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

Abstract

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.

Authors:
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:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1345153
Report Number(s):
LA-UR-16-24788
Journal ID: ISSN 0885-8950
Grant/Contract Number:
AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
IEEE Transactions on Power Systems
Additional Journal Information:
Journal Volume: 32; Journal Issue: 5; Journal ID: ISSN 0885-8950
Publisher:
IEEE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; Mathematics; Optimization Methods; Convex Quadratic Optimization; Semidefine Programming; Optimal Power Flow

Citation Formats

Coffrin, Carleton James, Hijazi, Hassan L, and Van Hentenryck, Pascal R. Strengthening the SDP Relaxation of AC Power Flows with Convex Envelopes, Bound Tightening, and Valid Inequalities. United States: N. p., 2016. Web. doi:10.1109/TPWRS.2016.2634586.
Coffrin, Carleton James, Hijazi, Hassan L, & Van Hentenryck, Pascal R. Strengthening the SDP Relaxation of AC Power Flows with Convex Envelopes, Bound Tightening, and Valid Inequalities. United States. doi:10.1109/TPWRS.2016.2634586.
Coffrin, Carleton James, Hijazi, Hassan L, and Van Hentenryck, Pascal R. Thu . "Strengthening the SDP Relaxation of AC Power Flows with Convex Envelopes, Bound Tightening, and Valid Inequalities". United States. doi:10.1109/TPWRS.2016.2634586. https://www.osti.gov/servlets/purl/1345153.
@article{osti_1345153,
title = {Strengthening the SDP Relaxation of AC Power Flows with Convex Envelopes, Bound Tightening, and Valid Inequalities},
author = {Coffrin, Carleton James and Hijazi, Hassan L and Van Hentenryck, Pascal R},
abstractNote = {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.},
doi = {10.1109/TPWRS.2016.2634586},
journal = {IEEE Transactions on Power Systems},
number = 5,
volume = 32,
place = {United States},
year = {Thu Dec 01 00:00:00 EST 2016},
month = {Thu Dec 01 00:00:00 EST 2016}
}

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Free Publicly Available Full Text
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