15 May 2007

The Glittering Future of Solar Power:
Prognostication of Photovoltaic Capacity Extrapolated from Historical Trends

Historically the photoelectric effect has been known for a couple hundred years ever since it was observed in elemental Selenium around the turn of the 19th century. It became practical to use the photoelectric effect to generate power with the development of the transistor in 1947 that lead directly to Germanium (and later Silicon) solar cells that could produce a useful amount of electricity. Early solar cells saw use in extreme applications, such as providing power for satellites. Serious efforts to develop photovoltaic cells for commercial power production wasn't undertaken until the Arab oil crisis's of the 1970s. The USA developed an early dominance in the technology, but that advantage withered as the memory of the oil crisis faded from public view and successive administrations ignored the technology. More recently interest in photovoltaics has been rekindled due to concern around global warming, predominately supported by programs in Germany and Japan, whose domestic manufacturers now produce the bulk of solar cells. Research and development in photovoltaic technology is proceeding at a frenzied pace, as triple-junction thin-film silicon and Copper-Indium-Gallium-Selenide (CIGS) cells are posed to take over market share from traditional polycrystalline silicon wafers sawed from solid ingots. In the future decades, nanotechnology and organic semiconductors offer the potential for new generations of solar power technology.

Photovoltaic cells are not like any other method humanity uses to collect and use energy. Existing techniques extract energy either from mechanical motion (wind, hydroelectric, tidal) or heat differentials (fossil fuels, nuclear, solar-thermal). Whereas all these systems produce useful work by the turning of a shaft photovoltaics convert sunlight directly into direct-current electricity. While photovoltaics are still beholden to the laws of thermodynamics and entropy, the difference still implies that they abide by difference rules. In particular, they have a total absence of moving parts and as a result are almost free of maintenance requirements. Photovoltaic cells degrade in performance only very slowly as they are bombarded by cosmic rays. Most manufacturers offer warranties that guarantee they will still reach 80 % of their rated power output after 25-years.

Photovoltaic Share of the Energy Pie

A report by Merill Lynch (Hat-tip to Clean Break) found that between 2200-2500 MWpeak worth of solar cells were manufactured in 2006 [1]. Taking the median value of 2350 MWpeak and a capacity factor (cf) of 0.2, which is typical, then the annual electricity capacity was 4 million kWh. According to the Energy Information Administration (US DoE), the world produced 16,400 billion kWh of electricity in 2004, and that figure is growing at 3.2 % a year since 1994. If we extrapolate to 2006 at 4 % growth then the total electricity production was an estimated 17,950 billion kWh. Photovoltaic power consists of only about 0.6 % of the annual growth in electricity capacity.

It seems minute, and it is, for now. However, solar production hasn't been growing at 3.2% per year. It has, in fact, been growing at 33 % per annum for the last decade [2], and it's expected to continue that trend for the immediate future. The cumulative installed capacity can be expressed as
C(t) = Co e(γ-δ)(t-to)/(γ-δ)
where C(t) is the cumulative installed PV electricity generation capacity, Co is the initial installed capacity, γ is the growth rate, δ is the degradation rate (10 % efficiency loss every 12.5 years or 0.008), and t is of course the time in years. Nothing fancy here, just pure exponential growth.
Figure 1: Scenarios for PV cumulative installed capacity as compared
to worldwide demand growth of 4 % per annum over the next 25 years.

As one can see from Figure 1, while the impact of solar may be trivial now, it will not be over the next 25 years. If solar can maintain the same growth rate is has for the past decade, solar can supply all of mankind's projected electricity demands 26 years from now.

Cost of Photovoltaic-derived Electricity

Generally speaking the cost of any technology declines with production capacity according to a power-logarithm law,
P(t) = Po ρlog2( Exp( γ (t-to) )
where P(t) is the price as a function of time, Po is the initial price, ρ is the learning rate, and C(t) is the capacity. Historically, ρ for photovoltaics has been very stable around 0.8 which corresponds to a learning rate of 20 % as depicted in Figure 2.
Figure 2: Learning rate for photovoltaic panels (reprinted from [3]).

