A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks

Shaojun Huang, Qiuwei Wu, Jianhui Wang, Haoran Zhao

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Abstract

This paper proposes a sufficient condition for the convex relaxation of AC Optimal Power Flow (OPF) in radial distribution networks as a second order cone program (SOCP) to be exact. The condition requires that the allowed reverse power flow is only reactive or active, or none. Under the proposed sufficient condition, the feasible sub-injection region (power injections of nodes excluding the root node) of the AC OPF is convex. The exactness of the convex relaxation under the proposed condition is proved through constructing a group of monotonic series with limits, which ensures that the optimal solution of the SOCP can be converted to an optimal solution of the original AC OPF. The efficacy of the convex relaxation to solve the AC OPF is demonstrated by case studies of an optimal multi-period planning problem of electric vehicles (EVs) in distribution networks.
Original languageEnglish
JournalIEEE Transactions on Power Systems
Volume32
Issue number2
Pages (from-to)1359 - 1368
ISSN0885-8950
DOIs
Publication statusPublished - 2016

Bibliographical note

(c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.

Keywords

  • AC optimal power flow (AC OPF)
  • Convex relaxation, convexity
  • Electric vehicle (EV)
  • Power distribution network
  • Second order cone program (SOCP)

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