The impact of large scale atmospheric circulation patterns on wind power generation and its potential predictability: A case study over the UK

Renewable Energy 36 (2011) 2087e2096

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Renewable Energy journal homepage: www.elsevier.com/locate/renene

The impact of large scale atmospheric circulation patterns on wind power generation and its potential predictability: A case study over the UK David James Brayshaw a, b, *, Alberto Troccoli c, Rachael Fordham b, John Methven b a

National Centre for Atmospheric Sciences Climate Directorate, University of Reading, P.O. Box 243, Reading, Berkshire, RG6 6BB, United Kingdom Department of Meteorology, Earley Gate, University of Reading, P.O. Box 243, Reading, Berkshire, RG6 6BB, United Kingdom c Commonwealth Scientific and Industrial Research Organisation (CSIRO), Pye Laboratory, GPO Box 3023, Clunies Ross Street, Canberra, ACT 2601, Australia b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 14 April 2010 Accepted 12 January 2011 Available online 24 February 2011

Over recent years there has been an increasing deployment of renewable energy generation technologies, particularly large-scale wind farms. As wind farm deployment increases, it is vital to gain a good understanding of how the energy produced is affected by climate variations, over a wide range of timescales, from short (hours to weeks) to long (months to decades) periods. By relating wind speed at specific sites in the UK to a large-scale climate pattern (the North Atlantic Oscillation or “NAO”), the power generated by a modelled wind turbine under three different NAO states is calculated. It was found that the wind conditions under these NAO states may yield a difference in the mean wind power output of up to 10%. A simple model is used to demonstrate that forecasts of future NAO states can potentially be used to improve month-ahead statistical forecasts of monthly-mean wind power generation. The results confirm that the NAO has a significant impact on the hourly-, daily- and monthly-mean power output distributions from the turbine with important implications for (a) the use of meteorological data (e.g. their relationship to large-scale climate patterns) in wind farm site assessment and, (b) the utilisation of seasonal-to-decadal climate forecasts to estimate future wind farm power output. This suggests that further research into the links between large-scale climate variability and wind power generation is both necessary and valuable. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: Climate variability Wind power Seasonal forecasting

1. Introduction It is widely accepted that near-surface wind speeds are highly variable over a wide range of time-scales, from gusts lasting a few seconds to slowly evolving climatological patterns (up to centuries and beyond). Developing an understanding of the impact of this variability on wind power production, over all time-scales, is important to the wind energy industry for many reasons, ranging from long-term site assessments to short-term operational grid management. Whilst maps of mean wind power potential for specific years are critical to the energy industry (e.g. [1]), the wind power output is also subject to multi time-scale wind variability. In this present paper, time-scales from hours up to months are considered. Research into wind speed variability in the context of wind energy on climatological time-scales is in its infancy. Much work

* Corresponding author. National Centre for Atmospheric Sciences Climate Directorate, University of Reading, P.O. Box 243, Reading, Berkshire, RG6 6BB, United Kingdom. Tel.: þ44 118 378 5585. E-mail address: [email protected] (D.J. Brayshaw). 0960-1481/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2011.01.025

has been done on lead times up to a few days (e.g., [2,3]) but, despite growing awareness of the importance of the large-scale atmospheric circulation [4,5], relatively little effort has been made to understand how the variability of the wind speed on intermediate time-scales (monthly to decadal) may affect wind power output. Indeed, [5] identifies that year-to-year variability in wind speed is “often the principal risk associated with. [long-term] production forecast[s]”. As indicated by [3], large-scale atmospheric circulation patterns may be good predictors for the statistics of short-term wind variability. More generally, such circulation patterns are important for two main reasons. Firstly, the statistics of near-surface wind speeds can be affected by slowly varying features of the climate system. A consequence of this is that wind speed climatologies based on short observational data sets (i.e., data sets that cover less than the period of variability) may lead to consistently inaccurate wind power output estimations, as illustrated by over the Baltic region by [6]. Secondly, knowing how short-term wind variability relates to these patterns may offer the potential for longer term (seasonal-todecadal) predictability of wind statistics, for instance by using predicted patterns from state-of-the-art climate forecasting systems.

