Wasserstein distance-based distributionally robust optimal scheduling in rural microgrid considering the coordinated interaction among source-grid-load-storage

We revisit Markowitz’s mean-variance portfolio selection model by considering a distributionally robust version, in which the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures is dictated by the Wasserstein distance. We reduce this problem into an empirical variance minimization problem with an additional regularization term. Moreover, we extend the recently developed inference methodology to our setting in order to select the size of the distributional uncertainty as well as the associated robust target return rate in a data-driven way. Finally, we report extensive back-testing results on S&P 500 that compare the performance of our model with those of several well-known models including the Fama–French and Black–Litterman models. This paper was accepted by David Simchi-Levi, finance.

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Distributionally robust chance constrained svm model with $\ell_2$-Wasserstein distance

Journal of Industrial and Management Optimization ◽

10.3934/jimo.2021212 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Qing Ma ◽

Yanjun Wang

Keyword(s):

Integer Programming ◽

Programming Problem ◽

Numerical Experiments ◽

Wasserstein Distance ◽

Mixed Integer ◽

Integer Programming Problem ◽

Discrete Form ◽

Svm Model ◽

Distributionally Robust ◽

Mixed Integer Programming Problem

<p style='text-indent:20px;'>In this paper, we propose a distributionally robust chance-constrained SVM model with <inline-formula><tex-math id="M1">\begin{document}$ \ell_2 $\end{document}</tex-math></inline-formula>-Wasserstein ambiguity. We present equivalent formulations of distributionally robust chance constraints based on <inline-formula><tex-math id="M2">\begin{document}$ \ell_2 $\end{document}</tex-math></inline-formula>-Wasserstein ambiguity. In terms of this method, the distributionally robust chance-constrained SVM model can be transformed into a solvable linear 0-1 mixed integer programming problem when the <inline-formula><tex-math id="M3">\begin{document}$ \ell_2 $\end{document}</tex-math></inline-formula>-Wasserstein distance is discrete form. The DRCC-SVM model could be transformed into a tractable 0-1 mixed-integer SOCP programming problem for the continuous case. Finally, numerical experiments are given to illustrate the effectiveness and feasibility of our model.</p>

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A Linear Programming Approximation of Distributionally Robust Chance-Constrained Dispatch With Wasserstein Distance

IEEE Transactions on Power Systems ◽

10.1109/tpwrs.2020.2978934 ◽

2020 ◽

Vol 35 (5) ◽

pp. 3366-3377

Author(s):

Anping Zhou ◽

Ming Yang ◽

Mingqiang Wang ◽

Yuming Zhang

Keyword(s):

Linear Programming ◽

Wasserstein Distance ◽

Distributionally Robust

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A Convex Optimization Approach to Distributionally Robust Markov Decision Processes With Wasserstein Distance

IEEE Control Systems Letters ◽

10.1109/lcsys.2017.2711553 ◽

2017 ◽

Vol 1 (1) ◽

pp. 164-169 ◽

Cited By ~ 11

Author(s):

Insoon Yang

Keyword(s):

Convex Optimization ◽

Markov Decision Processes ◽

Wasserstein Distance ◽

Decision Processes ◽

Optimization Approach ◽

Markov Decision ◽

Distributionally Robust

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An Optimal Scheduling Method of Virtual Power Plant Cluster Considering Generation-grid-load-storage Coordination

2021 6th Asia Conference on Power and Electrical Engineering (ACPEE) ◽

10.1109/acpee51499.2021.9436854 ◽

2021 ◽

Author(s):

Jun Wang ◽

Wei Du ◽

Dongmei Yang ◽

Gang Liu ◽

Hui Chen

Keyword(s):

Power Plant ◽

Optimal Scheduling ◽

Virtual Power ◽

Virtual Power Plant ◽

Scheduling Method ◽

Grid Load

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Sample Out-of-Sample Inference Based on Wasserstein Distance

Operations Research ◽

10.1287/opre.2020.2028 ◽

2021 ◽

Author(s):

Jose Blanchet ◽

Yang Kang

Keyword(s):

Financial Institution ◽

Wasserstein Distance ◽

Data Driven ◽

Risk Exposure ◽

Perfect Information Games ◽

Out Of Sample ◽

Distributionally Robust ◽

The One ◽

Estimated Error ◽

The Impact

Financial institutions make decisions according to a model of uncertainty. At the same time, regulators often evaluate the risk exposure of these institutions using a model of uncertainty, which is often different from the one used by the institutions. How can one incorporate both views into a single framework? This paper provides such a framework. It quantifies the impact of the misspecification inherent to the financial institution data-driven model via the introduction of an adversarial player. The adversary replaces the institution's generated scenarios by the regulator's scenarios subject to a budget constraint and a cost that measures the distance between the two sets of scenarios (using what in statistics is known as the Wasserstein distance). This paper also harnesses statistical theory to make inference about the size of the estimated error when the sample sizes (both of the institution and the regulator) are large. The framework is explained more broadly in the context of distributionally robust optimization (a class of perfect information games, in which decisions are taken against an adversary that perturbs a baseline distribution).

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