1
An Assessment of the Impact of
Reduced Averaging Time on Small Wind
Turbine Power Curves, Energy Capture
Predictions and Turbulence Intensity
Measurements
Douglas Elliott, Centre for Doctoral Training Centre in Wind Energy
Systems, Department of Electronic and Electrical Engineering, University of
Strathclyde, Glasgow.
David Infield, Centre for Doctoral Training Centre in Wind Energy Systems,
Department of Electronic and Electrical Engineering, University of
Strathclyde, Glasgow.
Key words: small wind turbine; performance assessment; power curve;
averaging; annual energy production; energy yield, turbulence intensity.
The effect of varying the averaging time of measured data used to calculate
wind turbine power curves is examined. The effects of reducing the averaging
time from 10 minutes to 1 minute, as recommended for small wind turbines
are investigated using power performance data recorded using a 15kW wind
turbine. Test site data have been processed according to IEC 61400-12-1 to
provide power curves and annual energy yield predictions [1]. A number of
issues are explored: the systematic distortion of the power curve that occurs as
averaging time is decreased, the errors introduced by the use of one minute
averaged power curves to calculate energy yield and the reduction of
turbulence intensity as averaging time is reduced. Recommendations for
improved small wind turbine testing and energy yield calculation are given.
1. Introduction
The dependency of a wind turbine power output on wind speed is described by a power
curve, determined by measurement and subsequent data analysis as described in the relevant
Standard; IEC 61400-12-1 [1]. Power curves are commercially important because they give
the purchaser a reliable means to calculate the expected yield of the turbine at any particular
site.
A wind turbine power curve would ideally be determined by measuring the wind speed
immediately before the rotor and then correlating these measurements with the electrical
power output from the turbine. However, measurement of wind speed at such close
Impact of Reduced Averaging Time on Small Wind Turbine Performance
2
proximity to the wind turbine is not possible due to the impact of the rotor on the local air
flow and therefore it is more commonly made multiple rotor diameters upstream of the rotor.
The separation between the wind turbine rotor and the point where wind speed is measured
reduces the correlation between the two measurands, potentially biasing the resulting power
curve. Achieving a good correlation is important for minimising this bias. The solution is to
suitably time average the data, increasing the correlation so that bias is no longer significant.
IEC 61400-12-1 states that the averaging time for large wind turbines should be 10 minutes,
coinciding with the averaging period for most contemporary meteorological data [1]. For
turbines with rotor diameter less than 16m, the averaging time has been reduced to 1 minute,
see Annex H of IEC 61400-12-1, [1]. A practical motivation of this change is to reduce the
length and cost of the measurement campaign required. The key concern here is the
anticipated reduction in correlation between the measured wind speed and power that results
and the potential for this to distort the power curve, increasing errors in yield prediction.
This paper quantifies the impact of reduced averaging through analysis of wind turbine
performance test data. This data is taken from the testing of a 15kW rated wind turbine
undertaken by TUV-NEL at East Kilbride in the UK. The test site was situated on the high
point of a hill with a south westerly prevailing wind direction, clear of any significant
obstruction. The terrain upstream in the prevailing direction is open moorland covered by
long grass and heather with an estimated surface roughness length in the range 0.05m to
0.2m. The wind speed was measured using a cup anemometer compliant with IEC 61400-121 located at turbine hub height and placed 34.9m (3.7 rotor diameters) upstream of the
turbine. Wind speed and power output data was sampled at 1Hz before averaging over one
minute time periods for data storage. These 1 minute averages and their standard deviations
collected over 2 months were made available for use in this study.
2. Data Processing
Data from the turbine has been used to determine power curves directly using the one minute
averaged data and also after further averaging over 5 and 10 minute periods to examine the
impact of averaging time.
The method of bins has been used to calculate the wind turbine power curve as prescribed in
IEC 61400-12-1; additional detail can be found in [2]. In all the work presented here
corrections based on procedures specified in IEC 61400-12-1 have been implemented.
Figure 1 shows a histogram of the data points that are present in each bin after the raw data
has been filtered to remove periods where the wind direction was invalid for data collection
(the valid region for the site is between 187° and 309°), as described in IEC 61400-12-1, and
also all periods where the turbine was non-operational during the measurement campaign [1].
