Development of a surrogate model for wind farm control

We present a method to derive a surrogate model for wind farm control. The procedure is based on a stochastic approach using generalized polynomial chaos (PC) and high-fidelity simulations. The turbine control law and the incoming wind conditions, such as speed and directions, are treated as uncertain variables. Wind farm power production is viewed as the random process depending on these uncertain variables. Thus, polynomial chaos expansion is used to obtain a response function that provides the wind farm power production as a function of the turbine control parameters and the wind speed and direction. The response function is obtained by using a finite set of deterministic realizations, which consist in highfidelity simulations for certain values of wind speed, direction and control parameters, interpolated by polynomials. In PC, the interpolating polynomial basis and the set of realizations are selected according to the probability density function of the uncertain parameters. This allows using a limited number of realizations to obtain an accurate response function and provides uncertainty bounds on the model. Thus, a mapping of the optimal control settings is obtained for any wind speed and direction to be employed for real-time wind farm operations. In this work, the procedure is validated against field measurements in a real wind farm in north Texas. The surrogate model is obtained by performing 64 simulations with our in-house code interpolated by 7th-order Hermite polynomials. The energy production computed with the surrogate model is accurate within 2% of the measured SCADA data. Once the response function has been obtained, an optimization problem is solved to find the control parameters maximizing the wind farm power production.