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For three-phase four-wire circuits, two compensation criteria have been established: one based on the instantaneous value concept and the other on the average value concept. Thus, according to the instantaneous value concept the non instantaneous power current is reduced, without altering the instantaneous active power. According to the average value concept, the nonactive average-current is reduced, without altering the average power. When the zero-sequence voltage component exists, both compensation types would not enable the zero-sequence (neutral) source current elimination. Then, two approaches are marked in this paper. The first one is for eliminating the non instantaneous power current or the nonactive average-current but the neutral current can still flow. The second one for eliminating the modified non instantaneous power current or the modified nonactive average-current, thus the neutral current component is compensated. According to recent recommendations in this work three-phase systems are considered as four-conductor systems. Experimental results are obtained to confirm the theoretical properties and to show the compensator performance.