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A commonly used indicator of large-scale atmospheric circulation patterns in the Atlantic/European sector, the North Atlantic Oscillation (NAO, [7]), is examined here in order to study the relationship between this pattern and the statistics of hourly- tomonthly mean wind speeds and their impact on hourly-tomonthly mean power output from an idealised wind turbine. By using a set of simple statistical and wind power models, this paper details the link between variations in the NAO on monthly time-scales to the power production from a hypothetical wind turbine at two different UK sites (Great Dun Fell and Stornoway, see below) during the extended Northern Hemisphere winter season (November to March). The extended winter season is chosen as it is within this season that the impacts of the NAO can be most clearly seen in western Europe. The potential benefits of using forecasts of the NAO state to produce improved monthahead statistical forecasts of monthly-mean wind power output are then explored. The paper begins with a discussion of the models used to generate the wind speed time-series and the power output forecasts (Section 2). The dependence of the power output on the NAO index is detailed in Section 3, and the utility of including NAO forecast information in wind power output predictions is examined in Section 4. Section 5 provides a discussion of the results and the conclusions. 2. Simulating power output distributions Having the ability to generate artificial time-series of wind speed and wind power is valuable for a variety of reasons. Two particular reasons are highlighted in the context of this present study. Firstly, direct measurements of wind speed rarely cover more than several years. It is therefore useful to be able to generate artificial wind speed records with similar statistical properties to the observed data (longer time series are useful for studying lowfrequency phenomena and obtaining “smoother” curves without the necessity of curve-fitting). Secondly, and more importantly, the ability to create artificial time-series enables the production of forecasts of wind power (or, in a similar manner, retrospective “hindcasts” of historical records can be created to validate the model). This latter property is used in Section 4 where the “potential predictability” of wind or wind power output given an NAO forecast is computed. When estimating the power output from a wind turbine, it is important that the temporal variability of the wind incident on the turbine is fully accounted for. In particular, while large-scale circulation patterns (such as the NAO) may be identified from monthly-mean fields and linked to a monthly-mean wind speed, the non-linear transformation between wind speed and power output from a turbine necessitates the use of higher frequency wind speed time-series (e.g., hourly). Furthermore, wind speed records in the UK clearly show persistence on synoptic (hourly to daily) time-scales (Fig. 1(d), described in more detail later). In order to generate accurate estimates of power generation (averaged over daily to monthly time-scales), it is vital to include this persistence in order to better estimate the variance of the output (consider, for example, the possibility of multi-day low-wind events which would be severely underrepresented by models of hourly-mean wind that failed to take account of inter-hourly persistence). In order to compute power distribution time-series at hourly resolution we therefore first generate a simulated wind speed timeseries (at hourly resolution) during a particular NAO state. We then transform it into the power output through a wind power model (also at hourly resolution). In the final stage the output power timeseries is averaged over different time-scales (between 1 and 30 days) and a probability distribution generated.

2.1. The wind speed model A two-stage approach to simulating the wind is adopted: 2.1.1. Stage 1: Binning wind speed data, based on the NAO For the purposes of this paper, monthly-mean NAO data is obtained from the US NOAA’s National Weather Service Climate Prediction Centre [8]. Qualitatively similar results are, however, obtained using the “traditional” definition of the NAO (the standardised anomalous surface pressure difference between Ponta Del Garda (26 W, 38 N) and Reykjavik (22 W, 64 N), as marked on 1(a) and (b)). As shown by Fig. 1(c), the NAO displays variability over a wide range of low frequencies (from seasonal to interannual and decadal, see [9]), and is closely related to the position of the North Atlantic storm track which describes the path of cyclonic weather systems moving eastward across the Atlantic. Consistent with the higher wind speeds associated with these storms, months with positive NAO anomalies tend to have higher near-surface wind speeds in North West Europe, with the reverse being the case for negative NAO anomalies (shading in Fig. 1(a) and (b)). The NAO index for each month in the extended winter season (NoveMar) is classified as “high” (NAO  þ0:5), “medium” (0:5 > NAO > þ0:5) or “low” (NAO  0:5). Hourly-mean 10 m wind speed data from the UK Met. Office MIDAS data set [10] are obtained for two UK sites: one at Great Dun Fell (GDF, North West England: 2.448 W, 54.684 N) and a second at Stornoway Airport (STORN, Isle of Lewis off North-West Scotland: 6.325 W, 58.214 N). These sites are chosen because they provide a long data record (GDF: 1969e2004, STORN: 1957e2002) and are highly exposed (GDF is in an exposed upland area 847 m above sea level, whereas STORN is at a coastal airport on an island to the north west of the Scottish mainland). They therefore represent somewhat “ideal” sites in that the impact of the large-scale climate variabilty is likely to be uncontaminated by local obstructions (this is particuarly true for GDF, although it is not unreasonable to expect that STORN may have been somewhat affected by changes in instrumentation or local building). The impacts of choosing different sites around the UK are discussed further in Section 5. Note that data from each of the two sites is always considered completely independently from the data from the other site. For each site, each month’s time-series of wind speed data is categorised according to whether the NAO index for the month was high, medium or low. This produces approximately 60 one-month long time-series of wind speed data in each NAO state (approximately 35 years of wind speed data with 5 months of extended winter in each, split roughly equally between the three NAO states gives 35  5=3z60 months in each NAO state). The characteristics of the wind speed distribution for each NAO category at the GDF site are shown in Fig. 1(e) (similar distributions are found for STORN, discussed later). In each NAO category, the wind speed distribution resembles the Weibull distribution (Fig. 1(e), c.f. [11]), a commonly used distribution for representing wind speeds. As expected, wind speeds are generally higher during high NAO than low NAO (compare the red and blue lines), with intermediate NAO in between (purple line). When the whole time-series is considered, i.e. irrespective of the NAO states, its distribution is closest to the intermediate NAO state (compare the yellow and purple lines). The persistence of the wind speed is clearly illustrated by the autocorrelation function (Fig. 1(d)). There is strong persistence (autocorrelation > 0.5) for the first 12e24 h, decaying to weaker values (<0.2) after approximately 2 days. This is physically consistent with the synoptic nature of the weather in this region, dominated by mid-latitude storms passing eastward through the area on day-to-day time-scales (hence the initially high autocorrelation values drop towards zero after two days).

