  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.
