Optimal power flow in four-wire distribution networks: Formulation and benchmarking

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. • We develop two quadratic optimization formulations for unbalanced four-wire grids. • The current–voltage formulation is superior to the power–voltage formulation. • Four-wire optimization models require about 30% more time to solve than three-wire ones. • Numerical results support the proposed relaxation and approximation hierarchies.