Análise topológica dos cortes da função de custo futuro baseada em geometria analítica: aplicação ao problema de despacho hidrotérmico

Abstract

The complexity associated with planning and scheduling the operation of a large system such as Brazil’s is enormous. This is mainly due to the number of hydroelectric plants arranged in cascades, the temporal coupling between decisions, the uncertainties associated with renewable energy sources and the energy market to be served, and the details of the system components. In general, to make the problem computationally tractable, it is divided into coordinated stages, which define long, medium and short-term studies. In Brazil, these studies use the NEWAVE, DECOMP and DESSEM models, respectively, developed by the Electric Energy Research Center (CEPEL). Coordination between them is carried out through the cost to go function (FCF), whereby the longer-term models transmit to the shorter-term models the expected value for the operation cost as a function of the state of the system, incorporating risk aversion. The NEWAVE and DECOMP models use algorithms based on Dynamic Programming (DP) to calculate the operating policy. These algorithms iteratively construct the FCF as a piecewise linear function using the Benders decomposition technique. In the course of the algorithms used by these models, it is common to construct cuts that become redundant in future iterations. From the point of view of Linear Programming (LP), the presence of redundant constraints does not alter the feasibility region, but can cause excessive effort in solving the problem. It is therefore essential that these constraints are identified and eliminated. This not only simplifies the problem, but also improves computational efficiency, reduces the probability of multiple solutions and maintains numerical stability, contributing to a more effective and robust approach to models. Furthermore, from the FCF provided by the longer-term models, information is inserted into the shorter-term model, especially economic information, which can lead to unexpected operations and significant deviations from the water values of the hydroelectric plants. This paper therefore applies a generic strategy for determining redundant FCF cuts. After defining these cuts, a methodology is proposed for defining what is called the region of activity of the cuts, applying concepts from Analytical Geometry. Next, the calculation of the distance between points in the state space and between a given point and the region of activity of each cut is defined. These developments make it possible to evaluate the distances between the coupling points of the models in which the cuts were built and were used when consulting the FCF associated with the same instant of time. All the analyses were carried out using tutorial examples and official cases from the models in order to be validated. The results thus contribute to improving the current process of coupling between models.