Linear power-flow models in multiphase distribution networks

This paper considers multiphase unbalanced distribution systems and develops approximate AC power-flow models wherein voltages, line currents, and powers at the point of common coupling are linearly related to the nodal net power injections. The linearization approach is grounded on a fixed-point interpretation of the AC power-flow equations, and it is applicable to distribution systems featuring a variety of connections for loads and generation units (e.g., wye and ungrounded delta, as well as line-to-line and line-to-grounded-neutral at the secondary of the distribution transformers). The approximate linear models can be naturally leveraged to facilitate the development of computationally-affordable optimization and control applications - from applications for advanced distribution management systems to online and distributed optimization routines. The approximation accuracy of the proposed method is evaluated on different feeders.