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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 turbine control via concurrent yaw misalignment and axial induction control has demonstrated potential for improving wind farm power output and mitigating structural loads. However, the complex aerodynamic interplay between these two effects requires deeper investigation. This study presents a modified blade element momentum (BEM) model that matches rotor-averaged quantities to an actuator disk model of yawed rotor induction, enabling analysis of joint yaw-induction control using realistic turbine control inputs. The BEM approach reveals that common torque control strategies such as K−Ω^2 exhibit sub-optimal performance under yawed conditions. Notably, the power-yaw and thrust-yaw sensitivities vary significantly depending on the chosen control strategy, contrary to common modeling assumptions. In the context of wind farm control, employing induction control which minimizes the thrust coefficient proves most effective at reducing wake strength for a given power output across all yaw angles. Results indicate that while yaw control deflects wakes effectively, induction control more directly influences wake velocity magnitude, underscoring their complementary effects. This study advances a fundamental understanding of turbine aerodynamic responses in yawed operation and sets the stage for modeling joint yaw and induction control in wind farms. 

Combined wake steering and induction control is a promising strategy for increasing collective wind farm power production over standard turbine control. However, computationally efficient models for predicting optimal control set points still need to be tested against high-fidelity simulations, particularly in regimes of high rotor thrust. In this study, large eddy simulations (LES) are used to investigate a two-turbine array using actuator disk modeling in conventionally neutral atmospheric conditions. The thrust coefficient and yaw-misalignment angle are independently prescribed to the upwind turbine in each simulation while downwind turbine operation is fixed. Analyzing the LES velocity fields shows that near-wake length decreases and wake recovery rate increases with increasing thrust. We model the wake behavior with a physics-based near-wake and induction model coupled with a Gaussian far-wake model. The near-wake model predicts the turbine thrust and power depending on the wake steering and induction control set point. The initial wake velocities predicted by the near-wake model are validated against LES data, and a calibrated far-wake model is used to estimate the power maximizing control set point and power gain. Both model-predicted and LES optimal set points exhibit increases in yaw angle and thrust coefficient for the leading turbine relative to standard control. The model-optimal set point predicts a power gain of 18.1% while the LES optimal set point results in a power gain of 20.7%. In contrast, using a tuned cosine model for the power-yaw relationship results in a set point with a lower magnitude of yaw, a thrust coefficient lower than in standard control, and predicts a power gain of 13.7%. Using the physics-based, model-predicted set points in LES results in a power within 1.5% of optimal, showing potential for joint yaw-induction control as a method for predictably increasing wind farm power output.