In recent years, the fractional order model has been employed to state of charge (SOC) estimation. The non integer differentiation order being expressed as a function of recursive factors defining the fractality of charge distribution on porous electrodes. The battery SOC affects the fractal dimension of charge distribution, therefore the order of the fractional order model varies with the SOC at the same condition. This paper proposes a new method to estimate the SOC. A fractional continuous variable order model is used to characterize the fractal morphology of charge distribution. The order identification results showed that there is a stable monotonic relationship between the fractional order and the SOC after the battery inner electrochemical reaction reaches balanced. This feature makes the proposed model particularly suitable for SOC estimation when the battery is in the resting state. Moreover, a fast iterative method based on the proposed model is introduced for SOC estimation. The experimental results showed that the proposed iterative method can quickly estimate the SOC by several iterations while maintaining high estimation accuracy.

Research on the heat transfer characteristics of lithium-ion batteries is of great significance to the thermal management system of electric vehicles. The electrodes of lithium-ion batteries are composed of porous materials, and thus the heat conduction of the battery is not a standard form of diffusion. The traditional heat conduction model is not suitable for lithium-ion batteries. In this paper, a fractional heat conduction model is used to study the heat transfer properties of lithium-ion batteries. Firstly, the heat conduction model of the battery is established based on the fractional calculus theory. Then, the temperature characteristic test was carried out to collect the temperature of the battery in various operating environments. Finally, the temperature calculated by the fractional heat conduction model was compared with the measured temperature. The results show that the accuracy of fractional heat conduction model is higher than that of traditional heat conduction model. The fractional heat conduction model can well simulate the transient temperature field of the battery. The fractional heat conduction model can be used to monitor the temperature of the battery, so as to ensure the safety and stability of the battery performance.