A truncated Gaussian mixture model for distributions of wind power ramping features

Wind power ramps (WPRs) are significantly impacting the power balance of the system operations. Better 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 truncated Gaussian mixture model (TGMM) to fit the probability distributions of different ramping features. The non-linear least square 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 to the actual probability distribution. A sign function is utilized to truncate the original GMM distribution and obtain the final TGMM. The cumulative distribution function (CDF) of TGMM is analytically derived. Numerical simulations on publically available wind power data show that the parametric TGMM can accurately characterize the irregular and multimodal distributions of each ramping feature.