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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
Article
  • 327 Downloads

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.

Keywords

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

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Copyright information

© 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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