Date: 05 June 2020, Friday
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“Tight-and-Cheap Conic Relaxations for Optimal Power Flow and Optimal Reactive Power Dispatch”
Miguel F. Anjos
School of Mathematics, University of Edinburgh
Abstract: The classical alternating current optimal power flow (ACOPF) problem is highly nonconvex and generally hard to solve. Computational speed and global optimality are key needs for practical OPF algorithms. In practice, solving large-scale ACOPF problems remains a challenge. We present a conic optimization approach to ACOPF that combines semidefinite optimization with the reformulation-linearization technique (RLT) to obtain a Tight-and-Cheap Relaxation (TCR) of ACOPF. We show conditions under which TCR is exact and can provide a global optimal solution for the ACOPF problem, theoretically and computationally. Computational experiments using standard test cases with up to 6515 buses (nodes) show that the time to solve TCR is up to one order of magnitude lower than for the chordal relaxation, a semidefinite relaxation technique that exploits the sparsity of power networks. We also consider the optimal reactive power dispatch (ORPD) problem. This is an extension of ACOPF where discrete control devices for regulating the reactive power, such as shunt elements and tap changers, are introduced. We model the ORPD problem as a mixed-integer nonlinear optimization problem, and apply the tight-and-cheap approach to it. We show that this relaxation, combined with a round-off technique, leads to near-global optimal solutions with very small optimality gaps. This is an improvement over the (nonconvex) continuous relaxation of ORPD. We report computational results on realistic test cases with up to 3375 buses. This is joint work with Christian Bingane and Sébastien Le Digabel.
Miguel F. Anjos holds the Chair of Operational Research at the School of Mathematics, University of Edinburgh, and an Inria International Chair. He is the Schöller Senior Fellow for 2020 at the University of Erlangen-Nuremberg. He received the B.Sc. degree from McGill University, the M.S. from Stanford University, and the Ph.D. degree from the University of Waterloo. His research interests are in the theory, algorithms and applications of mathematical optimization. He is particularly interested in the application of optimization to problems in power systems management and smart grid design. He is the Founding Academic Director of the Trottier Institute for Energy at Polytechnique, and President-Elect of the INFORMS Section on Energy, Natural Resources, and the Environment. Previous professional service elected positions include three-year terms on the Council of the Mathematical Optimization Society and as Program Director for the SIAM Activity Group on Optimization, and to a two-year term as Vice-Chair of the INFORMS Optimization Society. He served on the Mitacs Research Council since its creation in 2011 until 2017, and is now an Emeritus member. His allocades include IEEE Senior Membership, a Canada Research Chair, the NSERC-Hydro-Quebec-Schneider Electric Industrial Research Chair, the Méritas Teaching Award, 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