  DC power flow approximations are ubiquitous in the electricity industry.
However, these linear approximations fail to capture important physical aspects
of power flow, such as the reactive power and voltage magnitude, which are
crucial in many applications to ensure voltage stability and AC solution
feasibility. This paper proposes two LP approximations of the AC optimal power
flow problem, founded on tight polyhedral approximations of the SOC
constraints, in the aim of retaining the good lower bounds of the SOCP
relaxation and relishing the computational efficiency of LP solvers. The high
accuracy of the two LP approximations is corroborated by rigorous computational
evaluations on systems with up to 9241 buses and different operating
conditions. The computational efficiency of the two proposed LP models is shown
to be comparable to, if not better than, that of the SOCP models in most
instances. This performance is ideal for MILP extensions of these LP models
since MILP is computationally more efficient than MIQCP.
