Statistical Representation of Wind Power Ramps Using a Generalized Gaussian Mixture Model

Wind power ramps are significantly impacting the power balance of the system operations. Understanding the statistical characteristics of ramping features would help power system operators better manage these extreme events. Toward this end, this paper develops an analytical generalized Gaussian mixture model (GGMM) to fit the probability distributions of different ramping features. The nonlinear least-squares method with the trust-region algorithm is adopted to optimize the tunable parameters of mixture components. The optimal number of mixture components is adaptively solved by minimizing the Euclidean distance between the GGMM and the actual histogram distribution. The probability distribution of ramping features is generally truncated due to the ramp definition with a specific threshold. Thus, a sign function is utilized to truncate the GGMM distribution. Then, the cumulative distribution function of the GGMM is analytically derived and utilized to design a random number generator for ramping features. Numerical simulations on publicly available wind power data show that the parametric GGMM can accurately characterize the irregular and multimodal distributions of ramping features.