Real-world hydro-power unit-commitment: Dealing with numerical errors and feasibility issues

This article deals with feasibility issues of the hydro-unit commitment relative to units along a valley in the price-taker revenue-maximizing setting. The problem is formulated as a mixed-integer linear programming model. Besides physical constraints, we consider two additional specifications that apply to a subset of units and reservoirs within a valley, namely the power-flow curves of each unit feature discrete operational points and each reservoir level should meet target volumes. These specifications, together with the standard issues affecting real-world data, make our problem harder to solve, often infeasible. We follow a step-by-step approach to identify and repair one source of infeasibility at a time, namely numerical errors and model infeasibilities. The former is analyzed and fixed through tools like an exact solver and a model and data preprocessing. The remaining infeasibilities are eliminated with a 2-stage method. In the first stage, a minimal deviation from target volumes, i.e., strategic, thus relaxable, constraints, is computed to make the problem feasible. In the second stage, the original problem is solved with a possible deviation from the target volumes as defined in the first stage. Computational results confirm the effectiveness of the proposed method to recover feasibility on a challenging real-world test set.