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This paper proposes a methodology to determine the required level of spinning and nonspinning reserves in a power system with a high penetration of wind power. The computation of the required reserve levels and their costs is achieved through a stochastic programming market-clearing model spanning a daily time horizon. This model considers the network constraints and takes into account the cost of both the load shedding and the wind spillage. The methodology proposed is illustrated using an example and a realistic case study. Some conclusions are finally drawn.