Title: Convex Hull of the Quadratic Branch AC Power Flow Equations and Its Application in Radial Distribution Networks,
Abstract: A branch flow model (BFM) is used to formulate the AC power flow in general
networks. For each branch/line, the BFM contains a nonconvex quadratic
equality. A mathematical formulation of its convex hull is proposed, which is
the tightest convex relaxation of this quadratic equation. The convex hull
formulation consists of a second order cone inequality and a linear inequality
within the physical bounds of power flows. The convex hull formulation is
analytically proved and geometrically validated. An optimal scheduling problem
of distributed energy storage (DES) in radial distribution systems with high
penetration of photovoltaic resources is investigated in this paper. To capture
the performance of both the battery and converter, a second-order DES model is
proposed. Following the convex hull of the quadratic branch flow equation, the
convex hull formulation of the nonconvex constraint in the DES model is also
derived. The proposed convex hull models are used to generate a tight convex
relaxation of the DES optimal scheduling (DESOS) problem. The proposed approach
is tested on several radial systems. A discussion on the extension to meshed
networks is provided.