Network Flow and Copper Plate Relaxations for AC Transmission Systems
Abstract
Nonlinear convex relaxations of the power flow equations and, in particular, the Semi-Definite Programming (SDP), Convex Quadratic (QC), and Second-Order Cone (SOC) relaxations, have attracted significant interest in recent years. Thus far, little attention has been given to simpler linear relaxations of the power flow equations, which may bring significant performance gains at the cost of model accuracy. To fill the gap, this paper develops two intuitive linear relaxations of the power flow equations, one based on classic network flow models (NF) and another inspired by copper plate approximations (CP). Theoretical results show that the proposed NF model is a relaxation of the established nonlinear SOC model and the CP model is a relaxation of the NF model. Consequently, considering the linear NF and CP relaxations alongside the established nonlinear relaxations (SDP, QC, SOC) provides a rich variety of tradeoffs between the relaxation accuracy and performance.
Keywords
Cite
@article{arxiv.1506.05202,
title = {Network Flow and Copper Plate Relaxations for AC Transmission Systems},
author = {Carleton Coffrin and Hassan L. Hijazi and Pascal Van Hentenryck},
journal= {arXiv preprint arXiv:1506.05202},
year = {2015}
}
Comments
This article includes power flow background information similar to that in arXiv:1506.04773 and builds on the three bus example from arXiv:1502.07847