Parameter and order estimation algorithms and convergence analysis for lithium‐ion batteries

Abstract The fractional‐order equivalent circuit model can reflect the internal reaction mechanism of a lithium‐ion battery well. This article aims to design an effective model and optimization method to describe and analyze the operating characteristics of the lithium‐ion battery based on online measurement data. The fractional‐order controlled autoregressive model is derived by exploiting the memory superiorities of the fractional‐order, which comprises the electrochemical impedance spectroscopy and the ‐RC equivalent circuit model as the special cases. The utilization of polynomial properties reduces the difficulty of identification while preserving the ability of the controlled autoregressive model to fit the characteristics of the battery. To realize simultaneous parameter and the order estimation, a weighted gradient descent algorithm is proposed. The approach designs a new gradient direction and fully utilizes the data from the lithium‐ion battery by adding a suitable weighted factor. In addition, the forgetting factor is introduced to speed up convergence and produce more accurate parameter estimation. Furthermore, in order to analyze the convergence of the proposed algorithms, the convergence properties are proved by using martingale convergence theory and stochastic principle. Finally, the experimental simulation result shows the performance of the proposed algorithms.