Security constrained economic dispatch (SCED) is an important tool for ISOs/RTOs to achieve economic power system operation in day-ahead and real-time markets. However, the wind generation uncertainty varying within a large range may make the SCED model unsolvable under certain scenarios. Thus, curtailment is utilized in this work to avoid the infeasibility in the presence of wind power uncertainty. It is found that the uncertainty set is affected by the curtailment restriction which is modeled as an interval number. By the use of interval arithmetic and big M approach, we construct a mixed integer linear programming (MILP) with the objective of minimizing the total curtailment costs, while guaranteeing the SCED to be feasible when wind power varies within its uncertainty set. Numerical results from a 118-bus test system over 24 time periods verify the effectiveness of this proposed method.