  Power flow refers to the injection of power on the lines of an electrical
grid, so that all the injections at the nodes form a consistent flow within the
network. Optimality, in this setting, is usually intended as the minimization
of the cost of generating power. Current can either be direct or alternating:
while the former yields approximate linear programming formulations, the latter
yields formulations of a much more interesting sort: namely, nonconvex
nonlinear programs in complex numbers. In this technical survey, we derive
formulation variants and relaxations of the alternating current optimal power
flow problem.
