Approximate Branch Flow Models for Three-Phase Unbalanced Network: A Comparative Analysis

Optimal Power Flow (OPF) algorithms are crucial tools for Distribution Network Operators (DNOs) to ensure smooth system operation while transitioning to a decentralized, decarbonized, and digitized power grid. Within OPF algorithms, power flow equations that characterize three-phase distribution networks are essential but complex components. This paper evaluates the accuracy of three commonly used approximate models of the original branch flow-based three-phase power flow equations: the SOCP-based hybrid model, the linear model, and the approximated nonlinear model. Detailed formulations of these models are provided, including their underlying assumptions, approximations, and relaxations. These models are then tested on a 25-bus unbalanced distribution network, with their power flow results compared to those obtained from the standard backward forward sweep algorithm. A comprehensive comparative analysis is conducted, offering critical insights into the appropriate use of these models. This analysis aims to assist researchers in selecting the most suitable model for characterizing three-phase unbalanced distribution networks in their studies.