Monday, June 19, 2006

A Slim Chance for Solar Energy?

Such is the explosive growth of the solar power industry that manufacturers of polysilicon, which is moulded into a long ingot and then sliced into thin wafers for solar cells, can't keep up with demand for it. It appears that new supplies are not due to come on stream until 2008, and meanwhile the price of polysilicon has tripled in the past two years and could continue to rise. In the light of this circumstance, it is of interest to look over a few figures and facts about what might be extracted from sunlight, and on what scale this could be achieved. Indeed, is a solar economy possible?
The solar radiation flux (sunlight intensity) at the top of the atmosphere is 1,400 W/m2, but some of this energy is absorbed by the atmosphere as the radiation passes through it. At the equator, at sea level, and at noon on a clear day, the solar flux reaching the earth is attenuated to 1,000 W/m2. If the performance of the solar cell were perfect (i.e. 100% conversion of radiation to electricity) an electrical output of 1,000 W/m2 (i.e. kW/m2) would be obtained. However, the actual output is nearer 100 W, i.e. 10% efficiency. Undoubtedly, the technology will improve, and there are fuel cells in research labs that can generate electricity with an efficiency of more than 30%, but 10% is a reasonable figure for a commercial solar cell at present, so we will work with this. In the U.K., however, an average value for the received solar flux is nearer 150 W/m2, which at 10% efficiency means 15 W/m2.
This is of course during the day only. At night, the power output drops essentially to zero. In the early morning and late day, more of the sun's energy is absorbed by the atmosphere; clouds also reduce the power, and so the actual output is highly dependent on the weather conditions and hence the emphasis on finding ways to "store" the electricity produced by photovoltaic technology.
To get some rough numbers and a scale of what is required, let us consider generating capacities for the U.K., the U.S., China and the world as a whole, and hence the area of photovoltaic solar panels required to meet these outputs.
According to "The World Factbook (2003)", in that year the U.K. generated 360.9 billion kWh of electricity. Dividing by the number of hours in the year, this amounts to a generating capacity of 360.9 x 10*9 kWh/8760 h = 41.2 GW (41,200 MW). Hence, we would need:
41.2 x 10*9 W/ (15 W/m2) = 2.74 x 10*9 m2 of solar panel area to generate it. Since 1 square kilometer (km2) = 1 million m2, this amounts to 2,747 km2, which is only 1.2% of the total land area of the U.K. mainland (230,000 km2).
For the U.S., the total is 3.717 trillion kWh = 3.717 x 10*12 kWh/8760 h = 425 GW.
China generated 1.42 x 10*12 kWh/8760 = 162 GW.
And for the entire world, a grand total of 14.85 trillion kWh was generated, which translates to a generating capacity of 14.85 x 10*12/8760 = 1,695 GW.
The relative solar panel areas appear quite respectable. I leave the reader to work out the percentage of total area required for the U.S. and China, and confine myself to noting that for the whole world, 1,695 x 10*9 W/(15 W/m2) = 113,000 km2 is needed.
This is worked out on the basis of the U.K.'s sunshine and the area could be reduced considerably by placing the panels nearer to the equator, so probably, any solar-powered "local" electricity generating operation would be more efficient in the developing world, e.g. India, Africa, South America - China is more complex in terms of its climate.
Given that 30% of the surface of the Earth is land (i.e. not presently covered by sea - a value that might change if sea levels rise; although they appear to be falling in the Arctic for reasons no one understands), and assuming the planet to be a perfect sphere, we have a land area of:
0.3 x 4(pi) x r*2 = 0.3 x 4 x Pi x (6366)*2 = 153 x 10*6 km2.
This is a rough estimate made on the basis of a circumference of 40,000 km for the Earth, and hence a radius (r) of (40,000/pi)/2 = 6366 km.
Hence, we need "only" cover the earth to the extent of 113,000/153 x 10*6 = 0.07%, which doesn't sound much. Indeed, it corresponds to an area of about 300 kilometers by 380 kilometers, or 235 miles by 300 miles, which is almost exactly half that of the U.K. mainland. Not that I am suggesting we host the whole world's solar production capacity within these shores!
As noted, the sun only shines during the day, and we can expect a sizable output for, say, only 8 hours per day (on average: more in the summer, less in the winter). Therefore, some other means for providing our electrical power is necessary during the dark (night) period. Alternatively and in principle, we might have around three times the area of solar paneling ( 3 x 8 hours = 24 hours) to meet the total demand required, and store the extra in the form of an "energy carrier", either as electrons (batteries) or hydrogen.
If we need this energy in the form of electricity, then "electrons" stored in batteries would be the better bet, as getting electricity "back" from hydrogen via fuel cells would be overall less efficient.
How much silicon would be required to make the required swathe of solar panels? To estimate this, I shall assume that a silicon layer with a thickness of 200 microns (= 0.02 cm) is to be used (this is toward the "thin" end of the 180 - 350 micron range quoted in Wikipedia for solar cells).
The total required solar panel area of 113,000 km2 = 113,000 x 10*6 m2 = 113,000 x 10*6 x 10*4 cm2. This corresponds to a volume of 1.13 x 10*15 x 0.02 = 2.26 x 10*13 cm3 = 2.26 x 10*7 m3.
Assuming an average density of silicon of 2.3 tonnes/m3, this volume corresponds to:
2.26 x 10*7 m3 x 2.3 tonnes/m3 = 51.98 x 10*6 tonnes; i.e. about 52 million tonnes of pure silicon.
The manufacture of one tonne of silicon is reckoned to cause the release of 1.5 tonnes of carbon dioxide (Wikipedia). This, presumably, is reckoned on the basis of an overall mass balance as:

