We are familiar with assertions made about the number of homes which can be powered by new wind farms. The BBC never examines such statistics, presumably because it lacks the expertise to do so.
So - I'm handing over to an engineer with 40 years' experience who has done the necessary calculations.....
How many homes per turbine?
Reduced to its simplest form the calculation of how many houses can be powered by a wind turbine goes as follows:-
X = Number of houses
P = Rated power of turbine in kilowatts
E = Assumed availability per annum of power
Y = 8,760 = hours per annum of consumption
A = Assumed average power consumption of the house in kilowatts.
Note :- P. For turbines rated in Megawatts, multiply by 1,000.
A. This is the average electrical power consumption per household and is based on DECC figures of 4,700 kwh
E. This is the assumed percentage of rated power that the turbine will produce over the year and includes maximum and minimum figures averaged out. DECC use a figure of 0.3.
X = P x E x Y / A
For a 2-megawatt turbine we have
X = 2000 x 0.3 x 8760 / 4700
= 1,118.3 homes.
For simplicity, we can say that this calculation suggests that for every 1 megawatt of installed power we can expect to power 550 homes using average electricity. This says nothing about how many homes can be powered when there is no wind and does not say what happens when the weather is very cold and we need more power.
The 4,700 kilowatt-hours per annum is based on average consumption of an average house and assumes an average constant consumption of 536 watts. Actual instantaneous consumption varies greatly during the day when, for example one uses a kettle or an electric cooker.
The key figure is E because this reflects the actual annual power output of the turbine. In low wind areas this will be less than the assumed 0.3, whilst in high wind areas it may be more. For example, if we assume E as 0.25, the number of homes would be reduced to 930 homes.
When a huge offshore wind farm (consisting of a hundred turbines) was built near the North Kent coast, the operator, Vattenfall, said that its capacity was 300 megawatts. The project was launched with much publicity in September 2010, and we were told that it could power from 200,000 to 240,000 homes.
A more realistic figure can be obtained by using the method above....
The measured output is about 75MW so the load factor is 25%, not 30%.
Each megawatt of capacity services about 550 homes for load factor 30%.
So the number will be 550 x 300 x 25/30, or 137,500 homes.
The developer's figure, reported without comment by the BBC, is exaggerated by between 45% and 74%, depending on whether you use 200,000 or 240,000 as the claimed figure.