We investigate wake effects at the Anholt offshore wind farm in Denmark, which is a farm experiencing strong horizontal wind-speed gradients because of its size and proximity to land. Mesoscale model simulations are used to study the horizontal wind-speed gradients over the wind farm. From analysis of the mesoscale simulations and supervisory control and data acquisition (SCADA), we show that for westerly flow in particular, there is a clear horizontal wind-speed gradient over the wind farm. We also use the mesoscale simulations to derive the undisturbed inflow conditions that are coupled with three commonly used wake models: two engineering approaches (the Park and G. C. Larsen models) and a linearized Reynolds-averaged Navier–Stokes approach (Fuga). The effect of the horizontal wind-speed gradient on annual energy production estimates is not found to be critical compared to estimates from both the average undisturbed wind climate of all turbines' positions and the undisturbed wind climate of a position in the middle of the wind farm. However, annual energy production estimates can largely differ when using wind climates at positions that are strongly influenced by the horizontal wind-speed gradient. When looking at westerly flow wake cases, where the impact of the horizontal wind-speed gradient on the power of the undisturbed turbines is largest, the wake models agree with the SCADA fairly well; when looking at a southerly flow case, where the wake losses are highest, the wake models tend to underestimate the wake loss. With the mesoscale-wake model setup, we are also able to estimate the capacity factor of the wind farm rather well when compared to that derived from the SCADA. Finally, we estimate the uncertainty of the wake models by bootstrapping the SCADA. The models tend to underestimate the wake losses (the median relative model error is 8.75 %) and the engineering wake models are as uncertain as Fuga. These results are specific for this wind farm, the available dataset, and the derived inflow conditions.

The Anholt wind farm is currently the fourth largest offshore wind farm in
the world power-wise. The layout of the Anholt wind farm was optimized to
minimize wake losses. The number of wind turbines (111), the wind-turbine
type, and the maximum allowed wind-farm area for turbine deployment (88 km

So far the only reported studies on the wake effects of this wind farm are
those of

Engineering wake models are also often regarded as too simplistic for the
estimation of wake losses, yet they are those that are most used when
planning wind-farm layouts and for annual energy production (AEP)
estimations. This is because they can be easily implemented and optimized in
terms of computational performance. One cannot expect to characterize wakes
in detail with such models but for the estimation of power and energy
production means, they are sufficiently accurate when used properly

Wake models of all types have been mainly evaluated against offshore wind
farms that are well off the coast or where the effect of the land is assumed
to be minimal

Undisturbed refers to a wake-free condition in this study.

wind climates at some (or all) turbines' positions, in which the horizontal wind-speed gradient is embedded, with the wake models. To the authors knowledge, there have not been attempts to study the impact of the horizontal wind-speed gradient on wakes of wind farms using engineering wake models yet, although there is an attempt to include wind-direction gradientsIn this study, we first present (Sect.

We define the efficiency of the wind farm at a given wind speed

We define the power loss of the wind farm as

We define the relative wake model error as

The Anholt wind farm is located in the Kattegat strait between Djursland and
the island of Anholt in Denmark (Fig.

We have access to 10 min means of SCADA for the period from 1 January 2013 to 30 June 2015. Data include nacelle wind speed, yaw position, pitch angle, rotor speed, power reference, air temperature, rotor inflow speed, and active power. We also produce a filtered SCADA dataset by identifying periods when each turbine was grid connected and produced power during the entire 10 min period. The dataset excludes periods when any turbine was either parked or idling, those with starting and stopping events, and where power was curtailed or boosted. We find turbine nos. 1, 36, 65, and 68 to be boosted with power values 5 % above the rated value. The result is a time series of 7440 10 min values starting in July 2013 until December 2014.

Due to the lack of undisturbed mast measurements in the SCADA, we derive the
inflow conditions from the filtered SCADA dataset. We estimate an
“equivalent” wind speed based on either the 10 min SCADA's power or pitch
angle values in combination with the manufacturer's power curve or the
average pitch curve extracted from the SCADA. The inflow reference wind speed
is computed as the average equivalent wind speed for groups of four
undisturbed turbines as shown in Table

Free-stream turbines used to determine the inflow wind speed (first two columns) and the inflow wind direction (second two columns) as a function of an average yaw position.

We perform simulations of the wind climate over a region covering the Anholt
wind farm using the WRF version 3.5.1 model. Simulations are carried out on
an outer grid with horizontal spacing of 18 km

The wind climate at hub height in the middle of the Anholt wind farm for the year 2014 based on WRF simulations.

