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

Chen, Yuwei; Guo, Qinglai; Sun, Hongbin; Li, Zhengshuo; Wu, Wenchuan; Li, Zihao

doi:10.1109/tpwrs.2018.2797069

Cited by 155 publications

(100 citation statements)

References 34 publications

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“…However, there are few papers on its PSE applications in the existing literature [117,119]. As the trend of big data has fueled the increasing popularity of datadriven stochastic programming in many areas, DRO emerges as a new data-driven optimization paradigm which hedges against the worst-case distribution in an ambiguity set, and has various applications in power systems, such as unit commitment problems [125][126][127][128], and optimal power flow [129,130].…”

Section: Data-driven Stochastic Program and Distributionally Robust Omentioning

confidence: 99%

Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming

Ning

You

2019

Computers & Chemical Engineering

255

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This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and mathematical programming for decision-making under uncertainty, and identifies potential research opportunities. A brief review of classical mathematical programming techniques for hedging against uncertainty is first presented, along with their wide spectrum of applications in Process Systems Engineering. A comprehensive review and classification of the relevant publications on data-driven distributionally robust optimization, data-driven chance constrained program, data-driven robust optimization, and data-driven scenario-based optimization is then presented. This paper also identifies fertile avenues for future research that focuses on a closed-loop data-driven optimization framework, which allows the feedback from mathematical programming to machine learning, as well as scenario-based optimization leveraging the power of deep learning techniques. Perspectives on online learningbased data-driven multistage optimization with a learning-while-optimizing scheme is presented.

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Section: Data-driven Stochastic Program and Distributionally Robust Omentioning

confidence: 99%

Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming

Ning

You

2019

Computers & Chemical Engineering

255

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“…where P, P 0 are distribution functions in measure space Ω. Many scholars have studied the DRO based on KL divergence [31][32][33][34], and they put forward some reformulation methods in the research. In these studies, KL divergence has been used to solve problems such as unit commitment, and showed its advantages.…”

Section: Dro Model Based On Kl-divergencementioning

confidence: 99%

“…In general, the data are not fully utilized because the distribution knowledge contains more information than moments. Motivated by the deficiency of the moment-based DRO method, reference [24][25][26][27][28][29][30][31][32][33][34] investigated the distance-based DRO method. Usually, in a distance-based DRO model, the ambiguity set is constructed by probability distribution.…”

Section: Introductionmentioning

confidence: 99%

“…Different from the mature application of the Wasserstein metric, the application of Kullback-Leibler divergence needs further study. Under the volatile of wind power generation, [31] proposed a distance-based distributionally robust UC model via KL divergence. The objective function minimized the expected generation cost under the worst-case wind power generation distribution, and KL divergence was used to measure the distance between two distributions and to construct the ambiguity set.…”

Section: Introductionmentioning

confidence: 99%

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Distributionally Robust Model of Energy and Reserve Dispatch Based on Kullback–Leibler Divergence

et al. 2019

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This paper proposes a distance-based distributionally robust energy and reserve (DB-DRER) dispatch model via Kullback-Leibler (KL) divergence, considering the volatile of renewable energy generation. Firstly, a two-stage optimization model is formulated to minimize the expected total cost of energy and reserve (ER) dispatch. Then, KL divergence is adopted to establish the ambiguity set. Distinguished from conventional robust optimization methodology, the volatile output of renewable power generation is assumed to follow the unknown probability distribution that is restricted in the ambiguity set. DB-DRER aims at minimizing the expected total cost in the worst-case probability distributions of renewables. Combining with the designed empirical distribution function, the proposed DB-DRER model can be reformulated into a mixed integer nonlinear programming (MINLP) problem. Furthermore, using the generalized Benders decomposition, a decomposition method is proposed and sample average approximation (SAA) method is applied to solve this problem. Finally, simulation result of the proposed method is compared with those of stochastic optimization and conventional robust optimization methods on the 6-bus system and IEEE 118-bus system, which demonstrates the effectiveness and advantages of the method proposed.

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“…are commonly applied (see, e.g., [24]- [27]). Other distributional information based on, e.g., the Wasserstein distance [28], [29], the φ-divergence [11], [30], and the unimodality [16], [31], [32], have also been proposed to characterize the ambiguity set. Accordingly, DRO formulates a robust counterpart of SP and hedges against the worstcase probability distribution within the ambiguity set.…”

Section: Introductionmentioning

confidence: 99%

Distributionally Robust Co-Optimization of Power Dispatch and Do-Not-Exceed Limits

Jiang

Yan

2020

IEEE Trans. Power Syst.

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To address the challenge of the renewable energy uncertainty, the ISO New England (ISO-NE) has proposed to apply do-not-exceed (DNE) limits, which represent the maximum nodal injection of renewable energy the grid can accommodate.Unfortunately, it appears challenging to compute DNE limits that simultaneously maintain the system flexibility and incorporate a large portion of the available renewable energy at the minimum cost. In addition, it is often challenging to accurately estimate the joint probability distribution of the renewable energy. In this paper, we propose a two-stage distributionally robust optimization model that co-optimizes the power dispatch and the DNE limits, by adopting an affinely adjustable power re-dispatch and an adjustable joint chance constraint that measures the renewable utilization. Notably, this model admits a second-order conic reformulation that can be efficiently solved by the commercial solvers (e.g., MOSEK). We conduct case studies based on modified IEEE test instances to demonstrate the effectiveness of the proposed approach and analyze the trade-off among the system flexibility, the renewable utilization, and the dispatch cost.Index Terms-Power dispatch, renewable energy uncertainty, robust optimization, do-not-exceed limit, affine policy.

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

Cited by 155 publications

References 34 publications

Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming

Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming

Distributionally Robust Model of Energy and Reserve Dispatch Based on Kullback–Leibler Divergence

Distributionally Robust Co-Optimization of Power Dispatch and Do-Not-Exceed Limits

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