This paper presents the stability improvement results of a single-machine infinite-bus (SMIB) system using a series vectorial compensator (SVeC). A PID damping controller is designed by using modal control theory for the proposed SVeC to render adequate damping characteristics to the dominant modes of the studied SMIB system. To clearly compare the damping contributed by the proposed control scheme, both frequency-domain approach based on eigenvalue analysis and time-domain approach based on nonlinear-model simulations are systematically performed. It can be concluded from the simulation results that the proposed SVeC joined with the designed PID damping controller can offer better damping characteristics to both mechanical mode and exciter mode of the studied SMIB system under various operating conditions.