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Fig. 1. 10 m wind speeds and the NAO. (a) Near-surface wind speed (shading) and sea level pressure (contours) averaged over the months between 1948 and 2008 where NAO  0:5. Red lines indicate the locations of Ponta Del Garda and Reykjavik. (b) As (a) but for NAO  0:5. (c) A time-series of anomalies in the NAO pattern as defined in Section 2: black line shows monthly-mean values whereas the red line shows the mean of the extended winter season. (d) The autocorrelation of the hourly-mean wind speed at Great Dun Fell based on observations (solid line) and the wind speed model (dashed line). (e) A histogram of the observed hourly-mean wind speeds recorded at Great Dun Fell for different NAO conditions. (f) As (e) but using the wind speed model. The data for each plot is taken from the extended winter season (NoveMar), with blue, purple and red lines in (e) and (f) corresponding to months in the low, medium and high NAO categories respectively. For (c) and for the yellow lines in (e) and (f) data is used from all NAO states. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

2.1.2. Stage 2: Generating a synthetic wind speed time-series for each NAO category The wind speed data within a given NAO category are then used to generate conditional probabilities for a Markov chain [11]. This is achieved by:  Binning the wind speed data into 1.5 m se1 wide bins or “states” (i.e., <0  u < 1.5 m s1, 1.5  u < 3 m s1, etc.)  Using the resulting time-series of data to calculate the conditional probability that the wind speed at time t þ 1 occurs in state j given that the wind speed at time t was in state i (this is repeated for each possible i and j). The resulting conditional probabilities for each NAO state at the GDF site are shown in Fig. 2, and the strong diagonal orientation is indicative of the inter-hourly persistence of the wind speed (for any given state i at time t, the most likely states at time t þ 1 are generally j ¼ i  1, j ¼ i, or j ¼ i þ 1). As expected, the high NAO

category includes transitions to higher wind states than the low NAO category (compare Fig. 2(c) with (a)). Using data from all the NAO states together (i.e., without classifying the observed wind speed data by NAO value) produces a set of conditional probabilities that can be considered to be a combination of the other three cases (compare Fig. 2(d) with (a), (b) and (c)). Given a wind speed state at time t, a random number generator is then used to calculate the wind speed state at time t þ 1, based on the conditional probabilities shown in Fig. 2. A second random number is used to interpolate within the wind speed state (all wind speeds within the wind speed state are considered equally likely). The initial wind speed state (at t ¼ 0) is generated randomly, consistent with the observed wind state distribution for the relevant NAO category (the curves in Fig. 1(e)). The wind speed distributions generated by the model are shown in Fig. 1(f). These confirm that the wind speed statistical properties are preserved by the stochastic wind speed model. Indeed, this model captures much of the persistence of the observed wind

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Fig. 2. Conditional probabilities for the Markov models for each NAO category at the Great Dun Fell site. (a) Low NAO. (b) Medium NAO. (c) High NAO. (d) All NAO values. Darker shading indicates a higher probability of transfer from the state on the x-axis to the state on the y-axis (each state representing a 1.5 m se1 wide “bin” of wind speed), white squares indicate a conditional probability lower than 103 whereas the darkest colour indicates a conditional probability in the range 0.7e0.8.

speed time-series on time-scales of up to 24 h (Fig. 1(d)). Beyond this time-scale, however, the model tends to underestimate the wind speed persistence. This deficiency could perhaps be overcome by the use of a higher order Markov models but, given the length of the wind speed records available, robustly calibrating such a model would be extremely challenging. The implications of the underestimated persistence are discussed further in Section 3, but this feature of the model is not believed to have a significant impact on the conclusions presented here. 2.2. The wind power model A simple wind power model is used to convert the time-series of 10 m wind speed into a power output. This has two elements: a boundary layer scaling and a turbine model. 2.2.1. The boundary layer scaling Although large wind turbines are typically up to approximately 80e100 m tall (see, e.g., [12,13]), meteorological measurements of wind speeds are usually recorded at 10 m height above the ground (e.g. [10]). In general, the vertical wind shear is such that the wind further up in the boundary layer is stronger than it is at the surface and it is therefore necessary to adjust to the 10 m wind speed data to account for this. Accurately determining the boundary layer vertical wind shear is a complex problem, with the wind shear varying over a wide range of terrain conditions, time-scales and large-scale flow conditions. As

