Comparing the Performance of Three-Parameter Weibull and Lognormal Distributions in the Generation of Energy Inflows Synthetic Scenarios

A methodology based on tri-parametric Weibull distributions for modeling correlated residuals and generating synthetic series of monthly inflows (EIs) to hydropower reservoirs, using a periodic autoregressive model-PAR(p) in a SDDP scheme is proposed. The methodology and algorithm developed aim to preserve the EI historical mean, standard-deviation and skewness values. From an initial estimate of the location parameter, obtained through the method of 3rd order moments, estimates of the other parameters are calculated; then the algorithm iteratively refines the initial estimate to minimize the difference between the historical and synthetic skewnesses. The methodology was applied to 7 case-studies considering different reservoirs, months and PAR(p) model orders, and proved to be robust, presenting better performance than several methods found in the literature. Also, the proposed approach achieved superior performance in relation to the currently employed one (tri-parametric Lognormal distributions). The proposed approach is versatile and can also be applied in other areas.