Mean-variance mapping metaheuristic applied to stochastic hydrothermal optimization

Abstract

The optimal programming of a hydrothermal system is considered a complex problem, given its nonlinearity, dimension, and number of restrictions. In mid-term horizon, this complexity is also related to the uncertainty associated with some input parameters, such as demand and water inflow. Simplifications have been used in conventional models to solve this optimization problem; however, considering these reductions can lead to unrealistic solutions. Given the advantages of meta-heuristic tools, in terms of simplicity of their application to solve complex problems, obtaining a solution near to optimal and considering that models developed in the literature have addressed simple cases and have not exploited the advantages of metaheuristics, this paper proposes an application based on the Mean Variance Mapping metaheuristic technique to solve the optimal programming of a hydrothermal system in the mid-term horizon. A Numerical test on a system of cascaded reservoirs is presented, where the uncertainty of the water inflows was modeled by means of a scenario tree. The results are validated with Benders’ Decomposition model. It was assumed a single-node system, describe by both linear objective function and linear restrictions, however the proposed methodology can be applied to cases with a higher degree of complexity.