these complex effects are not the main focus of this paper, a simple approach was adopted, following the MonineObukhov boundary layer similarity theory, and the 10 m wind speed was multiplied by a constant scaling factor to approximate the flow at turbine height (approx 80 m). The estimated boundary layer shear scaling at the GDF site was taken to be a scaling of 1.25 (corresponding to a roughness length of 0.005 m or concrete/very open land). For STORN the scaling was taken to be 1.35 (corresponding to a roughness length of 0.025 m or open agricultural land). A discussion of the roughness classes corresponding to these scalings can be found at Ref. [14]. Both of these values may be overestimates of the shear at each site, particularly for GDF which is a hill-top site [the vertical wind shear can even be negative for flow over a hill which would imply a boundary layer shear scaling of less than unity, see [14]. Although there is some arbitrariness in the choice of the scaling parameter (which clearly affects the wind speed at the turbine height and consequently the energy it generates), sensitivity tests confirm that the general relationship of the power output to the NAO state (high NAO is related to high winds and high power output) was preserved when the scaling parameter was decreased (to 1.1, corresponding to a surface smoother than that expected over the ocean). However, when the scaling parameter is increased to very high values (beyond approximately 1.3e1.4 at the GDF site, or much higher values for STORN) this NAO-power relationship begins to break down as the wind speed frequently exceeds the safety cut-out speed of the turbine (see below). This break-down of the

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relationship is discussed in more detail in Section 3 where a sensitivity test at the GDF site but with a boundary layer scaling of 1.5 is presented (corresponding to a roughness length of 0.2 m or agricultural land with hedgerows etc).

3. Power output and the NAO The power output from three hypothetical turbines are now discussed as follows:  Great Dun Fell using its “best estimate” boundary layer scaling  Great Dun Fell using a “very rough” boundary layer scaling  Stornoway using its “best estimate” boundary layer scaling

2.2.2. The turbine model Following the information presented in [13], the hourly-mean power output, P, of a wind turbine is modelled according to the value of the hourly-mean wind speed, u, in the following four ranges:  P ¼ 0 for u< uci  P ¼ 12rair Ahu3 for uci  u< ur  P ¼ 12rair Ahu3r for ur  u< uco  P ¼ 0 for u  uco Here A is the area swept by the turbine blades (assumed to be a circle of 40 m in radius), rair is the density of air (taken to be 1.2 kgme3) and h is the efficiency (taken to be 0.3). uci (the “cut-in” speed), ur (the “rated” speed) and uco (the “cut-out” speed) are taken to be 3.5 m se1, 15 m se1 and 25 m se1 respectively for a standard turbine (these parameters are taken from the popular Vestas V90 turbine [12]). Only after the hourly power output for the turbine has been calculated is it then averaged over a range of different periods for display and interpretation (Section 3).

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3.1. Great Dun Fell using its “best estimate” boundary layer scaling A time-series of 1200 months (equivalent to 240 extended winter seasons) of wind speed data is produced using the model described in Section 2 for each of the high, medium and low NAO categories based on the data from the Great Dun Fell site. The characteristics of this distribution are shown in Fig. 1(f) and are discussed in Section 2.1. The resulting power output curves, averaged over a range of time periods, are shown in Fig. 3. As can be seen from each of the plots (i.e., over all averaging periods), including information on the state of the NAO has a significant impact upon the power output distribution (the distributions produced in the high NAO (red) and low NAO (blue) states differ from the distribution produced if the NAO is not classified (yellow)). Application of the Wilcoxon-MannWhitney rank-signifance test [11] confirms that each of the

