## 1 Introduction  
Megawatt-scale wind turbines are currently a mature technology. On one side, the current frontiers of research mainly deal with increasing the size of wind turbines and, therefore, the capacity factor, but there are still several open challenges (as, for example, the control of mechanical loads [1; 2]) and, therefore, wind turbines having a rated power above 7 MW are, at their present state, mainly prototypes. On the other side, considerable attention has recently been devoted to the optimization of operating wind farms featuring megawatt-scale wind turbines. The optimization problem can involve the mutual interaction between the wind turbines or can deal with the energy conversion efficiency of each wind turbine. As regards the former issue, the fields of research are layout optimization [3; 4; 5; 6; 7],cooperative wind turbine control [8; 9; 10], and yaw active control for wake mitigation [11; 12; 13; 14; 15]. As regards the latter issue, several types of wind turbines retrofitting for power production improvement are possible: They can be aerodynamic and based on the modification of the blade profile (installation of vortex generators, passive flow control devices, Gurney flaps, and so on [16; 17; 18; 19; 20]), or they can involve the control system and deal with the management of the blade pitch [21], the rotor rpm, the cut-out wind speed, and the high wind speed cut-in (defined as the wind speed at which the wind turbine starts producing again after a gust) [22; 23; 24]. Certain attention has therefore been recently devoted in the scientific literature to the study of wind turbine power upgrades: The scientific interest is basically motivated by the fact that wind turbines operate under nonstationary conditions because the source is stochastic. Therefore, the impact of an upgrade cannot be estimated by simply studying the total production in pre- and post-upgrade periods. At least some meaningful indication can be obtained by studying how the wind turbine power curve (i.e., the relationship between wind speed and power output) changes after an upgrade. However, as discussed, for example, in Reference [25], the study of the power curve might be insufficient for evaluating the impact of an upgrade. This can be due to the fact that the power of a wind turbine has multivariate dependencies (on climate conditions and on working parameters) and the study of the power curve disregards them all, except for wind speed and, possibly, air density [26]. Furthermore, another problem regarding the study of the power curve is that wind speed is commonly measured through cup anemometers placed behind the rotor and the undisturbed wind speed is estimated by the wind turbine control system through a transfer function, generally computed from field campaigns in flat terrain. This implies that the precision of the wind speed measurements in complex environments might not be enough in order to distinguish a variation of a wind turbine power curve that is of the order of few percents. This problem has therefore stimulated some interesting studies in the scientific literature about the ex-post assessment of wind turbine power upgrades through the analysis of operational data. For example, in Reference [25], a modification of the Gaussian kernel regression method [27] is proposed for computing the impact of two wind turbine upgrades: Pitch optimization and vortex generator installation on the wind turbine blades. The former test case is generated artificially by synthesizing the data according to the logic of pitch angle optimization; the latter test case, instead, is studied through the operational data of a wind turbine. Vortex generator installation is studied also in Reference [28]: The employed methods are the kernel plus of Reference [25] and the so-called power-power approach. The power-power approach is based on the study of the variation (before and after an upgrade) of the power difference between the wind turbine of interest (the target) and a reference wind turbine.