Managing Hydroelectric Reservoirs Over an Extended Horizon Using Benders Decomposition With a Memory Loss Assumption

Abstract

Traditional stochastic programming methods are widely used for solving hydroelectric reservoirs management problems under uncertainty. With these methods, random parameters are described using a scenario tree possessing an unstructured topology. Therefore, traditional methods can potentially handle high-order time-correlation effects, but their computational requirements grow exponentially with the branching level used to represent parameters (e.g., load, inflows, prices). Consequently, random parameters must be discretized very coarsely and, as a result, numerical solutions of mid-term optimization models can be quite sensitive to small perturbations to the tree parameters. In this paper, we propose a new approach for managing high-capacity reservoirs over an extended horizon (1-3 years). We partition the planning horizon in two stages and assume that a memory loss occurs at the end of the first stage. We propose a new Benders decomposition algorithm designed specifically to exploit this simplification. The low memory requirement of our method enables to consider a much higher branching level than would be possible with previous methods. The proposed approach is tested on a 104-week production planning problem with stochastic inflows.