skip to main content

Title: Strengthening the SDP Relaxation of AC Power Flows with Convex Envelopes, Bound Tightening, and Valid Inequalities

Here this work revisits the Semidefine Programming (SDP) relaxation of the AC power flow equations in light of recent results illustrating the benefits of bounds propagation, valid inequalities, and the Convex Quadratic (QC) relaxation. By integrating all of these results into the SDP model a new hybrid relaxation is proposed, which combines the benefits from all of these recent works. This strengthened SDP formulation is evaluated on 71 AC Optimal Power Flow test cases from the NESTA archive and is shown to have an optimality gap of less than 1% on 63 cases. This new hybrid relaxation closes 50% of the open cases considered, leaving only 8 for future investigation.
ORCiD logo [1] ;  [2] ;  [3]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Australian National Univ., Canberra, ACT (Australia)
  3. Univ. of Michigan, Ann Arbor, MI (United States)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 0885-8950
Grant/Contract Number:
Accepted Manuscript
Journal Name:
IEEE Transactions on Power Systems
Additional Journal Information:
Journal Volume: 32; Journal Issue: 5; Journal ID: ISSN 0885-8950
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; Mathematics; Optimization Methods; Convex Quadratic Optimization; Semidefine Programming; Optimal Power Flow