  With the potential to find global solutions, significant research interest
has focused on convex relaxations of the non-convex OPF problem. Recently,
"moment-based" relaxations from the Lasserre hierarchy for polynomial
optimization have been shown capable of globally solving a broad class of OPF
problems. Global solution of many large-scale test cases is accomplished by
exploiting sparsity and selectively applying the computationally intensive
higher-order relaxation constraints. Previous work describes an iterative
algorithm that indicates the buses for which the higher-order constraints
should be enforced. In order to speed computation of the moment relaxations,
this paper provides a study of the key parameter in this algorithm as applied
to relaxations from both the original Lasserre hierarchy and a recent complex
extension of the Lasserre hierarchy.
