Efficient Methods for Modeling Correlations Among Renewable Energy Sources in State-Space Sampling Monte Carlo Simulation

This paper compares two combined methods for modeling correlations among multiple random variables in the state-space sampling approach that is adopted in non-sequential Monte Carlo Simulation. The first method combines the Rank Score (Iman and Conover method) with Latin Hypercube sampling, while the second method combines Kernel Density Estimation with Bayesian Networks to represent dependency between variables. The methods are compared in terms of goodness-of-fit and computational efficiency, using statistical metrics, spatial correlation matrices, and scatter plots. The multiple time series were aggregated into single ones (Total and Net Generation) in order to validate the accuracy of each model in representing multi-dimensional correlated variables. The methods were evaluated for 3 large-dimensional cases based on the actual Brazilian energy system, with 10, 19 and 28 time series of 5-, 3- and 2-year horizons, respectively. The results show that the statistical dependencies of the historical data were accurately captured by both models, with comparable goodness-of-fit, but a higher computational efficiency of the first.