The reduction of produced emissions and the transition to renewable energy sources require a large increase in the installed capacity of wind. This leads to more and larger wind farms being built with ever-increasing turbine sizes. Offshore sites have a lot of benefits compared to onshore – i.e., higher wind speeds with lower turbulence, higher social acceptance, larger space availability, and larger energy density due to the possibility to install larger machines. Thus, offshore sites with favorable wind, soil, and depth conditions, like the North Sea, are being populated with wind farms that have to be spaced as close as possible.

Similar to single wind turbine wakes, the wind farms as a whole interact with the atmospheric boundary layer and create wakes that are propagated downstream . This phenomenon is more prominent in offshore farms where the machines used are larger, the ambient turbulence intensity (TI) is lower, and the surface roughness is lower than onshore sites. These effects need to be modeled and considered when planning the siting of wind farms as they can have a large impact on the operating conditions experienced by the neighboring wind farms. Neglecting such effects can lead to large deviations in the annual energy production (AEP) estimates, as well as the lifetime of the structural components .

Therefore, understanding these inter-farm interactions has been a topic of interest for research, as well as the industry. Previous studies based on airborne measurements have identified wind speed deficits and increases in turbulence downstream of offshore wind farms and clusters. They showed that these effects are visible up to a level of 50 km downstream, especially in neutral atmospheric conditions. In , measurements with synthetic aperture radars (SARs) and Doppler radars were performed showing a speed deficit of 4 % to 8 % up to 10 km downstream of the farms. The work of used also SAR measurements to investigate wind farm wakes in the North Sea and the Baltic Sea. They reported a speed deficit in the near wake, with full recovery at distances of 5–20 km depending on the free-stream wind speed, the atmospheric stability, and the number of operating turbines. In the study of , turbine data were used to identify the magnitude of the wake effects. They reported a detectable wind speed deficit and wake-induced turbulence due to neighboring farms at a distance of 4.2 km (38.8 D). In long-range lidar and satellite SAR measurements were used to investigate inter-farm wake effects for wind farms spaced at distances of 24 and 55 km. They identified wind speed deficits for the downstream farm to be higher in stable and weakly unstable atmospheric conditions, with mean levels of 20 % and 25 % for distances of 24 and 55 km, respectively. In data from the FINO1 platform are analyzed cumulatively to examine the wind speed and turbulence intensity distributions. The different periods of the Alpha Ventus (AV) wind farm project – preconstruction, single farm operation of Alpha Ventus, and cluster operation with the surrounding farms – are examined based on mean cumulative values and time series. The results show that the mean wind speed decreased by 1 ms-1 over the periods, and the mean turbulence intensity increased from 5.5 % to 8.5 % due to the farm wakes from the neighboring farms.

Moreover, numerical studies have been carried out to understand the underlying mechanisms of wind farm wakes. In large eddy simulations were performed to correlate atmospheric stratification, farm size, and layout with the flow inside and around a wind farm. They identified velocity deficits at a level of 3.5 % compared to free stream values at a 10 km distance for small vertical temperature gradients (1 Kkm-1) with the wake-induced turbulence propagating up to 10 km. Moreover, for a higher gradient of 5 Kkm-1, they report a full wake recovery at a distance of 5 km. studied the effects of large wind farms on the atmospheric boundary layer, showing that it is affected due to the enhanced mixing caused by the wakes. In a variety of numerical models, with ranging fidelity, were compared against supervisory control and data acquisition (SCADA) measurements for predicting the wake effects in a cluster of two wind farms separated by a distance of 3 km (30 D). The operational and wind data used were not of sufficient quality and quantity to draw meaningful conclusions. Nevertheless, the widespread results between the numerical models showed the need to further investigate the current capabilities and reduce the inherent uncertainty.

The need to include these effects in practical engineering studies has led to the development of engineering wind farm wake models with varying fidelity and requirements. suggested a simple analytical model to calculate the speed deficit accounting for atmospheric stability, surface roughness, the turbine's thrust coefficient, and the Monin–Obukhov length. Calibration and evaluation of the model can be found in . In an engineering model accounting for both speed deficits and wake-induced turbulence is suggested. It is based on the Jensen–Katic model , extended to include wake-induced turbulence and validated against measurements for power production.