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Fig. 3. Power output (averaged over different periods) histograms for the Great Dun Fell site, using the wind speeds generated by the statistical model described in Section 2 and the “best estimate” boundary layer scaling (see main text). (a) Over a 1 h period (no averaging). (b) Over a 1 day period. (c) Over a 10 day period. (d) Over a 30 day period. Blue and red lines in indicate power output under low and high NAO categories respectively, whereas the yellow line shows the power output using the same model but without classifying the NAO state (i.e., using all the wind data to train the wind speed model). Data for the intermediate NAO state (0:5< NAO< þ 0:5) is not shown, but is similar to the yellow line (unclassified NAO). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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distributions (high, medium and low) is statistically different from the others at the 99% significance level. Consider first the hourly-mean power production (Fig. 3(a)). Each of the curves show a strongly bimodal distribution indicating that, for any given hour, the turbine has a high probability of either producing no power (relative frequency 0.25) or its rated power (approximately 3 MW, relative frequency 0.35). This is consistent with the application of the wind power model (described in Section 2.2) to the wind speed distributions shown in Fig. 1(f) The NAO state has an impact on this distribution and, in particular, for the high NAO state the rated power is achieved in more than 40% of the hours simulated (red line) compared to the low NAO state, where the rated power is achieved in approximately 30% of the hours simulated (blue line). If information regarding the NAO state is ignored (the yellow line), then approximately 35% of the hours simulated achieve the rated output (similar to that seen in the intermediate NAO state, not shown). Averaging over a period of one day smooths the power output curves (compare Fig. 3(b) and (a)) and the bimodality is reduced (consistent with the inter-hourly variation of the wind speed) and a rather flat relative frequency distribution is produced. Nevertheless, the NAO state still has a noticable influence on the curves with the low NAO state tending to have a higher probability of lower mean power output than the high NAO state (compare the blue and red lines).

Fig. 3(c) and (d) show the impact of averaging the power output over longer periods (10 days and 30 days respectively). The distributions produced are approximately Gaussian in shape, with the distribution narrowing as the averaging period becomes longer. As before, the NAO state has a noticeable and statistically significant (99% confidence) impact on the distributions: the low NAO state is associated with generally lower power output (the mode of the distribution is 1.5 MW) than the high NAO (where the mode is 1.7 MW). A similar set of distributions can be seen if the observed wind speed data is used directly to produce the power output curve, as shown in Fig. 4(a) to 4(c). The consistency between the power output curve from the statistical wind speed model and the observational data (compare Fig. 3 with Fig. 4) indicates that the wind speed model is producing a good representation of the real wind speeds at these averaging time-scales, although the distributions based directly on the observed wind speed time-series are rather more noisy, particularly for the longer averaging periods, reflecting the relative sparsity of data (compare Fig. 3(d) with Fig. 4 (c): the curves in the former figure are smoother as a much greater number of sample time-points can be generated using the statistical model than are available directly from the observational record). As an additional test of the model, the variance of the power output using the simulated wind speed time-series was compared

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Fig. 4. Comparison between power output using the simulated and observed wind speed data at Great Dun Fell (using the “best estimate” boundary layer scaling: see main text). (a) Power output histogram using the observed data, averaging power output over 1 h period. (b,c) As (a) but over 1 day and 30 day periods respectively. (d) Variance of the power output distribution (averaged over different periods) using the observed wind speed data directly (solid line) and the statistical wind speed simulation (dashed line). For (a) to (c) blue and red lines in indicate power output under low and high NAO categories respectively, whereas the yellow line shows the power output using the same model but without classifying the NAO state (i.e., using all the wind data to train the wind speed model). Data for the intermediate NAO state (0:5< NAO< þ 0:5) is not shown, but is similar to the yellow line (unclassified NAO). For the observational data, any averaging period that contains missing wind speed data is completely rejected. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Table 1 Mean power output (averaged over whole simulated time-series) at different sites and with different boundary layer scalings for wind speed. Units MW, “GDF” and “STORN” indicate the Great Dun Fell and Stornoway sites respectively. Values in brackets indicate the equivalent value that is obtained if the observed wind time-series is used directly to drive the wind power model. The column marked “BL” indicates the boundary layer scaling parameter used (see Section 2.2). Site

BL

NAO  0:5

0:5 < NAO < þ0:5

NAO  þ0:5

All NAO

GDF GDF STORN

1.25 1.50 1.35

1.56 (1.59) 1.678 (1.655) 1.048 (1.026)

1.61 (1.65) 1.625 (1.605) 1.104 (1.083)

1.73 (1.77) 1.558 (1.514) 1.229 (1.217)

1.64 (1.68) 1.607 (1.582) 1.123 (1.115)

to that produced using the observational data directly over a range of different averaging periods (Fig. 4(d)). Despite the statistical wind speed model underestimating the autocorrelation of the wind speed at lags greater than 2e3 days (Fig. 1(d)), the variance of the power output distribution is well represented at time-scales from hourly-to-monthly (compare the dashed and solid lines in Fig. 4 (d)). This suggests that the model is not only reproducing the long-term mean power output from the turbine, but it is also capturing the variability in the wind power supply well (e.g., multiday persistent low-wind or high-wind events are being represented in the model to some extent, although it should be noted that the model probably fails to capture the most extreme cases of either). When the average over the whole (1200 month) simulated time-series is taken, the power output for the high NAO state is 1.73 MW, compared to 1.56 MW for the low NAO state (comparing well to the values of 1.77 MW and 1.59 MW if the observations are used directly to drive the turbine model, see Table 1). The difference between the high and low NAO values indicates that an error of up to approximately 10% in the wind power output could be

