# Considering Uncertainties of Key Performance Indicators in Wind Turbine Operation
## 6 Discussion
### Data Completeness  
* Missing measurements of the air density or air pressure result in considerable deviation in the mean wind power density and power curve. * The air density can be well approximated by a correction to the location altitude and the measured ambient temperature. The weather-related fluctuation of the air pressure leads to an uncertainty of about 0.013 kg/m\({}^{3}\). \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & & \multicolumn{5}{c}{**Key Performance Indicators**} \\ \hline
**Uncertainty Causes** & **Wind Speed** & **Capacity Factor** & **Wind Power Density** & **Power Curve** & **Production-Based Availability** \\ \hline Data Resolution & - & - &! &! &! \\ Data Availability &! &! &! &! &? \\ Data Completeness & - & - &! &? &? \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The effect of the evaluated uncertainty causes on different KPIs. * Measuring the ambient humidity is only of little additional use. It can be assumed to be 50%. * When approximating the air density, the uncertainty of the mean wind power density is approximately 1 W/m\({}^{2}\). At high wind speeds, this value may be higher. * If a density correction of the wind speed is carried out based on an approximated air density, the corresponding uncertainty of the calculated power curve leads to an uncertainty of about 0.25% when calculating annual energy yields. The results show that KPIs are affected by differing approaches and carefulness in data handling. In many cases, the resulting KPI uncertainties can be significantly reduced by simple measures, and the KPIs remain reliable. These are mostly systematic or epistemic uncertainties that can be largely corrected by additional effort. However, there are also substantial aleatoric uncertainties that depend, among other things, on the location and weather conditions but also on technical specifications and the operational behavior of WTs. The present work provides a quantification of the uncertainties wherever possible. However, uncertainties vary with site- and technology-specific conditions in many cases. These results cannot be generalized and require specific simulations for valid uncertainty quantification. Regardless, the presented results can be used to estimate the magnitude and relevance of the uncertainties. As shown in Section 3, there are additional potential causes for KPI uncertainties. Some of them are already part of previous publications and standards, while others require further research. Although this work covers the most important KPIs, there are many additional KPIs that could be of interest in the future. The mechanisms to simulate and test data handling-related uncertainties remain unchanged, and can be easily applied to additional KPIs. Furthermore, there is a need for additional research to quantify uncertainties due to decreasing data availability. A data quality index is required to describe the randomness and length of data gaps used to estimate the corresponding uncertainties more precisely. The current results provide a best- and worst-case scenario, which represent a starting point for future work. To consider KPI uncertainties in daily work, there is a need to incorporate the corresponding calculations and visualizations into operational management and business intelligence systems. As shown by the IEC standard 61400-12-1/2 [30,31] as a best practice example, guidelines to combine various uncertainty causes and default values need to be agreed upon. [PERSON], [PERSON], and [PERSON] designed the research question; [PERSON] performed the experiments, analyzed the data and wrote the paper; and [PERSON] and [PERSON] reviewed the paper. All authors have read and agreed to the published version of the manuscript. The research work of Fraunhofer IEE for this paper was funded by the German Federal Ministry for Economic Affairs through the WInD-Pool (grant No. 0324031A) project. Costs to publish in open access were covered by the Fraunhofer-Gesellschaft. The authors declare no conflicts of interest.