A Distributionally Robust Optimization Model for Unit Commitment Based on Kullback-Leibler Divergence

• Published in: IEEE transactions on power systems Vol. 33; no. 5; pp. 5147 - 5160
• Main Authors: Chen, Yuwei, Guo, Qinglai, Sun, Hongbin, Li, Zhengshuo, Wu, Wenchuan, Li, Zihao
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Ambiguity; Benders decomposition; Convergence; Distributionally robust; Divergence; Electric power generation; generalized Benders decomposition; Iterative algorithms; Iterative methods; Linear programming; Mathematical programming; Optimization; Optimization models; Robustness; Stochastic processes; Uncertainty; Unit commitment; Wind power; Wind power generation
• DOI: 10.1109/TPWRS.2018.2797069
• ISSN: 0885-8950

This paper proposes a new distance-based distributionally robust unit commitment (DB-DRUC) model via Kullback-Leibler (KL) divergence, considering volatile wind power generation. The objective function of the DB-DRUC model is to minimize the expected cost under the worst case wind distributions restricted in an ambiguity set. The ambiguity set is a family of distributions within a fixed distance from a nominal distribution. The distance between two distributions is measured by KL divergence. The DB-DRUC model is a "min-max-min" programming model; thus, it is intractable to solve. Applying reformulation methods and stochastic programming technologies, we reformulate this "min-max-min" DB-DRUC model into a one-level model, referred to as the reformulated DB-DRUC (RDB-DRUC) model. Using the generalized Benders decomposition, we then propose a two-level decomposition method and an iterative algorithm to address the RDB-DRUC model. The iterative algorithm for the RDB-DRUC model guarantees global convergence within finite iterations. Case studies are carried out to demonstrate the effectiveness, global optimality, and finite convergence of a proposed solution strategy.