The theoretical power in the wind varies as the third power of the wind speed, so small changes in wind speed could be expected to translate to rather larger changes in wind power. In fact, a modern MW-sized wind turbine wind turbine will start to regulate above ~9m/s, so the change in annual energy yield from a turbine will not increase as rapidly as the third power of the wind speed. The capacity factor of a wind turbine is defined as the average energy produced by a turbine over a representative period, e.g. a year, divided by that which would have been produced had the turbine operated at full output during that entire period. Using the power curve from a Vestas V80 2MW wind turbine, it is possible to calculate the expected capacity factor assuming a given average wind speed at hub height. The capacity factor will also depend on the distribution of capacity factor for a Vestas V80 2MW turbine is calculated and is shown as a function
of mean wind speed in Figure 16. It can be seen that the capacity factor goes up fairly linearly with mean wind speed until around 9m/s and then reduces more slowly, flattening off near 14m/s. This is due to a combination of the turbine regulating at 9m/s, reaching rated wind speed at around 14m/s and shutting down at 25m/s.
If a mean wind speed of 7m/s is assumed at 80m hub height, then a 4% variation (one standard deviation) in wind speed, as seen for the BADC-7 and BADC-57 indices, represents a variation in capacity factor and associated annual energy yield of 7%. A 7%
variation in wind speed, as seen for the ERA-40 index interpolated to the BADC-57 sites, would represent a variation in capacity factor and annual energy yield of 13%.
Figure 16: Capacity factor of a Vestas V80 2MW turbine as a function of mean wind speed.
7. CONCLUSIONS
This paper has presented two wind indices for the UK based on surface station observations of wind speed: one based on seven stations (BADC-7) over a 55-year period (1957-2011) and a second based on 57 stations (BADC-57) over a 29 year period (1983-2011). These indices have been compared with indices generated using a gridded dataset of values interpolated from UK stations, three indices calculated using the ERA-40 reanalysis dataset and another UK wind index. The directional wind speed at the BADC-7 stations was examined and there was found to be no obvious evidence of changes in site exposure or instrument location which could affect the continuity of wind speeds at these stations. There have, however, been notable changes in instrument
height at many of the stations included in the two indices and, as a result, wind speed observations at all stations were corrected to 10m above ground level. An attempt been made to assess trends in long term wind speed values for each of the indices and to investigate the degree of correlation between them. These trends have been identified using linear regression and their significance assessed using a Mann-Kendall test.
The principal findings of this paper are that:
The BADC-7 and BADC-57 indices agree reasonably well over the common
1983-2011 period with a correlation coefficient of 0.887 (0.917 when trends are removed);
The inter-annual variation of the BADC-7 and BADC-57 indices was found to be 4%;
This variation equates to a standard deviation in wind farm capacity factor of 7%;
From the late 1950s until the late 1960s, there was an apparent increase in annual
mean wind speeds followed by a rapid decrease and another increase throughout the 1970s into the early 1980s. Between the mid-1980s and 2011, there have been some notable low wind speed years including 1987, 2001 and 2010;
When compared to the other indices, similar trends in wind variability are seen,
though correlations vary between 0.60 and 0.92 (0.61 and 0.98 when trends are removed) reflecting the different levels of spatial smoothing, different averaging periods and site specific effects;
All of the indices show declining trends (between -0.05% per year to -0.71% per year) with the exception of the ERA-40 index calculated over the UK which shows
an increase (+0.1% per year), though not all of these trends were found to be
analysed, it is found to be relatively weak indicating that inter-annual variability is very localised;
Similarly, when the BADC-57 index is broken down by region, differences in
inter-annual variability are seen across the UK. In addition, there appears to be a general trend to decreasing wind speeds in all regions except the south-east and the largest decreasing trend is seen in the north-west. The greatest declines are seen in the Centre (BADC) who offered some interesting insights with respect to UK wind fields.
The authors would also like to thank the UK Met Office and the BADC for providing access to the UKCIP gridded dataset and the MIDAS data, respectively. The authors are
grateful to the staff of the Met. Office archive in Exeter for providing access to records related to the meteorological stations used in this research.
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Table 1. Summary of the parameters used in Equation 2 for calculation of the different
Year Bilinear interpolation to either BADC-7 or BADC-57 sites; average of grid points
Table 2. List of stations used in the 29- and 55-year Wind Indices. Those stations used to generate the 55-year index (BADC-7) are shown in italics.
Identifier Name Region Availability
54 Stornoway Airport North-West 99.0% 99.0%
113 Aviemore North-East 97.8%
132 Kinloss North-East 99.9%
137 Lossiemouth North-East 99.7%
161 Dyce North-East 94.7%
170 Peterhead Harbour North-East 93.2%
235 Leuchars North-East 99.3%
527 High Bradfield Central-East 89.0%
533 Church Fenton Central-East 99.3%
556 Nottingham, Watnall Central-East 99.0%
583 Wittering South-East 99.2%
847 Middle Wallop South-West 99.4%
886 Lyneham South-West 97.8%
1039 West Freugh Central-West 99.5%
1046 Ronaldsway Central-West 100.0%
1090 Blackpool, Squires Gate Central-West 98.4%
1145 Valley Central-West 99.5% 99.7%
1180 Bala Central-West 97.5%
1198 Aberporth South-West 99.5% 99.7%
1215 Milford Haven Conservancy Road South-West 99.1%
1302 Yeovilton South-West 98.8%
1336 Plymouth, Mountbatten South-West 96.4%
1346 Chivenor South-West 96.6%
1395 Camborne South-West 99.8%
1450 Aldergrove Central-West 99.6% 99.9%
1467 Ballypatrick Forest North-West 95.6%
1529 Orlock Head Central-West 95.3%
17414 Leeming Central-East 99.8%
18974 Tiree North-West 98.5% 99.5%
Table 3. Instrument changes since 1957 for the seven stations (BADC-7) used in the 55-year wind index. The last time changes, in either type of instrument or its effective
height, were checked was in December 2009. *Particular anemometer type not specified.
Site Dates Instrument Type Effective Height (m)
Lerwick 1957-1960
Table 4. The BADC Surface Wind Speed Indices.
1995 0.991 1.004 1.002
Table 5. Comparison of the trends of the different indices and standard deviation of each index (with and without tend removed). The F-statistic relates to the level of
significance of the trend according to the non-parametric Mann-Kendall test.
Wind index Trend (% yr-1) Period F St. dev (%) St. dev (%)
Table 6. Autocorrelations up to lag 10 for the de-trended indices. Those autocorrelations which are significant at the 5% level are marked in bold.
Lag
Table 7. Pearson correlation coefficients calculated using concurrent annual values for the different indices.
Wind index 1 Wind index 2 Concurrent
years Corr. coeff. Corr. coeff
Table 8. Pearson correlation coefficients calculated using annual mean wind speed values for combinations of the BADC-7 sites.
Aldergrove Boscombe Down
Lerwick Stornoway Tiree Valley
Aberporth 0.373 0.409 0.186 -0.130 0.547 0.441
Aldergrove 0.351 -0.071 0.270 0.731 0.529
Boscombe Down -0.277 -0.317 0.376 0.680
Lerwick 0.002 0.168 -0.089
Stornoway 0.241 0.119
Tiree 0.508