A multi-timescale estimator for state of energy and maximum available energy of lithium-ion batteries based on variable order online identification

The dynamic adjustment of the fractional orders for fractional-order models can improve the accuracy of modeling lithium-ion batteries, as a bridge between the state of energy (SOE) and the terminal voltage, the maximum available energy value will decay with changes in the charge-discharge rate and ambient temperature, so updating the predicted maximum available energy value in real-time can improve the accuracy of SOE estimation throughout the entire lifecycle. A multi-time scale combined estimation method for SOE and maximum available energy based on a fractional-order model is proposed to solve the asynchronous time-varying and coupling characteristics of maximum available energy and SOE estimation, which can effectively reduce the computational complexity of the algorithm by selecting different time scales. The results of dynamic stress test conditions show that the combined algorithm has high SOE prediction accuracy at different charge and discharge rates, with RMSE of 0.011 and 0.0175 respectively, which is better than the results under fixed maximum available energy. Furthermore, the experimental results under different time scales are verified, which further demonstrates that the multi-time scale framework can not only reduce the total running time of the algorithm by increasing the time scale but also ensure the accuracy of SOE estimation.