This article deals with the vector control in dq axes of a three-phase grid-connected photovoltaic system with single-stage topology and low-voltage-ride-through capability. The photovoltaic generator is built using an array of several series-parallel Suntech PV modules and is modeled as a Lookup Table (two-dimensional; 2-D). The requirements adopted when grid voltage sags occur are based in both the IEC 61400-21 European normative and the allowed amount of reactive power to be delivered according to the Spanish grid code, which avoids the disconnection of the inverter under grid faults by a limitation in the magnitude of the three-phase output inverter currents. For this, the calculation of the positive- and negative-sequences of the grid voltages is made and a conventional three-phase Phase-Locked Loop is used for the inverter-grid synchronization, allowing the control of the active and reactive powers solely with the dq components of the inverter currents. A detailed enhanced flowchart of the control algorithm with low-voltage-ride-through capability is presented and several simulations and experiments using Matlab/SIMULINK and the Controller Hardware-in-the-Loop simulation technique, respectively, are run for several types of one- and three-phase voltage sags in order to validate its behavior.