Experimental investigation of supercapacitor dynamics: charge–discharge performance analysis under system uncertainties

In this study, a comprehensive model of the charge and discharge behaviour of a supercapacitor was developed using both analytical and experimental methods in order to develop a compact model for use in energy storage and applications. The analytical portion includes a mathematical description and derivations of closed-form voltage versus time relationships for constant current and constant power operation. This model was validated experimentally using two different methods: an Arduino-based platform to measure the charging and discharging current and voltage under various loads, and a direct current (DC) electronic load platform to conduct controlled discharge experiments under various conditions. The discharge characteristics were mainly selected for analysis because they are related directly to the amount of usable energy; however, both charging and discharging measurements were obtained for analysis. Understanding how both charge and discharge work together allows the sizing and evaluation of supercapacitors for use in real-world systems. The experimental data confirmed a close correlation with the analytical data. The voltage dependence owing to the capacitive effect, as well as the equivalent series resistance (ESR) effect, contributes to the relatively small differences in the results when testing at higher discharge rates. A quantitative uncertainty analysis showed that instrumentation error accounts for only a small fraction of this deviation, with the effective capacitance decreasing to approximately 60%–77% of its nominal value at the highest discharge rates tested. The model was further validated under dynamically varying load conditions using a stitched analytical formulation, with close agreement obtained across successive resistance transitions. These results demonstrate that an analytical method, along with experimental validation, forms an excellent basis for supercapacitor characterisation and provides support for the development of a hybrid energy storage system (HESS) and other applications that require an accurate analysis of the charge‒discharge performance.