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

Abstract

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.

State‐of‐charge estimation of power lithium‐ion batteries based on an embedded micro control unit using a square root cubature Kalman filter at various ambient temperatures

“…The lithium‐ion battery (LIB) enjoys the merits of a longer cycle life and higher energy density and thus has been widely used in electric vehicles . While continuous efforts have been made towards cell optimization, the safe and efficient operation of LIB systems still relies on well‐designed BMSs that accurately estimate and adjust the SOC.…”

“…The lithium-ion battery (LIB) enjoys the merits of a longer cycle life and higher energy density and thus has been widely used in electric vehicles. [1][2][3][4] While continuous efforts have been made towards cell optimization, [5][6][7][8] the safe and efficient operation of LIB systems still relies on well-designed BMSs that accurately estimate and adjust the SOC. In spite of its importance, the SOC estimation based on an embedded MCU is still challenging because of the high computing cost and storage occupancy of most estimation algorithms.…”

Hydrogen ion supercapacitor cell construction and rational design of cell structure

“…Supercapacitors and secondary cells are regarded as promising candidates for energy storage and conversion devices. [23][24][25][26] In order to make it more extensively applied, the researchers were working on the improvement of the energy density without sacrificing the output power and operational life time. 22 Hybrid supercapacitors, however, merge the boundary between the supercapacitors and secondary batteries and possess several advantages over them, including high energy density, high power density, fast charge and discharge speed, and long cycle life.…”

“…Therefore, this device can be applied to many fields, where the supercapacitors and secondary batteries cannot meet the requirements. [23][24][25][26] In order to make it more extensively applied, the researchers were working on the improvement of the energy density without sacrificing the output power and operational life time. And the development of various asymmetric capacitor system has been the focus of attention.…”

Estimation and Fault Diagnosis of Lithium-Ion Batteries: A Fractional-Order System Approach

“…The first application of the fractional calculus was accomplished by Abel in 1823 while investigating the solution of the famous problem of tautochrone [9]. For almost two hundred years, fractionalorder models have been used to describe biology systems [10] in bioengineering, financial markets [11][12][13] in economics, and diffusion wave [14][15][16][17] and lead-acid battery or Li-ion battery [18][19][20][21] in physical engineering. Due to inherent properties of fractional-order calculus, fractional-order differential systems sometimes have a more appropriate mathematical description than integer-order differential systems for managing lithium-ion batteries.…”