This paper presents a new algorithm for a geometric approach to evaluate the boundaries of controllable power flow with a UPFC installed in a two-machine power system considering the constraints of converter ratings of the UPFC and also the line losses. Similar studies earlier had ignored the line losses due to resistance of the line. Using a geometrical approach, the analysis of the effect of placement of UPFC anywhere within the line is explored in the current plane. The main advantage of a geometric approach to evaluate the boundaries of controllable power flow in a power system with UPFC is that with a minimum computational effort, it gives a clear insight regarding the feasible operational area of the system subjected to a set of constraints. The significance of the proposed approach is that the method is more general and hence it can be extended to include the losses in the converters, the losses in the dc link capacitor etc., apart from the other equipment constraints. Using the proposed geometric approach, the P -δ curves of UPFC installed at any point along the transmission line can be determined. Further the paper presents a computational verification for the proposed algorithm and the geometric approach. This is based on the per-phase equivalent circuit representation of the two machine power system with UPFC. The two sets of results, viz., from the geometric approach and from the computational procedure, are in excellent agreement establishing the validity of the proposed algorithm. ©2008 IEEE.