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This paper presents a model-based controller for a three-phase four-wire shunt active filter, which uses a three-leg split-capacitor topology to implement the voltage source inverter. The controller is aimed to compensate reactive power and harmonic distortion in the general case of distorted and unbalanced source voltages and load currents, including distorted loads connected between a phase and the neutral line. In addition, the controller is able to compensate for the homopolar component of the load current, that is, the current flowing to the source via the neutral line can be considerably reduced without modifying the actual topology. The complete model in (fixed frame) alphabetagamma-coordinates is presented. Special attention is given to the homopolar component (referred here as the gamma-component) of the line current, source voltage and control input, which are instrumental for the control design purpose. Experimental results in a 2 kVA prototype are provided to illustrate the benefits of the proposed solution.