This paper presents an optimization approach to solve the short-term hydropower unit commitment and loading problem with uncertain inflows. A scenario tree is built based on a forecasted fan of inflows, which in turn comes from the weather forecast and the historical weather realizations. The tree-building approach seeks to minimize the nested distance between the stochastic process of historical inflow data and the multistage stochastic process represented in the scenario tree. A two-phase multistage stochastic model is used to solve the problem. One of the main features of the modeling of the problem is that the effect of varying water head on production is carefully heeded. The proposed approach is tested on a 31 day rolling horizon with daily forecasted inflows for three power plants situated in the province of Quebec, Canada, that belong to the company Rio Tinto.

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The authors investigate the complexity needed in the structure of the scenario trees to maximize energy production in a rolling-horizon framework. Three comparisons, applied to the stochastic short-term unit commitment and loading problem are conducted. The first one involves generating a set of scenario trees built from inflow forecast data over a rolling-horizon. The second replaces the entire set of scenario trees by the median scenario. The third replaces the set of trees by scenario fans. The method used to build scenario trees, based on minimization of the nested distance, requires three parameters: number of stages, number of child nodes at each stage, and aggregation of the period covered by each stage. The authors formulate the question of finding the best values of these parameters as a blackbox optimization problem that maximizes the energy production over the rolling-horizon. Numerical experiments on three hydropower plants in series suggest that using a set of scenario trees is preferable to using the median scenario, but using a fan of scenarios yields a comparable solution with less computational effort.