A copula method for simulating correlated instantaneous solar irradiance in spatial networks

This paper presents a method for generating correlated instantaneous solar irradiance data for an arbitrary set of spatially dispersed locations. Based on the empirical clear-sky index distribution for one location and the cross-correlation between clear-sky index data at all location pairs, a copula is used to represent the dependence between locations. The method is primarily intended for probabilistic simulations of electricity distribution grids with high penetrations of photovoltaic (PV) systems, in which solar irradiance data for nodes in the grid can be sampled from the model. The method is validated against a 10-s resolution solar irradiance data set for 14 locations, dispersed within an array of approximately 1 km × 1.2 km, at the Island of Oahu, Hawai'i, USA. The results are compared with previous results for along- and cross-wind pairs of locations, and with models for adjacent (completely correlated) and dispersed (completely uncorrelated) locations. It is shown that the copula approach performs better than the adjacent model for a majority of all location pairs and for all but one pair of locations separated more than 500 m. It outperforms the dispersed model for all pairs of locations. In conclusion, the proposed method can generate correlated data and estimate the aggregate clear-sky index for any set of locations based only on the distribution of the clear-sky index for a single location.