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

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 rest...

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Bibliographic Details
Published inIEEE 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
LanguageEnglish
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
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Summary: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.
ISSN:0885-8950
1558-0679
DOI:10.1109/TPWRS.2018.2797069