Reduced Scenario Tree Generation for Mid-term Hydrothermal Operation Planning

The optimal scheduling of hydrothermal systems requires the representation of future inflows uncertainties for basically two reasons. Firstly, to define the present day commitment of thermal plants in order to hedge against adverse low inflows, and, secondly, to specify the volume of water storage in reservoirs to avoid spillage if high inflows occur. An inflow scenario tree must be correctly dimensioned so as to provide a parsimonious - but still representative - sample of the multivariate process underlying possible future inflows. In this article we propose a methodology to generate such a tree. The idea is to use principal component analysis to reduce the effective dimensionality of the scenario specification problem so that a discretization technique can be used in a smaller dimensional space. A stochastic hydrothermal scheduling optimization model was applied to the Brazilian interconnected power system to illustrate the proposed methodology. The quality of the reduced sample was evaluated by considering not only hydrological aspects, but also the solution stability of the stochastic problem