We use three different wake models: the Park wake model with the
commonly used offshore value of

Due to the high computational efficiency of these wake models, we can easily
perform wake analyses over given wind-speed and wind-direction ranges and
AEP-like calculations using the values in the time series (no need for
distributions). For the latter calculations, we create lookup tables (LUTs)
for each wake model, which contain the total wind-farm power output for
specific undisturbed wind directions and wind speeds. Figure

The efficiency of the Anholt wind farm predicted by the wake models
at 5 m s

One way to account for the effect of the horizontal wind-speed gradient within a wind farm, which is not the result of wake effects themselves, on the wind-farm power output is by estimating the wake losses using the undisturbed wind speed and direction at each individual turbine position for each time realization as inflow condition instead of using a single undisturbed wind speed and direction as it is commonly performed. At each turbine position, we will therefore have both a time series of velocity deficits (and thus power values) because of the change with time of inflow conditions and a time series, with a number of members equal to the number of turbines in the farm, of velocity deficits for each inflow condition experienced by each turbine for each time realization. Then, the wind-farm power time series, as an example, can be estimated by averaging the power resulting from all inflow conditions for the same time realization (for the Anholt case this means 111 conditions) and then averaging the results of all turbines. This is hereafter known as a gradient-based analysis. The wind and inflow at each turbine must be undisturbed and so mesoscale model simulations over the wind-farm area (without the wind farm) are an obvious option to estimate the wind climate at each turbine position.

Due to the very high efficiency of the Park model (in a MATLAB script it takes milliseconds to perform one simulation of Anholt for a single inflow wind speed and direction), when using the WRF hourly time series, we can perform 111 simulations (i.e., 111 different inflow conditions that are interpolated from the WRF grid into the turbine positions) in a couple of seconds. Thus, we can perform a gradient-based AEP analysis with hourly WRF winds in just few hours. It is important to note that we can perform traditional (i.e., with a single inflow condition per time realization) AEP calculations with all wake models much faster using pre-computed LUTs.

We quantify the uncertainty of the wake models using a nonparametric
circular-block bootstrap similar to the approach of

The analysis of the influence of the horizontal wind-speed gradient in
Sect.

Figure

WRF-simulated mean wind speed at hub height in the Kattegat
area where the Anholt wind farm is deployed for the year 2014. All
data are shown in the left frame and data within the directions
270

In Fig.

Figure

The difference in AEP when accounting for the wind-farm gradient information
and when assuming a horizontally homogenous wind field

Estimated each hour by taking the average of the horizontal wind-speed gradient over each turbine of the farm.

is lower than 1 % when using the 2014 hourly WRF wind fields combined with the wake models (“average wind field” column in TableDifference (in percentage) between different types of AEP calculations and that using the horizontal wind-speed gradient information from the WRF simulations.

The difference in the AEP estimation by accounting for the wind-speed
gradient and that by using the wind climate of turbine no. 1, which is the
position with the lowest average wind speed, is larger than 1 % for the
engineering wake models. Such a difference is rather large considering that the
AEP of the wind farm is

Given the impact of the horizontal wind-speed gradient on the AEP estimations
(Sect.

Normalized average power of each turbine in the wind farm for
westerly flow conditions.

Since the horizontal wind-speed gradient does not seem to strongly impact the
wake behavior for broad wind-direction ranges, we compare the SCADA that
have been wind-speed and direction filtered with the wake models in Fig.

Figure

Normalized average power of the north–south row of turbines in the
middle of the wind farm for southerly flow conditions from SCADA and simulations
from the wake models within the range 168.7

Because the differences between SCADA and models in Fig.

Being able to estimate the AEP (Sect.

We use all the SCADA data that are available for 2014. Theoretically, there
should be 52 560 10 min samples for this year. However, the number of samples
per turbine available in the SCADA varies and is never the theoretical one;
the turbine with the highest number of samples is no. 7 (51 648) and that with
the lowest is no. 77 (49 512). The average availability, taking into account
all turbines, of observed samples is 98.10 %. Table

Observed and estimated (from the WRF-wake model setup) capacity factors of the Anholt wind farm for 2014. The estimated values account for the observed average availability of samples. The last column shows the power loss based on the SCADA and the power loss estimations from wake models without WRF coupling.

It is clear that we can estimate the observed capacity factor using the WRF-wake model setup fairly well. However, it is important to note that wind turbines are not always working and underperform when compared to the manufacturer's power curve. The predicted AEP or capacity factor of a combined mesoscale-wake model is typically higher than the observed value; however, we want to know the capacity factor of a wind farm regardless of the operating conditions.

Table

One way to show that the estimations of power of the free-stream turbines are
sound is to compare the manufacturer power curve with the SCADA-derived power
(averaging the power of the turbines in Table

However, this does not give us an idea about the validity of the
SCADA-derived inflow conditions for the turbines that are far from those we
use to derive the inflow conditions. By filtering the SCADA-derived inflow
conditions for westerly flow (270

Also based on the SCADA's 7440 10 min values, we find an optimal block length
for the circular bootstrap of 242 samples. On average, such sample length
corresponds to about 10 days, which is long enough to capture the correlation
between samples. We use 10 000 bootstrap replications and find that, for example,

Distribution of the relative model error

For the particular case of the Anholt wind farm and for the filtered SCADA
used in the analysis, Larsen linear has the distribution with lowest bias and
the second largest

It is important to note that some of our results depend on the methods we use
to derive the undisturbed inflow conditions of the wind farm. We show that
for power analyses of individual turbines, whose inflow conditions are
greatly affected by the horizontal wind-speed gradient (like turbine nos. 1
or 30), this is an important matter (see Fig.

