The increasing participation of renewables in power systems has forced system operators to strengthen grid codes requiring renewable power plants (RPPs) to provide fast frequency support such as inertia response and power oscillation damping. To cope with such new requirements, this article proposes the implementation of a virtual synchronous power plant controller (VSPPC) for RPPs. The VSPPC takes the most from emulating the behavior of a synchronous generator, especially in the case of grid events, as it permits emulating inertia and provides power oscillation damping capabilities. If compared with conventional control schemes, the main advantage of the VSPPC lays in the fact that it does not require to implement any modification in the existing controllers of the plant's converters, which are often controlled as grid-following generation units. This feature makes VSPPC attractive for incorporating advanced grid supporting functionalities in utility-scale RPPs. In this work, the main principles behind the VSPPC and comparative analysis based on simulation and experimental results are provided to validate its performance.