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This paper presents a shunt active power filter for four-wire power systems with unity power factor control (UPF), which operates in unbalanced and nonsinusoidal conditions. In these power systems it is interesting to use four-branch voltage source inverters (VSI) because they are capable of compensating load currents of nonzero average value. Most four-branch VSI control methods are based on a space vector generalization using Clarke's transformation. The switches of these inverters operate at variable frequency with the well-known disadvantages that this supposes. Here a fixed frequency current controller applied to four-branch VSI is presented. It is based on an extension of the space vector modulation from two-dimensional space to three-dimensional space using Clarke's transformation. With it, a fixed switch switching frequency is obtained that causes line current ripples to have a fixed frequency. These current ripples can be easily attenuated by means of appropriate filters. This current controller also is able to decrease the relationship between DC and AC voltages at a greater rate than the one in and at a much greater rate than the ones in. For obtaining the reference currents starting from load currents the UPF control method based on the domain analysis is used.