Local solutions of the optimal power flow problem

Waqquas A. Bukhsh, Andreas Grothey, Ken I.M. McKinnon, Paul A. Trodden

Research output: Contribution to journalArticlepeer-review

167 Citations (Scopus)


The existence of locally optimal solutions to the AC optimal power flow problem (OPF) has been a question of interest for decades. This paper presents examples of local optima on a variety of test networks including modified versions of common networks. We show that local optima can occur because the feasible region is disconnected and/or because of nonlinearities in the constraints. Standard local optimization techniques are shown to converge to these local optima. The voltage bounds of all the examples in this paper are between ±5% and ±10% off-nominal. The examples with local optima are available in an online archive (http://www.maths.ed.ac.uk/optenergy/LocalOpt/) and can be used to test local or global optimization techniques for OPF. Finally we use our test examples to illustrate the behavior of a recent semi-definite programming approach that aims to find the global solution of OPF.
Original languageEnglish
Pages (from-to)4780-4788
Number of pages9
JournalIEEE Transactions on Power Systems
Issue number4
Early online date15 Aug 2013
Publication statusPublished - Nov 2013


  • load flow
  • optimisation
  • global optimization techniques
  • optimal power flow


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