The integration of renewable energy resources (RES) in power systems is displacing conventional generation based on synchronous generators. RESs use voltage source converters as the main interface between the primary energy source and the grid. Therefore, these should guarantee in future converter-dominated power systems robust and secure operation through voltage and frequency regulation. Recently, the concept of a virtual synchronous generator (VSG) with grid-forming functionality has emerged in three-phase systems. However, the extension of this concept to single-phase devices has not been widely explored. Taking into account that a significant number of the new RES generation could be connected to distribution systems, it might be necessary to endow a certain number of single-phase RES with grid-forming capability. This paper presents the expansion of the three-phase VSG to a single-phase system including grid-forming functionality. Specifically, the paper proposes two possible implementations in the rotating and stationary reference frames. Both controllers are validated through experimental tests to substantiate their benefits and limitations.