Probabilistic Estimation of Wind Power Ramp Events: A Data-Driven Optimization Approach

Large-scale integration of renewable energy, such as wind and solar power generations, imposes an unprecedented challenge on power system operation, because wind/solar power output is volatile, while in the power system, the generation must balance load in real time. Failure of maintaining power balance may trigger contingency or even blackout, especially when renewable generation quickly increases or decreases during a certain period, which is called a ramp event. Since wind power cannot be predicted accurately, it is difficult to determine the incremental change in two consecutive time periods, not to mention the probability of a ramp event. This paper addresses this problem from the perspective of uncertainty quantification. The likelihood of a ramp event is cast as a data-driven robust probability inequality, which provides the probability of a random variable with unknown distribution belonging to a given polyhedron. To tackle the distributional uncertainty of wind output, we consider a collection of candidate distributions in an ambiguity set constructed from available data. The minimal requirements include the forecast value and the mean-absolute deviation, and the moment-based ambiguity set is comprised of all probability distributions that share the same values of mean and mean-absolute deviation. With more available historical data, a meaningful divergence-based ambiguity set can be set up which encapsulates all probability distributions that are close to an empirical distribution in the sense of Wasserstein metric. The proposed approach offers the probability upper bound of a ramp event in the worst-case wind power distribution, and the conservatism can be remarkably reduced when more historical data are at hand. The proposed methods are compared with the Gaussian mixture model, validating their effectiveness and advantage.