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This paper reports the investigations on the implementation of adaptive back stepping control technique in a power transmission system incorporating UPFC. The use of adaptive back stepping controller for controlling the operation of UPFC has not been reported earlier in the literature. The objective is to achieve effective control of the real and reactive power flows in the line, with minimum or zero dynamic interaction between them. A two bus power system with a UPFC is considered for the study. The system response to the power flow commands is investigated and the effectiveness of adaptive back stepping control is examined. Reference frame theory based mathematical models are used for analyzing the performance of the system in closed loop. The effectiveness of the proposed adaptive controller is demonstrated through digital simulations using MATLABSIMULINK and the results are compared using a PI based controller. It is found that the overall performance of the proposed controller is far superior especially with respect to dynamic interactions between real and reactive power.