Solving the Hydrothermal Unit Commitment Problem via Lagrangian Relaxation and Augmented Lagrangian

This paper considers the hydrothermal unit commitment problem of power systems with high proportion of hydraulic generation. In this sense, a large-scale mixed-integer nonlinear programming problem for the two day cost-optimal generation of system is developed. The model involves a large number of mixed-integer decision variables and constraints linking time periods and operation units. A Lagrangian Relaxation LR scheme, based on variable splitting technique, is designed by assigning multipliers to all constraints coupling. The resulting dual problem is solved by a Bundle method. As the LR method fails to find a feasible solution, a primal recovery phase is also developed. Starting of the dual solution, we use an Augmented Lagrangian technique to find a nearoptimal primal feasible solution. We assess our approach on real-life hydrothermal configuration extracted from Brazilian Hydrothermal power system, proving the conceptual and practical feasibility of the proposed algorithm.