Transient stability analysis of stochastic system mainly depends on Monte Carlo simulations which demand vast calculations over numerous trials to ascertain the behavior of the system. The uncertainty problems are usually solved as deterministic problems with the dynamics of the stochastic procedure ignored. A stochastic transient stability analysis method is proposed based on the quasi-Hamiltonian system theory and stochastic averaging method. Firstly

the perturbed stochastic power system is dynamically mapped into a perturbed two-machine system according to the extended equal area criterion(EEAC)theory. The stochastic differential algebraic equations of the system are established and the transient energy of the corresponding Hamiltonian system is derived. The security region of the system is determined according to its Hamiltonian energy function. Then

the stochastic averaging method is applied to analyze the quasi-Hamiltonian system and the averaged system and averaged equations are obtained. The diffusion procedure of the transient energy of the power system is studied in accordance with the diffusion theory while the conditional reliability function is calculated by the Kolmogorov equation. The influences of fault type

perturbation amplitude

and fault clearing time on the transient stability can be quantitatively investigated. The stochastic averaging method for quasi-generalized Hamiltonian system is applied in a four-generator and two-area system to verify its effectiveness. This work is supported by National Basic Research Program of China(973 Program)(No. 2013CB228204)and State Grid Corporation of China(No. SGJS0000DKJS1501031).