Subjects: Dynamic and Electric Engineering >> Electrical Engineering Subjects: Mathematics >> Control and Optimization. submitted time 2022-08-07
Xiaodong Zheng
Baorong Zhou
Xiuli Wang
Bo Zeng
Jizhong Zhu
Haoyong Chen
Peizheng Xuan
Waisheng Zheng
Abstract： Quick-start generation units are critical devices and flexible resources to ensure a high penetration level of renewable energy in power systems. By considering the wind uncertainty, and both binary and continuous decisions of quick-start units within the intraday dispatch, we develop a Wasserstein-metric-based distributionally robust optimization model for the day-ahead network-constrained unit commitment (NCUC) problem with mixed integer recourse. We propose two feasible frameworks for solving the optimization problem. One approximates the continuous support of random wind power with finitely many events, the other leverages the extremal distributions instead. Both solution frameworks rely on the classic nested column-and-constraint generation (C&CG) method. It is shown that due to the sparsity of L1-norm Wasserstein metric, the continuous support of wind power generation could be represented by a discrete one with a small number of events, and the extremal distributions rendered are sparse as well. With this reduction, the distributionally robust NCUC model with complicated mixed-integer recourse problems can be efficiently handled by both solution frameworks. Numerical studies are carried out, demonstrating that the model considering quick-start generation units ensures unit commitment (UC) schedules to be more robust and cost effective, and the distributionally robust optimization method captures the wind uncertainty well in terms of out-of-sample tests.
Subjects: Dynamic and Electric Engineering >> Electrical Engineering Subjects: Mathematics >> Control and Optimization. submitted time 2022-08-07
Abstract： 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.
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