Métodos de análise da função de custo futuro em problemas convexos: aplicação nas metodologias de programação dinâmica estocástica e dual estocástica

Abstract

The Brazilian National Grid (BNG) presents peculiar characteristics due to its huge territory dimensions and hydro-generation predominancy. As the water inflows to these plants are stochastic and a pluriannual regularization for system storage capacity is provided, the use of hydro-generation must be planned in an accurate manner such that it considersalongplanningperiod. So, thelong-termoperationplanning(LTOP)problemis generallysolvedbyachainofcomputationalmodelsthatconsideraperiodof5to10years ahead such that the primary model of this chain is based on Stochastic Dual Dynamic Programming (SDDP) technique. The main contribution of this thesis is to propose some improvements in Stochastic Dynamic Programming techniques usually settled on solving LTOP problems. In the fashion of an iterative cut selection, it is firstly proposed a LTOP problem solution model that uses an ecient state space discretization for Stochastic Dynamic Programming (SDP), called ESDP. The proposed model of SDP has a welldefined convergence criterion such that including CVaR does not hinder convergence analysis. Due to the lack of good upper bound estimators in SDDP when including CVaR, additional issues are encountered on defining a convergence criterion. So, based on ESDP convergence analysis, a new criterion for SDDP convergence is proposed such that it can be used regardless of CVaR representation with no extra computational burden. Moreover, the proposed convergence criterion for SDDP has a more detailed description such that forward paths can be individually assessed and then be accordingly discarded for computational time reduction, or even define paths to be replaced in a more particular resampling scheme in SDDP. Based on aggregate reservoir representation, the proposed methodsofconvergenceofSDDPandtheESDPwereappliedonLTOPproblemsrelatedto BNG. Results show improvements in SDDP based technique and eectiveness of proposed convergence criterion for SDDP when CVaR is used.