Optimal Power Flow in Four-Wire Distribution Networks: Formulation and Benchmarking

TL;DR

This paper develops and compares optimal power flow formulations for four-wire low-voltage distribution networks, emphasizing the advantages of current-voltage variables over power-voltage in terms of robustness and scalability.

Contribution

It introduces OPF formulations tailored for four-wire networks, including transformers and unbalanced loads, and evaluates their performance through extensive case studies.

Findings

Current-voltage formulations are more robust and scalable.

Kron reduction introduces modeling errors affecting solve time.

Current-voltage approach outperforms power-voltage in four-wire networks.

Abstract

In recent years, several applications have been proposed in the context of distribution networks. Many of these can be formulated as an optimal power flow problem, a mathematical optimization program which includes a model of the steady-state physics of the electricity network. If the network loading is balanced and the lines are transposed, the network model can be simplified to a single-phase equivalent model. However, these assumptions do not apply to low-voltage distribution networks, so the network model should model the effects of phase unbalance correctly. In many parts of the world, the low-voltage distribution network has four conductors, i.e. three phases and a neutral. This paper develops OPF formulations for such networks, including transformers, shunts and voltage-dependent loads, in two variable spaces, i.e. current-voltage and power-voltage, and compares them for robustness and scalability. A case study across 128 low-voltage networks also quantifies the modelling error introduced by Kron reductions and its impact on the solve time. This work highlights the advantages of formulations in current-voltage variables over power-voltage, for four-wire networks.