## 1 Introduction
Its weakness consists of the fact that it needs vast data sets in order to provide meaningful results: The authors of [28] have addressed this problem by employing time-resolved data sets with sampling time of the order of the second, rather than ten minutes, like the typical Supervisory Control And Data Acquisition (SCADA) data. Some proposals to overcome this issue have been formulated in References [21; 29]: The idea is that the power-power approach can be generalized by modeling the power of the wind turbine of interest as a function of operation variables of more than one reference near wind turbines. If an upgrade has a non-negligible effect on the performances of the wind turbine, it can be detected as a variation in the behavior of the residuals between model estimates (when the model is trained with pre-upgrade data) and measurements. A common lesson arises from the above discussed studies: It is important, when possible, to study wind turbine power curve upgrades in real environments because the flow conditions at the microscale level can be relevant for the efficiency of the upgrade. At the same time, it would be important and cost-saving to have reliable estimates of the impact of wind turbine power upgrades that are based on numerical models or simulations. The objective, on one hand, is having at our disposal a second piece of advice to the data-based validation. On the other hand, if a model is reliable for estimating the impact of an upgrade, it can be used as a first or preliminary piece of advice before the installation of the upgrade. The present work deals exactly with this kind of problems. A real test case is studied: A multi-megawatt wind turbine sited in Italy in a considerably complex terrain has undergone optimization of the rotor rpm management in order to reach the most appropriate induction level. The objective of the work is twofold:  
* Employing operational data to provide an estimate of the impact of the upgrade after some months of operation;
* validating a purely numerical framework (based on aeroelastic simulations of the wind turbine of interest) for estimating the impact of the control optimization. The data-driven method is formulated on the grounds of the discussion in Reference [30]: A multivariate linear model is selected, whose target is the power of the upgraded wind turbine and whose input variables are operation variables (power, rpm, blade pitches, and so on) of the nearby wind turbines. The input variables are selected based on their statistical significance by means of a stepwise regression algorithm [31]. The aeroelastic simulations were performed using the open-source FAST (fatigue, aerodynamics, structures, and turbulence) v8 software, developed at the National Renewable Energy Laboratory (NREL) in Golden, Colorado. The control upgrade was taken into account in the simulations based on the generator rpm-generator torque curve, by mimicking the operational curves before and after the upgrade. Several aeroelastic simulations were run: From these, it was possible to estimate an average pre- and post-upgrade power curve. By weighting these power curves against wind distribution, the impact of the control upgrade on the production was estimated. The main result of this work is that the data-driven and the numerical estimates of the upgrade display a good level of agreement. This result supports the use of numerical simulations for studying this kind of control upgrades, once they are fed with some input that is specific to the site (for example, turbulence intensity, wind intensity distribution) and to the technology (in this case, rotor rpm-power curves before and after the upgrade). Summarizing, the structure of the manuscript is the following: In Section 2, the test case is briefly described. Section 3 is devoted to the production improvement estimate based on operational data analysis: The method and the results are presented. Section 4 is devoted to the upgrade assessment based on the numerical simulations: The framework and the results are described.