This paper deduced the model of the synchronous generator (SG) dominated power system with energy storage system (ESS) over the electromechanical time scale. Then, by adopting the method of electrical torque analysis, this paper discussed the ESS control for electromechanical oscillation mitigation and its impact on the inertia and damping characteristics of SG dominated power system. The results show that P and D controllers affect the synchronous and the damping characteristics of the SG dominated system, respectively, with power angle feedback; when the rotor speed of SG is utilized as the feedback signal, P, I and D controllers affect the damping, synchronous and inertia characteristics, respectively. In addition, the principles of different control strategies that influence the system inertia and damping characteristics are explained, rendering a ground foundation for the design of ESS control strategies to enhance the inertia and damping of SG dominated grids. The simulation results show the correctness of the conclusions derived in this paper.