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A survey on conic relaxations of optimal power flow problem

Author

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  • Zohrizadeh, Fariba
  • Josz, Cedric
  • Jin, Ming
  • Madani, Ramtin
  • Lavaei, Javad
  • Sojoudi, Somayeh

Abstract

Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for power system operation. On the one hand, tractability is crucial due to the large size of modern electricity transmission grids. This is a result of the numerous interconnections that have been built over time. On the other hand, guarantees are needed to ensure reliability and safety for consumers at a time when power systems are growing in complexity. This is in large part due to the high penetration of renewable energy sources and the advent of electric vehicles. The aim of this paper is to review the latest literature in order to demonstrate the success of conic optimization when applied to power systems. The main focus is on how linear programming, second-order cone programming, and semidefinite programming can be used to address a central problem named the optimal power flow problem. We describe how they are used to design convex relaxations of this highly challenging non-convex optimization problem. We also show how sum-of-squares can be used to strengthen these relaxations. Finally, we present advances in first-order methods, interior-point methods, and nonconvex methods for solving conic optimization. Challenges for future research are also discussed.

Suggested Citation

  • Zohrizadeh, Fariba & Josz, Cedric & Jin, Ming & Madani, Ramtin & Lavaei, Javad & Sojoudi, Somayeh, 2020. "A survey on conic relaxations of optimal power flow problem," European Journal of Operational Research, Elsevier, vol. 287(2), pages 391-409.
    • Handle: RePEc:eee:ejores:v:287:y:2020:i:2:p:391-409
    DOI: 10.1016/j.ejor.2020.01.034
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    Cited by:

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    2. Martin Bichler & Johannes Knörr & Felipe Maldonado, 2023. "Pricing in Nonconvex Markets: How to Price Electricity in the Presence of Demand Response," Information Systems Research, INFORMS, vol. 34(2), pages 652-675, June.
    3. Mohammadi Fathabad, Abolhassan & Cheng, Jianqiang & Pan, Kai & Yang, Boshi, 2023. "Asymptotically tight conic approximations for chance-constrained AC optimal power flow," European Journal of Operational Research, Elsevier, vol. 305(2), pages 738-753.
    4. Skolfield, J. Kyle & Escobedo, Adolfo R., 2022. "Operations research in optimal power flow: A guide to recent and emerging methodologies and applications," European Journal of Operational Research, Elsevier, vol. 300(2), pages 387-404.
    5. Kirschner, Felix & de Klerk, Etienne, 2024. "A predictor-corrector algorithm for semidefinite programming that uses the factor width cone," Other publications TiSEM 957e76ec-7f75-4e6e-adc4-c, Tilburg University, School of Economics and Management.
    6. Martin Bichler & Hans Ulrich Buhl & Johannes Knörr & Felipe Maldonado & Paul Schott & Stefan Waldherr & Martin Weibelzahl, 2022. "Electricity Markets in a Time of Change: A Call to Arms for Business Research," Schmalenbach Journal of Business Research, Springer, vol. 74(1), pages 77-102, March.
    7. Hermann, Alexander & Jensen, Tue Vissing & Østergaard, Jacob & Kazempour, Jalal, 2022. "A complementarity model for electric power transmission-distribution coordination under uncertainty," European Journal of Operational Research, Elsevier, vol. 299(1), pages 313-329.
    8. Papadimitrakis, M. & Giamarelos, N. & Stogiannos, M. & Zois, E.N. & Livanos, N.A.-I. & Alexandridis, A., 2021. "Metaheuristic search in smart grid: A review with emphasis on planning, scheduling and power flow optimization applications," Renewable and Sustainable Energy Reviews, Elsevier, vol. 145(C).
    9. Martins Barros, Rafael & Guimarães Lage, Guilherme & de Andrade Lira Rabêlo, Ricardo, 2022. "Sequencing paths of optimal control adjustments determined by the optimal reactive dispatch via Lagrange multiplier sensitivity analysis," European Journal of Operational Research, Elsevier, vol. 301(1), pages 373-385.
    10. Wogrin, S. & Tejada-Arango, D. & Delikaraoglou, S. & Botterud, A., 2020. "Assessing the impact of inertia and reactive power constraints in generation expansion planning," Applied Energy, Elsevier, vol. 280(C).
    11. Bichler, Martin & Knörr, Johannes, 2023. "Getting prices right on electricity spot markets: On the economic impact of advanced power flow models," Energy Economics, Elsevier, vol. 126(C).

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