The limits of controllable power flow in the transmission line with the UPFC are determined by the equipment ratings and the line limits. In this paper, boundaries of controllable power flow in a simple two machine power system with UPFC based on a geometrical approach [3] are investigated. The main advantage of this geometrical approach is that even with a minimum computational effort, it gives a clear insight regarding the operational area of the power system with UPFC. However, certain subtle aspects of this geometrical method have not been addressed. A clear and comprehensive explanation of the mathematical basis is presented in this paper for the geometrical approach [3] for evaluating the controllable power flow. Although in a general sense, the location of UPFC within a line is not a crucial parameter affecting the overall performance, results of the geometric approach indicate discontinuities in the P-δ curves specifically in certain ranges of δ. Overall, the results indicate that there is no significant effect of the location of UPFC on the minimum and maximum real power transmitted at a given power angle within the boundaries of controllable power flow. However the corresponding reactive power and currents are affected by location of UPFC. Further, according to the geometrical approach, the feasible range of δ itself depends upon the location of UPFC. Also, the investigations reveal the restricted scope of the geometrical approach. Overall, it is observed that the geometrical approach [3] is appropriate and useful only for some ranges of power angle and location of UPFC. ©2006 IEEE.