Distributionally robust chance constrained optimal power flow assuming log-concave distributions

Bowen Li, Johanna L. Mathieu, Ruiwei Jiang

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

4 Scopus citations

Abstract

Optimization formulations with chance constraints have been widely proposed to operate the power system under various uncertainties, such as renewable production and load consumption. Constraints like the system's physical limits are required to be satisfied at high confidence levels. Conventional solving methodologies either make assumptions on the underlying uncertainty distributions or give overly-conservative results. We develop a new distributionally robust (DR) chance constrained optimal power flow formulation in which the chance constraints are satisfied over a family of distributions with known first-order moments, ellipsoidal support, and an assumption that the probability distributions are log-concave. Since most practical uncertainties have log-concave probability distributions, including this assumption in the formulation reduces the objective costs as compared to traditional DR approaches without sacrificing reliability. We derive second-order cone approximations of the DR chance constraints, resulting in a tractable formulation that can be solved with commercial solvers. We evaluate the performance of our approach using a modified IEEE 9-bus system with uncertain wind power production and compare it to standard approaches. We find that our approach produces solutions that are sufficiently reliable and less costly than traditional DR approaches.

Original languageEnglish (US)
Title of host publication20th Power Systems Computation Conference, PSCC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Print)9781910963104
DOIs
StatePublished - Aug 20 2018
Externally publishedYes
Event20th Power Systems Computation Conference, PSCC 2018 - Dublin, Ireland
Duration: Jun 11 2018Jun 15 2018

Other

Other20th Power Systems Computation Conference, PSCC 2018
CountryIreland
CityDublin
Period6/11/186/15/18

Keywords

  • Chance constraint
  • Distributionally robust optimization
  • Log-concave distribution
  • Optimal power flow
  • Uncertainty

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Computer Networks and Communications
  • Safety, Risk, Reliability and Quality

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  • Cite this

    Li, B., Mathieu, J. L., & Jiang, R. (2018). Distributionally robust chance constrained optimal power flow assuming log-concave distributions. In 20th Power Systems Computation Conference, PSCC 2018 [8442927] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/PSCC.2018.8442927