We study the effect of the uncertainty of wind power on the angular stability of power systems, including a single-machine, infinite-bus (SMIB) system, and a three-generator, nine-bus multi-machine system, which are subject to a self-clearing three-phase fault. Probability density function (PDF) and Monte Carlo (MC) methods are used to calculate the PDFs of states and the probability of the systems successfully clearing the fault as a function of the clearing time and the stochastic properties of the wind power fluctuations, namely the variance and correlation time of the fluctuations. Simulation results for both systems exhibit a significant effect of stochastic resonance between the system's small-signal fluctuation oscillation frequency around the synchronous equilibrium and the correlation time of the wind power fluctuations, amplifying generator state¹s fluctuations and decreasing the probability of successfully clearing the fault. This resonance effect is analytically verified by studying the dependence of the power system state¹s probability density function on the stochastic properties of the wind power fluctuations. For the multi-machine power system, we study the effect of the ratio of renewable-to-total generated power on the system¹s transient stability properties. We find that the probability of successfully clearing the three-phase faults considered decreases with increasing renewable-to-total power ratio. We also define stochastic critical clearing times as function of the desired confidence of successfully clearing the fault.