Multivariate Cross-Correlated Reliability Modeling of Wind Turbines using Pair-Copula Functions

Abstract

In this paper, the spatial-temporal correlation between wind turbines has been modeled. Due to the large dimension of the problem (spatial and temporal correlation) and the number of wind turbines, solving the copula-based correlation model is so complicated and requires a decomposition technique. The pair-copula function are employed to decompose the problem into bivariate copula functions and using goodness-of-fit indices, the most suitable copula families are evaluated and selected. This model has then been used to model uncertainties and generate cross-correlated scenarios around the short-term forecast values to include the correlation information in the error models. The generated samples are then represented as histograms, which later are fitted to optimal density functions. The most important contribution of this paper is the introduction of joint-reliability evaluation procedure that integrates the correlation models in the non-sequential Monte Carlo simulation method. The proposed joint-reliability model is applied to real wind farms in Lower Saxony in Germany. The results show that including the concept of correlation in the reliability evaluation lead to more realistic results, and allows to fulfill the ancillary services with a certain level of reliability through uncertain resources.