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Convex relaxations of the AC Optimal Power Flow (OPF) problem are essentialnot only for identifying the globally optimal solution but also for enablingthe use of OPF formulations in Bilevel Programming and Mathematical Programswith Equilibrium Constraints (MPEC), which are required for solving problemssuch as the coordination between transmission and distribution system operator(TSO/DSO) or optimal network investment. Focusing on active distribution gridsand radial networks, this paper introduces a framework that collects andcompares, for the first time to our knowledge, the performance of the mostpromising convex OPF formulations for practical applications. Our goal is toestablish a solid basis that will inform the selection of the most appropriatealgorithm for different applications. This paper (i) introduces a unifiedmathematical and simulation framework, (ii) extends existing methods to retainexactness in a wider number of cases and (iii) consider reactive powerinjections. We conduct simulations on the IEEE 34 and 123 radial test feederswith distributed energy resources (DERs), using yearly solar irradiation andload data.

Second-Order Cone Relaxations of the Optimal Power Flow for Active Distribution Grids