In this context, the goal of the present work is to investigate the effects of inter-farm wakes by analyzing measurement data. More specifically, metocean data from the FINO1 measurement platform along with SCADA and loads data from the closest machine of Alpha Ventus (AV) to the mast are analyzed for the period 2010–2019. Until 2015, AV was the only wind farm operating in the area. This setup allows us to observe how the metocean conditions – as measured by FINO1 – have changed in relation to the surrounding wind farm construction and how these changes impact the turbine's response at AV. The data are analyzed per direction and wind speed on an annual basis. This will give insight to researchers working on modeling the inter-farm interactions, as well as to practitioners focusing on optimizing wind farm siting and planning. Furthermore, the data presented here can be used by researchers doing research related to AV in order to represent the metocean conditions during the different operational periods of the project.

The rest of the paper is structured as follows: in Sect. 2 we describe the site and the locations of the farms and the met mast around the Alpha Ventus site. In Sect. 3 the measurement equipment and the data processing methods are discussed. Section 4 presents the results in terms of metocean conditions and turbine responses, followed by a discussion on the findings in Sect. 5.

Alpha Ventus is the first German offshore farm commissioned in 2010 and is located in the North Sea close to the island of Borkum. It consists of 12 fixed bottom wind turbines with a rated power of 5 MW. Half of the turbines are manufactured by REpower (renamed to Senvion) and have a jacket support structure, and the rest are manufactured by Adwen and use a tripod substructure. The research projects at AV are supported by the initiative Research at Alpha Ventus (RAVE) by coordinating the research activities and providing measurement data.

FINO1 is a research measurement platform including a fully equipped met mast erected in 2004 in the North Sea. It is located close to AV, at a 400 m (3.2 D) distance from the AV4 turbine. The data from both FINO1 and AV are processed and made available in one database operated by the Federal Maritime and Hydrographic Agency (BSH). Data have been collected since the pre-construction phase (2004–2010) of AV and also during the operational phase from 2010 to today.

As it was initially planned, new wind farms have been built around AV over time, operating at different distances and in different directions. Today, AV can be seen as a part of a larger wind farm cluster consisting of five wind farms equipped with similarly sized turbines. This allows us to observe how the site conditions have evolved during the years due to the interannual variability but also due to the presence of the neighboring wind farms.

An overview with all the wind farm information, the distances, and the directions relative to FINO1 are given in Table . A sketch intended to give the reader an impression of the topology of the area is given in Fig. . In 2015, two new wind farms started operating in the area. The closer one, Borkum Riffgrund 1 (BR1) , is located southwest of AV at distances between 2.8 and 7.6 km from FINO1, and the relevant directions are 70 to 244∘ (considering FINO1 as the origin of a clockwise system with north pointing up at 0∘). BR1 consists of 78 turbines of 4 MW with a rotor diameter of 120 m. The second, Trianel Borkum 1 (TB1) , is located northeast of AV at distances between 6 and 14 km and 253–315∘ direction relative to FINO1. The total installed capacity is 200 MW consisting of 40 turbines with rotor diameters of 116 m.

At the beginning of 2019, the Merkur (MRK) wind farm was commissioned. Merkur is the closest farm to FINO1 at relative distances between 1.4 and 8 km and with a relevant azimuth sector of 235–45∘. MRK consists of 66 turbines rated at 6 MW with 150 m rotor diameters and a total capacity of 396 MW. The second part of the Borkum Riffgrund project, the Borkum Riffgrund 2 (BR2) wind farm, started operating in mid-2019. It is the largest wind farm in the area with 448 MW capacity consisting of 8 MW machines with 164 m rotor diameters. The relevant directions to FINO1 are 80–250∘ at distances between 9 and 13 km. Finally, in 2020 the extension of the Trianel Borkum project, the Trianel Borkum 2 wind farm, started operating, but it is not in the scope of this study as we use data up to 2019.

Most of the information (e.g., construction/commissioning dates, geographic locations) shown here are gathered from publicly available sources which could not be fully verified. As is also explained in the following section regarding the data, some uncertainties exist due to imprecise information on dates, coordinates, maintenance logs, etc., which led us to be more conservative on the data filtering and to consider them in the interpretation of the results.

