# How many square kilometres of offshore wind farms would be required to replace the closing of a 4GW nuclear power station

A large nuclear power plant has a capacity of 4GW and a capacity factor of about 90%.

How much installed capacity of wind turbines with a capacity factor of 40% would be required to match that output?

Here is my attempt -

From the document "Capacity Densities of European Offshore Wind Farms" Capacity density of a wind farm is defined as the ratio of the wind farm’s rated capacity to its ground area. Capacity density is expressed in megawatts per square kilometer.

Average Europe capacity densities are in the range 5.0 - 5.4 MW/sq km

40% capacity factors from offshore wind would be considered a good result.

Taking these two values, the long term average power output from each square kilometer of offshore wind would be 2 - 2.16 MW

To match that large nuclear power plant output of 3,600 MW would require 1800 - 1667 sq km. (694 - 640 sq miles)

Approx 1,700 sq km (656 sq miles) area to match one power station seems a lot. That's more than the area of greater London (about 1,600 sq km)

Am I correct, or what have I done wrong?

• I am wondering if the decommissioning land use is being added to the estimated output of nuclear power plants? You need to add the number of years following the; what 25 year? use of the plant, until the land is safe for any other use, and compare this with the space taken up by wind farms which can be dismantled within weeks if necessary. Aug 7, 2019 at 13:12
• That 4GW, is that thermal (GWt) or electric (GWe) capacity? Do we actually have powerplants with 4 GWe?
– user2451
Aug 7, 2019 at 13:47

Your figures are a bit out, but broadly in the right area. Using observed figures for the numbers you've estimated, I get 1,246 km²

90% capacity factor for nuclear is probably optimistic, but some jurisdictions have achieved it. The global average in 2018 was 81%, but that's an overestimate, due to the way that reactors on long-term shutdown are handled.

Your offshore windfarm power yields per unit surface areas are a bit pessimistic. From calculations I did elsewhere, Denmark's offshore windfarms yield 2.2-3.3 W/m², averaging 2.6. Germany's yield 2.1-4.1, averaging 2.9. And the UK yields 1.4-5.7, averaging 2.6.

Using a 4GW nuke, 81% capacity factor, and 2.6 W/m², we get 1,246 km². Or roughly, a square that's 35.3km along the side. That's really not much - the sea is a very big place - and remember, almost all that sea is just area between turbines - very little of the seabed would be occupied. If we take a 45% capacity factor for offshore wind, it's an installed capacity of 7.22 GW, or 722 turbines each at 10 MW capacity. This is an eminently achievable engineering task.

Offshore wind does also have the virtue of being much cheaper now, per unit of electricity delivered, than nuclear; it also gets delivered on time and on or under budget!

Current high-end windturbines (WT) produce about 4.5 MW while being about 240 m high (top of rotor tip) and with a rotor diameter of 150 m.

When it comes to the distance between the WT, rule of thumb says 5 times rotor diameter in main wind direction, 3 times orthogonally, leaving us with 750 * 450 m per WT, which is about 0.33 km². So you can (if you place the WT rather conservative, usually rule of thumb is violated by 25 %) put 3 WT on a square kilometre, giving you 13.5 MW.

4000 MW / 13.5 MW/km² = 296.3 km² - which is not that much. Even if you consider your capacity factor (which to me seems a bit conservative) you end up with about 750 km² of windfarm.

Also, please consider that ideally, before replacing current power plants, the demand for energy should be reduced significantly and the usage should be more efficient. Only then renewables are supposed to meet all demands - something many people tend to "forget".

• I took my figure of 5 - 5.4 MW/sq km from an analysis of actual wind generation operating in Europe. Are there any installations actually achieving 15.5 MW/sq km? That's three times the European average. I understand that interference causes efficiency losses with closer spacing. My capacity factor was obtained by rounding up the average of 37% for European wind in 2018. (windeurope.org/wp-content/uploads/files/about-wind/statistics/…) Jun 26, 2019 at 8:50
• The European average takes into account WT built almost 20 years ago - those thingies have about 450 kW output. And since you're talking about replacing power plants, the WT would have to be built, and 13.5 MW/km² is what can be achieved currently.
– Erik
Jun 26, 2019 at 8:56
• As an example of what is possible, Scotlands brand new Hywind wind farm has a 65% capacity factor (so far, it's early days) and is generating 30MW from 5 turbines, meaning each is 6MW with a 150m rotor. This just about doubles the output relative to the answer by @Erik. Jun 27, 2019 at 4:57
• I disagree with reducing energy demand significantly. Energy is not evil. For example, converting the forest industry CO2 exhaust gases with hydrogen electrolysis + Fischer-Tropsch process to synthetic fuels would increase electricity consumption of the country where I live by 3x. Replacing coal with geothermal power would also increase electricity consumption. Electric cars also increase electricity consumption. Electricity consumption should go up, not down! Jul 9, 2019 at 15:19
• Why should it go up? Why always "more, more, more"? @juhist
– Erik
Jul 9, 2019 at 15:30