In the current power system dispatching, the high penetration of renewable energy sources has caused a lot of uncertainty. To cope with the issue, this paper proposes a data-driven stochastic optimization model as a solution to the unit commitment (UC) problem. This model integrates wind power and energy storage and considers the correlation among the forecast errors of multiple wind farms. Based on the Dirichlet process Gaussian mixture model (DPGMM), this paper first uses historical data to construct a probability density function (PDF) for the uncertainty and spatial correlation of wind power forecast errors. Then the simultaneous backward reduction (SBR) algorithm is used to select typical scenarios from the large number of simulated scenarios generated by sampling the PDF obtained previously. As such, the uncertainty of wind power is represented by the typical scenarios. After that, a stochastic UC model is proposed, the objective function of which is established considering the cost of wind curtailment and load shedding. Finally, taking a ten-unit system with two wind farms and energy storage devices as an example, the effectiveness of the above models and methods is validated by the results of comparative exemplifications.