The synchronverter is a device used in some microgrids to perform self-synchronization and represent the behavior of a synchronous machine. However, the original control has been proposed for balanced networks, which is not present in all distribution systems. In unbalanced networks, the negative sequence may appear and generate a double frequency oscillation when delivering power or a non-symmetrical current from the inverter; thus, it must compensate unbalanced load. Therefore, this article shows that a synchronverter can be synchronized using the positive sequence even when there are voltage unbalances. The proposed strategy was simulated in the Simulink-Matlab© software, considering an unbalanced power grid with a single inverter and a load. The results confirm the effectiveness of this strategy, as the synchronverter can follow the grid frequency and the wave shape amplitude after starting the frequency droop control.