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Abstract Despite substantial growth in wind energy technology in recent decades, aerodynamic modeling of wind turbines relies on momentum models derived in the late 19th and early 20th centuries, which are well-known to break down under flow regimes in which wind turbines often operate. This gap in theoretical modeling for rotors that are misaligned with the inflow and also for high-thrust rotors has resulted in the development of numerous empirical corrections which are widely applied in textbooks, research articles, and open-source and industry design codes. This work reports a Unified Momentum Model to efficiently predict power production, thrust force, and wake dynamics of rotors under arbitrary inflow angles and thrust coefficients without empirical corrections. The Unified Momentum Model is additionally coupled with a blade element model to enable blade element momentum modeling predictions of wind turbines in high thrust coefficient and yaw misaligned states without using corrections for these states. This Unified Momentum Model can form a new basis for wind turbine modeling, design, and control tools from first principles and may enable further development of innovations necessary for increased wind production and reliability to respond to 21st century climate change challenges. 

Wind farm design generally relies on the use of historical data and analytical wake models to predict farm quantities, such as annual energy production (AEP). Uncertainty in input wind data that drive these predictions can translate to significant uncertainty in output quantities. We examine two sources of uncertainty stemming from the level of description of the relevant meteorological variables and the source of the data. The former comes from a standard practice of simplifying the representation of the wind conditions in wake models, such as AEP estimates based on averaged turbulence intensity (TI), as opposed to instantaneous. Uncertainty from the data source arises from practical considerations related to the high cost of in situ measurements, especially for offshore wind farms. Instead, numerical weather prediction (NWP) modeling can be used to characterize the more exact location of the proposed site, with the trade-off of an imperfect model form. In the present work, both sources of input uncertainty are analyzed through a study of the site of the future Vineyard Wind 1 offshore wind farm. This site is analyzed using wind data from LiDAR measurements located 25 km from the farm and NWP data located within the farm. Error and uncertainty from the TI and data sources are quantified through forward analysis using an analytical wake model. We find that the impact of TI error on AEP predictions is negligible, while data source uncertainty results in 0.4%–3.7% uncertainty over feasible candidate hub heights for offshore wind farms, which can exceed interannual variability.