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This paper proposes a new unit commitment (UC) formulation for a power system with significant levels of wind generation. The proposed scheme departs from existing unit commitments in that it explicitly models the day-ahead predicted residual demand probability density function (PDF) including the effect of wind power curtailment. This PDF is then used to define a constraint on the probability of the residual demand exceeding the scheduled reserve, which is imposed in addition to the standard N-1 deterministic security criterion. This hybrid probabilistic/deterministic form maintains the mixed-integer linear structure that makes the proposed UC compatible with highly efficient commercially available solvers. Numerical examples illustrate the economical and technical benefits obtained by systematically including wind curtailment as decisions variables in the UC. In addition, the paper computes the hourly day-ahead UC schedule over the course of one year for a typical power system to illustrate the impact of wind power penetration on measures such as operation costs, incremental costs, emission levels, on/off unit switching operations, and reserve levels.