Skip to main content
SpringerLink
Log in

Power Network Design with Line Activity

  • Conference paper
  • First Online:
Book cover Optimization in Artificial Intelligence and Data Sciences

Part of the book series: AIRO Springer Series ((AIROSS,volume 8))

  • 472 Accesses

Abstract

We discuss the problem of optimally designing a power transportation network with respect to line activity. We model this problem as an alternating current optimal power flow with on/off variables on lines. We formulate this problem as a nonconvex MINLP in complex numbers, then we propose two convex MINLP relaxations. We test our formulations on some small-scale standard instances.

This paper has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement n. 764759.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Gendron, B., Crainic, T., Frangioni, A.: Multicommodity Capacitated Network Design. In: Sansò, B., Soriano, P. (eds.) Telecommunications Network Planning, pp. 1–32. Springer, New York (1999). https://doi.org/10.1007/978-1-4615-5087-7_1

    Google Scholar 

  2. Bruglieri, M., Liberti, L.: Optimal running and planning of a biomass-based energy production process. Energy Policy 36(7), 2430–2438 (2008). https://doi.org/10.1016/j.enpol.2008.01.009

    Article  Google Scholar 

  3. Glover, J., Sarma, M., Overbye, T.: Power System Analysis and Design. Cengage Learning, Stamford CT (2010)

    Google Scholar 

  4. Bienstock, D.: Electrical Transmission System Cascades and Vulnerability: an Operations Research Viewpoint. No. 22 in MOS-SIAM Optimization. SIAM, Philadelphia (2016). https://doi.org/10.1137/1.9781611974164

  5. Molzahn, D., Hiskens, I.: A Survey of Relaxations and Approximations of the Power Flow Equations. Foundations and Trends in Electric Energy Systems. Now Publishers, Hanover, MA (2019). https://doi.org/10.1561/3100000012

    Book  Google Scholar 

  6. Gilbert, J.C., Josz, C.: Plea for a semidefinite optimization solver in complex numbers. Tech. rep., HAL Archives-Ouvertes: hal-01422932 (2017)

    Google Scholar 

  7. Knight, U.: The logical design of electrical networks using linear programming methods. Proc. IEE 107(33), 306–314 (1960). https://doi.org/10.1049/pi-a.1960.0063

    Google Scholar 

  8. Adams, R., Laughton, M.: Optimal planning of power networks using mixed-integer programming. Part 1: Static and time-phased network synthesis. Proc. IEE 121(2), 139–147 (1974). https://doi.org/10.1049/piee.1974.0024

  9. Bienstock, D., Mattia, S.: Using mixed-integer programming to solve power grid blackout problems. Discrete Optimization 4(1), 115–141 (2007). https://doi.org/10.1016/j.disopt.2006.10.007

    Article  MathSciNet  Google Scholar 

  10. Bienstock, D., Verma, A.: The N-k problem in power grids: New models, formulations, and numerical experiments. SIAM J. Optim. 20(5), 2352–2380 (2010). https://doi.org/10.1137/08073562X

    Article  MathSciNet  Google Scholar 

  11. Ruiz, M., Maeght, J., Marié, A., Panciatici, P., Renaud, A.: A progressive method to solve large-scale AC optimal power flow with discrete variables and control of the feasibility. In: 2014 Power Systems Computation Conference (2014). https://doi.org/10.1109/PSCC.2014.7038395

  12. Salgado, E., Gentile, C., Liberti, L.: Perspective cuts for the ACOPF with generators. In: Daniele, P., Scrimali, L. (eds.) New Trends in Emerging Complex Real Life Problems, AIRO Series, vol. 1, pp. 451–461. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00473-6_48

    Chapter  Google Scholar 

  13. Salgado, E., Scozzari, A., Tardella, F., Liberti, L.: Alternating current optimal power flow with generator selection. In: Lee, J., Rinaldi, G., Mahjoub, R. (eds.) Combinatorial Optimization ISCO 2018, LNCS, vol. 10856, pp. 364–375 (2018). https://doi.org/10.1007/978-3-319-96151-4_31

