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Delegates are invited to meet and discuss with the poster presenters in this topic directly after the session 'How does the wind blow behind wind turbines and in wind farms?' taking place on Tuesday, 11 March 2014 at 16:30-18:00. The meet-the-authors will take place in the poster area.

Ajit Pillai The University of Edinburgh, United Kingdom
Ajit Pillai (3) F P John Chick (1) Vincent de Laleu (2)
(1) The University of Edinburgh, Edinburgh, United Kingdom (2) EDF Energy R&D UK Centre, , United Kingdom (3) The University of Edinburgh and EDF Energy R&D UK Centre, Edinburgh/London, United Kingdom

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Modelling wind turbine wakes at Middelgrunden wind farm


As part of a project to optimise offshore wind farm layouts, a comparative study of wind turbine wake models has been undertaken. Given that the optimisation tool seeks to quickly evaluate layout alternatives it is important to implement a fast, yet accurate model for accounting for wind turbine wakes. In this study, four wake models (three kinematic and one field model) have been applied to Middelgrunden Wind Farm outside of Copenhagen, Denmark to compare their relative accuracy and the computational times required. Middelgrunden wind farm poses a unique case study given the close spacing of turbines at only 2.4D.


In order to model the wakes at Middelgrunden it was decided to use a 10-minute averaged data set from 2001 to 2004, available courtesy of Virtual Wakes Laboratory and Middelgrundens Vindmøllelaug. As the wind farm is comprised of twenty Bonus B-76/2000 turbines placed along a single arc, the maximum wake effect would be expected when the wind is in line with this arc, roughly from the North [1]. Previous studies have looked at modelling the turbulence intensity and the wind velocity deficit at Middelgrunden using similar data sets, and therefore a similar approach in data selection was used to ensure that all turbines were operating, grid connected, and the wind was from the desired direction for each of the selected 10 minute intervals [1–3].

Since no met mast was deployed at the site during the operation of the turbines it was decided to use the anemometer reading at Turbine 1, the northernmost turbine, as the incoming wind speed to the wind farm. Using this wind speed measurement, the Jensen, Larsen, Ishihara, and Ainslie Eddy Viscosity wake models were implemented using the formulations available in the literature [4–13]. By implementing these models, the velocity deficits and therefore power deficits could be computed throughout the wind farm using the manufacturer thrust curve. Of the selected models, the Jensen, Larsen, and Ishihara models are kinematic wake models which parameterise the wake given an assumed shape of the wake expansion and the wake deficit. The Ainslie Eddy-Viscosity method is, however, a field model which requires solving the Reynolds-Averaged Navier Stokes equations with an eddy-viscosity closure. Since these wake models are all formulated as single wake models, a combination of a root-sum-square and weighting methods based on the fraction of the rotor plane that is operating within a wake were used to estimate the effect of superposition of wakes. By analysing the results for a range of incoming wind direction sectors it was possible to evaluate the models’ suitability for use at a site as densely packed as Middelgrunden as well as evaluate the computational time required for each model.

Main body of abstract

Wake models have previously not been compared at Middelgrunden; probably because the dominant wind direction is from the East and the turbines very rarely operate in wake affected flow (see fig. 1). Having said that, winds from the North result in an observable wake affect that does reduce the annual energy production (AEP) at the site. This reduction in AEP is not very significant for Middelgrunden; however, it does offer an opportunity to validate wake models for closely spaced turbines.

Figure 1: Wind Rose for Middelgrunden

Given that the first turbine is oriented at 357° relative to North, it was decided to look at sectors either ±30° or ±15° relative to this angle. For both of these sectors it was possible to compute the wake power deficit for each time and compute the average power output for each of the 20 turbines. These results were then compared to the actual output of the wind farm as given in the 10-minute averaged data.