made if the power output were estimated using a relatively short period observational baseline (say 1e2 years which have a strongly positive NAO state for example). Even simply considering the average of the long-term power output irrespective of the NAO states (1.64 MW, Table 1), and comparing that to the estimated power in the high and low NAO states suggests that NAO-induced changes could lead to mean power output errors of as much as 5e10%. This may represent a serious bias in the wind farm planning and/or operations given that, as noted in Section 2.1, the NAO is modulated by decadal variations comparable to the lifespan of a wind turbine. 3.2. Great Dun Fell using the “very rough” boundary layer scaling The procedure in Section 3.1 is repeated using a higher value of the boundary layer scaling parameter (1.5 rather than 1.25) as described in Section 2.2. The power output curves for different averaging periods are shown in Fig. 5, and the long-term mean power output (averaging over the whole 1200 month simulation) is shown in Table 1.

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Fig. 5. As Fig. 3 but showing the power output for the Great Dun Fell site using the “very rough” boundary layer scaling estimate.

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As before, for the 1-h averaging period (Fig. 5(a)) the high NAO state has a higher likelihood of reaching the rated power output (just over 3 MW) than the low NAO state (compare the red and blue lines). The difference in the probability of achieving the rated power output between the two extreme NAO states is, however, rather small (40% in high NAO vs. 38% in low NAO). There is now also a much greater chance of achieving no power output in the high NAO state than the low NAO state (35% compared to 23%, as shown by the red and blue histograms near the y-axis of the figure). As a consequence, when longer averaging periods are considered (1-day, 10-day or 30-day in Fig. 5(b)e(d)) the power output from the high NAO state is generally lower than that from the low NAO state (compare the red and blue lines in, e.g., Fig. 5(c) or the values in the second row of Table 1). This is because, in the high NAO state, the turbine spends more time inoperable due to high winds and thus the mean power output is lower than that expected from the low NAO state.

3.3. Stornoway using its “best estimate” boundary layer scaling The analysis for GDF was repeated using the observed wind speed data taken from the STORN site and is shown in Fig. 6 and Table 1. Fig. 6(a) shows the wind speed distribution recorded at the STORN site. As for GDF, the distribution appears to have the form of a Weibull curve, although the distribution is tighter than that for GDF with the 10 m wind speed rarely exceeding 20 m se1. As before, the high NAO state tends to correspond to higher wind speeds than the low NAO state (compare the red and blue lines) and the wind speed model is able to reproduce the overall characteristics of the distributions (compare Fig. 6(a) and 6(b)). As in Section 3.1 (GDF with the “best estimate” boundary layer scaling), the NAO has a positive relationship to the power output from the turbine (Fig. 6(c) to 6(f)). Table 1 shows that the simulated long-term mean output from the turbine is 1.23 MW in the high

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Fig. 6. 10 m wind speed and power output (averaged over different periods) histograms for the Stornoway site. (a) A histogram of the observed hourly-mean 10 m wind speeds recorded at Great Dun Fell for different NAO conditions. (b) As (a) but using the wind speed model. (c) Power output over a 1 h period (no averaging) using the simulated wind speed time series. (d,e,f) as (c) but averaged over 1 day, 10 day or 30 day periods. Blue and red lines in indicate low and high NAO categories respectively, whereas the yellow line shows the power output using the same model but without classifying the NAO state (i.e., using all the wind data to train the wind speed model). Data for the intermediate NAO state (0:5< NAO< þ 0:5 , purple line) is not shown in (c,d,e,f), but is similar to the yellow line (unclassified NAO). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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NAO state (1.22 MW if the wind speed observations are used directly to drive the turbine model) comparing with a simulated 1.05 MW for the low NAO state (1.03 MW if observations are used directly). As in the GDF site, there is a roughly 10e15% difference between the mean power output estimate in the high and low NAO states. 4. Using NAO information in wind power forecasts From the results presented in Section 3, it is clear that the state of the NAO has a noticeable impact on the power output that can be generated from a wind turbine at the sites examined. As noted in the introduction, there is therefore the potential to use a prediction of the state of the NAO at some future time to provide an improved statistical forecast of the power output from the turbine. The source of the NAO prediction is not the primary concern here (it can be based on persistence or from a true “prediction”), but rather, given such an NAO prediction, how much would it improve our knowledge of the power output from the turbine? To assess this, the wind speed model is used to create a synthetic wind speed time-series hindcast covering all of the extended winters in the period from which observed wind speed data is available for a particular site. The NAO state for each month is prescribed using either:  the actual NAO index value for the month (effectively a “perfect” NAO forecast), or  a “persistence” forecast of the NAO (the NAO index at month i is estimated to be the mean of the NAO for the previous two months: that is, NAOðiÞ ¼ 0:5  ðNAOðii  1Þ þ NAOðii  2ÞÞ , c.f., [15]). The NAO index at each month in these NAO forecasts is used to determine which Markov table the model uses for that month to generate the wind speeds (c.f., Section 2 and Fig. 2(a)e(c)). A third forecast is made where the NAO information is not included in the model (i.e. a single Markov table is used to calculate the wind speeds, as in Fig. 2(d)). This last forecast is termed the “No NAO information forecast”. Each of these three forecast wind speed time-series can then be converted to a forecast power time-series using the wind power model described in Section 2.2, and averaged over a 30 day period. The averaged wind speed or power output series from each forecast are then compared to the observed time-series at the same site. This comparison takes the form of calculating firstly the rootmean-square-error (RMSE) between the observed and forecast time-series and, secondly, the linear correlation between the observed and forecast time-series. Each forecast is repeated 50 times and the mean of the resulting ensemble of 50 estimates of the RMSE or linear correlation is calculated. The ensemble mean RMSE or ensemble mean linear correlation calculated for each forecasting method therefore represents a measure of the accuracy or value of the forecast method and, by comparing between the different methods, it is possible to assess whether or not including “persistence” or “perfect” NAO information quantitatively improves the power output forecast over the random “no NAO information” forecast. The results of this analysis are shown in Tables 2 and 3. Consider first the wind speed time-series in Table 2. As expected, the mean correlation between the “No NAO information forecast” and the observed time-series is negligible for each experiment listed in the table (essentially the “no NAO information” forecast is simply a random series but one which is consistent with the statistical wind speed properties at the site). At both sites, the “perfect NAO” and “persistence NAO” forecasts show statistically significant improvements in the mean correlation with observations compared to the “no NAO information” forecast.