SiO2 (60) + C (12) --> Si (28) + CO2 (44).

From the ratio of molecular/atomic masses for CO2 and Si, 44/28, a value of 1.57 is obtained, in close agreement with the above estimate. However, since the reaction occurs at 1,700 degrees C, a considerable input of energy is required in the form of electricity to make the reaction "go", with an additional amount of CO2 being unleashed skyward. Indeed, it is estimated that 13 MWh of electricity is used to make one tonne of pure silicon. To make the 52 million tonnes of silicon required for our global solar programme would demand 6.76 x 10*11 kWh. We are not of course going to make it all in one year, and perhaps over twenty years would be more realistic. However, that still means making 2.6 million tonnes of silicon every year, a figure to be compared with the current 30,000 tonnes currently produced, and in factories that make up to 10,000 tonnes per year each (some are far smaller than this). Hence, for a start we need something like 100 times the number of silicon factories that we now have!

What about the power requirement for them? To arrive at a per annum estimate we divide the total 6.76 x 10*11 kWh by 20 years, which gives us 3.38 x 10*10 kWh, and is to be compared with the world total electricity production of 14.85 x 10*12 kWh.
Hence, for a twenty year silicon programme, we would need at this rate to increase the world's annual electricity production by just 0.23%.
Nonetheless, building the number of factories necessary to manufacture "pure" silicon on 100 times the scale of current production is simply breathtaking, especially given the difficulty of even meeting the existing demand. Taken with the acquisition of the silica "ore" and the production of charcoal at the necessary grade to make "solar grade silicon", along with the fabrication of the solar panels themselves, the whole enterprise would be a stupendous undertaking.
The message is clear that solar will never become a sole producer of the world's electricity, although it will become increasingly important for stand-alone applications, particularly in the developing world.
I am not anti-renewables - I emphasise this - not in the slightest way! However, as with my earlier calculations on wind-power and biofuels, I am pointing out the sheer scale and energy density of human demand on the planet, which is not readily supplanted by renewable sources of energy. My considerations here are only made over current electricity production. If we try to factor in how much provision, e.g. by solar, would be required to produce electrons or hydrogen to run the world's transport systems at their current and rising size, we could easily multiply the above estimates by a factor of three or four: i.e. Renewables offer us little comfort in the absence of energy efficiency, which must be our leading step forward; then we may be in with a slim chance.

The best option for photovoltaic technology is through the development of thin-film technology, which uses perhaps 1/100th of the amount of semiconductor material, but the task is still monumental on the grand scale, while more localised applications are thus favoured. Other means to capture solar-energy are through roof-based water-heater systems, which use the heat from the Sun's rays to heat water - and of course, good old fashioned photosynthesis!


Kirk Sorensen said...

There's nothing like doing the numbers! Thank you, Chris...very interesting post!

Juan M said...

Chris, I think you are in a position to tell what the real energy balance of current PV panels is, I am posting this from Spain where currently there is a craze in installing PV panel farms. Myself I could be interested in buying a piece of a PV farm, but I have a healthy distrust on assuming that PV panels have a positive energy balance, there is not much information, y only have read that early on they had negative energy balance, and that of lately the energy balance is 4 (So the energy obtained from the PV panel during its life is 4 times the energy needed for the PV manufacturing).
Could you please give your estimate?

energybalance said...

