Fractional impedance of supercapacitor: an extended investigation

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.