We cannot derive the undisturbed horizontal wind-speed gradient from wake-affected turbines without a wake model.

and validate our findings.We also estimate the power loss and the uncertainty of the wake models based on a rather discontinuous and short filtered SCADA dataset. Therefore, our results might be biased and caution must be taken when generalizing our findings. A clear example is that related to the model uncertainty, where we find that most wake models underestimate the wake losses. With a longer dataset, the biases can change (and models might start to produce conservative results) but the relative position of the models will most probably be maintained, Park linear and Larsen quadratic being the most conservative and most optimistic models, respectively. If the same models are evaluated with SCADA from other wind farms, the biases will most probably change.

We show that our WRF-wake model setup is able to rather accurately predict the capacity factor of the Anholt wind farm. Anholt is the offshore wind farm with the highest all-life capacity factor in Denmark (49.4 %) and the highest in the world for a wind farm older than 2 years, outperforming Horns Rev II, which has, in principle, more favorable wind conditions. One of the reasons for this is the Anholt wind-farm layout, which highly minimizes the wake losses.

The results for the two flow cases illustrate what we already expected; Park linear shows the highest and Larsen quadratic the lowest wake deficits. This is mainly because of the values we choose for the wake decay coefficient. It is important to note that we can obtain similar wake deficits with both the Park linear and Park quadratic models when tuning the wake decays. Physically, it makes more sense to linearly sum the wake deficits but the quadratic approach is normally used due to a historical general good match of model predictions with observed power deficits, for the values normally suggested for the wake decay (0.04–0.05 for offshore conditions). The RANS model shows similar values to Fuga, as expected due to the similarity of the models' physics, both showing a better comparison to the SCADA for the two flow cases than the traditional Park quadratic model, also as expected.

For the Anholt wind farm, we show from both the SCADA and WRF model simulations that for a number of wind directions, there is a clear influence of the land on the free-stream wind speed at the positions of the turbines closer to the coast. However, for AEP calculations for which we run three different wake models using mesoscale model outputs as inflow conditions, accounting for the horizontal wind-speed gradient (also derived from the mesoscale model results) does not have a large impact on the results when compared to AEP calculations based on, first, a wind climate that is the average of all wind climates at the turbines' positions and, second, a wind climate correspondent to a position in the middle of the wind farm. It does, however, differ from the calculation using a wind climate that is strongly influenced by the horizontal wind-speed gradient particularly for the engineering wake models.

We look at two flow wake cases with two different engineering wake models and some of its variants and a linearized RANS model. The first case corresponds to westerly winds, for which the influence of the horizontal wind-speed gradient is largest. Here the wake models, and Fuga in particular, agree with the SCADA fairly well. The second case corresponds to southerly winds, for which the wake losses are highest. Here, the wake models tend to underestimate the wake deficit when compared to the SCADA. This is also translated into a wake-model tendency to underestimate the observed power loss, on average 0.31 % less than that derived from the SCADA.

Using our mesoscale-wake model setup, we find that the estimated capacity factors are 0.27–4.60 % biased when compared to those computed from the SCADA. Finally, using inflow conditions derived from the SCADA and by circularly block bootstrapping these, we estimate the relative error of the wake models. We find that these models tend to underestimate the wake losses, except for one wake model variant. The engineering wake models are found to be as good as the linearized RANS Fuga model. However, these are results that are wind farm and SCADA specific and that depend on the definition of inflow conditions; therefore similar analyses need to be reproduced at different wind farms, using more SCADA and different methods to derive the inflow conditions.

The Anholt SCADA can be made available by Ørsted upon request to Miriam Marchante Jiménez (mirji@orsted.dk). The WRF data can be made available by DTU Wind Energy upon request to Andrea N. Hahmann (ahah@dtu.dk).

The authors declare that they have no conflict of interest.

This article is part of the special issue “Wind Energy Science Conference 2017”. It is a result of the Wind Energy Science Conference 2017, Lyngby, Copenhagen, Denmark, 26–29 June 2017.

We would like to thank Ørsted and partners for providing the SCADA. Also, we thank Charlotte B. Hasager for promoting and leading the Anholt wind-farm internal project at DTU Wind Energy and Patrick Volker for making the mesoscale model simulation outputs easily accessible. Finally, we would like to thank the three anonymous reviewers and Nicolai Gayle Nygaard for their comments on the paper. Edited by: Julie Lundquist Reviewed by: three anonymous referees