  Linear active-power-only DC power flow approximations are pervasive in the
planning and control of power systems. However, these approximations fail to
capture reactive power and voltage magnitudes, both of which are necessary in
many applications to ensure voltage stability and AC power flow feasibility.
This paper proposes linear-programming models (the LPAC models) that
incorporate reactive power and voltage magnitudes in a linear power flow
approximation. The LPAC models are built on a convex approximation of the
cosine terms in the AC equations, as well as Taylor approximations of the
remaining nonlinear terms. Experimental comparisons with AC solutions on a
variety of standard IEEE and MatPower benchmarks show that the LPAC models
produce accurate values for active and reactive power, phase angles, and
voltage magnitudes. The potential benefits of the LPAC models are illustrated
on two "proof-of-concept" studies in power restoration and capacitor placement.
