Abstract: The power source stochastic fluctuation caused by renewable energy grid connection is an important problem affecting the stable operation of the power system. To explore this question,first of all,a power system model containing random disturbances is established and then based on the theory of quasi Hamiltonian system and using the stochastic average method and stochastic dynamic programming method,the theoretical analysis on the stochastic stability of the power system connected with renewable energy is conducted,and the optimal control design is made with the longest mean first-passthrough time as the objective,and the stability margin of the controlled system is examined. Finally,a single machine infinite numerical example is established based on the model,and the stochastic stability margin and optimal control law under different interference intensities are obtained. The feasibility and effectiveness of the proposed method are verified by digital simulation.