IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v64y2016i6p1177-1196.html

Strong SOCP Relaxations for the Optimal Power Flow Problem

Author

Listed:
  • Burak Kocuk

    (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • Santanu S. Dey

    (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • X. Andy Sun

    (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

Abstract

This paper proposes three strong second order cone programming (SOCP) relaxations for the AC optimal power flow (OPF) problem. These three relaxations are incomparable to each other and two of them are incomparable to the standard SDP relaxation of OPF. Extensive computational experiments show that these relaxations have numerous advantages over existing convex relaxations in the literature: (i) their solution quality is extremely close to that of the standard SDP relaxation (the best one is within 99.96% of the SDP relaxation on average for all the IEEE test cases) and consistently outperforms previously proposed convex quadratic relaxations of the OPF problem, (ii) the solutions from the strong SOCP relaxations can be directly used as a warm start in a local solver such as IPOPT to obtain a high quality feasible OPF solution, and (iii) in terms of computation times, the strong SOCP relaxations can be solved an order of magnitude faster than the standard SDP relaxation. For example, one of the proposed SOCP relaxations together with IPOPT produces a feasible solution for the largest instance in the IEEE test cases (the 3375-bus system) and also certifies that this solution is within 0.13% of global optimality, all this computed within 157.20 seconds on a modest personal computer. Overall, the proposed strong SOCP relaxations provide a practical approach to obtain feasible OPF solutions with extremely good quality within a time framework that is compatible with the real-time operation in the current industry practice.

Suggested Citation

  • Burak Kocuk & Santanu S. Dey & X. Andy Sun, 2016. "Strong SOCP Relaxations for the Optimal Power Flow Problem," Operations Research, INFORMS, vol. 64(6), pages 1177-1196, December.
    • Handle: RePEc:inm:oropre:v:64:y:2016:i:6:p:1177-1196
    DOI: 10.1287/opre.2016.1489
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2016.1489
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2016.1489?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Carleton Coffrin & Pascal Van Hentenryck, 2014. "A Linear-Programming Approximation of AC Power Flows," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 718-734, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sander Claeys & Marta Vanin & Frederik Geth & Geert Deconinck, 2021. "Applications of optimization models for electricity distribution networks," Wiley Interdisciplinary Reviews: Energy and Environment, Wiley Blackwell, vol. 10(5), September.
    2. Toplu-Tutay, Gizem & Hasenbein, John J. & Kutanoglu, Erhan, 2024. "Impact of power outages depends on who loses it: Equity-informed grid resilience planning via stochastic optimization," Socio-Economic Planning Sciences, Elsevier, vol. 95(C).
    3. Josif Figueroa & Kush Bubbar & Greg Young-Morris, 2024. "An Open-Source Tool for Composite Power System Reliability Assessment in Julia™," Energies, MDPI, vol. 17(20), pages 1-15, October.
    4. Neumann, Fabian & Hagenmeyer, Veit & Brown, Tom, 2022. "Assessments of linear power flow and transmission loss approximations in coordinated capacity expansion problems," Applied Energy, Elsevier, vol. 314(C).
    5. Sarid, A. & Tzur, M., 2018. "The multi-scale generation and transmission expansion model," Energy, Elsevier, vol. 148(C), pages 977-991.
    6. Saber, Hossein & Mazaheri, Hesam & Ranjbar, Hossein & Moeini-Aghtaie, Moein & Lehtonen, Matti, 2021. "Utilization of in-pipe hydropower renewable energy technology and energy storage systems in mountainous distribution networks," Renewable Energy, Elsevier, vol. 172(C), pages 789-801.
    7. Karimi, Ali & Aminifar, Farrokh & Fereidunian, Alireza & Lesani, Hamid, 2019. "Energy storage allocation in wind integrated distribution networks: An MILP-Based approach," Renewable Energy, Elsevier, vol. 134(C), pages 1042-1055.
    8. Xingpeng Li, 2020. "Fast Heuristic AC Power Flow Analysis with Data-Driven Enhanced Linearized Model," Energies, MDPI, vol. 13(13), pages 1-17, June.
    9. Amin Gholami & Kaizhao Sun & Shixuan Zhang & Xu Andy Sun, 2023. "An ADMM-Based Distributed Optimization Method for Solving Security-Constrained Alternating Current Optimal Power Flow," Operations Research, INFORMS, vol. 71(6), pages 2045-2060, November.
    10. Tómasson, Egill & Söder, Lennart, 2020. "Coordinated optimal strategic demand reserve procurement in multi-area power systems," Applied Energy, Elsevier, vol. 270(C).
    11. Subramanian, Vignesh & Feijoo, Felipe & Sankaranarayanan, Sriram & Melendez, Kevin & Das, Tapas K., 2022. "A bilevel conic optimization model for routing and charging of EV fleets serving long distance delivery networks," Energy, Elsevier, vol. 251(C).
    12. Sunil Chopra & Feng Qiu & Sangho Shim, 2023. "Parallel Power System Restoration," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 233-247, January.
    13. Sepúlveda, Juan & Brotcorne, Luce & Le Cadre, Hélène, 2025. "A reverse Stackelberg model for demand response in local energy markets," European Journal of Operational Research, Elsevier, vol. 327(1), pages 352-366.
    14. Wang, Shuaijie & Hou, Ye & Guan, Xin & Liu, Shu & Huo, Zhaoyi, 2024. "Resiliency-informed optimal scheduling of smart distribution network with urban distributed photovoltaic: A stochastic P-robust optimization," Energy, Elsevier, vol. 313(C).
    15. Nikoobakht, Ahmad & Aghaei, Jamshid & Khatami, Roohallah & Mahboubi-Moghaddam, Esmaeel & Parvania, Masood, 2019. "Stochastic flexible transmission operation for coordinated integration of plug-in electric vehicles and renewable energy sources," Applied Energy, Elsevier, vol. 238(C), pages 225-238.
    16. Grimm, Veronika & Grübel, Julia & Rückel, Bastian & Sölch, Christian & Zöttl, Gregor, 2020. "Storage investment and network expansion in distribution networks: The impact of regulatory frameworks," Applied Energy, Elsevier, vol. 262(C).
    17. Gideon Ude Nnachi & Yskandar Hamam & Coneth Graham Richards, 2022. "Appraising the Optimal Power Flow and Generation Capacity in Existing Power Grid Topology with Increase in Energy Demand," Energies, MDPI, vol. 15(7), pages 1-23, March.
    18. Kiszka, Adriana & Wozabal, David, 2025. "Stochastic dual dynamic programming for optimal power flow problems under uncertainty," European Journal of Operational Research, Elsevier, vol. 321(3), pages 814-836.
    19. Brent Austgen & Erhan Kutanoglu & John J. Hasenbein & Surya Santoso, 2025. "Comparisons of Two-Stage Models for Flood Mitigation of Electrical Substations," INFORMS Journal on Computing, INFORMS, vol. 37(2), pages 270-292, March.
    20. Peecock, Anna & Huang, Jiangyi & Martinez-Felipe, Alfonso & McKenna, Russell, 2025. "Reviewing sector coupling in offshore energy system integration modelling: the North Sea context," Renewable and Sustainable Energy Reviews, Elsevier, vol. 210(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:64:y:2016:i:6:p:1177-1196. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.