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 evalu...
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2025-01-01
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| author | Amir Shahirinia Zeinab Farahmandfar Mohammad Tavakoli Bina Hossein Hafezi Vincent Tanoe |
| author_facet | Amir Shahirinia Zeinab Farahmandfar Mohammad Tavakoli Bina Hossein Hafezi Vincent Tanoe |
| author_sort | Amir Shahirinia |
| collection | DOAJ |
| description | 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 <inline-formula> <tex-math notation="LaTeX">$\tau $ </tex-math></inline-formula> 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. |
| format | Article |
| id | doaj-art-37334d5c91e94714ace5079b1cb4e80b |
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| issn | 2169-3536 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
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| spelling | doaj-art-37334d5c91e94714ace5079b1cb4e80b2025-08-20T02:28:15ZengIEEEIEEE Access2169-35362025-01-0113795967960810.1109/ACCESS.2025.356521710979316Multi-Site Wind Farms Dependence Structure Using Vine Copulas: Impacts of Dataset Sizes and Employed CopulasAmir Shahirinia0https://orcid.org/0000-0002-0081-0674Zeinab Farahmandfar1https://orcid.org/0000-0001-8912-0401Mohammad Tavakoli Bina2https://orcid.org/0000-0001-9344-146XHossein Hafezi3https://orcid.org/0000-0003-1859-6263Vincent Tanoe4https://orcid.org/0000-0002-4195-579XSchool of Engineering and Applied Sciences, University of the District of Columbia, Washington, DC, USADepartment of Civil and Systems, Johns Hopkins University, Baltimore, MD, USAFaculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran, IranFaculty of Information Technology and Communication Sciences, Tampere University, Tampere, FinlandSchool of Engineering and Applied Sciences, University of the District of Columbia, Washington, DC, USAUsing 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 <inline-formula> <tex-math notation="LaTeX">$\tau $ </tex-math></inline-formula> 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.https://ieeexplore.ieee.org/document/10979316/R-vine copulasC-and D-vine copulasKendall’s τfrankGaussianclayton |
| spellingShingle | Amir Shahirinia Zeinab Farahmandfar Mohammad Tavakoli Bina Hossein Hafezi Vincent Tanoe Multi-Site Wind Farms Dependence Structure Using Vine Copulas: Impacts of Dataset Sizes and Employed Copulas IEEE Access R-vine copulas C-and D-vine copulas Kendall’s τ frank Gaussian clayton |
| title | Multi-Site Wind Farms Dependence Structure Using Vine Copulas: Impacts of Dataset Sizes and Employed Copulas |
| title_full | Multi-Site Wind Farms Dependence Structure Using Vine Copulas: Impacts of Dataset Sizes and Employed Copulas |
| title_fullStr | Multi-Site Wind Farms Dependence Structure Using Vine Copulas: Impacts of Dataset Sizes and Employed Copulas |
| title_full_unstemmed | Multi-Site Wind Farms Dependence Structure Using Vine Copulas: Impacts of Dataset Sizes and Employed Copulas |
| title_short | Multi-Site Wind Farms Dependence Structure Using Vine Copulas: Impacts of Dataset Sizes and Employed Copulas |
| title_sort | multi site wind farms dependence structure using vine copulas impacts of dataset sizes and employed copulas |
| topic | R-vine copulas C-and D-vine copulas Kendall’s τ frank Gaussian clayton |
| url | https://ieeexplore.ieee.org/document/10979316/ |
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