Parameter extraction method for fractional order supercapacitor system model

Accuracy, as one of the major concerns in control systems, can be better achieved by considering the system to be of fractional order than of integer order, since not all physical relationships are ideal in nature. The large internal capacitance of supercapacitor, which causes longer time constant, leads to a complex internal behavior. This study proposed an equivalent circuit of a supercapacitor with parameters consisting of ohmic loss, leakage resistance, capacitance in fractional order, and inductance for high frequency applications. Riemann-Lioville definition of fractional calculus was used in formulating the equivalent mathematical model and in solving the order of the system for varying frequency. The Panasonic's 10F and 30F gold capacitors were subjected to charge and discharge tests as well as in current-frequency test, and the resulting time responses and frequency responses were used in the parameter extraction.