Abstract. Waves have the potential to increase the power output of a floating wind turbine by forcing its rotor to move against the wind. Starting from this observation, we use four multi-physics models of increasing complexity to investigate the role of waves and platform movements in the energy conversion process of four floating wind turbines of 5–15 MW in the Mediterranean Sea. Progressively adding realism to our simulations, we show that large along-wind rotor movements are needed to increase the power output of a floating wind turbine; however, these are prevented by the current technology of spar and semi-submersible platforms. Wind turbulence is the main cause of power fluctuations for the four floating wind turbines we examined and is preponderant over the effect of platform motions due to waves. In a realistic met-ocean environment, the power curve of the floating wind turbines we studied is lower than that obtained with a fixed foundation, with reductions in the annual energy production of 1.5 %–2.5 %. The lower energy production is mainly ascribed to the platform mean tilt, which reduces the rotor's effective area.