Convex relaxations of non-convex optimal power flow (OPF) problems haverecently attracted significant interest. While existing relaxations globallysolve many OPF problems, there are practical problems for which existingrelaxations fail to yield physically meaningful solutions. This paper appliesmoment relaxations to solve many of these OPF problems. The moment relaxationsare developed from the Lasserre hierarchy for solving generalized momentproblems. Increasing the relaxation order in this hierarchy results in"tighter" relaxations at the computational cost of larger semidefiniteprograms. Low-order moment relaxations are capable of globally solving manysmall OPF problems for which existing relaxations fail. By exploiting sparsityand only applying the higher-order relaxation to specific buses, globalsolutions to larger problems are computationally tractable through the use ofan iterative algorithm informed by a heuristic for choosing where to apply thehigher-order constraints. With standard semidefinite programming solvers, thealgorithm globally solves many test systems with up to 300 buses for which theexisting semidefinite relaxation fails to yield globally optimal solutions.
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