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arXiv · 2505.12725

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

Yangyang Xu·Hongyu Zhao·Chengzhong Zhang·Chenglin Liao
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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).

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Yangyang Xu, Hongyu Zhao, Chengzhong Zhang, Chenglin Liao. 2025-05-19. A Control Oriented Fractional-Order Model of Lithium-ion Batteries Based on Caputo Definition. https://arxiv.org/abs/2505.12725

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