Two-stage distributionally robust optimal power flow with flexible loads

Yiling Zhang, Siqian Shen, Bowen Li, Johanna L. Mathieu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations


In this paper, we formulate a two-stage distributionally robust (DR) model for the optimal power flow (OPF) problem in the presence of uncertainties from wind power generation and load-based reserves. Assuming ambiguous distributions of the random variables, we minimize the costs of generation, reserves, and the worst-case expected value of the penalty cost of violating constraints. We consider a lifted support and a distributional ambiguity set parameterized by empirical means and absolute deviations of the random variables. We adopt an enhanced linear decision rule (ELDR) to derive a quadratic programming reformulation of the DR-OPF model, and compare its performance to that of a DR chance-constrained OPF model. We study the optimal solution patterns of the two approaches, compare their performance in out-of-sample simulations, and also numerically justify the use of the ELDR.

Original languageEnglish (US)
Title of host publication2017 IEEE Manchester PowerTech, Powertech 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781509042371
StatePublished - Jul 13 2017
Externally publishedYes
Event2017 IEEE Manchester PowerTech, Powertech 2017 - Manchester, United Kingdom
Duration: Jun 18 2017Jun 22 2017

Publication series

Name2017 IEEE Manchester PowerTech, Powertech 2017


Conference2017 IEEE Manchester PowerTech, Powertech 2017
Country/TerritoryUnited Kingdom

Bibliographical note

Funding Information:
This work was supported by NSF Grant #CCF-1442495.

Publisher Copyright:
© 2017 IEEE.


  • distributionally robust optimization
  • enhanced linear decision rule
  • load control


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