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This paper presents a stochastic cost model and a solution technique for optimal scheduling of the generators in a wind integrated power system considering the demand and wind generation uncertainties. The proposed robust unit commitment solution methodology will help the power system operators in optimal day-ahead planning even with indeterminate information about the wind generation. A particle swarm optimization based scenario generation and reduction algorithm is used for modeling the uncertainties. The stochastic unit commitment problem is solved using a new parameter free self adaptive particle swarm optimization algorithm. The numerical results indicate the low risk involved in day-ahead power system planning when the stochastic model is used instead of the deterministic model.