Quick Calculations on Solar Power

[Scottish Ninja]

I was hoping to get some useful information on solar power, as I was discussing the topic of energy sources with my friends today. One of them advocated solar power and other renewable energy sources; I pushed nuclear.

I decided to do some back of the envelop calculations, so that I could say something like "to replace all the nuclear power stations in the US with solar power, we'd need to cover the entirety of Arizona with solar panels". Well, according to what I got, I'm wrong. Very wrong. Which leads me to think I may have gotten my calculations wrong somewhere.

So, to start, I found on Howstuffworks, as an estimate, that one inch of solar panel generates 350 milliwatt-hours per day, and from the Energy Information Administration that the US produced 350 terawatt-hours in January, with 20% of that being from nuclear plants.

This gives us 70 terawatt-hours for nuclear power stations.

Next, I divided by 28 to get an estimate for per-day production; from this we get 2.5 terawatt-hours per day. I divided that by the 350 milliwatt figure to get approx 7.15e15 square inches of solar panels.

5280*12 gives me 63360 inches in a mile; squared, this is about 4 billion square inches in a square mile.

Dividing the previous figure of 7.15e15 by the 4 billion square inches gives me 1779269 square miles, about half the land area of the United States!

Is it really true we'd have to cover half the US with solar panels just to replace nuclear power alone? Coal is 50% of our power production; we'd need to invade Mexico to replace that. I knew solar power couldn't match other sources for power production but I didn't think it was this bad.

[Scottish Ninja]

Ghetto edit: I've figured out the problem with my calculations; stupid mistake as always. A terawatt is 10^12 watts, not 10^15, so I'm off by three orders of magnitude.

That puts the figure around 1800 square miles, which is somewhat less than the size of Delaware. This makes much more sense.

[Wyrm]

Next, I divided by 28 to get an estimate for per-day production; from this we get 2.5 terawatt-hours per day.

January has 31 days last time I looked.

Dividing the previous figure of 7.15e15 by the 4 billion square inches gives me 1779269 square miles, about half the land area of the United States!

A square mile of solar cells generates ~1405.0 MWhrs/day (350 mWhrs/day/sqin * (5280 ft/mi *12 in/ft)^2). Divide the total energy production in January (350 TWhrs) by the days in January (31 days) and by the production per 8035.4 sqmi. This is a plot of land 90 miles on its side.

Of course, we have this problem that on overcast days and at night, solar cells are just pretty black panels. Also, solar panels are still really really expensive per square inch. 285 square feet costs about $16,000, so the cost of this project is $12.5 trillion US. Ouchie.

[Kwizard]

(And manufacturing the solar panels introduces secondary problems like pollution from the process, and potentially, a lack of silicon on the large scale (not sure about that, since I haven't run the numbers), so even if it was enough energy for industry as well, these other problems shouldn't be ignored)

It's a few years away from any kind of commercial production, but isn't there a solar cell technology in the works which involves the use of titanium dioxide rather than the usual silicone-based substrate?

[TheKwas]

Monday view: Cheap solar power poised to undercut oil and gas by half
By Ambrose Evans-Pritchard
Last Updated: 11:31pm GMT 18/02/2007



Within five years, solar power will be cheap enough to compete with carbon-generated electricity, even in Britain, Scandinavia or upper Siberia. In a decade, the cost may have fallen so dramatically that solar cells could undercut oil, gas, coal and nuclear power by up to half. Technology is leaping ahead of a stale political debate about fossil fuels.

Anil Sethi, the chief executive of the Swiss start-up company Flisom, says he looks forward to the day - not so far off - when entire cities in America and Europe generate their heating, lighting and air-conditioning needs from solar films on buildings with enough left over to feed a surplus back into the grid.

The secret? Mr Sethi lovingly cradles a piece of dark polymer foil, as thin a sheet of paper. It is 200 times lighter than the normal glass-based solar materials, which require expensive substrates and roof support. Indeed, it is so light it can be stuck to the sides of buildings.

Rather than being manufactured laboriously piece by piece, it can be mass-produced in cheap rolls like packaging - in any colour.

The "tipping point" will arrive when the capital cost of solar power falls below $1 (51p) per watt, roughly the cost of carbon power. We are not there yet. The best options today vary from $3 to $4 per watt - down from $100 in the late 1970s.

Mr Sethi believes his product will cut the cost to 80 cents per watt within five years, and 50 cents in a decade.

It is based on a CIGS (CuInGaSe2) semiconductor compound that absorbs light by freeing electrons. This is then embedded on the polymer base. It will be ready commercially in late 2009.

"It'll even work on a cold, grey, cloudy day in England, which still produces 25pc to 30pc of the optimal light level. That is enough, if you cover half the roof," he said.

