Multi-Site Wind Farms Dependence Structure Using Vine Copulas: Impacts of Dataset Sizes and Employed Copulas

Using copulas in statistics evaluates the dependence between random variables. Copula modeling has significantly been used in many areas, especially in the search for multivariate distributions. As wind energy rapidly becomes an important renewable energy source, it is very important to deeply evaluate any potential existing dependencies among the data. This study introduces a comprehensive application of vine copulas in modeling multi-site wind speed dependencies for different sizes of datasets, offering a more flexible approach than traditional correlation-based methods. Unlike previous studies, this work systematically evaluates the impact of dataset sizes on the selection of the best-performing vine copula structures, providing valuable insights for improving wind forecasting and grid stability. These evaluations are studied using R-vine, C-and D-vine models by applying pair copulas families and the pairwise empirical Kendall’s $\tau $ values, where the appropriate model is selected based on the Akaike Information Criteria (AIC), the Bayesian Information Criteria (BIC), and the likelihood method (Log-likelihood). This study finds out the best vine copula model for three different wind speed datasets, namely hourly (large), daily (medium), and small (weekly). Also, using all pair copulas families (Clayton, Frank, Gumbel, Student’s t, and Gaussian), vine copula simulations provide guidelines for conceptual understanding of mutual impacts and correlations among multi-site wind farms. Simulations also show that the R-vine copula is the best structure for both large and small datasets, while the C-vine copula is the best structure for medium datasets.