Supercapacitor Model with Charge-Dependent Parameters Based on Experimental Frequency Response

The characterization of supercapacitors (SCs), particularly electric double-layer capacitors (EDLCs), is useful for the design of energy management systems. This article presents a five-parameter dynamic model based on electrochemical impedance spectroscopy (EIS) data. Unlike conventional fixed-parameter models, this study explores an approach that accounts for voltage dependence. The model was evaluated using four commercial 58-farad SCs over a frequency range of 10 mHz to 300 kHz and at voltages ranging from 6.25% to 93.75% of the nominal value. The results show that the parameters vary with the state of charge; for example, the effective capacitance increased by up to 24% when moving from 6.25% to 50% of the nominal voltage. The model, fitted using nonlinear optimization algorithms, has a mean square percentage error (MSPE) of less than 3%. This approach estimates the dynamic behavior of the SCs, facilitating the simulation and tuning of management and protection strategies.