Tightening McCormick Relaxations Toward Global Solution of the ACOPF Problem

Bynum, Michael Lee; Castillo, Anya R.; Watson, Jean-Paul; Laird, Carl Damon

doi:10.1109/TPWRS.2018.2877099

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:

Bynum, Michael Lee ^[1]; Castillo, Anya R. ^[1]; Watson, Jean-Paul ^[2]; Laird, Carl Damon ^[3]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Purdue Univ., West Lafayette, IN (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Publication Date:: Fri Oct 19 00:00:00 EDT 2018

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-2018-11431J; SAND-2018-3787J
Journal ID: ISSN 0885-8950; 669408

Grant/Contract Number:: AC04-94AL85000; NA0003525

Resource Type:: Accepted Manuscript

Journal Name:: IEEE Transactions on Power Systems

Additional Journal Information:: Journal Volume: 34; Journal Issue: 1; 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.

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                    Bynum, Michael Lee, Castillo, Anya R., Watson, Jean-Paul, & Laird, Carl Damon. Tightening McCormick Relaxations Toward Global Solution of the ACOPF Problem.  United States.  https://doi.org/10.1109/TPWRS.2018.2877099

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                    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.  https://doi.org/10.1109/TPWRS.2018.2877099.  https://www.osti.gov/servlets/purl/1485848.

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@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},

  number       = 1,

  volume       = 34,

  place        = {United States},

  year         = {Fri Oct 19 00:00:00 EDT 2018},

  month        = {Fri Oct 19 00:00:00 EDT 2018}

}

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https://doi.org/10.1109/TPWRS.2018.2877099

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Cited by: 22 works

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Figures / Tables:

TABLE I: Numerical results for relaxations of NESTA archive cases up to 300 buses (58 cases total). Highlighting indicates cases not closed to less than 0.1% gap. Nine cases are not listed due to the SOC relaxation alone reducing the gap below 0.1%.

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Works referencing / citing this record:

Evaluating demand response opportunities for power systems resilience using MILP and MINLP Formulations
journal, November 2018

Bynum, Michael; Castillo, Anya; Watson, Jean‐Paul
AIChE Journal, Vol. 65, Issue 7
DOI: 10.1002/aic.16508

Figures / Tables found in this record:

TABLE I (p. 3)

Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

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

Abstract

Citation Formats

Figures / Tables:

Evaluating demand response opportunities for power systems resilience using MILP and MINLP Formulations journal, November 2018

Evaluating demand response opportunities for power systems resilience using MILP and MINLP Formulations
journal, November 2018