A Copula-Based Scenario Generation Method for Renewable Wind Power Outputs of Two Wind Farms

Renewable wind power output is characterized by strong randomness, volatility, and spatial dependence, which makes accurate two-adjacent wind farm scenario generation essential for stochastic dispatch and secure operation of power systems. To describe the joint uncertainty of wind farm outputs without directly constructing a complicated joint probability distribution, this paper proposes a Copula-based scenario generation method for two correlated wind farm outputs. Historically measured output data of two wind farms are first transformed into pseudo-observations through non-parametric marginal distribution estimation. Six bivariate Copula tools, including Gaussian Copula, t-Copula, Empirical Copula, Frank Copula, Clayton Copula, and Gumbel Copula, are then compared in terms of correlation coefficient, Spearman coefficient, Kendall coefficient, degrees of freedom, and distance from the Empirical Copula. The results show that the Bivariate t-Copula achieves the smallest fitting distance among all parametric Copula models and can effectively characterize the strong correlation and tail dependence between the two wind farms. Based on the fitted t-Copula, random samples are generated in the Copula space, transformed into wind power output samples through inverse marginal functions, and reduced into six representative scenarios using K-means clustering. Finally, the generated scenarios are introduced into an optimal power flow model with wind scenarios on the IEEE 30-bus system. The calculation results show that the proposed method can provide representative wind power inputs and effectively reflect the influence of wind power uncertainty on conventional unit dispatch. The proposed approach provides a practical reference for scenario generation and stochastic operation analysis of power systems with two correlated wind farms.