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The flexible alternating current transmission systems (FACTS) devices are essential components of the transmission system to enhance the controllability and elevate the transfer capacity of the network. The unified power flow controller is known as the most versatile device in the FACTS family. This work studies a distinctive unified power flow controller (UPFC) structure based on the direct matrix converter to regulate the active and reactive power in a transmission system. In contrast to the conventional UPFC, there is no requirement for a bulky energy storage element in this structure. This results in various benefits including: decreased system volume, improved efficiency, prolonged lifetime, reduced maintenance and removal of the DC-link control. The full power controllable regions are analyzed and graphically obtained for the MC-UPFC, which facilitates the selection of proper UPFC ratings. The working principles and a model of the MC-UPFC are put forward and discussed, followed by explanations of direct space vector modulation (SVM) for this application. Based on the SVM modulation scheme, PID controllers are developed to control power flows in a double-line transmission system. In addition, decoupling controllers are derived by feeding back the coupling components into controllers. The numerical simulation results for a double-line transmission system corroborate the feasibility and effectiveness of the proposition. [ABSTRACT FROM AUTHOR]