The unified power flow controller (UPFC) is recognized as one of the most promising flexible ac transmission system (FACTS) devices for modern power systems, due to its versatile functionalities based on typical operation conditions, this project proposes the global and local power flow operation rules of the UPFC embedded transmission system theoretically. First, the detailed global power flow model (GPFM) and the local power flow model (LPFM) are established concerning several selected critical points (SCPs) in the system. The theoretical power flow operation rules for the ranges, the movements and the trajectories of GPFM and LPFM are analyzed, respectively. Then, the case study is performed based on the proposed simplified model, and the results are analyzed from GPFM and LPFM perspectives respectively. The operation rules and the power flow ranges is studied. Further case studies based on the proposed original mathematical model are also carried out, and the results are listed from different viewpoints of two-dimensional planes and three-dimensional spaces. All types of results are also analyzed from GPFM and LPFM perspectives, which verify that the UPFC is adaptive to various operation conditions for power flow regulation.