Prediction of oscillatory instability is a major concern in interconnected power system. One of the major causes for the power system oscillations is insufficient damping torque of synchronous machine which can damped using a Static Compensator (STATCOM) integrated with a Supplementary Modulation Controller (SMC). However, changes in SMC parameters can induce oscillatory modes to collide in eigenvectors and eigenvalues making the system highly sensitive to the changes and may lead to instability. The primary goal of this work is to discuss parametric modulation of STATCOM SMC and its effect on system stability in multimachine system. The analysis also finds system damping constraints for parametric variations of the controller without and with energy sources (ES) at STATCOM’s DC bus. The sensitivity of eigenmodes to changes in system parameters is thoroughly investigated for the various STATCOM working circumstances to determine the safe operating range of controller parameters.