Global optimization for optimal power flow over transmission networks

Y. Shi (), H. D. Tuan (), H. Tuy () and S. Su ()
Additional contact information
Y. Shi: University of Technology
H. D. Tuan: University of Technology
H. Tuy: Institute of Mathematics
S. Su: University of Technology

Journal of Global Optimization, 2017, vol. 69, issue 3, No 11, 745-760

Abstract: 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 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-017-0538-5

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