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Due to the increase of the distributed power generation in recent years, power system operators have updated their grid connection requirements, in order to include distributed power generation plants operation in the transient operation control of the overall electric power system. Among them, low voltage ride-through requirements demand wind power plant to remain connected to the network in presence of grid voltage dips, contributing to keep network voltage and frequency stable. Wind power technology points to increase voltage levels. Hence, multilevel converters are well suited for this application. The use of symmetrical components to control grid-connected voltage-source converters is simple and effective, but a sequence separation method is needed, which delivers inexact response during a lapse of time after a fault appearance or clearance. This inaccurate response can be a significant drawback. Predictive current control presents similar dynamic response and reference tracking than other well established control methods, but working at lower switching frequencies. In this work, predictive current control is applied to the grid-side NPC converter, in order to fulfil LVRT requirements. Then, a sequence separation method is not needed and inaccuracies after grid fault appearance and clearance are removed from the system performance. DC-link neutral point balance is also achieved by means of the predictive control algorithm, which considers the redundant switching states of the NPC. Simulation results confirm the validity of the proposed control approach.