Journal of Global Optimization

, Volume 69, Issue 3, pp 745–760 | Cite as

Global optimization for optimal power flow over transmission networks

  • Y. Shi
  • H. D. TuanEmail author
  • H. Tuy
  • S. Su


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.


Optimal power flow (OPF) Transmission networks Rank-one matrix constraint Nonsmooth optimization Semi-definite programming (SDP) Global optimization 


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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Faculty of Engineering and Information TechnologyUniversity of TechnologySydneyAustralia
  2. 2.Institute of MathematicsHanoiVietnam

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