With wind turbine system developing larger and lighter, the dimensions of time-varying complexity gradually increase. Meanwhile, the wind turbine loads suffer randomness, which results in stronger prolonged vibration. And then the stability of wind turbine system is seriously damaged. By integrating wind turbine model, deterministic load model and the impact of stochastic load, this paper establishes first-passage model with stochastic load. And combined with the electrical dynamic model of wind turbine, a unified electromechanical dynamic model is built up. By using stochastic averaging method of quasi-non-integrable- Hamiltonian systems, it sets up relevant Hamilton function and the stochastic model of one-dimensional diffusion process, which will lay a good foundation for following stability and reliability study. With an example of a domestic unit of 750 kW wind turbine, the corresponding unified electromechanical dynamic model is established. And the first-passage phenomenon is verified by a simulation in MATLAB. Simulation results show that the model has good applicability and operability.