Short-Term Hydrothermal Scheduling with Solar and Wind Farms Using Second-Order Cone Optimization with Chance-Box Constraints

Abstract

Short-Term Hydrothermal Scheduling (STHS) is a classic problem in power system operation where the aim is to decide the dispatch of both thermal and hydroelectric units. This problem is complex due to its non-linear non-convex nature, and the requirements for fast solving for daily operation. Technologies such as wind and solar generation introduce stochastic behaviors, which have to be considered within the mathematical model. Although the problem is frequently solved by traditional and heuristic techniques, this paper proposes a new formulation based on convex approximations, and in particular, Second-Order Cone optimization, which addresses the nonlinear relation among water discharge, reservoir volume, and hydropower generation in a rigorous mathematical approach. Moreover, the impact of wind and solar generation on the power system is analyzed, modeling their stochastic behavior in a robust way by using chance-box constraints. Numerical results demonstrate that the Second-Order Cone approximation is precise and faster than techniques proposed recently and that the chance-box constraint approach guarantees a robust solution.