A hybrid three-phase single-phase power flow formulation

This paper presents a hybrid power flow formulation unifying three-phase and single-phase (positive sequence) models. Positive sequence modeling is considered at the transmission level network and three-phase modeling is considered at the distribution level. A passive interface between these networks is proposed. The interface is based on a pi element that can represent transmission lines or transformers. The formulation allows both subsystems to be solved simultaneously using the classic Newton-Raphson method. The three-phase subsystem can either be represented in phase or sequence components. Tests in large-scale power systems indicate that the proposed hybrid formulation has the same robust convergence properties of the conventional all-single-phase or all-three-phase Newton-type methods. The use of the proposed formulation is motivated for studies where the focus of the analysis is in the unbalanced three-phase subsystem highly influenced by operating conditions in the single-phase-modeled subsystem.