Tight-and-Cheap Conic Relaxation for the AC Optimal Power Flow Problem

Christian Bingane, Miguel F. Anjos, Sebastien Le Digabel

Research output: Contribution to journalArticlepeer-review


The classical alternating current optimal power flow problem is highly nonconvex and generally hard to solve. Convex relaxations, in particular semidefinite, second-order cone, convex quadratic, and linear relaxations, have recently attracted significant interest. The semidefinite relaxation is the strongest among them and is exact for many cases. However, the computational efficiency for solving large-scale semidefinite optimization is lower than for second-order cone optimization. We propose a conic relaxation obtained by combining semidefinite optimization with the reformulation-linearization technique, commonly known as RLT. The proposed relaxation is stronger than the second-order cone relaxation and nearly as tight as the standard semidefinite relaxation. Computational experiments using standard test cases with up to 6515 buses show that the time to solve the new conic relaxation is up to one order of magnitude lower than for the chordal relaxation, a semidefinite relaxation technique that exploits the sparsity of power networks.
Original languageEnglish
Pages (from-to)7181-7188
JournalIEEE Transactions on Power Systems
Issue number6
Early online date21 Jun 2018
Publication statusPublished - 1 Nov 2018

Fingerprint Dive into the research topics of 'Tight-and-Cheap Conic Relaxation for the AC Optimal Power Flow Problem'. Together they form a unique fingerprint.

Cite this