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Title: Tightening McCormick Relaxations Toward Global Solution of the ACOPF Problem

Abstract

Here, we show that a strong upper bound on the objective of the alternating current optimal power flow (ACOPF) problem can significantly improve the effectiveness of optimization-based bounds tightening (OBBT) on a number of relaxations. We additionally compare the performance of relaxations of the ACOPF problem, including the rectangular form without reference bus constraints, the rectangular form with reference bus constraints, and the polar form. We find that relaxations of the rectangular form significantly strengthen existing relaxations if reference bus constraints are included. Overall, relaxations of the polar form perform the best. However, neither the rectangular nor the polar form dominates the other. Ultimately, with these strategies, we are able to reduce the optimality gap to less than 0.1% on all but 5 NESTA test cases with up to 300 buses by performing OBBT alone.

Authors:
 [1];  [1];  [2];  [3]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
  3. Purdue Univ., West Lafayette, IN (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1485848
Alternate Identifier(s):
OSTI ID: 1479492
Report Number(s):
SAND-2018-3787J; SAND-2018-11431J
Journal ID: ISSN 0885-8950; 663752
Grant/Contract Number:  
AC04-94AL85000; NA0003525
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
IEEE Transactions on Power Systems
Additional Journal Information:
Journal Name: IEEE Transactions on Power Systems; Journal ID: ISSN 0885-8950
Publisher:
IEEE
Country of Publication:
United States
Language:
English
Subject:
24 POWER TRANSMISSION AND DISTRIBUTION; ACOPF; bounds tightening; convex relaxation

Citation Formats

Bynum, Michael Lee, Castillo, Anya R., Watson, Jean -Paul, and Laird, Carl Damon. Tightening McCormick Relaxations Toward Global Solution of the ACOPF Problem. United States: N. p., 2018. Web. doi:10.1109/TPWRS.2018.2877099.
Bynum, Michael Lee, Castillo, Anya R., Watson, Jean -Paul, & Laird, Carl Damon. Tightening McCormick Relaxations Toward Global Solution of the ACOPF Problem. United States. doi:10.1109/TPWRS.2018.2877099.
Bynum, Michael Lee, Castillo, Anya R., Watson, Jean -Paul, and Laird, Carl Damon. Fri . "Tightening McCormick Relaxations Toward Global Solution of the ACOPF Problem". United States. doi:10.1109/TPWRS.2018.2877099.
@article{osti_1485848,
title = {Tightening McCormick Relaxations Toward Global Solution of the ACOPF Problem},
author = {Bynum, Michael Lee and Castillo, Anya R. and Watson, Jean -Paul and Laird, Carl Damon},
abstractNote = {Here, we show that a strong upper bound on the objective of the alternating current optimal power flow (ACOPF) problem can significantly improve the effectiveness of optimization-based bounds tightening (OBBT) on a number of relaxations. We additionally compare the performance of relaxations of the ACOPF problem, including the rectangular form without reference bus constraints, the rectangular form with reference bus constraints, and the polar form. We find that relaxations of the rectangular form significantly strengthen existing relaxations if reference bus constraints are included. Overall, relaxations of the polar form perform the best. However, neither the rectangular nor the polar form dominates the other. Ultimately, with these strategies, we are able to reduce the optimality gap to less than 0.1% on all but 5 NESTA test cases with up to 300 buses by performing OBBT alone.},
doi = {10.1109/TPWRS.2018.2877099},
journal = {IEEE Transactions on Power Systems},
issn = {0885-8950},
number = ,
volume = ,
place = {United States},
year = {2018},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on October 19, 2019
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