On full-life-cycle SOC estimation for lithium batteries by a variable structure based fractional-order extended state observer

Accurate SOC estimation of lithium batteries are crucial for the efficient operation of new energy storage systems. During the ageing of the battery, structure and parameters of the battery model, especially internal resistance, may change, which has a particularly significant impact on the accuracy of the model. For this reason, this paper proposes a SOC estimation method based on the extended state observer of the variable structure fractional order model. Firstly, an adaptive method for the structure and parameters of fractional order model through distribution of relaxation times (DRT) is proposed on full-cycle-life of lithium battery. The DRT is extracted from the Electrochemical Impedance Spectroscopy (EIS) of the lithium battery. The order and the initial parameters of the fractional order model of the lithium battery is determined by the characteristics of DRT during the ageing process of the lithium battery. Adaptive adjustment of model is realized by parameter identification combining with time domain data. Then, a fractional-order extended state observer is proposed to estimate SOC by treating internal resistance as an extended state, thus realizing online estimation of internal resistance uncertainty. The Lyapunov stability analysis proves that the estimation error of the observer is uniformly ultimately bounded. Finally, the experimental simulation analysis shows that the accuracy of the second-order model is significantly improved compared with the first-order model, and the accuracy improvement of the third-order model is limited compared with the second-order model. The MAE of the proposed algorithm is as low as 0.73%.