    MATH  Google Scholar 

  14. Ahmadi, A., Majumdar, A.: DSOS and SDSOS optimization: More tractable alternatives to sum of squares and semidefinite optimization. SIAM J. Appl. Algebra Geometry 3(2), 193–230 (2019). https://doi.org/10.1137/18M118935X

    Article  MathSciNet  Google Scholar 

  15. Bienstock, D., Verma, A.: Strong NP-hardness of AC power flows feasibility. Oper. Res. Lett. 47(6), 494–501 (2019). https://doi.org/10.1016/j.orl.2019.08.009

    Article  MathSciNet  Google Scholar 

  16. Fisher, E., O’Neill, R., Ferris, M.: Optimal transmission switching. IEEE Trans. Power Syst. 23(3), 1346–1355 (2008). https://doi.org/10.1109/TPWRS.2008.922256

    Article  Google Scholar 

  17. Molzahn, D., Holzer, J., Lesieutre, B., DeMarco, C.: Implementation of a large-scale optimal power flow solver based on semidefinite programming. IEEE Trans. Power Syst. 28(4), 3987–3998 (2013). https://doi.org/10.1109/TPWRS.2013.2258044

    Article  Google Scholar 

  18. Zimmermann, R., Murillo-Sánchez, C.: MatPower 7.0b1 User’s Manual. Power Systems Engineering Research Center (2018)

    Google Scholar 

  19. Bienstock, D., Escobar, M., Gentile, C., Liberti, L.: Mathematical programming formulations for the alternating current optimal power flow problem. 4OR 18(3), 249–292 (2020). https://doi.org/10.1007/s10288-020-00455-w

  20. Fourer, R., Gay, D.: The AMPL Book. Duxbury Press, Pacific Grove (2002)

    Google Scholar 

  21. Gerschgorin, S.: Über die abgrenzung der eigenwerte einer matrix. Izvestia Akademii Nauk USSR 6, 749–754 (1931)

    MATH  Google Scholar 

  22. Jabr, R.: Radial distribution load flow using conic programming. IEEE Trans. Power Syst. 21(3), 1458–1459 (2006). https://doi.org/10.1109/TPWRS.2006.879234

    Article  MathSciNet  Google Scholar 

  23. Babaeinejadsarookolaee, S., Birchfield, A., Christie, R., Coffrin, C., DeMarco, C., Diao, R., Ferris, M., Fliscounakis, S., Greene, S., Huang, R., Josz, C., Korab, R., Lesieutre, B., Maeght, J., Mak, T., Molzahn, D., Overbye, T., Panciatici, P., Park, B., Snodgrass, J., Tbaileh, A., Van Hentenryck, P., Zimmerman, R.: The power grid library for benchmarking AC optimal power flow algorithms. Tech. rep., (2019). arXiv:1908.02788

    Google Scholar 

  24. IBM: ILOG CPLEX 12.9 User’s Manual. IBM (2019)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IEOR, Columbia University, New York, NY, USA

    Daniel Bienstock

  2. LIX CNRS Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France

    Martina Cerulli, Mauro Escobar & Leo Liberti

Authors
  1. Daniel Bienstock
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Martina Cerulli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mauro Escobar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Leo Liberti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mauro Escobar .

Editor information

Editors and Affiliations

  1. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Lavinia Amorosi

  2. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Paolo Dell’Olmo

  3. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Isabella Lari

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bienstock, D., Cerulli, M., Escobar, M., Liberti, L. (2022). Power Network Design with Line Activity. In: Amorosi, L., Dell’Olmo, P., Lari, I. (eds) Optimization in Artificial Intelligence and Data Sciences. AIRO Springer Series, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-030-95380-5_17

Download citation

Publish with us

Policies and ethics

Search

Navigation