1AC OPF in Radial Distribution Networks- Part I: On the Limits of the Branch Flow Convexification and the Alternating Direction Method of Multipliers

Abstract—The optimal power-flow problem (OPF) has always played a key role in the planning and operation of power systems. Due to the non-linear nature of the AC power-flow equations, the OPF problem is known to be non-convex, therefore hard to solve. Most proposed methods for solving the OPF rely on approximations (e.g., of the network model) that render the problem convex, but that consequently yield inexact solutions. Recently, Farivar and Low proposed in [1,2] a method that is claimed to be exact for the case of radial distribution systems under specific assumptions, despite no apparent approximations. In our work, we show that it is, in fact, not exact. On one hand, there is a misinterpretation of the physical network model related to the ampacity constraint of the lines ’ current flows and, on the other hand, the proof of the exactness of the proposed relaxation requires unrealistic assumptions relate