An Overview of Semidefinite Relaxations for Optimal Power Flow Problem

I. A. Zorin, E. N. Gryazina

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The AC optimal power flow (AC OPF) problem is considered and five convex relaxations for solving this problem—the semidefinite, chordal, conic, and moment-based ones as well as the QC relaxation—are overviewed. The specifics of the AC formulation and also the nonconvexity of the problem are described in detail. Each of the relaxations for OPF is written in explicit form. The semidefinite, chordal and conic relaxations are of major interest. They are implemented on a test example of four nodes.

Original languageEnglish
Pages (from-to)813-833
Number of pages21
JournalAutomation and Remote Control
Issue number5
Publication statusPublished - 1 May 2019


  • convex relaxations
  • power flows
  • power systems
  • semidefinite programming

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