This paper presents a screening technique for greatly reducing the computation involved in determining the optimal location of a unified power flow controller (UPFC) in a power system. The first-order sensitivities of the generation cost with respect to UPFC control parameters are derived. This technique requires running only one optimal power flow (OPF) to obtain UPFC sensitivities for all possible transmission lines. To implement a sensitivity-based screening technique for guidance in optimally locating a single UPFC in a power system, we propose a new UPFC model, wrach consists of an ideal transformer with a complex turns ratio and a variable shunt admittance. In this model, the UPFC control variables do not depend explicitly on UPFC input and output currents and voltages. Accordingly, this model does not require adding extra buses for UPFC input and output terminals. IEEE five-, 14- and 30-bus systems were used to frustrate the technique. Index Terms-Flexible ac transmission systems (FACTS), FACTS location, first-order sensitivity, optimal power flow (OPF), screening technique, unified power flow controller (UPFC), UPFC ideal transformer model, UPFC placement, UPFC uncoupled model. This study focuses on the development of an Ideal Transformer Unified Power Flow Controller (UPFC) model and its integration with Optimal Power Flow (OPF) first-order sensitivities analysis for determining optimal UPFC locations in power systems. The abstract outlines the significance of UPFCs in enhancing power system stability and efficiency by controlling voltage and power flow. It highlights the objectives of the research, including the development of the UPFC model, analysis of OPF first-order sensitivities, and their combined application for screening optimal UPFC locations. The study aims to contribute to the improvement of power system operation and control through strategic UPFC placement. The abstract provides a concise overview of the study, summarizing the key aspects of the research. It outlines the development of an ideal transformer Unified Power Flow Controller (UPFC) model, the analysis of Optimal Power Flow (OPF) first-order sensitivities, and their application in determining optimal locations for UPFC installation in power systems