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This paper presents a model-based controller for a three-phase four-wire shunt active filter which uses a four-leg topology to implement the voltage source inverter. The proposed controller is able to compensate the homopolar current component due to an unbalanced load, thus, reducing the current flowing to the source via the neutral line, which is caused by distorting loads connected between a phase and the neutral line. In addition to the homopolar current compensation, the controller is able to compensate the usual issues found in three-wire systems, that is, reactive power and harmonic distortion in the general case of distorted and unbalanced source voltages and load currents. The complete model in (fixed frame) alphabetagamma-coordinates is presented. It is shown that the gamma component of the three legs input control acts in cooperation with the input control of the fourth leg to achieve the homopolar current compensation. This cooperative work has the effect of enlarging the range of the effective control action. Additionally, this opens the possibility of alternative modulation schemes for four-leg topologies. Numerical tests are provided to illustrate the benefits of our solution.