Two-Stage Stochastic Optimization of Large-Scale Hydrothermal System

One of the major challenges for planning and operation of complex hydrothermal systems is how to incorporate stochasticity in decision making; particularly, the stochasticity of inflows to reservoirs. The country of Brazil is subject to different climate regimes in different regions of the country. Consequently, great hydrological diversity is observed throughout the major watersheds. The Brazilian hydrothermal system consists of a completely linked network of 129 medium and large hydropower plants, 798 small hydropower plants, and 1469 thermal and 57 wind power plants, with a total installed capacity of 123,464 MW. The hydropower plants produce, on average, 91% of the total electricity consumed in the country, while the complementary thermal system is dispatched mainly during periods of drought. In our previous studies, we developed the HIDROTERM model to optimize the management and operation of the hydrothermal system. This deterministic model considers individual hydropower plants and is solved by nonlinear programming. The model is particularly useful for sensitivity analysis and has been applied to the planning and operation of the existing hydrothermal system. We now develop a new version of the model. The new model directly incorporates the stochasticity of the inflows in the formulation. The approach is based on a two-stage stochastic programming with recourse. The multi-stage inflow scenario tree is first built. The first stage is deterministic using inflow forecasts. The second stage branches out into possible scenarios. To reduce the size of the stochastic programming with recourse problem we are investigating different scenario tree reduction methods as well as methods that can be used to reduce the simulation time of the underlying hydrothermal model. The proposed methodology has been tested and verified on the Paranapanema basin, a representative subsystem of the Brazilian hydrothermal system.