The learning rate of photovoltaics is much higher than that of other energy technologies. In fact, it's more in-line with things like computers or DVD players. This fact should surprise no one; as I mentioned in the introduction, photovoltaics are different from all other forms of energy production. The small incremental nature of photovoltaics is a major advantage from a R&D perspective, as I've described previously. While coal and nuclear power plants are installed in increments of hundreds or thousands of megawatts, solar panels are measured in the hundreds of watts. Thus while a design change to a nuclear power plant can take a decade or more to manifest itself, solar manufacturers can do this in weeks. As a result, photovoltaic technology will go through hundreds of design revisions in the time it takes coal or nuclear plants to go through one. Some learning rates for various technologies are listed in Table 1. One thing to take from the table is not only that photovoltaics have a superior learning rate, but that they also have so much further to grow.

Table 1: Historical Learning Rates for Electricity Producing Technologies (extracted from [3]).


Learning Rate (%)

Correlation (R2)

Sample Period (years)













Gas Turbines












Laser Diodes




Current panel costs are treading at around $4.80/Wp, and the various extras such as frames, labour cost an addition $2.50/Wp. I'll use two locations to establish a baseline for the cost of photovoltaic power: Stuggart, Germany and Los Angeles, USA. A Retscreen analysis shows that the Stuggard location produces 1.089 MWh/year /kWp (which represents a capacity factor of 0.17) and LA produces 1.605 MWh/year /kWp (capacity factor 0.25). Simulations in RETSCREEN find that amortized over 25 years these locations can produce power at $0.24/kWh in Stuggart and $0.21/kWh in California [4]. Financial assumptions are: energy inflation is equal to monetary inflation, interest is 1.0 % above prime (government rates).

World residential electricity prices are generally lower than this [5]. France, which is primarily nuclear, has a rate of $0.144/kWh. The USA, which is coal based, has a mean rate of $0.095/kWh. Canada, which is mostly hydroelectric is one of the lowest at $0.068/kWh; another hydroelectric nation, Norway, comes in at $0.071/kWh. All of these numbers will include associated transmission costs. When we use the growth curves shown previously in Figure 1 with our equation for price, we find that the cost of PV drops below that of conventional electricity generation startlingly fast (Figure 3).
Figure 3: Cost of photovoltaic electricity for Stuggart and Los Angeles versus baselines
for France (nuclear-based), USA (coal-based), and Canada (hydroelectric-based).

Interestingly, the location of photovoltaics has little impact on their price over the long term. Rather it is the industy's growth rate which dictates the future price. One might be curious as to where the price point might be when the industry saturates.

The actual price decline of PV has stalled over the past year and a half. Essentially what happened is the PV industry eclipsed the microelectronics industry in terms of silicon consumption before thin-film silicon technologies were ready for commercial production. As a result, there's been a bit of a lag as silicon producers catch up to demand. I do not think that this will continue to be a problem, as I will explain below.

Limitations to Growth

For one to look at the curves in the previous sections, and believe that they are achievable then assurances that there won't be too many roadblocks in the future. This section will take a closer look at potential issues that could slow the growth of the photovoltaic industry.

Economic Incentives
One of the issue with photovoltaics is that as an emergent technology it isn't cost competitive with fossil fuels today. However, subsidy programs by governments of Japan and Germany have been generating tremendous demand growth by making solar cost competitive. Recently more jurisdictions have put forth subsidy programs, such as California, New Mexico, Ontario, Spain, Italy, and Portugal. One obvious question in looking at the exponential growth curves in Figure 1 is, "Just how much is all of this going to cost?" Combining the equations for the learning rate with the growth rate provides us with an answer.
Psubsidy = (Po ρlog2( exp() ) - 0.05)* C(t-to) e(γ-δ)(t-to) / (γ-δ)
This assumes that existing installations are amortized at the same rate as the price of new modules drops. This is not a bad assumption simply due to the massive growth rate, which has a doubling time of 2.1-2.7 years.
Figure 4: Annual cost to subsidize entirety of world PV production to a
rate of $0.05/kWh under 33 % annual growth scenario.

