Abstract
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.
Highlights
Hydroelectric power plants play a significant role in the generation scheduling of power systems because their operation is cheap, renewable, and flexible
The short-term generation scheduling (STGS) problem, which aims to efficiently determine the status of generating unit (GU) and their generation levels, usually in a day-head planning horizon, is one of the most important tasks for achieving an efficient operation because its solution is used in real-time to assist the operators in allocating the power production among the GUs
The main results of the mixed-integer linear programming (MILP) above for each time step t are as follows: a. the number of identical GUs that operate with equal power generation, gsjt, and turbined outflow wsjt; and b. the GUs that operate with power generation, gvvijt, turbined outflow, wvvijt
Summary
Hydroelectric power plants play a significant role in the generation scheduling of power systems because their operation is cheap, renewable, and flexible. To validate and verify the computational performance of the proposed strategy in this study, we compared the partitioning-based approach with two STGS formulations: one that linearizes each HPF through the nonconvex model LACC, the most efficient among the nonconvex models [13], and one that performs a concave approximation in each FPH via CH [4]. To facilitate the understanding of the proposed strategy, in this study, the formulation is developed for a run-of-river plant with many different types of GUs. The remainder of this paper is organized as follows: Section II presents the mixed-integer nonlinear programming formulation of the STGS problem, Section III presents the partitioning-based approach, and Section IV presents the results of a 50-unit hydroelectric plant with different operating characteristics.
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