Fractional impedance of supercapacitor: an extended investigation
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Fractional impedance of supercapacitor: an extended investigation Ravneel Prasad1 · Utkal Mehta1
· Kajal Kothari1
Received: 13 August 2020 / Revised: 31 October 2020 / Accepted: 16 November 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract There has been an impressive growth rate of supercapacitor’s applications, which urges a need for an in-depth investigation on modeling of supercapacitor in order to study the behavior and designing systems integrated with it. Studies have been carried out in multiple domains, but the time domain based modeling has been a simple and commonly adopted study. This research proposes the block-pulse based identification method for modeling the time response behavior of the supercapacitor. The proposed method for modeling supercapacitor simplifies fractional derivative into simple algebra rather than direct complex function like the Mittag-Leffler function. Furthermore, in this paper the critical observation is conducted with varied time duration of data collected for modeling of the supercapacitor of same brand and capacity. It shows how its parameters are affected by time length despite capturing full charge and discharge cycles. This may help in the crucial stage of determining the sample size or the data length for which modeling is to be performed. Some recommendations have been made after systematic observations on three different branded supercapacitors of same capacitance. Using the proposed technique, one can estimate the model parameters set to handle complexity posed by fractal behavior of supercapacitors. Keywords Supercapacitor · Impedance model · Fractional calculus · Time domain analysis · Block-pulse function · Operational matrix
1 Introduction Supercapacitor is an energy storage component that bridges the gap between standard batteries and conventional capacitors. It is able to store or dissipate large amounts of energy in a short span of time. The supercapacitor, also known as double-layer capacitor or ultracapacitor, can be categorized into two different classes depending on how the charges are stored in the system. A class of Electrostatic Double Layer Capacitor (ELDC) stores energy in a non-faradic process and does not involve any chemical reaction. On the other hand, Pseudo Capacitor is based on a faradic redox reaction which involves transfer of charges between the electrode and electrolyte [1]. Hence, depending on the capacitance and time response, it can be used in electric cars, renewable energy
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Utkal Mehta [email protected] Ravneel Prasad [email protected] Kajal Kothari [email protected]
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systems, biomedical sensors, memory backup, power regulators and etc. It is true that supercapacitor’s properties such as longer lifespan, greater power density over batteries and high energy density over conventional capacitors, are useful enough to replace the batteries in hybrid vehicles and power backup systems [1–4]. The aforementioned properties has been studied rigorously by researchers to understand internal beha
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