A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors
Review article, 2018

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 b attery/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.

Fractional-order models

Energy management


Electrochemical energy storage systems



Changfu Zou

Chalmers, Electrical Engineering, Systems and control

Lei Zhang

Beijing Institute of Technology

Xiaosong Hu

Chongqing University

Zhenpo Wang

Beijing Institute of Technology

Torsten Wik

Chalmers, Electrical Engineering, Systems and control

Michael Pecht

University of Maryland

Journal of Power Sources

0378-7753 (ISSN)

Vol. 390 286-296

Subject Categories

Other Engineering and Technologies not elsewhere specified

Energy Systems

Computer Systems



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