Analytical modeling of the induction, thrust, and power of a yaw misaligned actuator disk

Collective wind farm flow control, where individual wind turbines are operated in a suboptimal strategy to benefit the aggregate farm, has demonstrated potential to reduce wake interactions and increase wind farm energy production. However, existing wake models used for control often estimate the thrust and power of yaw misaligned turbines using simplified empirical expressions which require expensive calibration data and do not accurately extrapolate between turbine models. The thrust, velocity deficit, wake deflection, and power of a yawed wind turbine depend on its induced velocity. The induced velocity depends on both the yaw angle and thrust coefficient of the wind turbine. Here, we extend classical one-dimensional momentum theory to model the induction of a yaw misaligned actuator disk. Analytical expressions for the induction, thrust, initial wake velocity deficit, initial transverse velocity, and power are developed as a function of the yaw misalignment angle and the thrust coefficient. The analytical model is validated against large eddy simulations of a yaw misaligned actuator disk over a range of yaws and thrust coefficients. The implications of the developed, predictive model on wake steering, induction control, and joint steering and induction control are discussed.