## 4 Results
### Comparison against Benchmark Models
It was noticeable that, despite the simplifications of the proposed methods, the obtained average error metrics were competitive with the state-of-the-art in the literature, as can be argued by the discussion in Section 4.3 and by comparing against Table 1 in [33]. Furthermore, an analysis was devoted to monitoring the accumulated performance. The rationale for this analysis was that the order of magnitude of some performance changes possibly occurring in a wind turbine's lifetime is particularly small, but affects all the observations from a given moment. Therefore, monitoring small performance changes along long periods requires shifting the focus to the difference accumulated in a period against a reference one. To this aim, the target data set considered in this study was randomly split in two, and it was observed that the proposed method had a remarkably high sensitivity because the average accumulated percentage difference that it is possible to detect was of the order of 0.001%. Therefore, the main lesson from this study, which can be particularly useful in the wind energy practitioners community, is that for application purposes, a multivariate wind turbine power curve model does not need to be overly complicated, but should rather contribute intelligently to each of the critical points regarding this type of problem. The approach of this work was mainly methodological, but it should be emphasized that it has several practical applications. For example, a similar, albeit more complex method, was employed in [38; 53] for quantifying the effect of aging on wind turbine performance. A further application of the present study, which is being pursued at present, is the estimation of the effects of icing on wind turbine performance. Actually, the increasing exploitation of wind energy in harsh environments due to increasing demand for renewable energy production has been posing the issue of characterizing the performance of wind turbines in extreme conditions. Blade icing can likely be individuated as reduced rotor speed, and consequently extracted power, for a given wind speed [54; 55; 56]: therefore, a model similar to the one proposed in the present paper should be useful to individuate the behavior of a wind turbine in icing conditions. Furthermore, a topic that has been recently attracting attention in the wind energy literature is the effect of static and dynamic yaw error on wind turbine performance [57; 58; 59; 60]; the incorporation of such an effect in multivariate wind turbine power curve models would be a valuable development. Finally, a useful remark is that the the number of possible covariates could be enlarged quite arbitrarily; in that case, a dimension reduction algorithm such as principal component analysis [61] should be included in the modeling chain. **Author Contributions:** Conceptualization, D.A. and R.P. ; data curation, D.A. ; formal analysis, D.A. and R.P. ; investigation, D.A. and R.P. ; methodology, D.A. ; project administration, D.A. ; software, D.A. ; supervision, D.A. and R.P., validation, D.A. and R.P. ; writing--original draft, D.A. ; writing--review and editing, R.P. All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding. **Acknowledgments:** The authors thank the company Lucky Wind s.p.a. for the technical support and for providing the data sets employed for the study. **Conflicts of Interest:** The authors declare no conflict of interest.