A multitree approach for global solution of ACOPF problems using piecewise outer approximations
Abstract
Electricity markets rely on the rapid solution of the optimal power flow (OPF) problem to determine generator power levels and set nodal prices. Traditionally, the OPF problem has been formulated using linearized, approximate models, ignoring nonlinear alternating current (AC) physics. These approaches do not guarantee global optimality or even feasibility in the real ACOPF problem. We introduce an outerapproximation approach to solve the ACOPF problem to global optimality based on alternating solution of upper and lowerbounding problems. The lowerbounding problem is a piecewise relaxation based on strong secondorder cone relaxations of the ACOPF, and these piecewise relaxations are selectively refined at each major iteration through increased variable domain partitioning. Our approach is able to efficiently solve all but one of the test cases considered to an optimality gap below 0.1%. This approach opens the door for global solution of MINLP problems with AC power flow equations.
 Authors:

 Purdue Univ., West Lafayette, IN (United States). Davidson School of Chemical Engineering
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States). Center for Computing Research
 Purdue Univ., West Lafayette, IN (United States). Davidson School of Chemical Engineering; Sandia National Lab. (SNLNM), Albuquerque, NM (United States). Center for Computing Research
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
 OSTI Identifier:
 1570257
 Alternate Identifier(s):
 OSTI ID: 1582925
 Report Number(s):
 SAND201910860J
Journal ID: ISSN 00981354; 679386
 Grant/Contract Number:
 AC0494AL85000; NA0003525; KJ0401000
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Computers and Chemical Engineering
 Additional Journal Information:
 Journal Volume: 114; Journal Issue: C; Journal ID: ISSN 00981354
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 42 ENGINEERING; optimal power flow; outerapproximation; piecewise relaxation; global optimization; secondorder cone relaxation; ACOPF
Citation Formats
Liu, Jianfeng, Bynum, Michael, Castillo, Anya, Watson, JeanPaul, and Laird, Carl D. A multitree approach for global solution of ACOPF problems using piecewise outer approximations. United States: N. p., 2018.
Web. doi:10.1016/j.compchemeng.2017.10.018.
Liu, Jianfeng, Bynum, Michael, Castillo, Anya, Watson, JeanPaul, & Laird, Carl D. A multitree approach for global solution of ACOPF problems using piecewise outer approximations. United States. https://doi.org/10.1016/j.compchemeng.2017.10.018
Liu, Jianfeng, Bynum, Michael, Castillo, Anya, Watson, JeanPaul, and Laird, Carl D. Sat .
"A multitree approach for global solution of ACOPF problems using piecewise outer approximations". United States. https://doi.org/10.1016/j.compchemeng.2017.10.018. https://www.osti.gov/servlets/purl/1570257.
@article{osti_1570257,
title = {A multitree approach for global solution of ACOPF problems using piecewise outer approximations},
author = {Liu, Jianfeng and Bynum, Michael and Castillo, Anya and Watson, JeanPaul and Laird, Carl D.},
abstractNote = {Electricity markets rely on the rapid solution of the optimal power flow (OPF) problem to determine generator power levels and set nodal prices. Traditionally, the OPF problem has been formulated using linearized, approximate models, ignoring nonlinear alternating current (AC) physics. These approaches do not guarantee global optimality or even feasibility in the real ACOPF problem. We introduce an outerapproximation approach to solve the ACOPF problem to global optimality based on alternating solution of upper and lowerbounding problems. The lowerbounding problem is a piecewise relaxation based on strong secondorder cone relaxations of the ACOPF, and these piecewise relaxations are selectively refined at each major iteration through increased variable domain partitioning. Our approach is able to efficiently solve all but one of the test cases considered to an optimality gap below 0.1%. This approach opens the door for global solution of MINLP problems with AC power flow equations.},
doi = {10.1016/j.compchemeng.2017.10.018},
journal = {Computers and Chemical Engineering},
number = C,
volume = 114,
place = {United States},
year = {2018},
month = {6}
}
Web of Science
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