  Computational speed and global optimality are key needs for practical
algorithms for the optimal power flow problem. Two convex relaxations offer a
favorable trade-off between the standard second-order cone and the standard
semidefinite relaxations for large-scale meshed networks in terms of optimality
gap and computation time: the tight-and-cheap relaxation (TCR) and the
quadratic convex relaxation (QCR). We compare these relaxations on 60 PGLib-OPF
test cases with up to 1,354 buses under three operating conditions and show
that TCR dominates QCR on all 20 typical (TYP) test cases, on 18 out of 20
active power increase (API), and 12 out of 20 small angle difference (SAD).
Selected state-of-the-art conic relaxations are implemented in the new
MATLAB-based package CONICOPF available on GitHub.
