<p> The dynamics in single machine been connected to an infinite power system bus is analyzed in this paper. This analysis requires certain amount of system modeling level. The main components of the system models are excitation system, synchronous machine and the Power System Stabilizer. The Simulink /Matlab are used as the programming tool for analyzing this system performance. Design optimization arobust PSS based on Genetic Algorithm (GA) approach has been improvement. A proper design is required for this Power System Stabilizer (PSS) performance using the Particle Swarm Optimization (PSO) to archieve this. Then the implemented of the model and response of the dynamic system is been analyzed. The designed without PSS showed an unacceptable system response since as shown in the simulation results, system response with PSS proven to have improvements and PSS succeeding in  stabilizing an unstable system. Therefore this leads to stability of the performance of the generator.</p>