This paper proposes an expected value and chance constrained stochastic optimization approach for the unit commitment problem with uncertain wind power output. In the model, the utilization of wind power can be adjusted by changing the utilization rate in the proposed expected value constraint. Meanwhile, the chance constraint is used to restrict the probability of load imbalance. Then a Sample Average Approximation (SAA) method is used to transform the objective function, the expected value constraint, and the chance constraint into sample average reformulations. Furthermore, a combined SAA framework that considers both the expected value and the chance constraints is proposed to construct statistical upper and lower bounds for the optimization problem. Finally, the performance of the proposed algorithm with different utilization rates and different risk levels is tested for a six-bus system. A revised IEEE 118-bus system is also studied to show the scalability of the proposed model and algorithm.