Andrew Mason said:
To supply the equivalent of 1000 1000 MWe power plants using solar cells (ie. which would replace one nuclear plant) how much area would you need to have covered in solar cells?
Here is a ball-park calculation:
solar irradiance: 1367 w/m^2 (this is the solar energy falling on the Earth's upper atmosphere divided by \pi R_e^2. Of course, you have to take into account that the Earth is rotating and you cannot capture solar energy at this rate for 24 hours. And even if there are no clouds, some of this energy does not make it to the earth. The average on a sunny day would be no more than a quarter of this or about 340 w/m^2. On average, 30% would be reflected by clouds, so this reduces it to about 240 w/m^2.
Solar cells convert sunlight to electricity at a rate of around 20% with present technology. So a 1m^2 high efficiency solar panel could supply about 50 watts of electricity, on average. To produce 1000 GWe, you would need twenty billion of these panels. One square kilometre is 1 million square metres, so you would need 20,000 square kilometres of panels. This is about 140 km x 140 km to supply the entire country's electricity needs. If one used roofs of buildings you would not need to use valuable land.
Of course you would want to distribute these panels around the country. If you had 1000 sites of 20 square kilometers each, you could do it. You would also need some way of storing the electricity. But it does seem workable. At a cost of $2 per watt, the cost of the solar panels would be $2 trillion dollars. The cost of installation and infrastructure might be another trillion. Given the way governments seem to be throwing money around these days, that almost seems cheap.
AM
Although this is in the right ballpark, there are some extra's. The first problem is that your price: $2 per watt, is per watt PEAK POWER. However, depending on your location, there is a ratio of about 1:3 to 1:6 between peak power and average power (due to variability in solar illumination, cloudiness, etc...). So although you are about right that you could have 50W per square meter on average (I think it is closer to 30 W with affordable technologies and in temperate lattitudes, but ok), you would need to install about 300W peak power per square meter to obtain 50W average.
The second problem is the storage of electricity. It plays on 3 levels:
- day/night
- cloudy week/sunny week
- summer/winter
Now, there are techniques such as storage pumping stations and so on, but these are not always geographically possible, have a certain price, and are limited in capacity. They could eventually take care of day/night (at serious extra cost of about $2 per watt BTW).
However, it would be more problematic to have the cloudy week/sunny week variability.
And the only solution to the summer/winter variation would be to *increase* the solar capacity such that you reach average consumption not averaged over a year, but averaged over the darkest winter period. Now, depending on location, that can be a factor of up to 4 or 5 (meaning, averaged over, say, a month, the solar intensity during the darkest winter month is 4 or 5 times smaller than averaged over the whole year, summer included).
This means that you have to over-design your solar power system by the same factor in order to provide still the average power needed during winter (and have an equivalent surplus production in summer, with which you cannot do much for the moment, but which you could eventually use to do things like hydrogen production or anything else).
You could of course say that you will find a "long term storage" technique, like production of hydrogen or whatever in the summer, so that you can use it in winter. But then you will run into efficiency problems, which will give you easily a similar factor. So in any case, if solar is to provide for the bulk of the electricity, you will have to over-design your system (and its surface, and its cost) with a factor of 3-5 as compared to "yearly average production" AND provide for serious extra buffer capacity for the short-time variations (day/night ; cloudy/sunny).
EDIT: btw, your $2 per watt peak are optimistic:
http://www.solarbuzz.com/ModulePrices.htm