Hi Juan,

I have seen various estimates of the EROEI for PV, say between about 1 and 10, so as an average, 4 (I've read that one too) is probably reasonable? Producing enough silicon to really make a difference is one of the hard parts, but there is new technology e.g. dye-cells that might improve the situation for PV overall. However these are still very much at the research stage.

My wife and I considered the possibility of putting PV panels on the roof of our house but it was the cost that put us off, as we worked out it would take about 20 years to break-even on the outlay costs.

If other energy sources become increasingly expensive, e.g. gas, coal and oil (and nuclear) to make electricity, then you would break-even sooner and then be in profit for all the years following that the cells continued to work.

In terms of the environmental impact the situation is complicated. It takes resources to extract resources and if following the Peak Oil date, civilization "simplifies" and becomes highly non-technological, we might be better-off with mechanical devices like wind-turbines which could be adapted to grind corn!

But as an investment in a sunny part of Spain, I think you might do O.K. I'm not a financial advisor, but if you are interested in investing some money it might be fine. I would invest some cash there (probably)!

The upper limits of the EREOI for PV cells are always made by those who have a vested interest in them, and there are many web-sites that think it is not the best kind of technology - but having made the investment to set up a vast bank of PV cells around the world, as oil and gas (and maybe nuclear too, depending on how much uranium can be got) run out, it may be one of the world's greatest assets.

That's not a yes or no answer exactly, but what I'm saying is there are benefits just not quite to the extent some people may claim!

I hope that is of some help, at least.


Juan M said...

Thank you Chris,

this has nothing to do with business, has to do with being part of the solution, not part of the problem. I do not want to engage in anything that is unethical even if it has a good ROI.

Seems to me that politicians and manufacturers got together to tell lies to the public and/or hide information. In Spain subsidy for PV panel production is 600% for everty KWh. So it kind of makes business sense. But panel are being installed in the worst possible area, in Navarra with little insolation. The world leader is Germany (not much sun there)

Googleing on EROEI I found this:

Ultimately there is only one way to definitively answer this questions: The bootstrap challenge. I have previously stated that when I see an ethanol plant that distills their ethanol USING ethanol (not natural gas or coal), then I will seriously reconsider the merits of that alternative energy source. Likewise, when I see a PV production plant that is powered entirely by PV, containing machines manufactured at plants powered entirely by PV, machines composed of materials mined, refined, and shipped entirely under PV power, etc., then I will believe that PV has an EROEI greater than 1:1. With an EROEI like 30:1, this should be no problem . . . so the fact that this is not the case is yet another argument, at least in my mind, that reality stands closer to the 1:1 figure

Nanook said...

There's nothing like numbers, but use of accurate numbers would be a good start.

It is worth noting that thin film and amorphorus technologies cut the amount of raw materials required to a small fraction of monocrystaline cells.

But I don't expect solar photovoltiacs will ever be the universal source of the worlds energy either, why should they?

There are alternate technologies such as solar chimneys which use thermal mass to allow them to keep generating through the night.

Given that they're just brick or concrete chimneys with a turbine, the technology involved is not complex.

Never the less I do expect photovoltiacs will make a much larger contribution than you envision.

energybalance said...

Hello Nanook.

Constructive criticism is always welcome here, and so please tell me in what way are my numbers inaccurate, and suggest some alternative figures, whereupon I will write an updated article.

The purpose of this blog is to explore all possibilities regarding energy provision, so any rational input is appreciated.

Thin-film cells can use other materials than silicon - I agree that they are important in regard to consuming less resources than conventional cells do; that's the whole point of them, really - however, as I have discovered just recently, many of the raw materials are in potentially short supply, especially if new technologies are implemented which use them on the grand scale.

I think we will need all the renewables we can get as other energy sources begin to run-short. Dye-cells, eg. Gratzel cells with a dye-sensitizer and a TiO2 "hole-capture" medium are another possibility - there may be 200 years worth of TiO2 left at current rates of use, but less of course, if a new technology makes demands on it.

If you have more information/links etc. then please send them to me.



DantheMan said...

Very interesting figures!
Here's another figure:
6.76 x 10*11 kWh (Energy needed to make the 52 million tonnes of silicon required for our global solar programme)equals aprox 77 MW of generating capacity. (6,76 x 10*11 / 8760)
The worldwide energy consumption of the human race in 2004 was on average 15 TW* = 15 000 000 MW. * Source: Wikipedia "World energy resources and consumption". :)

energybalance said...

