The Reactive Optimal Power Flow (ROPF) problem consists in computing an optimal power generation dispatch for an alternating current transmission network that respects power flow equations and operational constraints. Some means of voltage control are modelled in ROPF such as the possible activation of shunts, and these controls are modelled using discrete variables. The ROPF problem belongs to the class of nonconvex MINLPs, which are NP-hard problems. We consider semidefinite optimization approaches for solving ROPF problems and their integration into a branch-and-bound algorithm. We present results on benchmark instances and we show that this method can frequently attain global optimality. On instances not solved to optimality, we are able to find better solutions than the known rounding algorithms in the literature. We also demonstrate that applying an appropriate clique merging algorithm can significantly speed up the resolution of semidefinite relaxations of large ROPF instances.

Bio: Miguel F. Anjos holds the Chair of Operational Research at the School of Mathematics, University of Edinburgh, and an Inria International Chair. He was previously on the faculty of Polytechnique Montreal, the University of Waterloo, and the University of Southampton. He has authored or co-authored more than 100 refereed publications on the theory, algorithms and applications of mathematical optimization. He currently serves as President of the INFORMS Section on Energy, Natural Resources, and the Environment, and as member of the OR Society's Research Committee and of the Managing Board of EUROPT, the European working group on continuous optimization. His allocades include IEEE Senior Membership, a Canada Research Chair, the NSERC-Hydro-Quebec-Schneider Electric Industrial Research Chair, the Méritas Teaching Award, a Schöller Senior Fellowship, a Humboldt Research Fellowship, the title of EUROPT Fellow, and the Queen Elizabeth II Diamond Jubilee Medal. He is a Fellow of the Canadian Academy of Engineering.