Power flow optimization using positive quadratic programming
The problem to minimize power losses in an electrical network subject to voltage and power constraints is in general hard to solve. However, it has recently been discovered that semidefinite programming relaxations in many cases enable exact computation of the global optimum. Here we point out a fundamental reason for the successful relaxations, namely that the passive network components give rise to matrices with nonnegative offdiagonal entries. Recent progress on quadratic programming with Metzler matrix structure can therefore be applied.
© 2011 IFAC. Published by Elsevier Ltd. The authors would like to gratefully acknowledge John C. Doyle for fruitful discussions on this topic. This research was supported by ONR MURI N00014-08-1-0747, ARO MURI W911NF-08-1-0233, the Army's W911NF-09-D-0001 and NSF NetSE grant CNS-0911041. The second author was supported by the Linnaeus grant LCCC from the Swedish Research Council.