An autocorrelation-based copula model for generating realistic clear-sky index time-series

This study presents a method for using copulas to model the temporal variability of the clear-sky index, which in turn can be used to produce realistic time-series of photovoltaic power generation. The method utilizes the autocorrelation function of a clear-sky index time-series, and based on that a correlation matrix is set up for the dependency between clear-sky indices at N time-steps. With the use of this correlation matrix an N-dimensional copula function is configured so that correlated samples for these N time-steps can be obtained. Results from the copula model are compared with the original data set and an uncorrelated model based on zero correlated clear-sky index data in terms of distribution, autocorrelation, step changes and distribution. The copula model is shown to be superior to the uncorrelated model in these aspects. As a validation the model is tested with solar irradiance for two different geographical regions: Norrköping, Sweden and Hawaii, USA. The copula model is also applied to a set of bins of daily mean clear-sky index and the use of bins is shown to improve the results.