Simulation of spatially correlated wind power in small geographic areas—Sampling methods and evaluation.

In clusters of wind generators spread over small geographic areas, the spatial correlation of wind power production is strong. Simulation of joint power production in such cases—such as for instance for determining the available power in a microgrid—is flawed if the correlation is not properly defined. Several methods have been proposed in the literature for producing scenarios of correlated samples; mostly focused on wind speed. In this paper we analyze three popular choices: classical Monte Carlo (with correlation induced by Cholesky factorization), Latin Hypercube Sampling (with correlation induced by rank sorting), and the recent copula theory. We put together a variety of statistical tools to transform an uncorrelated multivariate sample into a correlated one; and supplement other works by introducing a detailed definition of the wind power distribution and by expanding the Archimedean copula analysis to dimensions beyond the bivariate case analyzed in some related works. We analyze a year of wind production of 210 wind site from NREL data base. We cluster them to give a view of prospective microgrids, and employ several statistical techniques to measure the adequacy of the simulated samples to the original measured data. Our results show that, for generation in small geographic areas, the higher the number of generators, the better the wind power dependence structure is described by LHS. On the contrary, copulas—Gumbel or Gaussian for two- and three-dimensional problems, and Gaussian for higher dimensions—are better suited for representing correlated wind speed. The results are different when the generators are spread over large geographic areas. Compared with LHS endowed with rank sorting for inducing correlation, copula theory is in some sense cumbersome to apply for modeling and simulating wind power data. However, simulations can be performed in prospective microgrids in small geographical areas with larger accuracy by means of LHS if wind power is analyzed rather than wind speed. This advantage is lost for large distances or when small number of generators is considered. [ABSTRACT FROM AUTHOR]