Saturday, January 31, 2009

Power per unit land area of windfarms

As I've said in SEWTHA (the book), the average power per unit land area of a typical well-located onshore windfarm in Britain is about 2 watts per square metre. (Or 2 MW per square km.) This number is my estimate of the best that can be done in Britain, and, as I explained in the appendix, the theoretical power per unit land area doesn't depend very much on the size of the turbines used, because bigger turbines are spaced further apart.

I'm always keen to check my numbers and update them if necessary. Today the the New Scientist interview with James Lovelock prompted me to write a blog article giving explicit data from a real windfarm. James Lovelock says "to spoil all the decent countryside in the UK with wind farms is driving me mad. It's absolutely unnecessary, and it takes 2500 square kilometres to produce a gigawatt - that's an awful lot of countryside." That's a power per unit area of 0.4 W/m2, which is 5 times smaller than my 'best possible' 2 W/m2 estimate.

Let's look at some data. I picked a random windfarm in Britain with ten 27m-diameter turbines: Blood Hill windfarm. The helpful REF website gives exact energy-generation statistics for several years. The collage at the top of this page shows the data, and a map of the site, which is very close to the sea in Norfolk. What's the area of this site? The blue grid lines are 1km squares. I'd say the ten turbines 'occupy' about 0.3 km2 (including an appropriate strip of land around the turbines, where similar size turbines could not be placed). The average output of the ten turbines is 420 kW. So that is a power per unit area of 1.4 W/m2.

If anyone would like to repeat this calculation for real data from other windfarms around Britain or the world, we could collate the answers in the open-source wiki for Sustainable Energy - without the hot air.


Brendan said...

Hi David,

I think the REF as a data source is unreliable ... they are seen within the industry as an anti-wind energy lobby group, so data sourced from them may have the same bias,


Heather said...

Brendan - doesn't your argument strengthen David's - if an anti-wind group says that the farm gets three time's Lovelock's estimate, then the real number should be *at least* three times that efficiency...

David MacKay said...

I know that REF are perceived to be anti-wind, but please go and look at the data, and identify bias, instead of just libelling REF. I have looked at their data and I think that their data is factual and trustworthy. Please point me to another better source of data! Feel free to contact the owners of Blood Hill wind farm and see if they dispute the numbers reported by REF. I will happily eat my keyboard if they do. Just for clarity, the numbers from REF that I am here holding to be trustworthy are factual statements about the number of MWh generated by each windfarm. It would be extraordinary if the REF were faking these factual numbers.

Brendan said...

Hi David,

I doubt they are faking the numbers either. But I am not sure the Bloody Hill wind farm represents the "average" UK wind farm. From the data looks like Bloody Hill has a load factor of 18%, whereas the average onshore wind farm has a load factor of 27%.

(from Government Statistics:

That said, there is an argument that we've already used alot of the best sites, so 27% is not a realistic number at large wind penetrations.

I also understand you are trying to estimate a per unit area number, which load factor says nothing about.

Congrats on your blog/book, I enjoy reading your posts,


Andrew Smith-Gibbs said...

It's a common ploy by the anti-renewables lobby, such as REF, to say that wind turbines "take up" all this land, whereas arable and livestock farming can occur on all the land around and in between the turbines, so that very little productive land is actually taken out of farming use.

Elsewhere, say in the Welsh mountains, the land isn't used much anway. With around 18 million hectares of land available for agriculture, and plenty of mountains too, Britain has a huge onshore wind resource. And as for offshore, the 25GW from the Crown Estate's Round 3 is only just a beginning: there's an awful lot of windy North Sea out there.

As Brendan's pointed out, Blood Hill is a good choice if the agenda is to deliberately underestimate the wind generation from current wind farms, and that is a typical REF ploy.

A lot of windfarms have had planning permission refused at sites that would be expected to have high capacity; furthermore, development of onshore wind in Northern Scotland has been held back by a temporary lack of transmission capacity, so there are good solid reasons to believe that the capacity factor will hold up for quite a lot more GW of onshore yet.

In addition, we typically get a higher capacity factor from offshore, so the overall capacity factor for wind is likely to increase, rather than decrease, from its current level.

colinpalmer said...

