Fractional-order models of supercapacitors, batteries and fuel cells: a survey

Freeborn, Todd J.; Maundy, Brent; Elwakil, Ahmed S.

doi:10.1007/s40243-015-0052-y

Cited by 167 publications

(84 citation statements)

References 48 publications

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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%

Reevaluation of Performance of Electric Double-layer Capacitors from Constant-current Charge/Discharge and Cyclic Voltammetry

Allagui¹,

Freeborn

Elwakil

et al. 2016

Sci Rep

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171

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The electric characteristics of electric-double layer capacitors (EDLCs) are determined by their capacitance which is usually measured in the time domain from constant-current charging/discharging and cyclic voltammetry tests, and from the frequency domain using nonlinear least-squares fitting of spectral impedance. The time-voltage and current-voltage profiles from the first two techniques are commonly treated by assuming ideal SsC behavior in spite of the nonlinear response of the device, which in turn provides inaccurate values for its characteristic metrics. In this paper we revisit the calculation of capacitance, power and energy of EDLCs from the time domain constant-current step response and linear voltage waveform, under the assumption that the device behaves as an equivalent fractional-order circuit consisting of a resistance Rs in series with a constant phase element (CPE(Q, α), with Q being a pseudocapacitance and α a dispersion coefficient). In particular, we show with the derived (Rs, Q, α)-based expressions, that the corresponding nonlinear effects in voltage-time and current-voltage can be encompassed through nonlinear terms function of the coefficient α, which is not possible with the classical RsC model. We validate our formulae with the experimental measurements of different EDLCs.

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mentioning

confidence: 99%

Reevaluation of Performance of Electric Double-layer Capacitors from Constant-current Charge/Discharge and Cyclic Voltammetry

Allagui¹,

Freeborn

Elwakil

et al. 2016

Sci Rep

Self Cite

171

120

View full text Add to dashboard Cite

show abstract

“…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%

Stability regions for fractional differential systems with a time delay

Čermák

Horníček

Kisela

2016

Communications in Nonlinear Science and Numerical Simulation

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“…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%

Modeling of Heat Distribution in Porous Aluminum Using Fractional Differential Equation

et al. 2017

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Abstract:The authors present a model of heat conduction using the Caputo fractional derivative with respect to time. The presented model was used to reconstruct the thermal conductivity coefficient, heat transfer coefficient, initial condition and order of fractional derivative in the fractional heat conduction inverse problem. Additional information for the inverse problem was the temperature measurements obtained from porous aluminum. In this paper, the authors used a finite difference method to solve direct problems and the Real Ant Colony Optimization algorithm to find a minimum of certain functional (solve the inverse problem). Finally, the authors present the temperature values computed from the model and compare them with the measured data from real objects.

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Fractional-order models of supercapacitors, batteries and fuel cells: a survey

Cited by 167 publications

References 48 publications

Reevaluation of Performance of Electric Double-layer Capacitors from Constant-current Charge/Discharge and Cyclic Voltammetry

Reevaluation of Performance of Electric Double-layer Capacitors from Constant-current Charge/Discharge and Cyclic Voltammetry

Stability regions for fractional differential systems with a time delay

Modeling of Heat Distribution in Porous Aluminum Using Fractional Differential Equation

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