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The paper presents a direct and systematic method for determining the entire operating range of a UPFC in the presence of equipment and system operating limits. The method is inclusive of all limits: series converter voltage and current limits, shunt converter current limit, and voltage limits at the equipment terminals. The formulation is general and permits calculation of P-δ curves for a UPFC installed at any point along the transmission line. Equipment and system operating limits are shown to significantly impact the P-δ curves of the UPFC. The methodology presented in the paper provides system planners a means to realistically quantify potential benefits of a UPFC installation for a transmission system.