Center-node Unified Power Flow Controller (C-UPFC) is a recent developed Flexible AC Transmission System (FACTS) device. C-UPFC is a combined shunt-series controller that connected at the midpoint of transmission lines to control various parameters such as, voltage magnitude at midpoint of line, active and reactive powers flow at both ends of line. This paper proposed an efficient modelling with handling operating constraints of CUPFC device load flow solution. The proposed model based on power injection approach, where the parameters of C-UPFC are represented as function of the specified control values to keep the original structure of Jacobian matrix as it is. The operating constraints of C-UPFC including, the series injected voltages, the series current passing through converters, shunt injected voltage, the injected current of shunt converter, and exchanged power among converters are handled by an developed innovative methods. The developed handling methods based on modifying and updating the specified values as a function of maximum limit of the operating constraints. The proposed C-UPFC model with developed handling operating constraint methods implemented in IEEE 30-bus and IEEE 118-bus test systems. The obtained simulation results show the robustness and feasibility of the proposed model in load flow and superiority of the developed methods over the conventional methods for handling the operating constraints of C-UPFC.