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The authors analyse the operational profitability of a hydropower system selling both energy and reserve capacity in a competitive market setting. A mathematical model based on stochastic dynamic programming is used to compute the water values for the system considering different power plant configurations. The uncertainties in inflow and both energy and reserve capacity prices are considered through a discrete Markov chain. Subsequently, the system operation is simulated based on the obtained water values to assess system performance and expected revenues from the two markets. The model is applied in a case study for a Norwegian hydropower producer, showing how the power plant operation changes and profitability increases when considering sale of reserve capacity. The authors emphasise on how the water values are influenced by the opportunity to sell reserve capacity, and assess how the representation of non-convex relationships in the water value computations as well as simulation influence the profitability. P g max , P g min Max./Min. capacity, MW Q min minimum river flow, m 3 /s Q gm discharge in point m, m 3 /s T number of weeks in planning horizon V max , V min Max./Min. reservoir volume, Mm 3 V n reservoir volume at point n, Mm 3

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This study presents a two-stage stochastic linear programming (LP) model to calculate the water value in an isolated hybrid diesel/wind/pumped-storage power system with high wind power penetration and with a closed-loop pumped-storage power plant (i.e. there is no natural inflows in the upper pond), that takes into account in an approximate manner that the startup cost of the diesel units depends on the time passed since the previous shutdown. The proposed model is applied in the power system of El Hierro island in the Canary Archipelago. The water values provided by the proposed model have been used as input for the day-ahead generation scheduling. The results obtained in the study indicate that the day-ahead generation schedule obtained when using the water values provided by the proposed model is similar to the one obtained when using the water values provided by a detailed mixed integer LP (MILP) model. The computational time required to obtain the water value with the proposed model is several orders of magnitude lower than the one needed to solve the MILP model. 2 per unit power output/input of unit i ∈ V between P i and P i during the period t for the LP2 model

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