PROJECT TITLE :

Sparsity-Exploiting Moment-Based Relaxations of the Optimal Power Flow Problem

ABSTRACT:

Convex relaxations of non-convex optimal power flow (OPF) issues have recently attracted vital interest. While existing relaxations globally solve many OPF problems, there are practical problems for that existing relaxations fail to yield physically meaningful solutions. This paper applies moment relaxations to solve several of those OPF issues. The moment relaxations are developed from the Lasserre hierarchy for solving generalized moment problems. Increasing the relief order in this hierarchy results in “tighter” relaxations at the computational price of larger semidefinite programs. Low-order moment relaxations are capable of globally solving several tiny OPF problems for which existing relaxations fail. By exploiting sparsity and solely applying the higher-order relaxation to specific buses, global solutions to larger issues are computationally tractable through the utilization of an iterative algorithm informed by a heuristic for choosing where to use the upper-order constraints. With normal semidefinite programming solvers, the algorithm globally solves several take a look at systems with up to three hundred buses for that the present semidefinite relaxation fails to yield globally optimal solutions.