The design and financing of commercial-scale floating offshore wind projects require a better understanding of how power generation differs between newer floating turbines and well-established fixed-bottom turbines. In floating turbines, platform mobility causes additional rotor motion that can change the time-averaged power generation. In this work, OpenFAST simulations examine the power generated by the National Renewable Energy Laboratory's 5-MW reference turbine mounted on the OC3-UMaine spar and OC4-DeepCWind semisubmersible floating platforms, subjected to extreme irregular waves and below-rated turbulent inflow wind from large-eddy simulations of a neutral atmospheric boundary layer. For these below-rated conditions, average power generation in floating turbines is most affected by two types of turbine displacements: an average rotor pitch angle that reduces power, caused by platform pitch
and rotor motion upwind-downwind that increases power, caused by platform surge and pitch. The relative balance between these two effects determines whether a floating platform causes power gains or losses compared to a fixed-bottom turbine
for example, the spar creates modest (3.1%?4.5%) power gains, whereas the semisubmersible creates insignificant (0.1%?0.2%) power gains for the simulated conditions. Furthermore, platform surge and pitch motions must be analyzed concurrently to fully capture power generation in floating turbines, which is not yet universal practice. Finally, a simple analytical model for predicting average power in floating turbines under below-rated wind speeds is proposed, incorporating effects from both the time-averaged pitch displacement and the dynamic upwind-downwind displacements.