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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 todoi:10.15598/aeee.v17i3.3415 fatcat:vkwkrodb5nbe3f7y5c5edeq42q