This paper presents a novel power sharing control strategy for islanded mode microgrids (MG). The goal is to enable renewable power sources connected to the point of com- mon coupling (PCC) through three-phase three-wire inverters to cooperatively feed linear and non-linear local loads. The strategy contribution is two-fold. First, a centralized controller is designed to facilitate the power sharing capability of all inverters by means of data communications regardless of load changes and inverter faults. Second, a communication protocol is designed following an event-driven paradigm in such a way that the consumed bandwidth is reduced. Selected simulation results show the main features of the power sharing control strategy. ; Peer Reviewed ; Postprint (published version)