Exploring Symmetry in a Short-Term Hydro Scheduling Problem: The Case of the Santo Antônio Hydro Plant

Abstract

The Santo Antônio is the fifth largest hydro plant in Brazil. Due to the environmental constraints, the plant follows a run-of-river operation and, to handle inflow variability, possesses the 50 most oversized bulb generating units (GUs) in the world. These issues render a challenging short-term hydro scheduling problem (STHS), where the critical aspect is modeling the hydropower function (HPF). In this context, this article proposes a two-step strategy based on mixed-integer linear programming (MILP) to solve the STHS, that: (1) explores the symmetry related to the identical GUs by applying a binary expansion to find which units will be active, and (2) obtain the optimal load distribution by linearizing a series of nonlinear problems. In both steps, the HPF is linearized using the logarithmic aggregated convex combination (LACC) model. The symmetry exploration based on the binary expansion is new in the context of the STHS. The experiments show that the proposed strategy yields equal solutions to those obtained by an individual-LACC approach while providing, on average, a 74% reduction in computational time.