Data-Driven Distributionally Robust Unit Commitment With Wasserstein Metric: Tractable Formulation and Efficient Solution Method

Zheng, Xiaodong; Chen, Haoyong

doi:10.1109/tpwrs.2020.3014808

Cited by 40 publications

(31 citation statements)

References 6 publications

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“…The following lemmas establish (71) and the conditions under which it's right-hand side is well defined. Lemma 6.…”

Section: B Properties Of the Dual (48)mentioning

confidence: 99%

“…These assumptions typically relate to a specific form for the objective function or constraints in (2) (e.g. linear/convex functions/piecewise-convex objectives or constraints with support or density requirements, see [34,71,46,37,70,5,63] for additional examples). In this instance, such limitations preclude their applicability since, in general, a "gradient object" for a functional J (see Section 1) need not satisfy these conditions.…”

Section: Previous Workmentioning

confidence: 99%

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Frank-Wolfe Methods in Probability Space

Kent,

Blanchet,

Glynn

2021

Preprint

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We introduce a new class of Frank-Wolfe algorithms for minimizing differentiable functionals over probability measures. This framework can be shown to encompass a diverse range of tasks in areas such as artificial intelligence, reinforcement learning, and optimization. Concrete computational complexities for these algorithms are established and demonstrate that these methods enjoy convergence in regimes that go beyond convexity and require minimal regularity of the underlying functional. Novel techniques used to obtain these results also lead to the development of new complexity bounds and duality theorems for a family of distributionally robust optimization problems. The performance of our method is demonstrated on several nonparametric estimation problems.

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“…The following lemmas establish (71) and the conditions under which it's right-hand side is well defined. Lemma 6.…”

Section: B Properties Of the Dual (48)mentioning

confidence: 99%

Section: Previous Workmentioning

confidence: 99%

Frank-Wolfe Methods in Probability Space

Kent,

Blanchet,

Glynn

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…However, [2] does not consider the uncertainty associated with electricity prices. While [5] harnesses the Wasserstein distance, [3] capitalizes on moment information so as to construct ambiguity sets and develop DRO approaches for UC, yet neither approach jointly evaluates the uncertainty associated with VER generation and electricity prices.…”

Section: Related Workmentioning

confidence: 99%

“…Distributionally robust optimization (DRO)-albeit being initially proposed long ago-has recently gained traction as a paradigm that addresses the drawbacks of both SO and RO. Under the DRO paradigm, the probability distribution of uncertain parameters itself is considered to be uncertain and belong to an ambiguity set of probability distributions that may be constructed based on various methods, including using moment information [2,3], the Kullback-Leibler (KL) divergence [4], and Wasserstein distance [5]. Central to DRO is the formulation of an optimization problem that minimizes the expected cost brought about by the worst-case distribution in the ambiguity set.…”

Section: Introductionmentioning

confidence: 99%

A Distributionally Robust Optimization Approach for Unit Commitment in Microgrids

Yurdakul¹,

Sivrikaya²,

Albayrak³

2020

Preprint

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This paper proposes a distributionally robust unit commitment approach for microgrids under net load and electricity market price uncertainty. The key thrust of the proposed approach is to leverage the Kullback-Leibler divergence to construct an ambiguity set of probability distributions and formulate an optimization problem that minimizes the expected cost brought about by the worst-case distribution in the ambiguity set. The proposed approach effectively exploits historical data and capitalizes on the k-means clustering algorithm-in conjunction with the soft dynamic time warping score-to form the nominal probability distribution and its associated support. A two-level decomposition method is developed to enable the efficient solution of the devised problem. We carry out representative studies and quantify the relative merits of the proposed approach vis-à-vis a stochastic optimizationbased model under different divergence tolerance values.

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“…This is because any resulting UC model, when reformulated in a tractable form, may well have a scalability issue regarding the number of samples that make up the reference distribution. Indeed, most of the existing Wasserstein-DRO-based UC (WDRUC) models have this issue [12]- [15].…”

Section: Introductionmentioning

confidence: 99%

On Affine Policies for Wasserstein Distributionally Robust Unit Commitment

Cho¹,

Yang²

2022

Preprint

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This paper proposes a unit commitment (UC) model based on data-driven Wasserstein distributionally robust optimization (WDRO) for power systems under uncertainty of renewable generation as well as its tractable exact reformulation. The proposed model is formulated as a WDRO problem relying on an affine policy, which nests an infinitedimensional worst-case expectation problem and satisfies the non-anticipativity constraint. To reduce conservativeness, we develop a novel technique that defines a subset of the uncertainty set with a probabilistic guarantee. Subsequently, the proposed model is recast as a semi-infinite programming problem that can be efficiently solved using existing algorithms. Notably, the scale of this reformulation is invariant with the sample size. As a result, a number of samples are easily incorporated without using sophisticated decomposition algorithms. Numerical simulations on 6-and 24-bus test systems demonstrate the economic and computational efficiency of the proposed model.

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Data-Driven Distributionally Robust Unit Commitment With Wasserstein Metric: Tractable Formulation and Efficient Solution Method

Cited by 40 publications

References 6 publications

Frank-Wolfe Methods in Probability Space

Frank-Wolfe Methods in Probability Space

A Distributionally Robust Optimization Approach for Unit Commitment in Microgrids

On Affine Policies for Wasserstein Distributionally Robust Unit Commitment

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