In this section we present the measurement equipment used, the data filtering and calibration approaches used, and the post-processing methods applied to obtain the results shown in the next section. All data were obtained through the RAVE database which is publicly available under user agreements. The data used in this study were from the period 1 January 2011–31 December 2019.

The metocean data were collected from the FINO1 platform. The data were provided as 10 min statistics with corrections and calibration values applied as instructed by the providers to compensate for effects like mast shadowing (see also , and ). As these data are commonly used in the research community, we do not discuss all the sensors available and the specifics of the setups here. A thorough overview of the database and data quality considerations can be found in . In the study of , a comprehensive database of aggregated fitted distributions for different quantities is presented for the period 2004–2016. These data have been also used for examining the influence of stability on the loading spectrum of the Alpha Ventus turbines , as well as for the validation of aeroelastic farm-wide simulation tools .

For the wind conditions, we used the cup anemometers mounted at heights from 30 to 100 ma.s.l. (above sea level) at increments of 10 m. The wind speed and turbulence intensity (TI) measurements were taken from the top anemometer at 101.5 m. This is higher than the 92 m hub height of the Alpha Ventus turbines but was selected since there are fewer mast shadowing effects in the directions of interest more information on this can be found in. The data were corrected for shadow effects and calibration according to communication with the data providers and as explained in . The wind shear was calculated from all available heights assuming a power law exponent. The shear exponent α was fitted to the data by minimizing the least squares difference with the measured values. The wind direction statistics were obtained by the wind vane at 90 m with the relevant corrections applied as discussed in . The temperature and pressure data were also obtained as 10 min statistics. We used the thermometers on the mast at 34 and 52 ma.s.l., and the pressure was obtained by the barometer at 21 ma.s.l. The oceanographic data used here were also 10 min statistics and included sea surface temperature from the buoy and significant wave height (Hs) and peak period (Tp) from the radar mounted on the platform.

The turbine data used come from the AV4 turbine which is manufactured by Senvion and has a rated power of 5 MW, a hub height of 92 m, and a rotor diameter of 126 m. It is located at 92∘ azimuth relative to FINO1 at a distance of 3.2 D. The data were provided at a 50 Hz sampling rate. For the tower base loads, we used the strain gauges located above the transition piece and combined them with the nacelle yaw position signals to derive the fore–aft loads. Moreover, from the SCADA signals, we obtained the nacelle yaw position, blade pitch angle, generator power, and generator speed. For the nacelle yaw position sensor, a slow drift over time was observed. This was corrected by using events in which the turbine was not operating and the nacelle was rotated 360∘. We correlated the known locations of the strain gauges around the tower with the nacelle yaw signal in order to derive corrections of the offset and compensate for the sensor drift.

In order to filter the metocean statistics data we applied multiple criteria. The quality flags provided by the database were used. Data blocks with availability of less than 90 % for the 10 min period were rejected. Appropriate thresholds for minimum, maximum, and standard deviation values were implemented as an additional filtering criterion. More specifically, for the wind speed we accepted measurements with mean values between 1 and 30 ms-1, minimum value above 0.5 ms-1, maximum value below 40 ms-1, and standard deviation below 40 %. Similarly, for TI we accepted values between 1 % and 40 %. For the high-resolution turbine data, we applied the same filters for availability and statistics as before. Additionally, we only accepted events for which the nacelle yaw position and the met mast wind direction had a difference smaller than 3∘ to avoid including events for which the turbine was misaligned with the mast. Similarly, we rejected events for which the nacelle position signal's standard deviation was higher than 5∘ and events for which the difference between the maximum and minimum values was higher than 5∘ to avoid including the effect of yawing in the calculated loads. Furthermore, there were many periods in which the turbine was operated with curtailed power which affects loads (see, for example, ). We filtered out these periods by applying a filter involving combined thresholds for pitch angle, generator speed and power, and wind speed to make sure that the machine is operated invariably in full power. Turbine data from 2019 were not available to us at the time of this study.

