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For three-phase four-wire circuits, two compensation criteria are possible: one based on the instantaneous value concept and the other on the average value concept. Thus, according to the first concept the instantaneous reactive current is reduced, without altering the instantaneous active power (time instantaneous compensation). According to the second concept the nonactive current is reduced, without altering the average power (time average compensation). When the zero-sequence voltage component exists, both criteria would not enable the zero-sequence (neutral) source current elimination. Two approaches are distinguished in this paper. The first one is for eliminating the instantaneous reactive current or eliminating nonactive current components but neutral current can still flow. The second one proposes to eliminate the instantaneous pseudoreactive current or pseudo-nonactive current, then the neutral current component is compensated. Simulated results are obtained to confirm the theoretical properties and show the compensator performance.