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Distributionally robust optimal power flow with contextual information

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  • Esteban-Pérez, Adrián
  • Morales, Juan M.

Abstract

In this paper, we develop a distributionally robust chance-constrained formulation of the Optimal Power Flow problem (OPF) whereby the system operator can leverage contextual information. For this purpose, we exploit an ambiguity set based on probability trimmings and optimal transport through which the dispatch solution is protected against the incomplete knowledge of the relationship between the OPF uncertainties and the context that is conveyed by a sample of their joint probability distribution. We provide a tractable reformulation of the proposed distributionally robust chance-constrained OPF problem under the popular conditional-value-at-risk approximation. By way of numerical experiments run on a modified IEEE-118 bus network with wind uncertainty, we show how the power system can substantially benefit from taking into account the well-known statistical dependence between the point forecast of wind power outputs and its associated prediction error. Furthermore, the experiments conducted also reveal that the distributional robustness conferred on the OPF solution by our probability-trimmings-based approach is superior to that bestowed by alternative approaches in terms of expected cost and system reliability.

Suggested Citation

  • Esteban-Pérez, Adrián & Morales, Juan M., 2023. "Distributionally robust optimal power flow with contextual information," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1047-1058.
    • Handle: RePEc:eee:ejores:v:306:y:2023:i:3:p:1047-1058
    DOI: 10.1016/j.ejor.2022.10.024
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    References listed on IDEAS

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    1. Hong, Tao & Pinson, Pierre & Fan, Shu & Zareipour, Hamidreza & Troccoli, Alberto & Hyndman, Rob J., 2016. "Probabilistic energy forecasting: Global Energy Forecasting Competition 2014 and beyond," International Journal of Forecasting, Elsevier, vol. 32(3), pages 896-913.
    2. Bertsimas, Dimitris & McCord, Christopher & Sturt, Bradley, 2023. "Dynamic optimization with side information," European Journal of Operational Research, Elsevier, vol. 304(2), pages 634-651.
    3. Weijun Xie & Shabbir Ahmed, 2020. "Bicriteria Approximation of Chance-Constrained Covering Problems," Operations Research, INFORMS, vol. 68(2), pages 516-533, March.
    4. Arrigo, Adriano & Ordoudis, Christos & Kazempour, Jalal & De Grève, Zacharie & Toubeau, Jean-François & Vallée, François, 2022. "Wasserstein distributionally robust chance-constrained optimization for energy and reserve dispatch: An exact and physically-bounded formulation," European Journal of Operational Research, Elsevier, vol. 296(1), pages 304-322.
    5. Grani A. Hanasusanto & Vladimir Roitch & Daniel Kuhn & Wolfram Wiesemann, 2017. "Ambiguous Joint Chance Constraints Under Mean and Dispersion Information," Operations Research, INFORMS, vol. 65(3), pages 751-767, June.
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    Cited by:

    1. Álvaro Porras & Concepción Domínguez & Juan Miguel Morales & Salvador Pineda, 2023. "Tight and Compact Sample Average Approximation for Joint Chance-Constrained Problems with Applications to Optimal Power Flow," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1454-1469, November.

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