For the post-processing of the loads, we used the rainflow algorithm and Miner's rule with a Wöhler exponent of 4 and a reference cycle number of 600 to derive the 1 Hz damage equivalent loads (DELs). Due to the non-disclosure agreement with the turbine manufacturer, the DEL values shown are normalized with values close to the maximum. For the wind speed distributions, we binned the data and fitted the Weibull parameters k and C using least squares. In all the plots that include bands, they represent the 15th and 85th percentiles. Finally, we do not show the scatter but only the mean value and the band to avoid congestion and improve clarity for the reader.

Regarding the periods of measurements, we decided to use full years for all the quantities. This was done to facilitate the analysis of the wake effects which is the main objective of this study and also to avoid bias due to seasonal variability. To achieve this, we rejected measurements that had large continuous gaps in the year and also years with less than 80 % availability in total. In other analyses that are based on binning (e.g., directional or wind speed bins), we accepted only bins that included 25 points or more to avoid statistical bias.

There are some known sources of uncertainty affecting the results shown here. We do not have access to the service log of the turbines; hence, we are not aware of maintenance or replacement activities on the turbine components (or measurement devices) that might have influenced the results. We tried to compensate for these with the filtering approaches mentioned earlier. We also do not have access to operational information of the neighboring farms in order to know when the farms might have stopped operating or when they were curtailed, which is expected to have an impact on the wake effects. Finally, availability varies significantly from sensor to sensor. Especially in turbine data for which the filters required a combination of sensors, the resulting availability was much lower.

Another known uncertainty comes from the measurements relevant to the 30–190∘ directions. There, FINO1 is in the direct wake of Alpha Ventus. Thus, we should not consider them as free-stream directions and should take into account that wind speeds are probably underestimated and TI is overestimated compared to the real free-stream wind speeds seen by Alpha Ventus in this sector. Nevertheless, this sector is useful for our analysis as there have been no changes in the surroundings since AV started operating. Thus, this sector can be used as a validation sector influenced only by the interannual variability and the measurement uncertainties but not by wake-related effects.

The results from FINO1 and the AV4 turbine will be presented in two sections. The first is dedicated to metocean conditions and the second to the turbine's response. We are going to analyze these in terms of azimuth directions, as shown in Fig. . This figure can be used as a reference for the reader for the positioning of the farms and the azimuth sectors relative to FINO1, which is used as the origin. Additionally, we use a color code with shades of blue for the years when Alpha Ventus was the only operating farm in the area (2011–2014) and shades of red for the years 2015–2018 when the TB1 and BR1 farms were also operating. The yellow color refers to the year 2019 when MRK and BR2 wind farms started operating too.

We will focus the analysis on the 200–320∘ sector as it is the relevant one for investigating the inter-farm wakes. In the 30–170∘ direction the mast measurements are directly influenced by the wakes of AV. The directions around 180 and 360∘ are influenced by the mast's own shadowing as previous studies have also shown see, for example,. Hence, we decided to exclude these sectors which also have a low probability of occurrence.

Having a fully equipped offshore measuring platform located near a farm and capturing data for long periods while the surroundings are changing is rare and very beneficial for assessing offshore wind farm wake effects. Nevertheless, still a lot of uncertainties come into play, as explained in Sect. . The directional results are subject to uncertainty as the sectors of influence of the neighboring farms are not strict. This is due to possible errors in the exact locations of the turbines and the measurement equipment, but it is more significantly influenced by the wake expansion itself and the possible meandering of the farm wake. Moreover, this could also be influenced by a possible yaw misalignment of the upstream turbines. Additionally, as offshore farms are becoming larger, reaching several kilometers, and turbine wakes are not linear features, a single point of measurement is probably not enough to fully characterize the inflow that could be varying across the wind farm.

Another important aspect relevant to this study is the consideration of atmospheric stability classification. It is well established by research that the wake effects (both at turbine and farm level) are directly correlated with stability. In this study, we decided not to add this dimension to the data processing as we focused on the analysis of the results cumulatively per year. The temperature difference results shown are an indicator that the annual stability distributions are similar over the different years. Moreover, the boundary layer is more affected by the mixing taking place through the interaction with the upstream farms, making it difficult to characterize atmospheric stability based on turbulence intensity or vertical shear. Common stability measures like the Monin–Obukhov length based on similarity theory might not be applicable due to the wake (not ideal free-stream) conditions. The chosen approach allows us to examine the cumulative effect of the inter-farm interactions on the mean annual conditions experienced by the turbines. This is of practical interest when assessing or simulating the conditions and performance of a turbine at the site.

