Generalized formulation to estimate the Supercapacitor’s R-C series impedance using fractional order model

Abstract

The main objective of this paper is to develop a new technique for the supercapacitor’s parameter identification that can handle the issue of initial voltage. An effective approach is proposed using the fractional-order derivative for accurate identification of a well-known series Resistance-Capacitance (R-C) model. An expression is derived using the Caputo definition and the Haar wavelet operational matrix, which is sufficient for both charging and discharging phase data of supercapacitors. To extract impedance parameters, voltage stimulated step response is utilized and parameters are calculated despite random initial voltage stored in a supercapacitor. This operational matrix approach transforms complex fractional derivative terms into simple algebraic expressions and reduces the overall complexity. The proposed technique shows a very good agreement with experimental data that exhibit different initial voltages and different time-frames. Investigations and experiments with various supercapacitors clearly reveal the importance of the developed equation for a fractional R-C model.

Keywords

• Fractional-order models
• Supercapacitor
• Haar operational matrix of derivative
• Impedance model
• Caputo definition.