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 aπelement 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.