IEC 61400-12-1 requires that a minimum of 30 minutes worth of data be recorded for each
wind speed bin and a total of 180 hours of sampled data, this translates to 30 points and
10,800 points of 1 minute averaged wind speed data respectively [1]. It can be observed that
the first requirement is met throughout the majority of the operating range and the total
number of valid data points is 37,520 which satisfies the second requirement. IEC 61400-12-
Impact of Reduced Averaging Time on Small Wind Turbine Performance
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1 requires at least 30 data points in each bin, up to a wind speed 1.5 times the wind speed at
which the turbine produces 85% of the rated power of the turbine (16.5m/s), this is also found
to be satisfactory.
Number of data points
2000
1500
1000
500
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Wind Speed [m/s]
Figure 1: Histogram showing the number of data points in each wind speed bin after filtering and air density corrections.
3.0 Selection of Averaging Time
Applying insufficient averaging results in correlation between measured wind speed and
measured power that is too low, leading to distortion known as ‘errors in bins’ [3]. To gain
an understanding of how the errors in bins distortion affects the power curve, consider that
the anemometer has just measured a very high wind speed, associated with a short gust, and
that no or little averaging is applied to the data. Due to wind turbulence, the value of the
wind speed at the rotor (for simplicity consider the wind at the centre of the rotor disc) will
not be the same as that measured by the anemometer at that instant. In fact it is likely that
the wind speed at the rotor will be lower, therefore the power generated will also be lower
than the power output corresponding to the anemometer measurement according to an ideal1
power curve. This gives rise to a power curve data point that is too low. The reverse effect
happens for very low wind speeds measured by the anemometer and the power curve is
distorted upwards there. The result is illustrated qualitatively in, [3] (page 201).
To correct for this distortion, [4] suggests shifting the measured wind speed values towards
the mean before binning by an amount determined by the correlation. The fact that these
corrections have been successfully applied in the past to power curves using short averaging
times (see for example [3] pages 202 and 203) suggests that this statistical analysis of errors
in bins is correct and that this form of distortion is the result of errors in bins. The impact of
reducing the averaging period of the data from 10 minutes to 1 minute is investigated to
assess the severity of the errors in bins distortion.
1
This is ideal in the sense that it would be the same as a power curve measured in an ideal wind tunnel with
steady wind and thus no turbulence and also no tunnel blockage affects.
Impact of Reduced Averaging Time on Small Wind Turbine Performance
4
4.0 Results from data analysis
In order to provide a base case to compare the effects of varying the averaging time, a
standard power curve based on 10 minute averaged data has been generated (Figure 2), the
error bars for both wind speed and power have been calculated in the standard way.
Predictions of the annual energy production have also been determined using this power
curve, for mean wind speeds of 5m/s and 7m/s, following IEC 61400-12-1, Table 1.
14
12
Power [kW]
10
8
6
4
2
0
0
2
4
6
8
10
12
Wind Speed [m/s]
14
16
18
20
Figure 2: Base case power curve derived using a 10 minute data, showing standard uncertainty.
4.1 Effect of averaging time variation on a wind turbine power curve
Power curves derived from data averaged over periods of 1 and 5 minutes are compared with
the 10 minute averaged base case in Figure 3 (uncertainties have been omitted for clarity of
presentation). It is evident from these curves that the variation of averaging time has little
overall impact upon the general shape of the power curve.
To show the differences between these curves more clearly, the 1 minute and 5 minute curves
have been normalised against the base case curve. This is presented in Figure 4 where the 1
minute and 5 minute normalisations are shown as percentages of the base case curve. The
uncertainties of each point in the normalisation are also shown as percentages of the base
case. There appear to be small systematic differences indicative of some errors in bins
distortion, although the uncertainties are larger than these differences.
Impact of Reduced Averaging Time on Small Wind Turbine Performance
5
14
12
Power [kW]
10
8
6
4
1min
5min
10min
2
0
0
2
4
6
8
10
12
14
Wind Speed [m/s]
16
18
20
22
Figure 3: Power curves derived using data averaged over 1, 5 and 10 minute periods.
