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This paper explores the application of modular multi-level converters (MMC) as a means for harnessing the power from off-shore wind power plants. The MMC consists of a large number of simple voltage sourced converter (VSC) submodules that can be easily assembled into a converter for high-voltage and high power. The paper shows that the MMC converter has a fast response and low harmonic content in comparison with a two-level VSC option. The paper discusses the modeling approach used, including a solution to the modeling challenge imposed by the very large number of switching devices in the MMC.