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Center for Nonlinear Studies |
Due to the potential for finding globally optimal solutions, significant research interest has focused on the application of semidefinite optimization techniques to problems in the field of electric power systems. This seminar discusses a semidefinite relaxation of the non-convex AC optimal power flow (OPF) problem, which seeks to minimize the operating cost of an electric power system subject to both engineering inequality and network equality constraints. The convex semidefinite relaxation is capable of finding globally optimal solutions to many OPF problems. By exploiting power system sparsity, semidefinite relaxations of practically sized OPF problems are computationally tractable. The semidefinite relaxation is “tight” for many but not all OPF problems. For practical problems where the semidefinite relaxation is not tight, results show small active and reactive power mismatches at the majority of load buses while only small subsets of the network exhibit significant mismatch. This suggests that the relevant non-convexities in these problems are isolated in small subsets of the network. Examination of the feasible spaces for small test cases illustrates such non-convexities and explains the semidefinite relaxation’s lack of tightness. Finally, preliminary results from the application of higher-order “moment” semidefinite relaxations show promise in obtaining globally optimal solutions to these small test cases.
Host: Marian Anghel