Wind power generation is becoming increasingly important in order to meet rising energy demand. Doubly-fed induction generator (DFIG)-based wind power generation is recent and used in many countries due to its better power controllability. The controllers, like proportional integral (PI) controllers, are used for the stabilization of the waveforms of the supply system. The change in controllers has produced better oscillation damping in recent days. The effect of varying the wind input to generate power using the wind turbine results in instability in the power system because the control is done on a grid supply. This paper aims to propose an optimum First Order Proportional Integral Derivative (FOPID) controller for damping power system instability using a static synchronous series compensator (SSSC) system that takes into account the dynamics of wind energy conversion systems (WECS) connected to an infinite grid. The WECS model, which includes variations in wind supply to the wind turbine, has been developed to test the durability of the optimized controller that was developed to damp power system oscillations. The controller was used to take the power system dynamics into account. A new controller is being designed to include a corrective measure for damping the oscillations to adjust the instability caused by wind supply variations. The controller helps to tune the controller settings that lead to the achievement of the power oscillation damping objectives. These results are compared with those of a conventional Permanent Magnet Synchronous Machine (PMSM) based wind turbine system.