2020
DOI: 10.1149/1945-7111/aba1a6
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Optimal Charging and Discharging of Supercapacitors

Abstract: In this paper, we discuss the optimal charging and discharging of supercapacitors to maximize the delivered energy by deploying the fractional and multivariate calculus of variations. We prove mathematically that the constant current is the optimal charging and discharging method under R s -CPE model of supercapacitors. The charging and round-trip efficiencies have been mathematically analyzed for constant current charging and discharging.

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Cited by 20 publications
(8 citation statements)
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“…So far, the highest achievable capacitance [13][14][15] and energy densities 16 have been obtained with nanometre-sized pores. Hence, an extensive research effort has been dedicated to understanding the properties of such nanoporous supercapacitors 12,[17][18][19][20][21][22][23][24][25][26][27] , with an overarching goal being to maximize the stored energy density [28][29][30][31][32][33][34][35] and the speed of charging and discharging [36][37][38][39][40][41][42][43][44] .…”
mentioning
confidence: 99%
“…So far, the highest achievable capacitance [13][14][15] and energy densities 16 have been obtained with nanometre-sized pores. Hence, an extensive research effort has been dedicated to understanding the properties of such nanoporous supercapacitors 12,[17][18][19][20][21][22][23][24][25][26][27] , with an overarching goal being to maximize the stored energy density [28][29][30][31][32][33][34][35] and the speed of charging and discharging [36][37][38][39][40][41][42][43][44] .…”
mentioning
confidence: 99%
“…Nowadays, the demand for energy storage equipment is greatly increased due to the rapid development of the global economy, and the rapid consumption of fossil fuels such as coal, oil, and natural gas. The development and utilization of renewable and clean energy have received more and more attention, and new technologies for energy conversion and storage are urgently needed 1–3 . In recent years, supercapacitors have attracted wide attention as a new trend in energy storage applications compared to conventional capacitors and batteries because of their unique properties, such as higher energy storage capacity, high specific power, and good life cycle, etc 4–6 .…”
Section: Introductionmentioning
confidence: 99%
“…The inception of the fractional calculus extends to the time integer calculus was known. It has become omnipresent in various fields such as bioengineering [1,2], agriculture [3], viscoelasticity [4], filters [5,6,7], control theory [8], electronics [9], and circuits [10]. In the latter decades, Fractional Order Models FOM attracted the researchers' attention, because of being accurate and compact compared to their equivalent integer-order models [11].…”
Section: Introductionmentioning
confidence: 99%