The convex hull of the AC power flow equations in rectangular coordinates

Abstract

Obtaining the convex hull of the alternating current (AC) power flow equations is largely beneficial in the convexification of the optimization problems in power systems where the AC power flow constraints are taken into account. In this paper, the AC power flow formulation in rectangular coordinates which is a non-convex quadratic equality is equivalently decomposed into four quadratic inequalities whose coefficient matrices are positive semidefinite. Two of the quadratic inequalities are convex while the other two are not. The proposed decomposition facilitates the convexification of the power flow equations much. A convex hull formulation is proposed for the resulting non-convex quadratic inequalities. This formulation is applied to study the convex hull of the AC power flow.