Uma nova metodologia para geração de séries sintéticas de vazão natural afluente usando modelo periódico autorregressivo com erro multiplicativo baseada em otimização não linear

Abstract

The Mid-Term Energy Operation Planning of the Brazilian National Interconnected System (SIN) is a complex decision-making problem under uncertainty, involving intricate spatial and temporal interactions. The optimal policy is currently determined through the Stochastic Dual Dynamic Programming (SDDP) algorithm, which models hydrological uncertainty through a Periodic Autoregressive (PAR) process using the Box and Jenkins method. However, the PAR model estimated by Box and Jenkins has a significant limitation: the possibility of generating synthetic series with negative inflow values, which can lead to unfeasiblities in the optimization problem. To address this issue, the official methodology employs a three-parameter Lognormal transformation, which, while avoiding negative results, introduces an undesirable nonlinearity into the model, affecting the effectiveness of the SDDP. This work proposes an alternative, simple, and flexible methodology for estimating the coefficients of the PAR model. The approach is based on the direct minimization of multiplicative errors, combined with a mean constraint on the generated residuals and subsequent scale adjustments, aiming to generate synthetic scenarios that meet the essential assumptions for the optimal functioning of the SDDP.