Since the loading speed of the pumped storage unit is not controllable after the pumping phase is transferred to the pumping condition, the load jumps violently during the start-up and shutdown process, which may easily affect the stability of the power grid frequency during the isolated period. In order to solve the problem has long plagued frequency stability of Hainan power grid under the "big machine small net" and eliminate the possible threats to safety and stability, according to the mathematical models of the synchronous machine, the water turbine and its governor of the pumped storage unit, this paper establishes the dynamic feedback linearization model of the turbine governor link and the rotor motion link of the synchronous machine. The influence of turbine governor dynamics on the frequency stability of pumped storage units was studied by BPA simulation. By calculating the frequency stability and power Angle stability of Hainan power grid, the maximum capacity of pumped storage unit is determined. This study provides a reliable reference for the future stable operation of Hainan power grid and isolated operation of pumped storage units.