Distributionally Robust Chance-Constrained Approximate AC-OPF with Wasserstein Metric

Chao Duan*, Wanliang Fang, Lin Jiang, Li Yao, Jun Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

179 Scopus citations


Chance constrained optimal power flow (OPF) has been recognized as a promising framework to manage the risk from variable renewable energy (VRE). In the presence of VRE uncertainties, this paper discusses a distributionally robust chance constrained approximate ac-OPF. The power flow model employed in the proposed OPF formulation combines an exact ac power flow model at the nominal operation point and an approximate linear power flow model to reflect the system response under uncertainties. The ambiguity set employed in the distributionally robust formulation is the Wasserstein ball centered at the empirical distribution. The proposed OPF model minimizes the expectation of the quadratic cost function w.r.t. the worst-case probability distribution and guarantees the chance constraints satisfied for any distribution in the ambiguity set. The whole method is data-driven in the sense that the ambiguity set is constructed from historical data without any presumption on the type of the probability distribution, and more data leads to smaller ambiguity set and less conservative strategy. Moreover, special problem structures of the proposed problem formulation are exploited to develop an efficient and scalable solution approach. Case studies are carried out on the IEEE 14 and 118 bus systems to show the accuracy and necessity of the approximate ac model and the attractive features of the distributionally robust optimization approach compared with other methods to deal with uncertainties.

Original languageEnglish (US)
Article number8294298
Pages (from-to)4924-4936
Number of pages13
JournalIEEE Transactions on Power Systems
Issue number5
StatePublished - Sep 2018


  • Optimal power flow
  • ambiguity
  • chance constraints
  • distributionally robust optimization
  • uncertainty

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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