The supercapacitor is among the elements commonly used to store energy as an important component in sustainable energy systems. In doubly fed induction generators (DFIGs), the supercapacitor is used to compensate voltage dips and damping oscillations. In this study, a different supercapacitor model was developed for system stability in a DFIG-based wind turbine connected to an infinite bus. In the development of the mathematical supercapacitor model, the lookup table was realized with the voltage-capacity relationship and sliding mode control. DFIG modeling with/without the developed supercapacitor was performed for symmetrical and asymmetrical fault situations, and the findings were then compared and interpreted in detail. The simulation study analysis was conducted in a MATLAB/SIMULINK environment. The developed supercapacitor model yielded impressive results in symmetrical and asymmetrical faults.