Generalized Unified Power Flow Controller (GUPFC) is a member of the flexible alternating current transmission system (FACTS) devices family that operates based on voltage source converter (VSC) and is known as the most efficient FACTs device. GUPFC can control the voltage of one bus and the active and reactive power flows on at least two transmission lines with equal voltage levels. This paper presents the mathematical modeling of power injection by GUPFC for the first time. Besides, the accurate design and details of the control system for series and shunt converters of a GUPFC, along with a new mathematical function for pulse generation based on a 48-pulse VSC when the GUPFC is placed in the middle point of a parallel transmission line, are presented in this study. The power injection modeling introduced in this paper is very useful and efficient in Newton-Raphson power flow studies and in modeling different parts of the control system and power electronics converter in dynamic and transient studies. The modeling is implemented in MATLAB/Simulink for a 400 km, 230 kV, and 60 Hz nominal frequency double-circuit transmission line. The satisfactory results provided in the simulations section of the paper verify the validity and accurate performance of the proposed model.