Nested extremum seeking control for wind farm power optimization

Large-Eddy Simulations (LES) of an array of wind turbines have been carried out to design and evaluate a model-free approach, extremum-seeking control (ESC), for power maximization. This paper shows how to coordinate the action of the extremum seeking controllers (at each turbine) by nesting the objective functions used for optimization so that the power of the overall array is maximized. The paper illustrates how to select the frequencies of the dither signals (used by the ESCs) to reduce the sensitivity to turbulent wind fluctuations in the estimation of the gradients used for real-time power maximization. The results are compared with the results from a baseline configuration where each turbine is set to operate at its individual optimum tip speed ratio; i.e., at the nominal design condition. The comparison shows that a properly designed nested ESC can yield nontrivial improvements in power production relative to the baseline.