Figures 2 and 3 below show the normalised average power produced from each turbine under the two scenarios. From this it can be observed that all the wake models correctly predict a decrease in the power produced relative to the first turbine in the arc due to the wake effect. For these two scenarios, the Larsen model was found to be the most accurate when considering the larger sector (12.48% RMS error), while the Jensen model was the most accurate for the smaller sector (8.09% RMS error). The smaller sector size was found to have lower RMS errors for each of the models compared to the larger sector size indicating the models are generally more suitable for the smaller sector size. The Jensen and Ishihara models showed the greatest improvement with their RMS errors decreasing 10.62 percentage points and 8.15 percentage points respectively. The Larsen and Ainslie Eddy-Viscosity models, however, only showed a 1.28 percentage point and 3.04 percentage point decrease.

Figure 2: Wake Deficit 357°±30°
Figure 3: Wake Deficit 357°±15°

Unfortunately, smaller sector sizes yield no periods of valid data from 2001-2004 and therefore it cannot be confirmed if this trend continues as the sector size decreases. The data selection does, however, play a key role in the levels of error of the wake models. In an effort to increase the data that was selected and allow for less uniform flow through the wind farm, the wind direction requirement was relaxed such that only the wind direction observed by Turbine 1 needed to be in the sector of interest. Compared to the stricter requirement, it was found that the ±30° scenario (fig. 4) had a reduction in RMS error for all wake models, while for the ±15° scenario (fig. 5) an increase in RMS error was observed for all the wake models. The inconsistency observed here is likely to be due to only 25 data points being selected by the ±15° scenario with strict constraints.

Figure 4: Wake Deficit 357°±30° (Relaxed Constraint)
Figure 5: Wake Deficit 357°±15° (Relaxed Constraint)

Selecting data in this manner was similar to the methodology used by Gaumond et al. [14, 15] and Crasto & Castellani [16] in their analyses of wakes at Horns Rev. Both of these studies found that the Larsen model best described the power deficit at Horns Rev. These studies also found that decreasing the sector size beyond ±15° led to higher levels of error. Smaller sectors such as ±5° or ±1° therefore led to an over-estimation of the wake effect and the power deficits down a single line of turbines at Horns Rev. Similarly in the present study, smaller sectors such as and ±10° or ±5° led to higher levels of RMS error.

The computational time was found to be directly dependent on the number of data points and therefore the data selection criteria. Within each study, however, the Larsen and Ishihara models were consistently the fastest with very little between the two. As expected, the implemented field model was consistently the most computationally intensive model requiring on the order of 5-10 times more time to run than any of the individual kinematic models. The relative speeds of the models are shown in the figure below.

Figure 6: Computational Time


This study explored modelling the wake effect at Middelgrunden wind farm. The study considered four different wake models, none of which are recommended for turbine spacing below 5D. This study has, however, shown that for turbines spaced at 2.4D all four models can give results on the order of 8-15% RMS error.

Though each wake model has different errors for each incoming wind velocity, the overall performance of the models was considered here. From this analysis it was found that the lowest RMS errors were on the order of 8% and achieved using either the Jensen or Larsen wake models depending on the data selection criteria. With the exception of one of the data selection scenarios, the Larsen wake model was consistently the most accurate. The Ainslie Eddy-Viscosity field model had RMS error values close to that of the Larsen model; however, they were consistently higher indicating that for the extra computational time there was no gain in accuracy. These preliminary results suggest that of the four models considered, the Larsen wake model constitutes the best compromise between accuracy and computational time regardless of the data selection criteria, and therefore would be best suited for implementation as part of a layout optimisation tool. Although the Ishihara model was often one of the quickest, it did consistently result in some of the highest errors, consistent with previous work at Horns Rev [11–13]. It is likely that the Jensen model required additional computational time compared to the other kinematic models due to the fact that it computes the fraction of the rotor plane that is within the wake of another turbine rather than including a radial term. It was also found that the computational time for each model could be approximated as a linear function of the number of 10-minute data points under consideration.

This work has, however, been unable to identify the most appropriate data selection criteria for these models. Further work should validate these models against additional wind farms and explore the data selection criteria at greater depth.

Learning objectives
This study seeks to compare four wake models at Middelgrunden wind farm in order to assess their suitability for use in a layout optimisation tool. From this study it was found that the Larsen wake model offers the best compromise between accuracy and computational time. This is an agreement with previous results from Horns Rev.

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