Sensitivity analysis on the definition of stages for the Multi-stage Benders decomposition approach applied to hydrothermal scheduling

Multi-stage Benders decomposition (MSBD), also known as dual dynamic programming, has been proposed previously in the literature to solve hydrothermal scheduling problems. The MSBD methodology, contrary to traditional dynamic programming approaches, solves the problem by iterative forward and backward recursions, approximating the cost-to-go function for each stage by Benders cuts. The classical definition of the stages in the MSBD approach is to assign a stage for each time step. In this paper, we propose a new strategy to decompose the problem, where each stage comprises all variables and constraints of several time steps. Numerical results of the application of this strategy to the short-term hydrothermal scheduling problem are presented. These results confirm the advantages of this strategy in terms of CPU time, as compared to the classical stage definition. We show that there is an "optimal aggregation factor", which best balances the trade-off between the CPU time to solve each subproblem generated by the decomposition and the number of iterations until convergence of the MSBD algorithm.