With the increasing proportion of power electronic devices in the power grid, the power system generally suffers from problems such as reduced inertia and diminished damping, resulting in weak stability of the power system. Due to the susceptibility of distributed power sources to external factors, it is imperative to deploy energy storage systems with sufficient capacity to safeguard the stable operation of the power grid. Energy Storage Converter (ESC) serves as a key interface between the energy storage system and the power grid, and the research on its control strategy is of great importance. Flexible control strategies not only enable microgrids to operate as a whole unit connected to the grid, but also support their independent operation when necessary. This article summarizes the control strategies of energy storage inverters in different modes and identifies the problems that need to be solved in current power grid energy storage systems.