  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.
