State of Charge Estimation of Supercapacitors with Fractional Order Modelling

Supercapacitors are widely employed for substituting/assisting batteries for various applications like electric vehicles, traction, micro grids and so on. Design of efficient and cost effective energy management schemes for these applications demands accurate estimation of the State of Charge (SOC) of the supercapacitors. If the behavior of supercapacitors can be modelled using a simple RC circuit, then SOC can be directly calculated from the open circuit voltage. However, because of the porous nature of their electrodes, supercapacitors are subjected to charge redistribution during/following every charge/discharge cycle. Consequently, the value of the capacitance exhibits a nonlinear relation with the voltage, frequency, magnitude of the charge/discharge current and temperature. This paper presents some interesting observations regarding the charge and discharge mechanisms of the supercapacitors. The SOC of key commercial supercapacitors is calculated based on a fractional order model and the results are verified using Ampere counting method. Further the effect of the charge redistribution on defining the utilizable capacity limits is analyzed and an empirical method for calculating the utilizable SOC is presented.