An indicator for the electrode aging of lithium-ion batteries using a fractional variable order model

The fractional order expressed as a function of recursive factors defines the fractional morphology of charge distribution on porous electrodes. Electrode aging causes the fractality of charge distribution to gradually deviate from the original fractal dimension, consequently, the fractional order of the fractional order model varies with the cycle number of batteries. This paper aims to determine the relationship between the fractional order and electrode aging, and use the fractional order as an indicator for electrode aging. The transient discharge dataset of fully charged lithium-ion batteries is taken as the input signal of the identification system of the fractional order model. The identification of the fractional order is then performed with the least squares method. The results show that there is a stable monotonous relationship between the fractional order and the cycle number of batteries. Using the fractional order as an indicator for electrode aging can quickly evaluate the degradation level of electrodes without destroying the battery. Moreover, it is significant to find that the electrode life is terminated when the fractional order tends to be stable, and therefore, the fractional order is used to recognize the ongoing or abrupt degradation of batteries. The effectiveness of the proposed method is verified by the dataset of National Aeronautics and Space Administration (NASA) Ames Prognostics Center of Excellence and the dynamic stress test. (C) 2018 Elsevier Ltd. All rights reserved.