Figure 5: Annual cost to subsidize entirety of world PV production to a rate of $0.05/kWh under 25 % annual growth scenario.

The total cost of these subsidies run to about US$90 billion for the 33 % growth model and US$154 billion for the 25 % model until the price of solar power drops below the desired $0.05/kWh. It's not an insignificant amount of money, but neither is it a particularly onerous cost for transforming our energy structure; the USA alone budgets $24 billion a year to the Department of Energy.

It's probably worth noting that return rate is over one trillion dollars a year by 2031 against the $0.05/kWh baseline. This can be construed either as potential tax revenue or additional income that will be contributed to GDP.

Intermittency is the problem that renewable energy sources suffer from due to the natural fluctuations of their power source. Any transmission grid that relies on renewable sources as a primary input will require a substantial amount of storage, deferrable demand, or load-following spare capacity. The severity of intermittency can be thought of as a combination of its predictability, correlation to demand, and variance. Compared to its chief competitor, wind, solar is far more predictable. One can be assured of the position of the sun in the sky every day with the mitigating factor being cloud cover. However, integrated over a large area the portion of the sky covered with cloud can be reliably estimated. In comparison, wind velocity is nearly impossible to predict. It also correlates relatively well to the natural daily peak in demand, for a noisy real-world system. The variance of wind and solar are roughly equal, which is a little surprising given the dinural cycle of night and day that solar has to deal with. In addition to their daily variance both solar and wind are subject to seasonal variations.

It is my opinion that the concern over intermittency of solar power is exaggerated. This is due to the fact that the learning rate of photovoltaics dictates that the cost of solar will fall below that of the main established sources of power (coal, nuclear) well before solar will constitute a significant fraction of our energy consumption. I think most people will agree, when the price of solar energy drops below that of the competition, the game changes. When you have power to burn, simple and low-capital techniques of storing or transmitting solar electricity become practical. At $0.05/kWh solar would have a margin of $0.04/kWh or more to work within for charging electric vehicles, filling deferrable demand, storage techniques such as Vanadium redox batteries, or long distance high-voltage direct-current transmission.

Resource Limitations
One of the factors limiting photovoltaic growth at the moment is a shortage of electrical-grade refined silicon. Silicon itself is not in short supply, being the second most abundant element in the Earth's crust after Oxygen. This limitation is likely to fall away as new cell designs that use less silicon are deployed commercially. Traditional cells are made by sawing a solid block of polycrystalline silicon and then polishing the surfaces. This results in a cell that is 300 μm with around 50-100 μm of material wasted. New techniques such as ribbon growth can reduce that figure to 100 μm. Furthermore, thin film silicon cells grown by chemical vapour deposition, such as Sharp's triple-junction cells, can achieve the same performance as polycrystalline cells with only 10 μm of silicon. As these techniques reach market penetration (ribbon growth is proprietary, thin-film techniques are not), they should reduce the strain on silicon refiners.

The other resource restriction is due to geographical limitations. Some renewable resources (hydroelectric, tidal) are tightly limited to certain terrain, such as tidal basins or river valleys. Wind is a somewhat more diffuse, but the best resources where the wind blows most strongly and consistently are still limited compared to humankind's energy consumption.

Figure 6: Global Solar Energy Abundance Map [6].

World insolation (incoming solar radiation) on the other hand is massive and relatively evenly distributed. The sun outputs 1026 watts of power and our tiny little planet intercepts about a billionth of that. Right now the human race consumes around 18 TW of energy, or 1/10,000th of what strikes the Earth. Roughly 1/3rd of that is useful work, the rest is lost to entropy. The 24-hour average insolation for the inhabited world spans 150-300 W/m2. That implies we would need 3.5-7 m2 of 10 % efficient panels per person, to supply all of our energy needs from solar power.

