A Control Oriented Fractional-Order Model of Lithium-ion Batteries Based on Caputo Definition

TL;DR

This paper introduces a fractional-order lithium-ion battery model based on the Caputo definition, providing a simple recursive solution that balances accuracy and computational efficiency for real-time battery management.

Contribution

It presents a novel Caputo-based fractional-order model with a closed-form solution suitable for online implementation, improving upon traditional methods.

Findings

Achieves voltage prediction accuracy comparable to second-order models

Reduces memory usage compared to Grünwald-Letnikov method

Suitable for real-time battery management systems

Abstract

This letter proposes a fractional-order battery model based on the Caputo definition. A closed-form time-domain solution is derived, enabling a simple recursive expression for discrete-time implementation. The model requires only the current and previous time-step states in each iteration, significantly reducing memory usage compared to the conventional Gr\"{u}nwald--Letnikov (G-L) method. This recursive structure is highly compatible with filter design and online parameter identification. Experimental validation on a 40.2~Ah NCM622 cell shows that the proposed first-order model achieves voltage prediction accuracy comparable to a second-order integer-order model. The results demonstrate that the Caputo-based model offers a practical balance between accuracy and computational efficiency, making it well suited for real-time battery management systems (BMS).