A parsimonious bootstrap method to model natural inflow energy series

Abstract

The Brazilian energy generation and transmission system is quite peculiar in its dimension and characteristics. As such, it can be considered unique in the world. It is a high dimension hydrothermal system with huge participation of hydro plants. Such strong dependency on hydrological regimes implies uncertainties related to the energetic planning, requiring adequate modeling of the hydrological time series. This is carried out via stochastic simulations of monthly inflow series using the family of Periodic Autoregressive models, PAR(p), one for each period (month) of the year. In this paper it is shown the problems in fitting these models by the current system, particularly the identification of the autoregressive order 'p' and the corresponding parameter estimation. It is followed by a proposal of a new approach to set both the model order and the parameters estimation of the PAR(p) models, using a nonparametric computational technique, known as Bootstrap. This technique allows the estimation of reliable confidence intervals for the model parameters. The obtained results using the Parsimonious Bootstrap Method of Moments (PBMOM) produced not only more parsimonious model orders but also adherent stochastic scenarios and, in the long range, lead to a better use of water resources in the energy operation planning.