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With the increasing Complexity of Modern Interconnected Power Systems, Low Frequency inertial Oscillations after a disturbance in a Power System are becoming one of the major problem. This paper provides a systematic approach for designing a Supplementary Excitation Controller to damp the Low frequency oscillations observed in the system using an Innovative Particle Swarm Optimization (PSO) Algorithm. In Power systems, a good measure of damping is the Damping Ratio. The proposed Controller design is formulated as a Damping ratio enhancement based Optimization problem to compute the Optimal damping controller parameters, which aid in improving system stability. To validate the effective damping action of the proposed controller, Non linear Time domain simulations has been carried out in this work. The contrasting feature of this work is the implementation of Dynamic Sensitivity Analysis. A detailed Sensitivity analysis reveals that the system dynamic performance with the proposed PSO based controller is quite robust to wide variations in system loading conditions and also variation in System model parameters compared to the conventionally designed Lead lag Controller.