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A predictive control algorithm specially developed for shunt active power filters aimed to compensate reactive power and current harmonics components is presented and analyzed. The proposed predictive control algorithm is implemented in a three-phase four-leg voltage-source inverter (4L-VSI). The use of a 4L-VSI allows the compensation of current harmonics, reactive power and neutral current harmonics generated by single-phase non-linear loads. A detailed mathematical model of the filter, including the effect of the power system equivalent impedance is derived and used to design the proposed predictive control algorithm. The proposed active power filter and associated control scheme performance and compensation effectiveness are demonstrated by simulation and with experimental results.