Fractionalorder models of supercapacitors batter

Authors: Todd J Freeborn Brent Maundy Ahmed S Elwakil

Publish Date: 2015/06/14

Volume: 4, Issue: 3, Pages: 9-

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Abstract

This paper surveys fractionalorder electric circuit models that have been reported in the literature to best fit experimentally collected impedance data from energy storage and generation elements including supercapacitors batteries and fuel cells In all surveyed models the employment of fractionalorder 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 deviceModeling of energy storage and generation elements used in hybrid and renewable energy sources is crucial for future development of these sources 1 Of specific importance are supercapacitors batteries and fuel cells 2 A survey of published fractionalorder models has been carried out and is presented in this work These models provide best fit to experimentally measured impedances and/or transient responses and employ one or more constant phase element CPEs 3 also known as the fractionalorder capacitor 4From a circuit theory perspective it is possible to define a general frequencydomain electrical impedance which is proportional to salpha s=jomega This device is known as a fractance 5 from which classical circuit elements are special cases of the general device when the order alpha is 1 0 and 1 for a capacitor resistor and inductor respectively A CPE or fractionalorder capacitor is characterized by the impedance Z CPE=1/C alpha salpha where C alpha is termed pseudocapacitance with units F/sec1alpha and alpha is the order These units were originally proposed in 6 A CPE has a phase angle phi CPE=alpha pi /2 which is constant independent of frequency and dependent only on the order alpha While alpha in mathfrak R is mathematically possible the values from experimentally collected data of CPEs are in the range of 0alpha le 1 therefore it has also become known as a fractionalorder capacitorA number of recent surveys and special issues have focused on the applications of fractionalorder circuits and systems in general 7 and particularly in industrial automation 8 Meanwhile energy storage components and particularly electrochemical doublelayer capacitors 9 fabricated to provide high and very high capacitances supercapacitors as well as batteries are critical components in hybrid energy systems which require accurate models for these devices 10 Although there exists a considerable mass of research on the modeling of these devices a survey focusing on fractionalorder models has not been conducted It is the purpose of this paper to fill this gap

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