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Fractional Calculus and Applied Analysis

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Volume 22, Issue 6


State-of-art survey of fractional order modeling and estimation methods for lithium-ion batteries

YaNan Wang
  • Power Electronics and Mechatronics, Control Laboratory, Dept. of Automation, Beijing Institute of Technology, Beijing, 100081, China
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/ YangQuan Chen
  • Mechatronics, Embedded Systems and Automation Laboratory, Dept. of Engineering, University of California, Merced, CA 95343, USA
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/ XiaoZhong Liao
  • Power Electronics and Mechatronics, Control Laboratory, Dept. of Automation, Beijing Institute of Technology, Beijing, 100081, China
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Published Online: 2019-12-31 | DOI: https://doi.org/10.1515/fca-2019-0076


This paper presents a state-of-art survey of the research on fractional-order (FO) modeling with parameter identification, and FO estimation methods for state of charge (SOC), state of health (SOH), and remaining usage life (RUL) of lithium-ion batteries (LIBs) mainly in recent five years. FO electrochemical models and six different types of FO equivalent circuit models (ECMs) are introduced in detail. Then, the corresponding tuning algorithm for parameters of these FO models are also provided in brief. Moreover, FO estimation methods for SOC are listed and analyzed, mainly including FO observers, and FO Kalman filters (FO-KFs). SOH and RUL estimation is another vital aspect for LIBs ageing and degradation monitoring, thus FO estimation methods proposed in recent research within five years are all listed. Finally, some suggestions that may be helpful for further research are proposed in conclusion.

MSC 2010: Primary 26A33; Secondary 34A08; 60G22; 93A30; 93C95; 93E10; 93E12

Key Words and Phrases: fractional-order modeling; lithium-ion batteries; constant phase elements; state of charge; state of health; fractional-order Kalman filters

This paper is dedicated to the memory of late Professor Wen Chen


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About the article

Received: 2019-07-15

Published Online: 2019-12-31

Published in Print: 2019-12-18

Citation Information: Fractional Calculus and Applied Analysis, Volume 22, Issue 6, Pages 1449–1479, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2019-0076.

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