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This paper proposes a practical approach to the theory of instantaneous power in non-sinusoidal and unbalanced-three-phase systems. This approach is based on the symmetrical components theory in instantaneous state. General equations relating both the instantaneous powers and the symmetrical components in instantaneous state are developed. These developed equations are fundamental in elucidating some important characteristics of the instantaneous powers and useful to understand the control algorithms used for the UPFC and the active filtering. A control strategy based on this approach is applied to the third generation of flexible ac transmission system. A typical arc furnace and UPFC model have been implemented in digital simulator to demonstrate the capability of the UPFC to compensate all disturbances. Theory and computer simulations using Simulink of Matlab are developed to demonstrate the practicality of the approach.