Second-order cone relaxations of the optimal power flow for active distribution grids: Comparison of methods

Lucien Bobo*, Andreas Venzke, Spyros Chatzivasileiadis

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


Convex relaxations of the AC Optimal Power Flow (OPF) problem are essential not only for identifying the globally optimal solution but also for enabling the use of OPF formulations in Bilevel Programming and Mathematical Programs with Equilibrium Constraints (MPEC), which are required for solving problems such as the coordination between transmission and distribution system operator (TSO/DSO) or optimal network investment. Focusing on active distribution grids and radial networks, this paper introduces a framework that collects and compares, for the first time to our knowledge, the performance of the most promising convex OPF formulations for practical applications. Our goal is to establish a solid basis that will inform the selection of the most appropriate algorithm for different applications. This paper (i) introduces a unified mathematical and simulation framework, (ii) extends existing methods to retain exactness in a wider number of cases and (iii) consider reactive power injections. We conduct simulations on the IEEE 34 and 123 radial test feeders with distributed energy resources (DERs), using yearly solar irradiation and load data.

Original languageEnglish
Article number106625
JournalInternational Journal of Electrical Power and Energy Systems
Number of pages9
Publication statusPublished - May 2021

Bibliographical note

Publisher Copyright:
© 2020 Elsevier Ltd


  • Convex relaxation
  • Distributed energy resources
  • Distribution networks
  • Optimal power flow


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