The convex hull of the AC power flow equations in rectangular coordinates

Qifeng Li, Vijay Vittal

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

6 Scopus citations

Abstract

Obtaining the convex hull of the alternating current (AC) power flow equations is largely beneficial in the convexification of the optimization problems in power systems where the AC power flow constraints are taken into account. In this paper, the AC power flow formulation in rectangular coordinates which is a non-convex quadratic equality is equivalently decomposed into four quadratic inequalities whose coefficient matrices are positive semidefinite. Two of the quadratic inequalities are convex while the other two are not. The proposed decomposition facilitates the convexification of the power flow equations much. A convex hull formulation is proposed for the resulting non-convex quadratic inequalities. This formulation is applied to study the convex hull of the AC power flow.

Original languageEnglish (US)
Title of host publication2016 IEEE Power and Energy Society General Meeting, PESGM 2016
PublisherIEEE Computer Society
Volume2016-November
ISBN (Electronic)9781509041688
DOIs
StatePublished - Nov 10 2016
Event2016 IEEE Power and Energy Society General Meeting, PESGM 2016 - Boston, United States
Duration: Jul 17 2016Jul 21 2016

Other

Other2016 IEEE Power and Energy Society General Meeting, PESGM 2016
CountryUnited States
CityBoston
Period7/17/167/21/16

Keywords

  • AC power flow
  • Convex hull
  • Convex relaxation
  • Non-convex quadratic equality
  • Rectangular coordinates

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Nuclear Energy and Engineering
  • Renewable Energy, Sustainability and the Environment
  • Electrical and Electronic Engineering

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  • Cite this

    Li, Q., & Vittal, V. (2016). The convex hull of the AC power flow equations in rectangular coordinates. In 2016 IEEE Power and Energy Society General Meeting, PESGM 2016 (Vol. 2016-November). [7741777] IEEE Computer Society. https://doi.org/10.1109/PESGM.2016.7741777