A Study on the Strong Duality of Conic Relaxation of AC Optimal Power Flow in Radial Networks

TL;DR

This paper establishes conditions for strong duality in SOCP formulations of AC power flow in radial networks and validates them through numerical tests on standard and real-world networks.

Contribution

It introduces closed-form conditions that guarantee strong duality in the SOCP relaxation of AC power flow problems in radial networks.

Findings

Proposed conditions ensure strong duality in radial networks.

Numerical tests validate the effectiveness of the conditions.

Applicable to both test and real-world distribution networks.

Abstract

This paper proposes a set of closed-form conditions to ensure the strong duality of second-order cone program (SOCP) formulation for AC power flow in radial power networks. In addition, numerical evaluations on IEEE 33-bus test networks and a real-world distribution network are performed to demonstrate the validity of the proposed conditions.