15
Power difference [%]
10
5
0
-5
-10
-15
1min
5min
4
6
8
10
12
14
Wind speed [m/s]
16
18
20
Figure 4: Percentage difference between the base case power curve and the 1 and 5 minute averaged power curves.
Pearson moment coefficients have been calculated to quantify the correlation between the
wind speed and power measurements as a function of averaging time, in the region between
5m/s and 7m/s, where the power curve is approximately linear. The coefficients for data with
averaging times of 1 minute and 10 minutes are shown in Figure 5, where it is evident that
the coefficient for the one minute averaged data is 18% lower than for the ten minute
averaged data. The decline in correlation with averaging time is to an extent mitigated by the
reduced distance between the anemometer and the rotor for such a small turbine, which
increases the correlation of measurements before averaging is applied.
Impact of Reduced Averaging Time on Small Wind Turbine Performance
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0.95
Correlation coefficient
0.9
0.85
0.8
0.75
1
2
3
4
5
6
Averaging times [mins]
7
8
9
10
Figure 5: Correlation coefficient between wind speed and electrical power in the linear region of the power curve, between
5m/s and 7m/s, with increasing averaging time.
In conclusion, it is clear that ‘error in bins’ distortion caused by reducing the averaging time
to 1 minute is minor. At the peak of the power curve the difference between the 1 and 10
minute averaging would appear to result in a drop of about 200 Watts (1.7%). It is possible
that the limited error in bins distortion is a result of the reduced distance between the
anemometer and the turbine mentioned above.
4.2 Effect of averaging time variation on annual energy yield
In practice, the annual energy production (AEP) of a wind turbine is calculated for a known
site by applying the measured power curve to a reference wind speed frequency distribution.
IEC 61400-12-1 does not deal with measured wind speed distributions, but states that
indicative annual energy yields can be calculated using the Rayleigh distribution [1].
Although not specified in the Standard, this long term distribution must be based on an
averaging period, the choice of which can affect the yield results. The averaging period used
to determine the long term probability distribution is almost universally either ten minutes or
one hour. In practice there is little difference between the results obtained for each. Selection
of a smaller averaging period however, such as one minute, can cause errors in the yield
predictions.
The annual energy production has been calculated using the power curves derived from the
differently averaged data and Rayleigh distributions corresponding to annual mean wind
speeds between 4m/s to 11 m/s [1]. It is important to note that, as apparent from Figure 7,
changing the averaging period affects the upper bound of the wind speed range to which the
power curve extends. For this reason IEC 64100-1-12 suggests that power curves that do not
cover the full range of operational wind speeds should be suitably extrapolated. The resulting
AEP’s are plotted in Figure 6, indicating that at lower wind speed sites the AEP is not
strongly dependent on the averaging period (the difference is approximately 1-2% for annual
mean wind speeds below 8 m/s), with some slightly larger differences at windier sites.
Impact of Reduced Averaging Time on Small Wind Turbine Performance
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4
Predicted Annual Energy Production [kwh]
8
x 10
7
6
5
4
1 min
5min
10 min
3
2
1
4
5
6
7
8
Site Mean Wind Speed [m/s]
9
10
11
Figure 6: Predictions of annual energy production with power curves extrapolated to 25m/s.
Using the turbine performance test data, the consequence of calculating the AEP from a one
minute averaged power curve using a standard 10 minute averaged based wind speed
distribution, can also be assessed. Ideally a long term wind distribution calculated from one
minute data should be used for consistency, but this will not always be available. The
question therefore is how much error in yield using a 10 minute averaged based distribution
as opposed to a 1 minute average based distribution could introduce. Figure 7 compares 10
minute with 1 minute frequency distributions for the data set used in the preceding analysis.
2500
1min averaged data
10min averaged data
Time [mins]
2000
1500
1000
500
0
0
5
10
15
Wind Speed [m/s]
20
25
Figure 7: Frequency distribution of measured wind speed averaged over 1 minute and 10 minute periods, derived using data
recorded for the performance measurements.
The differences apparent in the distributions result in different calculations of energy yield,
shown in Table 2. The yields are calculated using the power curve based on 1 minute
averaged data and multiplied by the frequency distributions for data averaged over both 1
minute and 10 minutes. The results show that there is a small but significant difference, over
Impact of Reduced Averaging Time on Small Wind Turbine Performance
8
1%, between the energy yields calculated with the different frequency distributions. This
difference is solely due to the different averaging time applied to calculate the frequency
distributions.
