## 1 Introduction  
Wind power is currently considered as the most promising source of renewable electricity in the world. Nevertheless, due to the non-stationary conditions to which wind turbines are subjected, performance monitoring and early fault diagnosis are non-trivial tasks. For this reason, despite wind turbines' substantially constituting a mature technology, the O&M costs can still reach the order of 25% of the overall life-cycle costs [1, 2]. In the wind energy practitioners' community, the standard for the evaluation of wind turbine performance is the analysis of the power curve, i.e., the curve displaying the relation between the wind flow intensity and the power output: the IEC recommends the binning method [3], consisting of averaging the power measurement per wind speed intervals of 0.5 m/s or 1 m/s. In general, the averaging or discretisation of wind turbine data [4] provides meaningful indications. The power curve analysis has the great advantage of simplicity, but the drawback is that it does not account for the fact that the power of a wind turbine has a multivariate dependence on the environmental conditions and working parameters [5]. Furthermore, the undisturbed wind flow is not measured directly: it is estimated through a nacelle transfer function based on downwind measurements collected behind the rotor span [6; 7; 8]. The widespread diffusion of Supervisory Control And Data Acquisition (SCADA) has been a turning point and has projected wind energy into the era of data. SCADA systems record a vast set of environmental, operational, mechanical, electrical, and thermal data with a frequency in the order of Hertz and store them upon averaging with a time basis of a few minutes (typically ten). Wind turbine performance monitoring and fault diagnosis have been therefore gradually evolving into data analysis problems: the general concept is that anomalous performance or incoming damages are individuated by analyzing the residuals between the measurements and data-driven normal behavior model [9; 10; 11; 12; 13; 14; 15; 16; 17]. The critical points as regards this kind of approach are repeatability, generalization, supervision, and absence of theoretical standards, and the literature is focused on these aspects. Given these considerations, also the study of wind turbine power curves has become substantially a problem of data analysis and interpretation [18; 19; 20; 21; 22; 23; 24]. A recent line of research about wind turbine power curves regards multivariate approaches [25; 26; 27; 28; 29; 30; 31]: the general idea is that the power of a wind turbine is the output of a data-driven model, which has further input variables in addition to the wind speed. Despite it have been shown that the wind speed can account for up to the 99% of the variance of the power [32] and therefore further input variables can explain not more than the residue of 1%, this can be decisive in order to obtain data-driven models whose average error metrics are sufficiently low to guarantee a robust monitoring of wind turbine performance. For a recent review about multivariate wind turbine power curves, refer to [33]. From the discussion in [33], it arises that the literature about wind turbine multivariate power curves is at its early stages, but some evidence has been gradually accumulating:  
* Due to the complexity of the wind flow at the microscale level, meteorological mast data can be useful only for modeling the power of a wind turbine that is sited extremely close to the mast [6]. For application in real-world large wind farms, meteorological mast data are not appropriate for wind turbine power curve models [34];
* Consequently, the most meaningful additional input variables for modeling the power of a wind turbine are the working parameters. In regard to the latter point, the blade pitch and the rotational speed have been individuated as the most relevant operation variables to be employed in a multivariate wind turbine power curve model.