In this paper, a study of the day-ahead unit commitment problem with stochastic wind power generation is presented, which considers conditional, and correlated wind power forecast errors through a distributionally robust optimization approach. Firstly, to capture the characteristics of random wind power forecast errors, the least absolute shrinkage, and selection operator (Lasso) is utilized to develop a robust conditional error estimator, while an unbiased estimator is used to obtain the covariance matrix. The conditional error, and the covariance matrix are then used to construct an enhanced ambiguity set. Secondly, we develop an equivalent mixed integer semidefinite programming (MISDP) formulation of the two-stage distributionally robust unit commitment model with a polyhedral support of random variables. Further, to efficiently solve this problem, a novel cutting plane algorithm that makes use of the extremal distributions identified from the second-stage semidefinite programming (SDP) problems is introduced. Finally, numerical case studies show the advantage of the proposed model in capturing the spatiotemporal correlation in wind power generation, as well as the economic efficiency, and robustness of dispatch decisions.

This paper applies modern statistical nonparametric methodology to the problem of prediction of the transient stability boundary of large-scale power engineering systems. The stability issue is characterized by the critical clearing time (CCT) that is employed to determine whether a precontingency steady-state condition is stable for a given fault in the power system. The multidimensional mapping between the precontingency steady-state conditions and the corresponding CCT is modeled as an additive structure of one-dimensional functions. Nonparametric kernel estimation methods are applied to the assumed additive model yielding the boundary prediction algorithm that is easily interpretable and avoids the curse of dimensionality. The precision of our additive nonlinear modeling is demonstrated in the context of fault prediction of the 470-bus power network. For the specified fault type, we demonstrate a stronger prediction accuracy compared to other large-scale machine learning methods that have been used for the transient stability boundary problem so far.

This paper utilizes modern statistical and machine learning methodology to predict the oscillation mode of interest in complex power engineering systems. The damping ratio of the electromechanical oscillation mode is formulated as a function of the power of the generators and loads as well as bus voltage magnitudes in the entire power system. The celebrated Lasso algorithm is implemented to solve this high-dimension modeling problem. By the nature of the L1 design, the Lasso algorithm can automatically render a sparse solution, and by eliminating redundant features, it provides desirable prediction power. The resultant model processes a simple structure, and it is easily interpretable. The precision of our sparse modeling framework is demonstrated in the context of an IEEE 50-Generator 145-Bus power network and an online learning framework for the power system oscillation mode prediction is also provided.