4.3 Effect of averaging time variation on measured turbulence intensity
The turbulence intensity for a wind turbine site is calculated using the time averaged wind
speed and standard deviation. Conventionally, the averaging time period used is 10 minutes.
The spectral density function for short term wind speed variations, often simply called the
turbulence spectrum, has been extensively studied, but the exact spectrum is site dependent
and commonly peaks at around one minute, therefore a large difference can be expected if an
averaging period of one minute is used to calculate the turbulence intensity at a given site.
To quantify the impact for the site used in this study, the turbulence intensity has been
calculated for a range of averaging periods from 1 to 10 minutes. The results are shown in
Figure 8. 10 minute averaging gives a turbulence intensity that is 22% higher than with 1
minute averaging. Care must therefore be taken in interpreting the turbulence intensities
stated with small wind turbine performance test results. It would be more meaningful for the
associated turbulence intensities to be calculated in the conventional manner averaged over
10 minutes, even if the power curve is to be based on 1 minute averages.
0.155
0.15
Turbulence Intensity
0.145
0.14
0.135
0.13
0.125
0.12
0.115
1
2
3
4
5
6
7
Averaging Period Length [min]
8
9
10
Figure 8: A graph showing the relationship of turbulence intensity and averaging period.
5.0 Conclusions
Commercial pressure to reduce uncertainties and errors in energy yield estimation indicates
that the decrease in accuracy caused by the use of one minute averaging should be of
concern.
The results of the investigations reported in this paper confirm some systematic distortion of
power curves as a result of errors in bins, resulting from shorter averaging times, but indicate
that for small wind turbine testing the effect is minor and can probably be ignored. It has also
Impact of Reduced Averaging Time on Small Wind Turbine Performance
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been shown that the use of a 1 minute averaged power curve as recommended for small
turbines can lead to an error in yield calculation (greater than 1%), if the wind distributions
are based on ten minute or hourly data, as is the standard practise. It is suggested that the
Standard be amended to require that the wind probability distribution used in energy yield
calculations with one-minute power curves should be based on one-minute data. Finally it is
shown that the calculated turbulence intensity depends strongly on averaging period and
therefore it is suggested that the Standard should be amended to require that turbulence
intensity is calculated in the usual manner using 10 minute data, even if the power curve is
based on 1 minute data.
In conclusion it can be stated that IEC 61400-12-1 provides a reasonable basis for the
calculation of power curves for small wind turbines and one minute averaging provides
sufficient correlation between wind speed and power to reduce errors in bins to an acceptable
level, however changes should be made to the recommended energy yield calculation and the
way that site turbulence is assessed.
Acknowledgements
The authors would like to thank TUV-NEL and Proven Energy for their cooperation and for
making available the turbine test data. This work was funded by the EPSRC.
References
1.
2.
3.
4.
IEC, 61400-12-1:2006 Wind turbines — Part 12-1: Power performance measurements of electricity producing
wind turbines, 2006.
Akins, R.E., Performance Evaluation of Wind Turbines. ASCE, Transportation Engineering Journal, 1980. 106: p.
19-29.
Burton. T, S.D., Jenkins. N, Bossanyi E, The Wind Energy Handbook. Vol. 1. 2008: Wiley.
Dragt, J.B., Error analysis in the determination of the power performance of wind energy conversion systems,
1989, Netherlands Energy Research Foundation, ECN.
Impact of Reduced Averaging Time on Small Wind Turbine Performance
Mean Wind Speed of Rayleigh
Distribution
5m/s
7m/s
10
23,742kWh
45,691kWh
Table 1; Base case annual energy predictions (AEP) calculated with 10 minute averaged power curves as shown in Figure
2, using Rayleigh distributions with means of 5 and 7 m/s.
15kW Turbine
Energy yield based on the Energy yield based on raw data Difference
raw data averaged over 10 averaged over 1 minute
minutes.
263.61MWh
260.58MWh
1.15%
Table 2; Energy yields calculated using 1and 10 minute averaged wind speed frequency distributions with the 1 minute
averaged power curve.