A microgrid consists of a grid capable of operating in connection to the main interconnected power system or in island mode. This paper deals with a microgrid containing a small hydroelectric power plant (HPP), a battery energy storage system (BESS), a wind energy conversion system (WECS), and a photovoltaic array (PV). The WECS and PV systems are connected to the grid through one full-power voltage source converter (VSC). In order to provide frequency and voltage supports to the microgrid, the VSC is controlled by a virtual synchronous generator (VSG) technique of synchronverter. The considered scenario was divided into three parts: first, the microgrid operates connected to the main system and then it starts operating in island mode; posteriorly, frequency and voltage variations occur due to load variations in the microgrid; finally, the microgrid returns to operate connected to the interconected system. Simulation results have shown that the synchronverter is an alternative to provide efficient frequency and voltage control to a microgrid for both connected and island modes, considering a hybrid generation unit.