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A synchronverter is an inverter that mimics synchronous generators, which offers a mechanism for power systems to control grid-connected renewable energy and facilitates smart grid integration. Similar to other grid-connected inverters, it needs a dedicated synchronization unit, e.g., a phase-locked loop (PLL), to provide the phase, frequency, and amplitude of the grid voltage as references. In this paper, a radical step is taken to improve the synchronverter as a self-synchronized synchronverter by removing the dedicated synchronization unit. It can automatically synchronize itself with the grid before connection and track the grid frequency after connection. This considerably improves the performance, reduces the complexity, and computational burden of the controller. All the functions of the original synchronverter, such as frequency and voltage regulation, real power, and reactive power control, are maintained. Both simulation and experimental results are presented to validate the control strategy. Experimental results have shown that the proposed control strategy can improve the performance of frequency tracking by more than 65%, the performance of real power control by 83%, and the performance of reactive power control by about 70%.