TITLE: Strong SOCP Relaxations for Optimal Power Flow Problem

ABSTRACT:

Optimal Power Flow is a fundamental optimization problem in electrical power systems analysis. Although local optimal solution methods are generally successful, they do not provide guarantees on the quality. Recently, much research has focused on Semidefinite Programming (SDP) relaxations to obtain strong lower bounds. In this work, we instead utilize Second Order Cone Programming (SOCP) relaxations due to their superior computational power. However, since SOCPs are weaker than their SDP counterparts, we propose three improvements to strengthen SOCP relaxation and show that two of them are incomparable to SDP relaxation. Finally, we present extensive computational experiments with standard benchmark instances from literature to demonstrate the accuracy and efficiency of SOCP-based methods.

This is joint work with Santanu S. Dey and X. Andy Sun