Personnel Shortfall
Running short of trained people in a rapidly growing industry is always presents a problem. Take, for example, nuclear engineers. There aren't many of them, training one takes about four years, and their skills are not easily transferred to other disciplines. The photovoltaics industry is similar enough to the microelectronics industry that they can trade personnel, however. The microelectronics industry has already built up strong education programs that photovoltaics can piggy-back.

If chemical vapour deposition (CVD) for thin-film silicon becomes the dominant production method, this still should not present too great a problem. CVD is a common manufacturing technique used for all sorts of coatings, such as tribological (hardness) coatings for tools, or even aluminized mylar. It's also used in microelectronics. It does happen to be more of an art then a science, which means that learning requires experience.

Ancillary Costs
Installing a rack of PV modules on a garage is not simply a matter of fixing them down with some twist-ties. Typically they need a metal frame so they present an optimum azimuth to the sun, they need electrical wiring, they need an inverter to transform DC to AC power, they may need a net-meter to sell power back to the utility, and of course, there's the labour required for installation. As many readers will know, there's quite an argument in California as to whether or not a licensed electrician is required for installations. One might also consider the 3 mm layer of glass (glazing) that protects the cells from hail also 'ancillary' although it is included in the sticker price.

The main question is whether or not ancillary costs have a similar learning rate to that of the modules themselves. My analysis has assumed that they do. We will probably see declines in the ancillary costs by better product integration and standardization. Rugged encapsulation combined with light-trapping surface patterning will probably slowly replace the standard glazing. Inverters should improve drastically both in terms of cost and lifespan. There's also always been the idea of incorporating solar cells into dual-use products, such as solar shingles or skylights.

Consumer Acceptance
Unlike just about every other source of electrical generation, photovoltaic power doesn't have any "Not In My Backyard" (aka NIMBY) issues. `Nuff said.


Many people will look at the graphs in disbelief that the easy path photovoltaic power has been travelling can continue. All I can really say in reply is, those are the historical numbers. The learning rate is exceptionally stable. The growth rate has been, if anything, accelerating in the face of a industry silicon shortage. Thin-film technologies seem well positioned to cause the price to continue to fail into the near future. Solar power doesn't have very far to fall in many European nations before it's cheaper than residential rates. As residential solar becomes the cheapest power available that will continue to push demand upward and fuel growth. There's nothing obvious to me that says 'Stop' in solar's future and it's a fact of exponential growth that the early years matter the most. Even if the growth rate drops 1 % a year over the next 25-years the eventually outcome seems predetermined, it's just a question of the timing.


[1] S. Pajjuri, M. Heller, Y.S. Tien, I. Tu, B. Hodess, "Solar Wave - Apr-07 Edition" Merill Lynch (2007).
[2] W. Hoffmann, "PV solar electricity industry: Market growth and perspective", Solar Energy Materials & Solar Cells 90 (2006), pp. 3285-3311.
[3] A. McDonald, L. Schrattenholzer, "Learning rates for energy technologies", Energy Policy 29 (2001), pp. 255-261.
[4] RETScreen International Clean Energy Project Analysis Software, National Resources Canada.
[5] Electricity Prices for Households, Energy Information Administration, February 28,2007.
[6] Matthias Loster, Solar land area, Wikipedia.org, 2006.


Adam MacKillop (Hadeon's and Stjepan's Dad) said...
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Daniel said...

Sounds like you have been reading "Solar Revolution" by T. Bradford. If not, the book makes the same point as you do in many more pages.

Using your 0.8 learning curve/production doubling, we need to see 3 more production doublings to get to pairity with utility prices in most markets (assuming solar is twice as expensive today). This implies ~10x today's production rate or about 20,000 MWp/yr. I'm confident we can get there in about 10 years.

Of course I am a true believer in solar.

Robert McLeod said...

No I haven't read that book or I would have referenced it.

