On the Tightness and Scalability of the Lagrangian Dual Bound for the Alternating Current Optimal Power Flow Problem

Weiqi Zhang, Kibaek Kim, Victor M. Zavala

Published 2021-04-08Version 1

We study tightness and scalability properties of a Lagrangian dual (LD) bound for the nonconvex alternating current optimal power flow (ACOPF) problem. We show that the LD bound is as tight as that provided by the powerful and popular semidefinite programming relaxation. However, a key advantage of the proposed bound is that it can be computed in a parallel, decentralized manner. Specifically, in the proposed approach we partition the network into a set of subnetworks, we dualize the coupling constraints (giving the LD function), and we maximize the LD function with respect to the dual variables of the coupling constraints (giving the desired LD bound). The dual variables that maximize the LD are obtained by using a bundle method and we provide a proof of convergence for such method. We demonstrate our developments using PGLib test instances.