The Application of Bio Inspired Algorithms to complicated Power System Stability Problems has recently attracted the researchers in the field of Artificial Intelligence. Low frequency oscillations after a disturbance in a Power system, if not sufficiently damped, can drive the system unstable. This paper provides a systematic procedure to damp the low frequency oscillations based on Bio Inspired Genetic (GA) and Particle Swarm Optimization (PSO) algorithms. The proposed controller design is based on formulating a System Damping ratio enhancement based Optimization criterion to compute the optimal controller parameters for better stability. The Novel and contrasting feature of this work is the mathematical modeling and simulation of the Synchronous generator model including the Steam Governor Turbine (GT) dynamics. To show the robustness of the proposed controller, Non linear Time domain simulations have been carried out under various system operating conditions. Also, a detailed Comparative study has been done to show the superiority of the Bio inspired algorithm based controllers over the Conventional Lead lag controller.