With the large-scale integration of distributed generators, the power distribution areas face new risks such as voltage violations. New power electronic devices represented by soft open point (SOP) facilitate the development of flexible interconnected power distribution areas, bringing urgent demand for coordinated operation of power distribution areas. In this paper, considering the integration of SOP, flexible interconnection of distribution areas is constructed. a distributed operation optimization method for flexible interconnected power distribution areas based on proximal atomic coordination (PAC) is proposed. The distribution area variables are divided into internal variables and boundary variables. The distributed optimization model is transformed into atomized distributed optimization model based on PAC. The accuracy and effectiveness of the distributed operation optimization method is validated on a modified practical flexible interconnected distribution area with a multi-terminal SOP.