I learned two things from this research: that the price of PV will drop below that of the status quo before it runs into serious intermittency issues and that the cost to subsidize that is not excessively expensive. I've certainly seen growth curves before, and log-log plots of the price, but I hadn't seen anyone combine the two to estimate the cost of a worldwide subsidy program.

Anonymous said...

Nice work, although I was under the impression that PV is still around 5 times more expensive than grid electricity. I think one will still need most of the transmission &distribution network with PV, since PV is a variable source of energy and I haven't so far seen storage costs that would beat the costs of having a grid. Certainly batteries can improve, but they have a long way to go and they have a slower learning curves than PV.

Another issue is that wind is quite close to solar when it comes to learning curves. There's around 15 times more wind power than PV and it is being installed at a rate that's about ten times higher than that of PV. Growth rate for wind is also above 20% per year and poised to stay there at least for the next 3-4 years. With current rate of doubling wind power could be the biggest source of new power production in 10-15 years and I think PV won't be there so soon.

Learning curve of wind power is slower than that of PV though. What makes this up is that wind is already close to costs of producing electricity from fossil fuels (or actually beating them in good places). However, currently we are seeing supply side restrictions from wind power manufacturers and prices are up due to that. It will be interesting to see where they go once there's enough manufacturing capacity once again. That might take several years though.

Ultimately PV could triumph, since it is easier to imagine that PV could one day be really cheap due to the semi-conductor nature of the technology whereas wind power cannot go down forever mostly due to material cost issues. However, there are regions in the world that don't get much sun during the winter and wind can provide a very good partner for PV.

Wind is also often put down by saying that there is not big enough resource, but this picture has been changing fast. New higher turbines reach good enough winds in places where we previously thought too poor for wind. Compare wind resource maps for 70 meter and 100 meter at http://www.eere.energy.gov/windandhydro/windpoweringamerica/wind_maps.asp for instance.

Anonymous said...

I am interested in what you think of the Global warming ney sayers.

This is from Sen J Imhof's website.

The media's climate fear factor seemingly grows louder even as the latest science grows less and less alarming by the day. (See Der Spiegel May 7, 2007 article: Not the End of the World as We Know It ) It is also worth noting that the proponents of climate fears are increasingly attempting to suppress dissent by skeptics. (See UPI May 10, 2007 article: U.N. official says it's 'completely immoral' to doubt global warming fears )

As I install solar pv and thermal for a living these thoughts, both yours and Mr Imhof's have a substantial effect on my business.

Fred Pittenger
Simplicity Solar
Grand Junction, Co

Robert McLeod said...

I don't mean to discount wind power, it's more so that it has already arrived. Wind is already the bulk of new electricity installations in North America and Europe. The raw cost of wind power can be as low as $0.04/kWh. That said, I don't think it will attain the eventual market penetration that solar can. I think the intermittency drawbacks for wind are much more severe. It also doesn't have as far to grow.

From the data I've worked with it's not obvious that wind is stronger at night but I'll take your word for it. I could always apply a histogram to check that. It does blow stronger in the winter. When it comes to statistics, when you add two noisy sources together you end up summing the noise as well.

Increasing the altitude of the turbines is going to exacerbate the NIMBY issues associated with wind power. A 75 m tower can be seen from 31 km away, 100 m from 36 km. You increase the height by 25 % and it's visible to a 25 % larger area. Offshore wind will be able to take advantage of taller towers.

Anonymous said...

You seem to imply that global warming is not or should not be believed, yet it has been one of the main thrusts driving the incentives across the world which in turn inspired solar market investment of billions of dollars.

Those in Colorado who pushed Amendment 37 REP through did so largely with reasoning based on global warming. There was not and would not be a market here without this incentive. We live in an area that still enjoys dirt cheap electricity, although it is starting to creap up. Cost of power is not a significant driver here. But Federal tax incentives are and Standard Rebate Offers.

Seems like you are pissing on your glitter.

Fat Man said...

Impressive piece of work. I am sorry it took me so long to respond, but i had to print it and clear a half hour to read it.

If you are right, then we have no further worries about energy shortages or CO2 surpluses.

