2015
DOI: 10.1007/s40243-015-0052-y
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Fractional-order models of supercapacitors, batteries and fuel cells: a survey

Abstract: This paper surveys fractional-order electric circuit models that have been reported in the literature to best fit experimentally collected impedance data from energy storage and generation elements, including super-capacitors, batteries, and fuel cells. In all surveyed models, the employment of fractional-order capacitors, also known as constant phase elements, is imperative not only to the accuracy of the model but to reflect the physical electrochemical properties of the device.

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Cited by 171 publications
(84 citation statements)
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“…a Cooper Bussmann PowerStor supercapacitor (denoted PS, rated as 2.7 V with 3 F nominal capacitance and 0.060 Ω maximum equivalent series resistance (ESR) at 1 kHz) and a NEC/TOKIN supercapacitor (denoted NEC, rated as 5.5 V with 1 F nominal capacitance and 65 Ω maximum ESR at 1 kHz). The impedance response of the PS device is typical for an equivalent series resistance ( R s ) in series with a constant-phase element (CPE) behavior212223242526, as it consists of a straight line of slope 13.17 Ω/Ω (i.e. 85.6°) with R s  = 40 mΩ (Im( Z ) = 0) at 5.3 kHz.…”
mentioning
confidence: 99%
“…a Cooper Bussmann PowerStor supercapacitor (denoted PS, rated as 2.7 V with 3 F nominal capacitance and 0.060 Ω maximum equivalent series resistance (ESR) at 1 kHz) and a NEC/TOKIN supercapacitor (denoted NEC, rated as 5.5 V with 1 F nominal capacitance and 65 Ω maximum ESR at 1 kHz). The impedance response of the PS device is typical for an equivalent series resistance ( R s ) in series with a constant-phase element (CPE) behavior212223242526, as it consists of a straight line of slope 13.17 Ω/Ω (i.e. 85.6°) with R s  = 40 mΩ (Im( Z ) = 0) at 5.3 kHz.…”
mentioning
confidence: 99%
“…This originally purely theoretical idea of fractional-order controllers was recently supported and justified by several papers studying experimentally collected impedance data of supercapacitors whose underlying electrochemical dynamics can be described and captured using of fractional-order models (see, e.g. [7] and the papers cited therein).…”
Section: Introductionmentioning
confidence: 97%
“…Various phenomena in nature can be modeled using fractional derivatives [8][9][10][11][12][13][14][15][16]-for example, in [9,11], the authors surveyed fractional-order electric circuit models, Reference [12] shows applications of fractional derivatives in control theory, and, in [13,14,16,17], we can find information about application fractional derivatives in heat conduction problems. In [16], the authors present an algorithm to solve the fractional heat conduction equation.…”
Section: Introductionmentioning
confidence: 99%