2095

Table 2 Ensemble mean RMSE and linear correlations between the simulated monthlymean wind speed time-series created using “perfect”, “persistence” and “no” NAO forecasts and the observed wind speed record (see main text). “GDF” and “STORN” indicate the Great Dun Fell and Stornoway sites respectively. The first value in each column is the RMSE (units m se1) while the second (bracketed) value denotes the linear correlation. Values in bold indicate correlations that are significantly different to the equivalent “no NAO forecast” simulation at the 99% level. For the observational data, a moderate amount of missing data is allowed within each month (up to 240 h per month) and the average is calculated from the remaining non-missing data. Site

Perfect

Persistance

No forecast

GDF STORN

3.30 (0.338) 2.36 (0.077)

3.46 (0.254) 2.39 (0.043)

4.04 (0.004) 2.45 (0.002)

The correlations are generally stronger at GDF than STORN (for the “perfect NAO” forecast, compare 0.077 for the monthly-mean wind at STORN with 0.338 at GDF). The mean RMSE provides a slightly different picture. The mean RMSE of the wind speed is significantly reduced by including NAO information (compare, e.g., the “no NAO” forecast RMSE of 4.04 m se1 at GDF against 3.30 m se1 for the “perfect” and 3.46 m se1 for the “persistence” forecasts: a reduction of approximately 15%). The “persistence NAO” forecast clearly adds less skill than the “perfect NAO” forecast but nevertheless indicates that even a simple practical NAO forecasting methodology has the potential to add value to statistical predictions of monthly-mean wind speed (a mean RMSE of 3.46 m s1 at GDF (correlation 0.254) compared to 4.04 m s1 (and effectively zero correlation) if the NAO information is not included). Examining the monthly-mean power time-series correlations in Table 3 reveals a similar picture. As with the wind speed data, including NAO information improves the ensemble mean correlation between the observed and forecast power output time-series (e.g., the “perfect NAO” monthly-mean forecast at STORN has a correlation of 0.080 compared to effectively zero if NAO information is not included). The differences are statistically significant at 99% confidence. Consistent with the wind speed time-series, GDF tends to show stronger correlations than STORN (although the difference is less pronounced for the power output time-series). At both sites including NAO information acts to reduce the RMSE compared to the “no NAO” forecast (e.g., at GDF: compare 0.333 MW with the “perfect” and 0.344 MW with the “persistence” against 0.375 MW with the “no NAO” forecasts, a reduction of around 10%). The evidence presented here therefore suggests that the “persistence” forecast adds some skill over the random “no NAO information forecast” on monthly averaging periods and is generally more noticable at the GDF site. Even the simple “persistence NAO” forecast is a statistically significant improvement to the power output forecast over these averaging time-scales. The “perfect NAO” forecast produces further improvements in the power output forecast at both sites, suggesting that there is also additional potential for adding further valuable information if the NAO state can be accurately forecast (up to a site- and averaging-period- dependent maximum “potential predictability” that can be derived from the NAO). Table 3 As for Table 2, but for monthly-mean power output (in MW). For Great Dun Fell (GDF) and Stornoway (STORN) the “best estimate” boundary layer scalings of 1.25 and 1.35 are used respectively (see Section 2.2). Site

