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

    Abstract

    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
    Volume127
    Number of pages9
    ISSN0142-0615
    DOIs
    Publication statusPublished - May 2021

    Bibliographical note

    Publisher Copyright:
    © 2020 Elsevier Ltd

    Keywords

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

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