Chapter 3 - Uncertainty modeling

Abstract

Chapter 3 proposes new uncertainty modeling methods for wind power output both in stochastic programming and robust optimization. In stochastic programming, a scenario generation method considering spatial-temporal correlation is proposed for uncertainty representation of multiple wind farms. The Gaussian mixture model and exponential function are used to construct the spatial correlation and temporal correlation, respectively, and Gibbs sampling is utilized to reduce the sampling complexity. In robust optimization, a partition-combine uncertainty set is proposed to reduce the conservativeness. The partition is to reduce the size of the original box-like uncertainty set and generate a new uncertainty set no longer limited to a specific shape. The combination is to utilize nonempty subsets to describe the irregular shape of the new uncertainty set. The scale of uncertainty variables is reduced with quick identification of inner subsets. The simulation results validated that the proposed scenario generation method and partition-combine uncertainty set modeling method can properly fit the probability distribution and boundaries of the historical dataset.