A Two-level Sddp Solving Strategy with Risk-averse Multivariate Reservoir Storage Levels for Long Term Power Generation Planning

Power generation planning in large-scale hydrothermal systems is a complex optimization task, specially due to the high uncertainty in the inflows to hydro plants. Since it is impossible to traverse the huge scenario tree of the multi-stage problem, stochastic dual dynamic programming (SDDP) is the leading optimization technique to solve it, originally from an expected-cost minimization perspective. However, there is a growing need to apply risk-averse formulations to protect the system from critical hydrological scenarios. This is particularly important for predominantly hydro systems, because environmental issues prevent the construction of new large reservoirs, thus reducing their water regulating capability. This paper proposes a two-level SDDP / Benders decomposition approach to include risk-aversion in power generation planning. The upper level problem is a SDDP solving strategy with expected-cost minimization criterion, where recourse functions for each time step are built through forward/backward passes. The second level consists in multi-period deterministic optimization subproblems for each node of the scenario tree, which are solved to ensure a desired level of protection from a given critical scenario several months ahead. We apply an inner iterative procedure for each stage/scenario of the overall SDDP approach, where feasibility cuts for the feasible region of the second-level subproblems are included in the upper level problem. Such cuts yield the so-called riskaverse storage level surfaces, which are multidimensional rule curves for reservoir to ensure that the policy provided by the SDDP algorithm becomes risk-averse against such critical scenarios. Results are presented for the real large-scale Brazilian system.