The findings here show the dependency of the perceived wake effects on the distance and size of the farms. We summarize here some of the points we observed that need more investigation. The operation of the farm BR2, located directly upwind of BR1, did not seem to affect further the measurements at FINO1 both in terms of wind speed and TI. Furthermore, the wake-induced turbulence from the closest farm, MRK, was found to be more sensitive to wind speeds. This could be correlated to the distance and also to the fact that the machines are larger than the other farms examined and operate with a larger variation in the thrust coefficient. Additionally, the characterization and modeling of the vertical wind shear, especially when the distances between the farms are smaller, have to be evaluated. In general, more research is needed to understand the correlation between wind farm size and layout, turbine capacity and size, and their effect on the strength of the wakes, the distance they can propagate, and their influence on the local microclimate of the downstream farm.

Another factor to consider is the weighting, in terms of probability of occurrence, of wind speeds and directions when assessing the overall effect of the inter-farm interactions. As seen from the wind rose and the Weibull distributions, the wind speed and directional bins where the wake effects are stronger are the most probable ones. This means that the impact they have on lifetime loading and revenue is expected to be more significant when calculating the aggregated values. This holds true for the specific site used in this study but shows that in general considering this weighting is important in the cases when inter-farm wakes are accounted for in decision-making for processes like initial siting, maintenance planning, end-of-life strategies, and operational and bidding strategies.

To facilitate further research on this topic, it could be very useful to have measurements from the inflow of both the upstream and downstream farms, ideally in a distributed manner. Moreover, at least some information such as operational status or power production from both interacting farms (upstream and downstream) would be very useful. Another aspect that could be worth investigating in future scenarios, with higher wind farm density and even closer spacing in favorable sites, is the coordinated operation of wind farm clusters. It may be that, by adjusting sector-wise the operation of the upstream farms according to their size, layout, and relative orientation, one could increase the overall power production and even reduce the overall structural loading.

In the present work we used metocean and turbine data to evaluate the effects of the inter-farm interactions at the offshore site Alpha Ventus. The nearby measurement platform FINO1 allowed us to examine how the local conditions have changed from the period when AV was the only farm in the region to the later period when four larger wind farms started operating at distances varying from 1.4 to 9 km. The data were analyzed on an annual basis and with regards to directions and wind speeds.

Systematic changes in the flow conditions and the turbine response were found that can be attributed to wind farm wakes. This was validated by the agreement of trends and magnitudes in the values examined for the two distinct periods, as well as the directional results. Moreover, the general atmospheric conditions were found not to be changed over the years in terms of temperature or pressure.

The wind speeds were found to be reduced, with the shape parameter of the fitted Weibull distributions being reduced by 15 % on average. For a theoretical 5 MW wind turbine this translates to 15 %–20 % reductions in AEP. The increase in measured turbulence intensity was found to be highly correlated with the distances between the farms, reaching a maximum mean increase of 120 % for the closest farms (1.5 km) in below-rated conditions. The vertical wind shear as expressed by the fitted power law exponent was found to be reduced, although, especially in the sectors related to the closest farms, it seemed to deviate from the power law approximation. The oceanographic measurements suggested no correlation between the presence of farm wakes and the values of significant wave height and wave period.

Turbine measurements were used to investigate how the changed flow conditions are experienced by the turbine of Alpha Ventus closest to FINO1. The tower bottom fore–aft loads were influenced by the closer wind farm reaching an increased level of 30 %–40 % for below-rated wind speeds. Both generator speed variation and blade pitch activity were found to be increased as well, even in sectors where loads did not change. This suggests that inter-farm wake effects have to be considered for all the systems and components of the turbine and not only for the structural loads.

The measurement results presented here show the possible technical and financial impacts of inter-farm wakes which have to be considered when planning the siting of wind farm clusters. Moreover, it shows the need for analytical and simulation models that will be able to reproduce these effects and take into account the layout, sizing, and relative distances of neighboring farms.