# Considering Uncertainties of Key Performance Indicators in Wind Turbine Operation
## 5 Results
### Data Resolution  
For KPIs with a linear dependence, changes of the data resolution showed hardly any impact. The smoothing effect of the averaging process when resampling the data did not affect KPIs, such as the average wind speed or capacity factor. Minor deviations were caused by missing data points, which led to a different weighting of the remaining data points. Different aggregation time periods led to changing allocations and weightings of the data and thus to slight deviations. The observed deviations can be considered negligible given the number of samples per aggregation period do not deviate too much.  
Equations of the second- or a higher-degree were affected by the smoothing effect. Missing information on extreme values led to lower KPI results since losing higher values has a greater impact than losing lower values. For the wind power density, one can correct this systematic deviation if the standard deviation of the wind speed is available, see Figure 3a. The correction assumes a normally distributed wind speed within the aggregation period as used to describe wind speed turbulences [31]. Of note, this is only valid for short periods. Long term wind speed distributions are generally characterized by Weibull or Rayleigh distributions. The correction algorithm showed an uncertainty of \(\sim\)0.1% for the investigated examples since this assumption is not always met. This is still fifteen times lower than the observed systematic deviation when switching from 1 Hz data to hourly data.  
The smoothing effect also affected the calculation of empirical power curves. Systematic deviations were witnessed in the transition area to the rated power, where high resolutions show a kink while lower resolutions smooth the transition and give the power curve its expected look. The IEC standard 61400-12-1/2 [30; 31] requires 10 min data for empirical power curves. Different data resolutions led to deviations in the power curves and thus uncertainties when calculating energy yields. A relative standard deviation of approximately 0.4% was observed when calculating potential annual energy productions using power curves based on different resolutions over various wind speed distributions. Although this result should not be considered to be generally valid, its order of magnitude is expected to be correct.  
This uncertainty also propagates into the calculation of the potential energy yield when assessing the production-based availability, but can be neglected due to its low impact. Much more important is the effect shown in Figure 2(b). Initiatives such as the WInD-Pool, derive downtimes from wind speed and power measurements because distinct event information is often times missing. Although high-resolution data allows a clear distinction between operating times and standstill, this distinction becomes blurred at lower resolutions. The high-resolution area of Figure 2(b) shows a dropping in availability. This behavior can be explained by the assimilation of time steps adjacent to downtime because the negative power of several non-operational time steps can negate the positive power of single time steps. As the resolution further decreases, this behavior reverses. Short downtimes, such a five min-long reset of a WT, disappear in 10-min data. Of course, the behavior depicted in Figure 2(b) strongly depends on the distribution and length of downtimes, but the overall message is clear: Deriving downtime events from operational data is afflicted with significant uncertainties. Instead, distinct event information should be used whenever possible.