Implementable Three-Phase OPF Formulations for MV-LV Distribution Networks: MILP and MIQCP

The increasing uptake of distributed energy resources (DER) poses significant operational challenges to Distribution Network Operators (DNOs). In this context, AC Optimal Power Flow (OPF)-based approaches have the potential to aid DNOs' decision-making, to enable the operational orchestration of DER and network elements, improving performance while catering for network constraints. However, the classical OPF formulation is non-linear, and consequently, suffers scalability issues when dealing with realistic distribution networks as they can have over thousands of nodes, require three-phase modelling and contain discrete devices. This work extends the authors' previous works by proposing and comparing two implementable OPF formulations (linear and quadratically-constrained) for operational usage in distribution networks considering D-Y transformers. Results using a realistic MV-LV network show that both formulations can successfully orchestrate the operations of DER and network elements. While the linear OPF offers speed advantages when handling discrete variables, the quadratically-constrained OPF has better accuracy with acceptable speeds.