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Discussion and mathematical proof on necessary and sufficient conditions for the application of the {p-q} theory for compensating the harmonic currents consumed by non-linear load using a shunt active filter are presented. These conditions over instantaneous active and reactive powers were not addressed before and must be considered on the design of new control strategies based on {p-q} theory. Theoretical demonstration is proposed and an application example with simulations results is used to validate the theoretical results.

On the Use of the p-q Theory for Harmonic Current Cancellation with Shunt Active Filters