Wind farm dynamics and power optimization in realistic atmospheric boundary layer conditions
Keywords: Mechanical Engineering.

The study of wind farms within realistic atmospheric boundary layer (ABL) conditions is critical to understand the governing physics of the system and to design optimal operational protocols. Aerodynamic wake interactions between individual wind turbines typically reduce total wind farm energy production 10-20% and increase the cost of electricity for this resource. Further, in large wind farms, the collective farm efficiency is in part dictated by the interaction between the wind farm and the turbulent ABL and, correspondingly, the vertical transport of kinetic energy into the turbine array. Coriolis forces, arising from the projection of Earth's rotation into a non-inertial rotating Earth-fixed frame, modify the interaction of a wind farm with the ABL. The traditional approximation made in typical ABL simulations assumes that the horizontal component of Earth's rotation is negligible in the atmospheric boundary layer. When including the horizontal component of Earth's rotation, the boundary layer and wind farm physics are a function of the geostrophic wind direction. The influence of the geostrophic wind direction on a wind farm atmospheric boundary layer was characterized using conventionally neutral and stable boundary layer large eddy simulations (LES). In the Northern hemisphere, geostrophic winds from west-to-east establish the horizontal component of Earth's rotation as a sink term in the shear Reynolds stress budget whereas the horizontal component manifests as a source term for east-to-west geostrophic winds. As a result, the magnitude of entrainment of mean kinetic energy into a wind turbine array is modified by the direction of the geostrophic wind, and correspondingly, the boundary layer height and wind speed and direction profiles depend on the geostrophic wind direction. Historically, wind farm control protocols have optimized the performance of individual wind turbines which results in aerodynamic wake interactions and a reduction in wind farm efficiency. Considering the wind farm as a collective, a physics- and data-driven wake steering control method to increase the power production of wind farms is developed. Upwind turbines, which generate turbulent energy-deficit wake regions which impinge on downwind generates, are intentionally yaw misaligned with respect to the incident ABL wind. While the yaw misaligned turbine may produce less power than in yaw aligned operation, the downwind generators may significantly enhance their production, increasing the collective power for the farm. The wake steering method developed combines a physics-based engineering wake model with state estimation techniques based on the assimilation of the wind farm power production data, which is readily available for control decisions at operational wind farms. Analytic gradients are derived from the wake model and leveraged for efficient yaw misalignment set-point optimization. The open-loop wake steering control methodology was tested in a multi-turbine array at a utility-scale operational wind farm, where it statistically significantly increased the power production over standard operation. The analytic gradient-based wind farm power optimization methodology developed can optimize the yaw misalignment angles for large wind farms on the order of seconds, enabling online real-time control. The dynamics of the ABL range from microscale features on the order of meters to mesoscale meteorological scales on the order of hundreds of kilometers. As a result of the broad range of scales and diversity of competing forces, the wind farm interaction with the turbulent ABL is a complex dynamical system, necessitating closed-loop control which is able to dynamically adapt to the evolving wind conditions. In order to rapidly design and improve dynamic closed-loop wind farm controllers, we developed wind farm LES capabilities which incorporate Coriolis and stratification effects and which permit the experimentation of real-time control strategies. Dynamic, closed-loop wake steering controllers are tested in simulations with full Coriolis effects and, altogether, the results indicate that closed-loop wake steering control can significantly increase wind farm power production over greedy operation provided that site-specific wind farm data is assimilated into the optimal control model