Nonnegative Wind Speed Time Series Models for SDDP and Stochastic Programming Applications

Stochastic dual dynamic programming (SDDP) is a popular method for hydro-thermal planning and recently has been applied to energy optimization problems in smart grids involving wind energy resources. In this method, there is a need for incorporating dynamic models in order to take into account time correlations of uncertainties. The models used should posses certain linearity properties to conserve the convexity of the optimization problem to be solved. This is crucial for the convergence of the SDDP algorithm. In the past, especially in hydro-thermal planning, linear autoregressive (AR) models were usually used for this purpose. However, they can produce negative values which is not realistic and can lead to difficulties in SDDP computations. As a remedy, one can employ additive or multiplicative AR models which are capable of producing nonnegative time series. Despite of this fact, the works using such models in SDDP based wind energy applications are very rare and model estimation methods were not elaborated. Moreover, their accuracy in representing real wind uncertainty was not studied well. Motivated with these facts, in the present study, modeling of wind speed distribution by such AR models is investigated. The parameters of the models were estimated by solving constrained least squares optimization problems. In order to asses the accuracy of corresponding distributions, a nonparametric method for computing the K-L divergence between probability density functions was utilized. Finally, the models were compared in terms of accuracy of their distributions and features of their parameter estimation algorithms.