A Simple Adaptive Fractional Order Model of Supercapacitor for Pulse Power Applications

Abstract

The porous nature of the electrodes results in complex dynamics of the supercapacitors. Consequently, the value of the capacitance varies with the voltage level, frequency and magnitude of the charging/discharging current. Conventional RC models or ladder RC network models are not apt for accurate representation of such dynamics. This paper investigates the suitability of a simple fractional order model for accurately representing such characteristics of the supercapacitors for pulse power applications. The identification of the fractional order model parameters from constant resistance charge/discharge test, constant current charge/discharge test and impedance spectroscopy is discussed. Based on the test results, the shortcomings of the simple fractional order model in representing the pulse power applications, owing to the variation of the fractional order model parameters are examined. An adaptive fractional order model considering the nonlinear voltage and frequency dependence on the parameters is then deduced. A procedure for identifying the model parameters is presented and the validity of the model is verified using various test profiles.