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Global optimization for optimal power flow over transmission networks

Author

Listed:
  • Y. Shi

    (University of Technology)

  • H. D. Tuan

    (University of Technology)

  • H. Tuy

    (Institute of Mathematics)

  • S. Su

    (University of Technology)

Abstract

The optimal power flow (OPF) problem for power transmission networks is an NP-hard optimization problem with nonlinear constraints on complex bus voltages. The existing nonlinear solvers may fail in yielding a feasible point. Semi-definite relaxation (SDR) could provide the global solution only when the matrix solution of the relaxed semi-definite program (SDP) is of rank-one, which does not hold in general. Otherwise, the point found by SDR is infeasible. High-order SDR has recently been used to find the global solution, which leads to explosive growth of the matrix variable dimension and semi-definite constraints. Consequently, it is suitable only for OPF over very small networks with a few buses. In this paper, we follow our previously developed nonsmooth optimization approach to address this difficult OPF problem, which is an iterative process to generate a sequence of improved points that converge to a global solution in many cases. Each iteration calls an SDP of moderate dimension. Simulations are provided to demonstrate the efficiency of our approach.

Suggested Citation

  • Y. Shi & H. D. Tuan & H. Tuy & S. Su, 2017. "Global optimization for optimal power flow over transmission networks," Journal of Global Optimization, Springer, vol. 69(3), pages 745-760, November.
    • Handle: RePEc:spr:jglopt:v:69:y:2017:i:3:d:10.1007_s10898-017-0538-5
    DOI: 10.1007/s10898-017-0538-5
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    References listed on IDEAS

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    1. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
    2. H. Tuy & H. Tuan, 2013. "Generalized S-Lemma and strong duality in nonconvex quadratic programming," Journal of Global Optimization, Springer, vol. 56(3), pages 1045-1072, July.
    3. Barry R. Marks & Gordon P. Wright, 1978. "Technical Note—A General Inner Approximation Algorithm for Nonconvex Mathematical Programs," Operations Research, INFORMS, vol. 26(4), pages 681-683, August.
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    Cited by:

    1. Shi, Ye & Tuan, Hoang Duong & Savkin, Andrey V. & Lin, Chin-Teng & Zhu, Jian Guo & Poor, H. Vincent, 2021. "Distributed model predictive control for joint coordination of demand response and optimal power flow with renewables in smart grid," Applied Energy, Elsevier, vol. 290(C).

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