Distributionally robust chance-constrained optimal power flow assuming unimodal distributions with misspecified modes

Bowen Li, Ruiwei Jiang, Johanna L. Mathieu

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


Chance-constrained optimal power flow (CC-OPF) formulations have been proposed to minimize operational costs, while controlling the risk arising from uncertainties like renewable generation and load consumption. To solve CC-OPF, we often need access to the (true) joint probability distribution of all uncertainties, which is rarely known in practice. A solution based on a biased estimate of the distribution can result in poor reliability. To overcome this challenge, recent work has explored distributionally robust chance constraints, in which the chance constraints are satisfied over a family of distributions called the ambiguity set. Commonly, ambiguity sets are only based on moment information (e.g., mean and covariance) of the random variables; however, specifying additional characteristics of the random variables reduces conservatism and cost. Here, we consider ambiguity sets that additionally incorporate unimodality information. In practice, it is difficult to estimate the mode location from the data and so we allow it to be potentially misspecified. We formulate the problem and derive a separation-based algorithm to efficiently solve it. Finally, we evaluate the performance of the proposed approach on a modified IEEE-30 bus network with wind uncertainty and compare it with other distributionally robust approaches. We find that a misspecified mode significantly affects the reliability of the solution, and the proposed model demonstrates a good tradeoff between cost and reliability.

Original languageEnglish (US)
Article number8771187
Pages (from-to)1223-1234
Number of pages12
JournalIEEE Transactions on Control of Network Systems
Issue number3
StatePublished - Sep 2019


  • Chance constraint
  • distributionally robust optimization
  • misspecified mode
  • optimal power flow (OPF)
  • α-unimodality

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Control and Optimization


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