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Cédric Josz(Cedric.Joszrtefrance.com) Abstract: Finding a global solution to the optimal power flow (OPF) problem is difficult due to its nonconvexity. A convex relaxation in the form of semidefinite programming (SDP) has attracted much attention lately as it yields a global solution in several practical cases. However, it does not in all cases, and such cases have been documented in recent publications. This paper presents another SDP method known as the momentsos (sum of squares) approach, which generates a sequence that converges towards a global solution to the OPF problem at the cost of higher runtime. Our finding is that in the small examples where the previously studied SDP method fails, this approach finds the global solution. The higher cost in runtime is due to an increase in the matrix size of the SDP problem, which can vary from one instance to another. Numerical experiment shows that the size is very often a quadratic function of the number of buses in the network, whereas it is a linear function of the number of buses in the case of the previously studied SDP method. Keywords: Global optimization, moment/sumofsquares approach, optimal power flow, polynomial optimization, semidefinite programming. Category 1: Applications  Science and Engineering Category 2: Network Optimization Category 3: Global Optimization (Applications ) Citation: Research report, INRIA ParisRocquencourt, BP 105, F78153 Le Chesnay, France. Download: [PDF] Entry Submitted: 11/19/2013 Modify/Update this entry  
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