  Convex relaxations of the power flow equations and, in particular, the
Semi-Definite Programming (SDP) and Second-Order Cone (SOC) relaxations, have
attracted significant interest in recent years. The Quadratic Convex (QC)
relaxation is a departure from these relaxations in the sense that it imposes
constraints to preserve stronger links between the voltage variables through
convex envelopes of the polar representation. This paper is a systematic study
of the QC relaxation for AC Optimal Power Flow with realistic side constraints.
The main theoretical result shows that the QC relaxation is stronger than the
SOC relaxation and neither dominates nor is dominated by the SDP relaxation. In
addition, comprehensive computational results show that the QC relaxation may
produce significant improvements in accuracy over the SOC relaxation at a
reasonable computational cost, especially for networks with tight bounds on
phase angle differences. The QC and SOC relaxations are also shown to be
significantly faster and reliable compared to the SDP relaxation given the
current state of the respective solvers.