"We don't need subsidies, we just need governments to get out of the way and do no harm. They've spent $170bn subsidising nuclear power over the last thirty years," he said.

His ultra-light technology, based on a copper indium compound, can power mobile phones and laptop computers with a sliver of foil.

"You won't have to get down on your knees ever again to hunt for plug socket," he said

Michael Rogol, a solar expert at Credit Lyonnais, expects the solar industry to grow from $7bn in 2004 to nearer $40bn by 2010, with operating earnings of $3bn.

The sector is poised to outstrip wind power. It is a remarkable boom for a technology long dismissed by experts as hopelessly unviable.

Mr Rogol said he was struck by the way solar use had increased dramatically in Japan and above all Germany, where Berlin's green energy law passed in 2004 forces the grid to buy surplus electricity from households at a fat premium. (In Britain, utilities may refuse to buy the surplus. They typically pay half the customer price of electricity.)

The change in Germany's law catapulted the share price of the German flagship company SolarWorld from €1.38 (67p) in February 2004 to over €60 by early 2006.

The tipping point in Germany and Japan came once households twigged that they could undercut their unloved utilities. Credit Lyonnais believes the rest of the world will soon join the stampede.

Mike Splinter, chief executive of the US semiconductor group Applied Materials, told me his company is two years away from a solar product that reaches the magic level of $1 a watt.

Cell conversion efficiency and economies of scale are galloping ahead so fast that the cost will be down to 70 US cents by 2010, with a target of 30 or 40 cents in a decade.

"We think solar power can provide 20pc of all the incremental energy needed worldwide by 2040," he said.

"This is a very powerful technology and we're seeing dramatic improvements all the time. It can be used across the entire range from small houses to big buildings and power plants," he said.

"The beauty of this is that you can use it in rural areas of India without having to lay down power lines or truck in fuel."

Villages across Asia and Africa that have never seen electricity may soon leapfrog directly into the solar age, replicating the jump to mobile phones seen in countries that never had a network of fixed lines. As a by-product, India's rural poor will stop blanketing the subcontinent with soot from tens of millions of open stoves.

Applied Materials is betting on both of the two rival solar technologies: thin film panels best used where there is plenty of room and the traditional crystalline (c-Si) wafer-based cells, which are not as cheap but produce a higher yield - better for tight spaces.

Needless to say, electricity utilities are watching the solar revolution with horror. Companies in Japan and Germany have already seen an erosion of profits because of an effect known "peak shaving". In essence, the peak wattage of solar cells overlaps with hours of peak demand and peak prices for electricity in the middle of the day, crunching margins.

As for the oil companies, they are still treating solar power as a fringe curiosity. "There is no silver bullet," said Jeroen Van der Veer, Shell's chief executive.

"We have invested a bit in all forms of renewable energy ourselves and maybe we'll find a winner one day. But the reality is that in twenty years time we'll still be using more oil than now," he said.

Might he be wrong?

http://www.telegraph.co.uk/money/main.j ... view19.xml

I would be wary of believe too much of it, everyone has their own vested interests but there is reason to believe that solar-power would be more effective to subsidize at this point. I'm not against Nuclear power by any means, but I do think a restructuring of subsidization is in order (I'm pretty sure that all nuclear power plants are heavily subsidized, if not state owned) and I've read a few interesting articles recently arguing that the returns of solar power initiatives are far out-stripping their nuclear rivals. Meaning that diminishing marginal returns in the nuclear sector make further investment inefficient. There seems to be a lot more technological progress to be made in the solar field than in the nuclear field.

[bz249]

I would be wary of believe too much of it, everyone has their own vested interests but there is reason to believe that solar-power would be more effective to subsidize at this point. I'm not against Nuclear power by any means, but I do think a restructuring of subsidization is in order (I'm pretty sure that all nuclear power plants are heavily subsidized, if not state owned) and I've read a few interesting articles recently arguing that the returns of solar power initiatives are far out-stripping their nuclear rivals. Meaning that diminishing marginal returns in the nuclear sector make further investment inefficient. There seems to be a lot more technological progress to be made in the solar field than in the nuclear field.

Have you heard about a really minor issue called Fourt-Generation Reactor?

http://en.wikipedia.org/wiki/Generation_IV_reactor

I would say there is tiny potential in the nuclear industry too.

[TheKwas]

Generation IV reactors (Gen IV) are a set of theoretical nuclear reactor designs currently being researched. These designs are generally not expected to be available for commercial construction before 2030.

I agree that there is still potential in the Nuclear power industry, and still much progress to be made, but at the moment it's a lot less dynamic than the solar industry.