equivalent circuit models. Meanwhile, five other cycles are adopt here to validate the prediction error of the two models, and final results indicate that the fractional model has better generalization ability.


Fractional order state space model Equivalent circuit model Time domain system identification HPPC test Lithium-ion modelling 



This research work is supproted by CERC-CVC: U.S. - China Clean Energy Research Center Clean Vehicles Consortium (2010DFA72760-305). The Sinopoly Battery Ltd, a sponser of the battery cells for experimental test, is also gratefully acknowledged. And many thanks are also given to the authors whose papers were refered here.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.National Engineering Laboratory for Automotive Electronic Control TechnologyShanghai Jiao Tong UniversityShanghaiChina

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