Low-voltage problem emerges in cases of symmetrical and asymmetrical fault in power systems. This problem can be solved out by ensuring low-voltage ride-through capability of wind power plants, through a static synchronous compensator (STATCOM). The purpose of this study is to reveal that the system can be recovered well by inserting a STATCOM with energy storage to a bus where a double-fed induction generator (DFIG)-based wind farm has been connected, so the bus voltage is maintained within desired limits during a fault. Moreover, a supercapacitor is used as an energy storage element. Modeling of the DFIG and STATCOM along with the nonlinear supercapacitor was carried out in a MATLAB/Simulink environment. The behaviors of the system under three- and two-phase faults have been compared with and without STATCOM-supercapacitor, by observing the parameters of DFIG output voltage, active power, speed, electrical torque variations, and d-q axis stator current variations. It was found that the system became stable in a short time when the STATCOM-supercapacitor was incorporated into the full-order modeled DFIG.