To control the complex powers emanating from a bus in power system, there are two solutions. The obvious solution is to equip each of the n lines radiating from the node with its own UPFC. The next evolution of the idea is to equip with a multi-terminal UPFC. First, the configuration and the principle of the Two-terminal UPFC (when n=2) are presented. In consideration of the existing shortages of output model-constructing method and topological model-constructing method for T-UPFC, a switching function mathematical model of this device is constructed by introducing the concept of switching function. It has more generality than the output and the topological model with the consideration of the internal switching character and the physical course of the T-UPFC.