Modelling of ultracapacitor using a fractional-order equivalent circuit

Research shows many dynamic systems such as ultracapacitors are better characterised using fractional–order system. This paper models ultracapacitor through electrochemical impedance spectroscopy (EIS) measurement. Ultracapacitor response to this measurement is used to determine the parameters of its equivalent circuit. Constant phase elements (CPEs) are incorporated in the equivalent circuit model to better describe ultracapacitor dynamic behaviour. The ultracapacitor impedance response is modelled by zones and the circuit elements are connected in congruence with its response at the respective zone. The proposed modelling approach permits obtaining a model that has parameters that are associated with ultracapacitor physical process. Consequently, this approach leads to a fractional–order model. Simulation of a fractional–order model in MATLAB/SIMULINK is given in detail and the model performance is compared with experimental data. Results reveal that the voltage evolution during current turn–off is better described. The voltage decay at this period is influenced by the CPE exponent, n.