Applications of Lifted Nonlinear Cuts to Convex Relaxations of the AC Power Flow Equations

Bugosen Tannous, Sergio Ivan; Parker, Robert Brunato; Coffrin, Carleton James

doi:10.1109/tpwrs.2024.3470428

Applications of Lifted Nonlinear Cuts to Convex Relaxations of the AC Power Flow Equations

Journal Article · Mon Oct 07 00:00:00 EDT 2024 · IEEE Transactions on Power Systems

DOI:https://doi.org/10.1109/tpwrs.2024.3470428· OSTI ID:2478624

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Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Here, we demonstrate that valid inequalities, or lifted nonlinear cuts (LNC), can be projected to tighten the Second Order Cone (SOC), Convex DistFlow (CDF), and Network Flow (NF) relaxations of the AC Optimal Power Flow (AC-OPF) problem. We conduct experiments on 38 cases from the PGLib-OPF library, showing that the LNC strengthen the SOC and CDF relaxations in 100% of the test cases, with average and maximum differences in the optimality gaps of 6.2% and 17.5% respectively. The NF relaxation is strengthened in 46.2% of test cases, with average and maximum differences in the optimality gaps of 1.3% and 17.3% respectively. We also study the trade-off between relaxation quality and solve time, demonstrating that the strengthened CDF relaxation outperforms the strengthened SOC formulation in terms of runtime and number of iterations needed, while the strengthened NF formulation is the most scalable with the lowest relaxation quality improvement due to these LNC.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 2478624

Report Number(s):: LA-UR--24-23960

Journal Information:: IEEE Transactions on Power Systems, Journal Name: IEEE Transactions on Power Systems Journal Issue: 1 Vol. 40; ISSN 0885-8950

Publisher:: IEEECopyright Statement

Country of Publication:: United States

Language:: English

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TABLE II(p. 5)

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Related Subjects

24 POWER TRANSMISSION AND DISTRIBUTION
AC-OPF
Computer Science
Convex Relaxations
Energy Sciences
Mathematics
Valid Inequalities

Applications of Lifted Nonlinear Cuts to Convex Relaxations of the AC Power Flow Equations

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References (15)

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