Monday, May 21, 2007

Comparative Solar Power.

When statistics are quoted, it is often helpful to know the various measurements and assumptions behind them, especially in relation to environmental matters, and particularly solar energy. I have just encountered a statistic that photovoltaic (PV) cells covering an area of desert 10 miles by 15 miles could generate 20,000 MW (megawatts) of electricity. That is 20 GW, or about half the amount of electricity that is normally generated in the UK. In metric units, this is 16 kilometers x 24 km = 384 square kilometers (km^2).

Since 1 km^2 = 10^6 m^2, we may deduce that the useful solar power amounts to: 20,000 x 10^6 W/384 x 10^6 m^2 = 52.1 W/m^2. If the solar irradiance is 350 W, that means the cells are working at an efficiency of 52.1/350 x 100 = 14.9% (15%).

Now the same article quotes that a similarly PV-stacked area of 100 miles by 100 miles could provide enough electricity to run the whole of the US. So this is 160 km x 160 km = 25,600 km^2. Simple division indicates that the total electricity generated in the US is 25,600/384 x 20 GW = 1,333 GW, which is rather in excess of the 425 GW that I understood it to be. Indeed, to provide 425 GW of electricity under "desert" conditions would take:

425 x 10^9/52.1 (W/m^2) = 8.16 x 10^9 m^2 = 8,160 km^2 or a square with sides (8,160)^1/2 = 90.3 km.

I will estimate the amount of electricity that could be generated under UK sunlight from 25,600 km^2 of solar panels. Here an average of 150 W/m^2 is reasonable, and assuming an efficiency of 10% (which is a fair value for working solar cells - there are more efficient research-stage cells that are reckoned at 30% but they are not available yet), we have 15 W/m^2 of usable light for PV generation.

Hence, 25,600 x 10^6 m^2 x 15 = 384 x 10^9 W. Now this is only 10.7% less than the 425 GW US national electricity consumption, and indeed the discrepancy can be taken-up by (a) 166 W/m^2 (cf. 150 W/m^2) or (b) an efficiency of 11.1% (cf. 10%), so we are close either way. My main point is that obviously the 10 mile x 15 mile "desert" PV estimate does not apply to the same conditions that the 10o mile x 100 mile "US total" figure was estimated from, which must refer to less sunny climes!

As a matter of interest, let's consider how much silicon would be required to provide this much PV using prevailing technology. If the thickness of the silicon is 180 microns (which is the lower end of the 180 350 micron range quoted in wikipedia for solar cells), that is .18 mm = 180 x 10^-6 m.

Therefore the volume of silicon = 25,600 x 10^6 m^2 x 180 x 10^-6 m = 4.6 x 10^6 m^3 (cubic metres). Silicon has a density of 2.2 tonnes/m^3 and so this amounts to 4.6 x 10^6 x 2.2 = 10.1 million tonnes of silicon.

In the entire world, there is just 30,000 tonnes of pure silicon produced annually, and so it would take 10.1 x 10^6/30,000 = 337 years to produce enough of it to turn the US over to solar in total! Even that little patch in the desert intended to provide 20 GW of PV needs 384 x 10^6 x 180 x 10^-6 x 2.2 = 152,064 tonnes of silicon, which would require 152,064/30,000 = 5 years worth of the entire world supply of pure silicon to install it. I am not being flippant here, but trying to show that there is a limit on resources and that many more silicon manufacturing plants will be needed if the world is to move over to PV seriously.

In a previous posting "Slim Chance for Solar Energy" I estimated that to make all the world's electricity from PV would require an approximate one hundred times the silicon production capacity that exists now, in order to provide this raw material with which to match current electricity generation. Thin-film cells and dye (Gratzel) cells would require different and far less resources to fabricate them, but can they be brought on-line soon enough to make a difference either in terms of depleting natural gas reserves (much electricity is made from gas, certainly in Europe) or in trying to avert our contribution to global warming? It is all a moot point.

Related Reading. ("U.S. Department of Energy - Energy Efficiency and Renewable Energy Solar Energy Technologies Program").


TB said...

Chris, is it just me or are you tending towards pessimism in the last few weeks?

I don't dispute your figures. The issues you raise are real. I'm just curious about your personal outlook.

Professor Chris Rhodes said...

Hi TB,

mmm, I am not so much pessimistic but it does seem that each "solution" when examined more closely is beset with pitfalls. For example, I remain optimistic that we might be able to make a lot of biodiesel from algae, but that technology does seem to be more complex that at first might appear.

The real point that does bother me "personally" is that whatever technology is to be implemented must be brought on-line against the backdrop of cheap conventional oil running out, i.e. a timescale of 10 - 15 years. That doesn't leave us much time.

It also irks me just how much resource is being spent on the "hydrogen economy" which will never amount to much, and certainly little in a decade or so. Governments and research councils should stop squandering depleting resources on phantoms.

So, I think we might "make it" but only through a planned reduction in total energy use and the serious implementation of alternatives but on the full-scale not just at the research-level. Otherwise we are on a hiding to nothing.

If the world carries-on as now, there will come the rapid loss of energy resources and that is the most painful scenario I can envisage. Surely this is to be avoided, but there is no clear indication other than the threat of further wars over resources.


TB said...

OK then, thanks for that.

It's such a shame that global warming has captured so much of the public's attention when arguably the issue of energy resources is far more critical and may even make CO2 emmissions a non-issue in a shorter time than most people could imagine.

I'm inclined to agree with you that a planned reduction in energy consumption - on a massive scale - is probably the only hope for the long-term continuation of a high technology society. But I haven't heard anything even remotely like that from the major political parties here in Australia, not even the Greens.

Have you (or any other readers) heard of substantial energy reductions being made part of public policy anywhere in the world?

Professor Chris Rhodes said...

Hi TB,

this is the latest I am aware of about Australian energy policy:

All else I have found is about energy-efficient light bulbs! i.e,. about the same as the UK!

I am watching closely to see some government policy in either of our nations... or anywhere else for that matter. The "powers that be" must know what we are headed for and so I expect some "guidelines" quite soon!


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