The optimal power flow (OPF) problem minimizes the operating cost of an
electric power system. Applications of convex relaxation techniques to the
non-convex OPF problem have been of recent interest, including work using the
Lasserre hierarchy of "moment" relaxations to globally solve many OPF problems.
By preprocessing the network model to eliminate low-impedance lines, this paper
demonstrates the capability of the moment relaxations to globally solve large
OPF problems that minimize active power losses for portions of several European
power systems. Large problems with more general objective functions have thus
far been computationally intractable for current formulations of the moment
relaxations. To overcome this limitation, this paper proposes the combination
of an objective function penalization with the moment relaxations. This
combination yields feasible points with objective function values that are
close to the global optimum of several large OPF problems. Compared to an
existing penalization method, the combination of penalization and the moment
relaxations eliminates the need to specify one of the penalty parameters and
solves a broader class of problems.Comment: 8 pages, 1 figure, to appear in IEEE 54th Annual Conference on
Decision and Control (CDC), 15-18 December 201