I noticed the same numbers and have written to New Scientist - remains to be seen if they will publish the letter. My numbers suggest a higher power density of around 8MW per square km. This is based on 2MW turbines with 80m diameter and 500m spacing (roughly 6 times diameter.)

This of course is rated capacity. As wind farms in the UK run at 30% to 40% capacity factor, the 'equivalent' when compared to higher capacity factor conventional plant (say > 80%) is still 3 - 4MW per square km.


Colin Palmer
Wind Prospect Group

Paul said...

I would perhaps ask someone like Dale Vince of Ecotricity (he has a relevant post on is blog) for a set of figures to compare to the ones provided by the inappropriately named 'Renewable Energy Foundation' - no slander or libel intended, but for those that look beyond the name - it is obvious there is bias.

Andrew Smith-Gibbs said...

Hi Paul,
if one wanted to pick the other extreme, to counter one case of cherry-picking by doing the same in the other direction, then one might look at Burradale, with a typical annual capacity factor of the order of 50-60%

pmcc said...

Taking a new windfarm site near my house in central Scotland, Greenknowes, the following data is available:

"...broadly crescent shaped, about 4.7 kilometres long and varying in width between 200 and 500 metres...". Let's take 750 metres as the width, to provide enough separation between turbines for a future adjacent windfarm.
Area = 3.525 km2
No of turbines = 18
MW peak = 27
Anticipated load factor = 30%
MW anticipated mean output = 8.1
So, MW mean output per km2 = 2.3

The spacing factor above is somewhat arbitrary, because the site is on a high ridge and additional turbines are unlikely to be built in the glen itself. A more reasonable 'spacing' factor would be to estimate windfarm width as the gap between ridges. Looking at the map a reasonable figure for this would be 2km, giving MW per km2 of 0.86.

A small amount of googling turned up the data below data for Scottish Power wind sites. Map grid references can be found at for estimation of land area.

Site / MW capacity / Year operational / Load Factor:
Barnesmore 15 1997 15 1997 33%
Beinn an Tuirc 30 2002 30 2002 35%
Black Law I 97 2005 97 2005 30%
Callagheen 17 2006 17 2006 32%
Carland Cross (45% owned) 3 1992 3 1992 28%
Coal Clough (45% owned) 4 1992 4 1992 26%
Coldham 16 2005 16 2005 29%
Corkey 5 1994 5 1994 37%
Cruach Mhor 30 2004 30 2004 22%
Dun Law 17 2000 17 2000 26%
Elliots Hill 5 1995 5 1995 37%
Hagshaw Hill 16 1995 16 1995 30%
Hare Hill 13 2000 13 2000 41%
P&L (50% owned) 15 1992 15 1992 24%
Rigged Hill 5 1994 5 1994 37%
Black Law II 27 2006 27 2006 25%
Beinn Tharsuinn 29 2006 29 2006 29%
Total (April 2007) 344 30%

Paul said...

Hi Andrew,

Well - that is indeed a very high annual capacity! You are right - that best case scenario should counterbalance the cherry picking of the REF ;)

David MacKay said...

People, people! The idea that REF is cherry-picking is ridiculous! The REF publishes data for every single wind farm in the country! The selection of Blood Hill was done by me, and the way in which I chose it was essentially at random: I was teaching about windturbines and wanted to work out the power per unit area of a windfarm with a decent number of turbines of diameter 27m. So I hunted for a farm with 10+ turbines of that diameter. Please feel free to repeat the whole calculation for other windfarms. Don't just report the load factor, since that does not reveal the power per unit area. Don't rely on predicted outputs: please use real data. Please stop ignorantly attacking REF's data. The only responsible way to attack their data is to point out what is wrong with it, and as I already said, I will eat my keyboard if you find anything wrong with it. They publish the energy produced by every windfarm in the country, and it is absurd to ignore these factual data for some ad-hominem reason.

David MacKay said...

When I discuss the power per unit area of windfarms, there's always someone who says "ah, but you can use the area between the wind turbines for farming!" Yes yes yes, do I have to say that every single time I mention wind farms? This reminds of this hilarious New Scientist article which says "the US could replace all its cars and trucks with electric cars powered by wind turbines taking up less than 3 square kilometres" - hahahahahahaha! - which is the sort of helpful answer you get when you take into account only the literal footprint of the turbines.
Yes, the gaps between the turbines can be used for other stuff; but people still need to know the facts about the land area that must be associated with wind farms if they are to make a difference, which is James Lovelock's point, and is what this post is about.

