Supercapacitor (SC) is completely valuable as an energy storage device for different applications such as electric vehicles and hybrid renewable systems. A simple SC model that composed of series RC circuit is insufficient to precisely characterize its dynamic performance. Consequently, an accurate mathematical model must be created for reliable and safe operation of SC. The equivalent circuit model that contains three RC branches, immediate, delayed and long is considered, the first branch includes voltage-dependent capacitance. The second one determines the terminal behavior in minutetime range while the last branch determines the behavior for time longer than 10 min. Such model has eight unknown parameters to be determined. A new formula to estimate the SC voltage is derived. For first time Interior Search Algorithm (ISA) is employed to identify these parameters. The obtained results are compared with those obtained by other different optimization algorithms like Genetic Algorithm (GA), Moth Flam Optimization (MFO), Antlion Optimizer (ALO), Gray Wolf Optimizer (GWO), Whale Optimization Algorithm (WOA), and Artificial ecosystem-based optimization (AEO). Two different capacitors with values of 470-F and 1500-F are considered during the validation process. Extensive statistical analysis is carried out to prove the reliability of the proposed methodology. The results confirmed high level of agreement between experimental data and optimized model circuit.