Large Eddy Simulations of the turbulent flow over an array of wind turbines have been performed to evaluate a model-free approach to power optimization. Two different implementations have been tested: (i) individual extremum-seeking control (IESC), which optimizes the power of the single turbines individually; (ii) nested ESC (NESC), which coordinates the single controllers to seek a farm-level optimum. Both schemes provide a gain over the baseline, which operates all the turbines with ideal design set points. These settings are found to be sub-optimal for waked turbines. The NESC provides a slightly larger power production than the independent ESC, albeit it has a slower convergence to the optimum. Therefore, depending on wind variability, both strategies may be employed. IESC is more appropriate for sites with wind conditions changing on a short time scale, while NESC should be preferred when the wind conditions are quite stable. Since the extremum-seeking algorithm is model-free, uncertainties in atmospheric conditions, aging of the turbine or numerical dissipation due to the sub-grid model should not change the general conclusions reached in this paper. This methodology can provide reliable results and permits to gain, through the analysis, a useful knowledge on the mechanisms leading to the performance enhancement. (C) 2017 Elsevier Ltd. All rights reserved.