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Lagrangian Duality and Branch-and-Bound Algorithms for Optimal Power Flow

Author

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  • Dzung T. Phan

    (Department of Business Analytics and Mathematical Sciences, IBM T. J. Watson Research Center, Yorktown Heights, New York 10598)

Abstract

This paper investigates a Lagrangian dual problem for solving the optimal power flow problem in rectangular form that arises from power system analysis. If strong duality does not hold for the dual, we propose two classes of branch-and-bound algorithms that guarantee to solve the problem to optimality. The lower bound for the objective function is obtained by the Lagrangian duality, whereas the feasible set subdivision is based on the rectangular or ellipsoidal bisection. The numerical experiments are reported to demonstrate the effectiveness of the proposed algorithms. We note that no duality gap is observed for any of our test problems.

Suggested Citation

  • Dzung T. Phan, 2012. "Lagrangian Duality and Branch-and-Bound Algorithms for Optimal Power Flow," Operations Research, INFORMS, vol. 60(2), pages 275-285, April.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:2:p:275-285
    DOI: 10.1287/opre.1110.1036
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    Cited by:

    1. Kursad Derinkuyu & Fehmi Tanrisever & Nermin Kurt & Gokhan Ceyhan, 2020. "Optimizing Day-Ahead Electricity Market Prices: Increasing the Total Surplus for Energy Exchange Istanbul," Manufacturing & Service Operations Management, INFORMS, vol. 22(4), pages 700-716, July.
    2. Guanglei Wang & Hassan Hijazi, 2018. "Mathematical programming methods for microgrid design and operations: a survey on deterministic and stochastic approaches," Computational Optimization and Applications, Springer, vol. 71(2), pages 553-608, November.
    3. 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.

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