Assessing solution quality and computational performance in the hydro unit commitment problem considering different mathematical programming approaches

• A comprehensive formulation for the HUC problem with extensive modeling details.
• Detailed explanation of the LR, MILP, and MINLP for solving the HUC problem.
• Comparative analysis of LR, MILP, and MINLP based on the cost and computational burden.

This paper presents a comparative analysis of different mathematical programming approaches for optimizing the hydro unit commitment (HUC) problem with cascaded plants, multiple generating units, and a head-dependent hydropower model. Regarding the HUC problem related to this paper, the objective is to minimize the cascade outflow while satisfying all constraints, including a power target for each plant, in a day-ahead planning horizon. The decision variables are the on/off status of the units and the respective generation levels. Rigorously, the HUC is a mixed-integer nonlinear programming (MINLP) problem, and several strategies can be used to compute near-optimal solutions. In this paper, we are interested in accessing the solution quality, as well as the computational performance when the HUC problem is solved using the following mathematical programming approaches: (i) the Lagrangian relaxation that represents a decomposition technique that exploits the HUC modeling structure, (ii) a MINLP solver that can handle the size and the non-concavity of the problem, and (iii) a mixed-integer linear programming (MILP) approach obtained by means of the hydropower model linearization. To perform the proposed analysis, numerical results are presented related to a real hydro system with eight cascaded reservoirs and 29 generating units.