Solving Stochastic Hydrothermal Unit Commitment with a New Primal RecoverycTechnique Based on Lagrangian Solutions

The high penetration of intermittent renewable generation has prompted the development of Stochastic Hydrothermal Unit Commitmentc(SHUC) models, which are more difficult to be solved than their thermal-basedccounterparts due to hydro generation constraints and inflow uncertainties.cThis work presents a SHUC model applied in centralized cost-based dispatch, where the uncertainty is related to the water availability in reservoirs and demand. The SHUC is represented by a two-stage stochastic model, formulated as a large-scale mixed-binary linear programming problem. The solution strategy is divided into two steps, performed sequentially, with intercalated iterations to find the optimal generation schedule. The first step is the Lagrangian Relaxation (LR) approach. The second step is given by a Primal Recovery based on LR solutions and a heuristic based on Benders' Decomposition. Both steps benefit from each other, exchanging information over the iterative process. We assess our approach in terms of the quality of the solutions and running times on space and scenario LR decompositions. The results show the advantage of our primal recovery technique compared to solving the problem via MILP solver. This is true already for the deterministic case, and the advantage grows as the problem’s size (number of plants and/or scenarios) does