Geração de séries sintéticas com fatores aditivos e multiplicativos a partir de modelos autorregressivos ajustados via algoritmo de otimização aritmética

Abstract

The efficient coordination and operation of the National Interconnected System (NIS) depend on adequate electro-energy planning, whose main objective is to attend all loads in their entirety at the lowest possible cost, balancing operational cost and service quality. To plan the Brazilian electrical system, the planning stages are divided into medium, short, and very short terms, differentiated by the planning horizon and the representation of system components. Medium-term planning, with a horizon of five years ahead and monthly discretization, represents the top of electro-energy planning, as it encompasses the largest horizon, and its results serve as the basis for short-term planning and daily scheduling. For medium-term planning support, the NEWAVE model is currently used in Brazil to define the best operational policy, employing Stochastic Dual Dynamic Programming (SDDP). Due to the five-year horizon, there is a need to represent inflow scenarios or natural energy inflow due to intrinsic stochasticities. Thus, the GEVAZP model uses the autoregressive PAR(p) model to generate synthetic inflow series and, additionally, a Lognormal transformation to prevent the generation of negative series. In this context, this work aims to present a new methodology to calculate the best coefficients and optimal monthly order of a periodic autoregressive model through a Mixed-Integer Nonlinear Programming problem, iteratively solved by the Arithmetic Optimization Algorithm metaheuristic. The proposed optimization problem’s objective function is to minimize the standard deviation of the error vector, represented by the difference between the estimated value and the consolidated historical real value in the NEWAVE deck. Therefore, the arithmetic optimization, for each month, will calculate the best positive coefficients and determine the best order to be considered so that the standard deviation between the calculated errors is as low as possible. Finally, with all coefficients calculated and the optimal order considered for each month, synthetic water inflow or natural energy inflow series are generated, using a simple alternation between additive and multiplicative factors to construct exclusively positive artificial scenarios. The simulations considered the NEWAVE deck from July 2024 and the PySDDP library for reading the data of the plants and Equivalent Energy Reservoirs of the SIN. Finally, the results show the applicability of the developed methodology through comparisons with models adjusted via Box & Jenkins and through statistical analyses of the generated synthetic series. The methodology was tested for both hydroelectric plants and Equivalent Energy Reservoirs of the SIN represented in the medium term.