A Graph Theory Based Approach to Modeling Dynamic Wind Turbine Yaw*

Yaw control has shown great potential as a method for increasing the power output of wind farms but there have been relatively few efforts to model the dynamic behavior of an array of dynamically yawing turbines. When a turbine is dynamically yawed, the wake created by that turbine is deflected and its shape changes, which also affects the dynamics of turbines that encounter the changed wake downstream.  To capture these dynamics, we model the wind farm as a graph in which each turbine is a node and the dynamic changes in wake interactions between turbines within the farm are represented through time-varying edge weights.  These edge weights are represented using a normalized velocity deficit coefficient describing the individual velocity deficits between each pair of turbines.  The deficits are then superposed linearly to find the local velocity at each turbine, according to the relationships defined by the graph.  This enables us to estimate the time-varying effect of dynamic yawing at each turbine and to determine the impacts on the overall farm power output. As a first step, the model is validated through comparisons to statistically steady state results from large eddy simulations.