This study focuses on a virtual synchronous machine (VSM) based on voltage source converters to mimic the behavior of synchronous machines (SMs) and improve the damping ratio of the power system. The VSM model is simplified according to some assumptions (neglecting the speed variation and the stator transients) to allow for the possibility of dealing with low-frequency oscillation in large-scale systems with many VSMs. Furthermore, a virtual power system stabilizer (VPSS) structure is proposed and tuned using a method based on a linearized power system dynamic model. The linear and nonlinear analyses examine the stability of two modified versions of a 16-machine power system in which, in the first case, partial classical machines are replaced by VSMs, and in the second case, all SMs are replaced by VSMs. The simulation results of the case studies validate the efficiency of the proposed control strategy.