Perfect

Persistance

No forecast

GDF STORN

0.333 (0.097) 0.395 (0.080)

0.344 (0.062) 0.401 (0.039)

0.375 (0.010) 0.410 (0.004)

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5. Discussion and conclusion This study has combined a series of simple statistical meteorological and wind power models to produce synthetic time-series of hourly-mean power output for hypothetical wind turbines situated at two sites in the UK (Great Dun Fell and Stornoway) under different large-scale winter atmospheric conditions (represented by one of three NAO states: high, medium or low). These timeseries were then time-aggregated to estimate the hourly- to monthly-mean power output distributions from the turbine. The model reproduces inter-hour to inter-day persistence in wind speed, and produces a good representation of the power output distributions when compared directly against meteorological data. On each of the time-scales examined (hourly- to monthlymeans) the statistical properties of both the power and wind distributions are significantly affected by the slowly varying, large scale atmospheric circulation. These results have implications for commercial wind farms. For example, consider the financing of a wind farm where the long-term mean (monthly or longer) power output is estimated based on a relatively short time period of wind speed observations (say, 1e2 years). If this observational period occurred under a high NAO background state (as in the early 1990’s, see Fig. 1(c)) then the power forecast would tend to overestimate the actual power output once the NAO anomaly reduced back to its neutral climatological level (as in the mid-2000’s, Fig. 1(c)). For this reason it is now “relatively common practice to exclude the early 1990’s from long-term reference data sets” in the wind energy industry [16]. This approach does, however, lead to other problems. In particular, if a wind speed record runs from, say, 1988e2008, then excluding data from the early 1990’s will only lead to a more accurate forecast of the mean power output in the period 2008e2018 if the NAO remains neutral. There is, however, no reason to expect that the NAO will remain neutral over this period and the exclusion of wind speed data from the early 1990’s therefore clearly underestimates the uncertainty in the anticipated power output from a wind farm site over lead times comparable to the lifetime of the turbine. The relationship between large-scale climate patterns and wind power generation at a particular site does, however, present new opportunities for stakeholders in the wind energy industry. Forecasting large-scale climate patterns at lead times of seasons to decades is often more successful than directly simulating point data and there is growing evidence that some large-scale patterns can be predicted a few months in advance. Although this is especially valid for the major El Niño Southern Oscillation [17], the NAO state may be predicted too, though with a lower accuracy, and even by using simple statistical procedures (e.g. a moving average of the observed NAO [15]). Initial testing with one such simple procedure indeed suggests that this seasonal forecasting could offer a way to improve monthlymean wind speed and wind power forecasts at month-ahead lead times (the findings for the wind speed forecasts were particularly robust although, for averaging periods much shorter than one month (not shown), it should be noted that the improvements in the power output forecasts were less noticable). The “skill” test described here was designed to focus solely on monthly-mean output but further tests could developed more sophisticated metrics, e.g., the probability of a given hour within a month achieving rated output. Although this study has focussed on just two sites, the results presented here suggest that the relationship between the NAO and the wind distribution may be subtlely different at different sites, even within the UK. This may be partially be an artefact of data quality (e.g., changes in the configuration of the meteorological site where windspeed data is collected perhaps associated with new buildings or trees), which may perhaps explain the relatively weak relationship between surface wind speed and NAO at the Stornoway site compared to GDF (recall that STORN is sited at an airport whereas

GDF is at a more remote site). Nevertheless, it is reasonable to expect that there will be geographical variation in the relationship between large-scale atmospheric patterns (such as the NAO) and surface wind speed, emphasising the need for a fuller understanding of the atmospheric processes at work on both local (i.e., site specific) and regional levels (e.g., the differing behaviour may relate to the position of the western end of the North Atlantic storm track over Europe and the centres of action of the NAO pattern). It is also worth noting that preliminary reseach for this paper [18] found a strong relationship between the NAO and wind speed using observational data from a site at Blackpool (3.04 W, 53.77 N; close to GDF but at sea level near the coast) while the NAO-wind relationship was much weaker at London Heathrow (0.45 W, 51.48 N; South East England). The relationship between the NAO and the power output is further complicated by the non-linear relationship of the wind power generated by a turbine to the wind speed, and the current model does not take into account the impacts of wind variability on time-scales of less than 1 h or the possibilities of damaging extreme wind gusts. The sensitivity of the model to the wind shear in the boundary layer (and its relationship to the large-scale climate) is clearly another area requiring much further research. Nevertheless, this simple model has been shown to illustrate the potential for linking wind power generation in midlatitude regions to large-scale climate patterns suitable for seasonal-to-decadal prediction techniques. Similar statistical techniques could also be explored for other renewable resources (e.g., wave and solar) and climate patterns (e.g., the East Atlantic pattern).

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