An Online Identification Algorithm to Determine the Parameters of the Fractional-Order Model of a Supercapacitor

Supercapacitors exhibit different capacitance values under varying operating conditions, due to the porous nature of their electrodes. As a result, the conventional resistor-capacitor (R-C) model or ladder R-C network models fail to accurately represent the dynamics of the supercapacitors. Fractional-order models (FOMs) that have been utilized in recent times, to represent these dynamics are more accurate. But, they too, are prone to inaccuracies because their parameters vary due to the changes in the operating voltage, current, and frequency. To address this issue, this article presents an online FOM for supercapacitors, which employs a two-stage least square fitting algorithm for identifying the parameters in real time. The first stage of the algorithm identifies the derivative order, "alpha" whereas the second stage calculates the capacitance and resistance values based on the voltage and current measurements. The proposed online FOM is implemented using Grunwald-Letnikov derivative in a DSP and the effectiveness is verified with experimental results. Furthermore, comparison of the online FOM with an existing offline FOM for state of charge estimation is presented. Additionally, certain issues related to the choice of the initial values and sampling time, encountered in the real time implementation of the proposed FOM, are also reported.