Paul said...


From the operators site:

"Blood Hill Wind Farm is our smallest development. It can generate enough power to supply over 1000 homes, displacing the emission of 2542 tonnes of carbon dioxide annually.

The wind farm has been operating since December 1992 and took just under four months to construct in a project involving local contractors. In 2005 it saved around 15 tonnes of sulphur dioxide and five tonnes of oxides of nitrogen from being released into the atmosphere.

The site covers an area of 3 hectares, but less than 1% of this land is taken up by the turbines and access tracks."

I never questioned the figures for Bloodhill though - just the REF, and your reference of them.

The REF report (funded by Mr Vincent Tchenguiz and produced by Oswald Consultancy Ltd on behalf of the REF) you used to not cherry pick your data from for the Bloodhill site goes from 2002 - 2008.

The Bloodhill site was already a decade old when that report began.

Perhaps it would be worth looking at a more modern installation of 10+ devices of that diameter, for the sake of accuracy, or perhaps just for the sake of argument? :)

David Pollard said...

In defence of James Lovelock's estimate...

He says it is unnecessary to "spoil all the decent countryside in the UK with windfarms..." So he seems to be referring specifically to maximal onshore use. (Hence comparisons with offshore sites are not appropriate. Note also that Dave Cameron almost installed a chimney turbine not so long ago with a potential yield of possibly 0.5; 'Not A Good Thing' is the appropriate technical term in these parts I believe.)

Actual production at a typical commercial site has been 1.4 W/m^2, and this was presumably carefully sited. Extensive use of onshore wind, besides possibly including a few better sites, would have to include a significant proportion of less optimal sites. And, besides less favourable winds, the "appropriate strip of land around the turbines, where similar size turbines could not be placed" would also be larger in many instances if enough onshore farms were built to supply a major part of demand. (Some sites would be inconvenient, and others would have only one or two turbines, so would have a relatively larger surrounding strip.)

But another aspect has been almost entirely ignored: the cost of providing energy when the wind isn't blowing. Perhaps the best that could be done would be to use pumped hydroelectric storage, with an efficiency each way of 80%; maybe 50% energy efficiency overall when transmission losses and capital/maintenance costs (energy) are taken into account. At 1/3 capacity factor, if the supply is to be continuous, for every kWhr supplied directly another 4 have to be put into the storage system of which only 2 are delivered.

My rough sums suggest a 2:3 ratio between delivered continuous and generated power. Even then, additional provision has to be made for the times when calm extends beyond the capacity of the storage system.

These factors seem to me to explain the discrepancy between 'best case theoretical peak' onshore of 6 W/m^2 and Lovelock's estimate of 0.4 W/m^2 if, as it seems, he is referring to widespread deployment, which would lead to diminishing returns, with provision to meet continuous demand.

Personally, I can see how he came to the view that Gen 4 fission and thorium is the way to go for energy generation, even without considering the opportunity this provides to dispose of plutonium stocks and to transmute long-lived waste.

Now, does anyone know who is working on microwave pyrolysis? It looks as though the biochar from domestic and agricultural waste is commercially viable in terms of reduced fertiliser use alone, and it's said to have an energy yield of 2 to 5 through increased food production. If microwave pyrolysis will work with intermittent power, this looks to be a neat way to put to use all that cheap but erratic wind energy; with syngas, biodiesel and chemical feedstocks as a bonus by-product.

James Lovelock's appraisals seem to be not far wide of the mark.

Martin Williams said...

As far as I can make out, a 3MW wind turbine occupies - at most - about 400 square metres. The rest of the area occupied by the wind farm can be used for agriculture as it was before the wind farm was installed. If you assume the actual output of a turbine is about a third of its rated output we have 1MW generated from about 400 square metres. 2500 watts per square metre.

This figure compares well with the land area occupied by a conventional coal station, eg Drax, where about 3.25 square kilometres produce 4GW - about half that of the wind turbines! If you include the area of the coal mines needed to feed this station the figure drops even lower.

It is clearly unfair to assume, as seems to have been done, that the land between the turbines is unusable for anything else. In the majority of cases the arrival of the wind farm has only a tiny impact on the agricultural use which can carry on as before.