In the near future a large part of traditional generation based on conventional synchronous machines (SM) will be replaced by renewable generation based on voltage source converters (VSC). In this sense, power system operators have begun to demand VSC-based power plants be able to participate in the frequency and voltage regulation, and are also interested in services like inertia emulation and damping of power oscillation, functions that today are carried out by large synchronous generators. Therefore, several studies have suggested new ways to control voltage source converters, that try to emulate the behavior of synchronous generators and are known generically as Virtual Synchronous Machines. The synchronous power controller (SPC) is a flexible solution that emulates the classical swing equation of a synchronous machine and improves its response. The SPC inherits the advantages of conventional synchronous generators, while it fixes many of its drawbacks. In this work, a sensitivity analysis of a VSC connected to the grid and controlled by SPC is performed. In this sense, a non-linear mathematical model of the system is first developed. This non-linear model is then linearized, obtaining a linear model from which the eigenvalues and sensitivities of the system to some relevant parameters are calculated. Finally, time-domain simulations are performed to confirm the results of the sensitivity analysis.