Nice one, Dan!

So the amount of "electricity" required to make the 52 million tonnes of silicon should be no problem at all!

The main effort needed is to build those 100 or so x the present number of factories, new, to install the technology over say a 20 year period. A huge task, however, but surely the world needs to start building them now.

Thin-film cells would reduce the amount of silicon (or other PV-material) considerably, and perhaps coincidentally by a factor of 100! However, to the best of my knowledge these are not commercially available?

Dye-sensitized cells also offer an improvement in the quantity of "mineral" material, i.e. TiO2, required so that is another possibility.

Regards, Chris.

DantheMan said...

Thanx for fast feedback!
The future of global energy is sunny, that's for sure!
However, I'd rather bet my money on CSP (in the Sahara!) than PV -read this interesting article!,,1957908,00.html#article_continue

Have a sunny day! :)

Yordan Georgiev said...

Great post! You should add couple of charts and Diagrams since most of the fanatic renewables advocates are kind of mathematically illiterate ...

And yes Kirk, he could also add how-many tons of Thorium and all the metals needed for the LFTR's would be required to achieve the same goal ...

energybalance said...

Hi Yordan,

I like to do the sums! The numbers are usually a bit staggering in their vastness however. Thin-film cells look good since they use far less and amorphous material and Quantum Dot cells if they can be brought to fruition promise up to 65% light conversion efficiency and need a lot less semiconductor material.

I don't know how the figures stack up for LFTRs, but as you say Kirk is likely to be the man to know.



Anonymous said...

The present temperatures in the Northern Hemisphere lead me to believe that the CO2 bogey will be annihilated. An increase of 0.002% in atmospheric CO2 will no longer be significant. Large investment in solar cells is not advised.

pulmonary disease said...

I agree that they are important in regard to consuming less resources than conventional cells do that's the whole point of them, really

Pravin said...

Hi Cris nice blog post. Still I am not sure on the energy balance for Silicon, some one at one conference said that energy balance of silicon is negative ( what ever energy is consumed in producing a unit of silicon is more that that it would generate over its life). Do u hv any numbers on that, This would be pure science.

By now everybody would hv realised that single energy solution is hypothetical. So it would hv to be a portfolio of various kind of solutions.

What u hv said id right, efficiency has to precede these solutions. and demand management has to precede efficiency.

It is the human race which causing the demand to explode. the materialistic habit of consumption centric society has to go.

The whole marketing would hv to go. the concept of created need which is causing the consumption has to go.

no body knows whether the human race can be controlled or its' on the ways to dynos :)

But as long as we are there, as logicla entities, I can not fathom the fact that, if most of the energy in any form is from the radiation energy of sun and probably other bodies in the universe, tapping that source directly would be more sensible than waiting for millions of years for that energy to create fossile fules then spend hell lot of money and resurces t oextract them and then burn them to get energy and on the way screw up the planets natural system

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Solar energy is the best natural resource that we have this time even more that fuel is too expensive. In fact i want to approach costa rica investment opportunities and look all the alternative this country can have because it climate. We must to find the way to save our planet and to use solar energy could be the first step.

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energybalance said...

On the personal level roof-based solar water heating systems are more efficient than pv panels.



Anonymous said...

Chris, to be more realistic, did you consider the worlds production capacity of photovoltaic panels in squre meters? How is the relation of the production capacity to the demand you estimated? Can you estimate the correction to be necessary for the efficiency of the photovoltaic panels available today? Is there any potential to I crease the efficiency? How high is that?

I could probably do all the estimates myself, but my ambitions are not so high as yours. Please excuse me for challenging you and assume it as my respect to your competence.


energybalance said...


this is an old one now! I did work it all out in square metres, and probably a 15% efficiency for standard solar panels might be obtained, at least when they are new. I took a modest 10% so maybe you could "downscale" the areas and materials by 1.5. For thin-film cells I believe the efficiency is about 8%, but this is an emerging technology.

The leaders in PV are Japan and Germany mainly because of earlier government subsidies. The present manufacturing output for solar pv is still minute compared to the full-scale demand.

Thermal solar power has the higher efficiency and there are major programmes in Portugal and Spain. There is also the DESERTEC project for generating solar electricity by thermal and some PV in north Africa to bring to Europe but that is still under development.

The article was mainly intended to be indicative since my impression is that most people are completely unaware of the amount of material and length of time necessary to implement "green" technology on a scale necessary to make any difference to our use of fossil fuels.


Chris Rhodes

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