Don’t build downwind, chump

Because wind turbines take energy from the air that flows over their blades, there is the obvious possibility of wake effects, i.e. where downwind turbines experience lower wind speeds. (The power at the turbine is related to the wind speed by a cubic function, so a small decrease in wind speed could lead to a large loss of power.)

Bearing in mind the incipient industrialisation of the North Sea, I wondered what the scale of such effects might be. Instinct said that they would be negligible. Are they?

Wind turbines are well spaced within farms. The wind farm visible from the beach at Gt Yarmouth (Scroby Sands) is fairly old and small. Its turbines are 60 m tall and have 40 m blades. Their files, as you look from shore, are 350 m apart, and the ranks are 500 m apart. These distances, a casual observer might surmise, are chosen to minimise or eliminate interference between turbines, and that the layout is chosen to favour performance from the prevailing wind direction. So you might think that if the wind blows directly from shore along the line of two turbines 500 m apart (about 6 turbine diameters), that the second turbine would suffer no performance loss.

Searching Google Scholar for an answer to this question I came across Nygaard et al 2020. The first thing these authors present is a within-farm wake model. The previous standard apparently represented a wake as an expanding regular cone, whereas a better fit to real-world data was obtained by Nygaard et al using a model where wake expansion slowed down over distance. Anyway the relevant observation for me was that in the real world (Westermost Rough wind farm), second and subsequent turbines only had 80% of the power of the foremost turbine if the wind was blowing directly along the line (ranks at Westermost Rough, like at Scroby Sands, are 6 turbine diameters apart, which for turbines with a 154 m diameter, means they are 900 m apart).

That sounds quite a large drop in performance, but the wind is not likely to be blowing exactly perpendicular to the ranks or files of turbines. What about cluster wakes: the effect of one wind farm on a completely different wind farm? One might naively think that if the power loss at 6 turbine diameters (c. 900 m in the case of Westermost Rough) was 20%, that when you start putting clear blue water between them the effect will end up being negligible.

Well, Nygaard et al have data on this too. There is another wind farm fairly close (15 km) to Westermost Rough: Humber Gateway, a set of 73 turbines with a rotor diameter of 112 m. That makes Westermost Rough 130 (15000/112) turbine diameters from Humber Gateway. What happened when the wind blew through Humber Gateway before it reached Westermost Rough?

This is the surprising (to me at least) result:

Figure 3 from Nygaard et al, with original legend

Humber Gateway is to the south, & Westermost Rough is the square with some turbines missing from the centre. The graph shows the power ratio between the two end turbines as the wind direction changes. Real world data is orange dots, their emulations are the lines. Of particular interest is where one and not the other is in the Humber Gateway’s cluster wake: a 30% loss of power results.

Nygaard et al go on to model blockage (the upstream effect of wind turbines on wind speed), which seems to be a minor problem compared to wakes, & then they combine the two effects to try to get a better estimate of wind speeds at turbines. They point out that neglecting wind turbine interactions, and even interactions between different wind farms, will lead to overestimation of energy production.

Conclusion

Presumably as the North Sea fills up with bird munchers, everyone will want their farms to upwind of their competitors.

A snap of a casualty on Gt Yarmouth North Denes taken about a year and a half ago. Scroby Sands wind farm is barely visible on the horizon. It is, however, close enough that the juxtaposition of the two were rather suspicious, in my eyes, at least. I think it’s a female sparrowhawk, but I didn’t flip it over to check.

Reference

Nygaard et al is available here.

5 Comments

  1. Funnily enough, I can’t remember anyone in Government, mainstream media, wind turbine companies, “environmental” pressure groups or anyone else pushing wind turbines at us, mentioning Nygaard et al, and the potential negative implications for the great claims being made on behalf of offshore wind.

    I’m sure the wind turbine companies themselves must be very well aware of it, on the other hand, yet the seem to be keeping quiet. Funny that.

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  2. There’s the memorable image of the wake at Vattenfall’s Horns Rev Offshore Wind Farm, Denmark:

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  3. I always thought that there needed to be 10D spacing to stabilise the flow downstream of obstructions. That is what it is for orifice plates in compressible fluids. The data you analysed indicates that this rule of thumb seems correct.

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  4. It seems to me that any rule governing the required spacing of wind turbines not only has to offset the downwind turbulence caused by upstream turbines but also the loss of energy within the wind; energy extracted from the wind by the upstream turbines. Or is the turbulence in the wake caused by this extraction? I seem to recall that no more than a third of the energy within the wind intersected by the turbine blades can be extracted.

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  5. Alan, the Betz limit is at the maximum value of 4a(1-a)^2 where a is the fractional decrease in wind velocity at the turbine. It maxes out at 0.59 ish when a = 1/3, which is when the wind speed has been reduced by 2/3. But I don’t know how well this works in the real world.

    Chris, I suppose the spacing used is a compromise between the available area and the wake effect. If there are fewer turbines in the same space, each will perform better, but additional turbines might still be profitable.

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