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The power quality of a three-phase photovoltaic (PV) inverter drastically deteriorates in the presence of grid faults with unbalanced voltages. A ripple in the injected power and an increase in the current harmonic distortion are the main noticeable adverse effects produced by this abnormal grid situation. Several grid-fault control schemes are nowadays available for operating under unbalanced grid voltage. These control schemes usually have extreme power quality characteristics. Some of them have been conceived to completely avoid power ripple during unbalanced voltage sags, but at an expense of high current harmonic distortion. With other schemes, the harmonic distortion is totally eliminated but at an expense of high ripple in the injected power. This paper further explores the performance of PV inverters under unbalanced voltage sags. It has three theoretical contributions: 1) a generalized control scheme, which includes the aforementioned grid-fault controllers as particular cases; 2) a control strategy based on the use of continuous values for the control parameters. This original approach gives adjustable power quality characteristics that cannot be achieved with the previous control schemes; 3) three different control algorithms for calculating the continuous values of the control parameters. These contributions are experimentally validated with a digital signal processor-based laboratory prototype.