Processo iterativo de construção da função de custo futuro na metodologia PDE-ConvexHull

Abstract

The Brazilian National Grid (BNG) presents peculiar characteristics due to the huge territory dimensions and by the fact that the electricity generation is predominantly originated from hydraulic plants that provide for the system the capacity of a pluriannual regularization of the reservoirs. The water inflows to these plants are stochastic and often present complementary behavior among the regions of the country, stimulating the existence of big amounts of energy exchanges between the subsystems through the national grid. The long term operation planning problem (that includes a period of 5 to 10 years ahead with monthly discretization) is made by a chain of computational models that are validated by the main agents that act on BNG (commercialization, generation, transmition and distribution of energy). The primary model of this chain, which is developed by Electric Energy Research Center/ELETROBRÁS, is the NEWAVE model, which is based on the Stochastic Dual Dynamic Programming (SDDP) for electroenergetic policy determination on a long term horizon. Thisworkhastheobjectiveofimplementacomputationalmodelforthemid/longtermoperation planning using the Stochastic Dynamic Programming (SDP) together with the Convex Hull algorithm (PDE-ConvexHull) in a computationally efficient way (Fast-PDE-ConvexHull). This is because it was observed that when utilizing the PDE-ConvexHull technique, an elevated amount of hyperplanes are obtained for the composition of the cost-to-go function. So, the different linear programming problems to be solved during the iterative process can be turned larger, increasing the execution time for the operational policy calculus in a considerably manner. Thus, the main contribution of this work is to present a new methodology (FastPDE-ConvexHull) for the representation of the cost-to-go function on the linear programming problems where the computational time become less sensible to the number of hyperplanes obtained from the Convex Hull algorithm. It is highlighted that techniques of parallel computing was employed in order to turn the process more efficient. The methodology was utilized for the BNG’s long term planning calculus, based on the equivalent subsystems of energy. The methodology Fast-PDE-ConvexHull was incorporated to a computational platform, developed in C++/Java programming language, that is able to consider the same data set used by the official models acting on the BNG, compounding a robust model for the resolution of the problem. Firstly, in order to validate the proposed methodology, the results obtained from the FastPDE-ConvexHullarecomparedwiththoseobtainedfromtheutilizationofthePDE-ConvexHull technique aiming to verify the computational gain and the adherence between both results. Finally, as the elaborated computational platform is capable to use the official data set availablefortheNG,itwaspossibletheutilizationoftheMonthlyOperationalProgram(MOP) of January 2011, released by the Independent System Operator (ISO), as the study case for comparingtheresultsobtainedbytheproposedmethodologywiththeresultsobtainedfromthe NEWAVE model.