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

TL;DR

This paper evaluates second-order cone relaxations of the AC optimal power flow problem in active distribution grids, comparing their performance and extending methods for broader applicability with reactive power considerations.

Contribution

It introduces a unified framework for convex OPF relaxations, extends existing methods for greater exactness, and considers reactive power injections in distribution grids.

Findings

The framework effectively compares different convex relaxations.

Extensions improve the exactness of relaxations in practical scenarios.

Simulations demonstrate the applicability on IEEE test feeders with DERs.

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.