Domain Partition of the Hydro Production Function for Solving Efficiently the Short-Term Generation Scheduling Problem

Short-term generation scheduling (STGS) is a fundamental task in the operational planning analysis of hydroelectric plants. For the multi-unit case, the STGS is represented as a large-scale nonconvex mixed-integer nonlinear optimization model. Then, considering the (usual) short time for providing a solution, it is vital to exploit all the structural properties of the problem at hand. The main issue for exploiting this problem is the hydro production function (HPF), which is a nonlinear nonconvex relationship between power, head, and turbined outflow of a generating unit (GU). Nevertheless, the HPF usually presents operating regions where the function is convex and regions in which it is concave due to physical reasons. Inspired by sequential convex mixed-integer nonlinear programming techniques, this paper proposes partitioning the domain of the HPF in regions in which it is convex and those in which it is concave. The HPF is approximated by a piecewise linear function using the logarithmic aggregation convex combination (LACC) model in convex regions. In turn, in the concave regions, the HPF is replaced by a convex hull approach, which, combined with symmetry strategies, reduces the number of binary variables in the resulting optimization problem. Using several computational instances of a 50-unit hydroelectric plant, we show that the partitioning-based proposed strategy significantly reduces the computational time compared to two other efficient MILP formulations.