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Fluctuating wind production over short time periods is balanced by adjusting generation from thermal plants to meet demand. Thermal ramp rates are limited, so increased variation in wind output as wind penetration increases can add to system operating costs because of the need for more thermal operating reserves. Traditional deterministic modeling techniques fail to fully capture these extra costs. We propose a stochastic dynamic programming (SDP) approach to unit commitment and dispatch, minimizing operating costs by making optimal unit commitment, dispatch, and storage decisions in the face of uncertain wind generation. The SDP solution is compared with two other solutions: 1) that of a deterministic dynamic program with perfect wind predictions to find the cost of imperfect information, and 2) that of a simulation model run under a decision rule, derived from Monte Carlo simulations of the deterministic model, to assess the cost of suboptimal stochastic decision making. An example Netherlands application shows that these costs can amount to several percent of total production costs, depending on installed wind capacity. These are the conclusions of a single simplified case study. Nonetheless, the results indicate that efforts to improve wind forecasting and to develop stochastic commitment models may be highly beneficial.