2014/04/20 by Daniel K. Molzahn, Molzahn, Daniel K., Ian A. Hiskens +1 · 4 citations
Decision Sciences · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimal Power Flow Distribution #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.1404.5071
openalex publication_date 2014/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Convex relaxations of non-convex optimal power flow (OPF) problems have\nrecently attracted significant interest. While existing relaxations globally\nsolve many OPF problems, there are practical problems for which existing\nrelaxations fail to yield physically meaningful solutions. This paper applies\nmoment relaxations to solve many of these OPF problems. The moment relaxations\nare developed from the Lasserre hierarchy for solving generalized moment\nproblems. Increasing the relaxation order in this hierarchy results in\n"tighter" relaxations at the computational cost of larger semidefinite\nprograms. Low-order moment relaxations are capable of globally solving many\nsmall OPF problems for which existing relaxations fail. By exploiting sparsity\nand only applying the higher-order relaxation to specific buses, global\nsolutions to larger problems are computationally tractable through the use of\nan iterative algorithm informed by a heuristic for choosing where to apply the\nhigher-order constraints. With standard semidefinite programming solvers, the\nalgorithm globally solves many test systems with up to 300 buses for which the\nexisting semidefinite relaxation fails to yield globally optimal solutions.\n