A Linear-Programming Approximation of AC Power Flows

This paper presents linear-programming models (the LPAC models) for approximating the AC power flow equations. The LPAC models capture both the voltage phase angles and magnitudes which are coupled through equations for active and reactive power. The cold-start LPAC models use a piecewise-linear approximation of the cosine terms in the AC equations, as well as a Maclaurin approximation for the remaining nonlinear terms. Experimental comparisons with AC solutions on a variety of standard IEEE and MatPower benchmarks shows that the LPAC models are highly accurate for active and reactive power, phase angles, and voltage magnitudes. The potential benefits of the LPAC models are illustrated on two case studies in power restoration and capacitor placement.