Power generation of the hydropower groups is integrated with power transmitted through long distance and extra high voltage transmission lines. Hydropower groups may be isolated from the outage of transmission lines and confront with such serious stability issues as frequency control and voltage control. Combining with the actual operation conditions in Sichuan power grid， the simulation model is built based on PSASP and MATLAB to reproduce the operation accidents of the isolated hydropower groups in Sichuan power grid. Main factors resulting in system instability under isolated operation mode are explored with studying high frequency and high voltage characteristic of the isolated hydropower groups. The security and stability control strategies are accordingly proposed. Simulations in Sichuan power gird verify effectiveness of the proposed control strategies.