A Copula Enhanced Convolution for Uncertainty Aggregation

A promising approach to managing the uncertainty of renewables is probabilistic forecasting. However, a key challenge associated with the integration of probabilistic forecast into real-world applications is to estimate the distribution of the aggregation of several correlated variables given their individual distributions. This study presents a copula enhanced convolution technique that accounts for cross-variable correlations. The method approximates the distributions of the convolved variables with piecewise polynomial functions and the correlations are represented with copula functions, which are then discretized and factorized for better computation performance. The method is demonstrated by applying it to the convolution of two correlated variables as well as multiple correlated variables. Our results indicate the copula enhancement effectively improve the results by reducing deviations from the actual distributions in the case of net load forecasting in California.