A wind turbine-permanent magnet synchronous generator (WT-PMSG) system includes a variable speed permanent magnet synchronous generator and utilizes a static synchronous compensator (STATCOM) connected on the grid side of the system. A PI/PID controller is designed to apply modulation index control signals to the generator side-converter since the modulation index of the generator side-converter has been determined to have the higher controllability to damp the oscillatory modes of the system when the STATCOM is located at the grid side converter. The controller gains are tuned through a frequency based optimization procedure. This configuration dampens voltage instabilities to provide LVRT compliance.