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

TL;DR

This paper investigates the tightness of the Lagrangian dual bound for the nonconvex ACOPF problem, proposing a decentralized computation method and comparing its tightness to existing relaxations.

Contribution

It introduces a parallelizable approach to compute the LD bound for ACOPF by partitioning the network and dualizing coupling constraints, and compares its tightness to SDP and SOCP relaxations.

Findings

LD bound is less tight than SDP relaxation

LD bound is as tight as SOCP relaxation

Proposed method enables decentralized computation of LD bound

Abstract

We study tightness properties of a Lagrangian dual (LD) bound for the nonconvex alternating current optimal power flow (ACOPF) problem. We show an LD bound that can be computed in a parallel, decentralized manner. Specifically, the proposed approach partitions the network into a set of subnetworks, dualizes the coupling constraints (giving the LD function), and maximizes 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 proximal bundle method. We show that the bound is less tight than the popular semidefinite programming relaxation but as tight as the second-order cone programming relaxation. We demonstrate our developments using PGLib-OPF test instances.