2015/06/17 by Carleton Coffrin, Coffrin, Carleton, Hassan Hijazi +3 · 2 citations
Engineering · #FOS: Electrical engineering #FOS: Mathematics #Microgrid Control and Optimization #Optimal Power Flow Distribution #Optimization and Control (math.OC) #Power System Optimization and Stability #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1506.05202
openalex publication_date 2015/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.