Multi-modular converters (MMC) are an emerging and promising option for high voltage direct current (HVDC) transmission, connection of offshore wind farms and FACTS. For such converters, two new strategies for current control are proposed, in which a band is defined around the reference current of the three phases, and modules to be turned ON are chosen to keep the three phase currents within the bands. In the first strategy, only the voltage levels adjacent to the grid voltage level are chosen; this is called "constant excitation" and it is the most appropriate when the number of modules per arm is small. The second strategy uses an excitation proportional to the current error, and it is the most appropriate when the number of modules per arm is great. The theoretical foundation of the strategies and the simulation results within an external active and reactive power control loop are presented. Finally, the current control strategies were applied to HVDC transmission from offshore wind farm to the onshore grid. (C) 2015 Elsevier Ltd. All rights reserved.