This paper presents an investigation and visualization of the effect of UPFC on power flow characteristics by incorporating it in a simple twobus system. The UPFC is represented by two ideal voltage sources each of them is connected in series with a reactance. This model investigates the nonlinearity of UPFC on the power system load flow problem. Since the various UPFC variables equations are non-linear, a form of vector presentation in complex power plane is used to visualize the effect of different control variables of UPFC on line power transfer. This visualization helps to identify the effectiveness of each one of control variables on power control region.