Exactness of OPF Relaxation on Three-phase Radial Networks with Delta Connections

TL;DR

This paper investigates the inexactness of semi-definite relaxations of AC optimal power flow in three-phase radial networks with delta connections, identifying causes and proposing algorithms to recover exact solutions.

Contribution

It reveals the origin of inexactness due to non-uniqueness and introduces algorithms that achieve exact solutions in networks with delta connections.

Findings

Algorithms recover exact solutions up to numerical precision.

Inexactness is caused by solution non-uniqueness and numerical errors.

Proposed methods work on IEEE test systems with delta connections.

Abstract

Simulations have shown that while semi-definite relaxations of AC optimal power flow (AC-OPF) on three-phase radial networks with only wye connections tend to be exact, the presence of delta connections seem to render them inexact. This paper shows that such inexactness originates from the non-uniqueness of relaxation solutions and numerical errors amplified by the non-uniqueness. This finding motivates two algorithms to recover the exact solution of AC-OPF in the presence of delta connections. In simulations using IEEE 13, 37 and 123-bus systems, the proposed algorithms provide exact optimal solutions up to numerical precision.