Journal of Power Sources Vol. 390, 30 June 2018, pp. 286-296, DOI:

A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors

Changfu Zou1, Torsten Wik1, Lei Zhang2, Zhenpo Wang2, Xiaosong Hu3, Michael Pecht4
1Department of Electrical Engineering, Chalmers University of Technology, Gothenburg 41296, Sweden
2National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology, Beijing 100081, China
3State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China
4CALCE, Center for Advanced Life Cycle Engineering, Department of Mechanical Engineering, University of Maryland, College Park, Maryland 20740, USA


Electrochemical energy storage systems play an important role in diverse applications, such as electrified transportation and integration of renewable energy with the electrical grid. To facilitate model-based management for extracting full system potentials, proper mathematical models are imperative. Due to extra degrees of freedom brought by differentiation derivatives, fractional-order models may be able to better describe the dynamic behaviors of electrochemical systems. This paper provides a critical overview of fractional-order techniques for managing lithium-ion batteries, lead-acid batteries, and supercapacitors. Starting with the basic concepts and technical tools from fractional-order calculus, the modeling principles for these energy systems are presented by identifying disperse dynamic processes and using electrochemical impedance spectroscopy. Available battery/supercapacitor models are comprehensively reviewed, and the advantages of fractional types are discussed. Two case studies demonstrate the accuracy and computational efficiency of fractional-order models. These models offer 15–30% higher accuracy than their integer-order analogues, but have reasonable complexity. Consequently, fractional-order models can be good candidates for the development of advanced battery/supercapacitor management systems. Finally, the main technical challenges facing electrochemical energy storage system modeling, state estimation, and control in the fractional-order domain, as well as future research directions, are highlighted.

This article is available online here and to CALCE Consortium Members for personal review.

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