Analytical model for the power-yaw sensitivity of wind turbines operating in full wake

Wind turbines are designed to align themselves with the incoming wind direction. However, turbines often experience unintentional yaw misalignment, which can significantly reduce the power production. The unintentional yaw misalignment increases for turbines operating in the wake of upstream turbines. Here, the combined effects of wakes and yaw misalignment are investigated, with a focus on the resulting reduction in power production. A model is developed, which considers the trajectory of each turbine blade element as it passes through the wake inflow in order to determine a power-yaw loss exponent. The simple model is verified using the HAWC2 aeroelastic code, where wake flow fields have been generated using both medium- and high-fidelity computational fluid dynamics simulations. It is demonstrated that the spatial variation in the incoming wind field, due to the presence of wakes, plays a significant role in the power loss due to yaw misalignment. Results show that disregarding these effects on the power-yaw loss exponent can yield a 3.5% overestimation in the power production of a turbine misaligned by 30 degrees. The presented analysis and model is relevant to low-fidelity wind farm optimization tools, which aim to capture the combined effects of wakes and yaw misalignment as well as the uncertainty on power output.