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

Journal Article · Wed Nov 30 23:00:00 EST 2016 · IEEE Transactions on Power Systems

DOI:https://doi.org/10.1109/TPWRS.2016.2634586· OSTI ID:1345153

Coffrin, Carleton James ^[1]; Hijazi, Hassan L ^[2]; Van Hentenryck, Pascal R ^[3]

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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)

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.

• Research Organization: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC52-06NA25396
• OSTI ID: 1345153
• Report Number(s): LA-UR--16-24788
• Journal Information: IEEE Transactions on Power Systems, Journal Name: IEEE Transactions on Power Systems Journal Issue: 5 Vol. 32; ISSN 0885-8950
• Publisher: IEEE
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
97 MATHEMATICS AND COMPUTING
Convex Quadratic Optimization
Mathematics
Optimal Power Flow
Optimization Methods
Semidefine Programming