Measurement of Supercapacitor Fractional-Order Model Parameters From Voltage-Excited Step Response

In this paper, we propose using a numerically solved least squares fitting process to estimate the impedance parameters of a fractional order model of supercapacitors from their voltage excited step response, without requiring direct measurement of the impedance or frequency response. Experimentally estimated parameters from low capacity supercapacitors of 0.33, 1, and 1.5 F in the time range 0.2-30 s and high capacity supercapacitors of 1500 and 3000 F in the time range 0.2-90 s verify the proposed time domain method showing less than 3% relative error between the simulated response (using the extracted fractional parameters) and the experimental step response in these time ranges. An application of employing supercapacitors in a multivibrator circuit is presented to highlight their fractional time-domain behavior.