Technical Report ERGO 13-018

Local solutions of the optimal power flow problem
W.A. Bukhsh, A. Grothey, K.I.M. McKinnon and P.A. Trodden


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 ( and can be used to test local or global optimization techniques for OPF. Finally we use our test examples to illustrate the behaviour of a recent semi-definite programming approach that aims to find the global solution of OPF.




Submitted for publication


  1. This is a preprint of a paper published in IEEE Transactions on Power Systems, Vol. 28, No. 4, November 2013 (link).
  2. Another technical report covering the issue of local optima in OPF problems is ERGO 11-017.
  3. Test case archive for optimal power flow problems with local optima is at