2013/11/25 by Cédric Josz, Jean Maeght, Josz, Cédric +5 · 1 citation
Engineering · Mathematics · #Advanced Optical Network Technologies #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimal Power Flow Distribution #Optimization and Control (math.OC) #Power System Optimization and Stability #math.OC
paper · pdf · doi:10.48550/arxiv.1311.6370
16 pages, 4 figures, 2 matlab source code files included in the zip version
openalex publication_date 2013/11/25 · arxiv created 2016/03/03 · arxiv updated 2016/03/04 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
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 moment-sos (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.