My question to you is which of your assumptions is weak or unrealistic, i.e. why won't this come true?

Robert McLeod said...


Please point out to me where I've implied that global warming "is not or should not be believed."

Anonymous said...

Is it really neccessary to have the inverters?
If we are going to transition to solar, can't we also transition our appliances to DC?
With the exception of the synchronous motors in washing machines and fridges (etc), most of our appliances really run on DC... and surely we can make fridges etc with DC motors?

Robert McLeod said...

Certainly DC appliances exist. If you want to live off the grid, 24V DC appliances are probably the way to go. However, it's more so rectifiers (AC to DC) that are inefficient rather that inverters (DC to AC). I don't really see a method of 'graduating' to DC appliances since the electrical distribution is AC, and all other forms of electricity generation are AC (with the exception of fuel cells). It's not something I would push before PV is supplying the majority of the world's energy (as opposed to just electricity).

Anonymous said...

I just discovered your blog and have added it to my iGoogle page. Good stuff!

Your analysis of solar power is fascinating. I particularly like Figure 3. But I'm having a bit of a hard time accepting that solar will continue to grow at a 33% rate for the next 25 years. I just don't think you can extrapolate that far into the future. Even at a 25% growth rate (which still strikes me as highly optimistic), installed capacity of solar wouldn't catch up to other sources for many decades, as your chart shows. And a piddly 17% growth rate (still phenomenal if maintained for 25 years straight) would appear to push the Solar Era well into the next century.

I also wonder about the environmental impact of this exponential growth in solar power. Just how much land is it going to require to switch to solar? How many resources will it require to manufacture all of these panels, batteries, frames, etc.? I honestly don't know if this is a significant impact, but I'd be curious to see what your opinion is.

Fat Man said...
This comment has been removed by the author.
Fat Man said...

Orygunner: Historically, new technologies have had explosive growth periods. The first airplane flew in 1903. 55 years later the 747 was rolled out. Computers were invented in the 1940s, within 60 years they were desktop staples. Does Robert's prediction require faster growth than those examples?

Anonymous said...

Fat man, I'm sure those technologies did have fast growth rates, but it's an empirical question as to whether they sustained 33% or more for 25 years straight. I don't know if they did, and apparently neither do you, otherwise you'd cite the figures. There were also few substitutes for airplanes and computers when they rose to dominance, but electricity can be generated using a multitude of different methods.

All I'm saying is that a 33% growth rate sustained for 25 straight years just strikes me as a tad optimistic. I'm a pessimist by nature, so best-case-scenario thinking doesn't do much for me, and I don't think it makes for good policy.

Robert McLeod said...


I'll try to address your points one at a time.

In terms of sustaining the growth rate, I can see a few of means for continued strong demand.

One would be any sort of greenhouse gas legislation in the major economies of the world. A carbon trading system or simple tax will certainly favour solar and other renewables over coal and natural gas. Even if some nations do not get on-board the CO2 wagon, we will likely eventually see the developed nations applying a carbon tariff to imported goods. Since CO2 sequestration is largely vapourware, and it will definitely be expensive, nations, their industry and citizens, will look to solar and wind as being most competitive supply-side method of curtailing greenhouse gas emissions to meet mandates.

Another thing that could push solar is local depletion of coal and natural gas. We've already seen depletion of the coal resources in the UK and Germany, and if it continues to expand at its current rate in China we'll see it there too within my lifetime. Coal depletion is more an issue of declining quality than tonnes but it will still give solar a competitive advantage. Low-heat coal is expensive to ship over long distances. Of the major coal producers, only Australia exports a major fraction of their production.

Natural gas depletion will all have local effects even if there's large quantities available elsewhere in the world. Cryogenic liquefaction will work, and reasonably well, but it will be a lot more expensive than our current oil tanker method.

Lastly, we should not discount the impact on the developing world. Most developing nations are resource-poor, while the OECD countries are all resource rich (with the notable exception of Japan). For a lot of these countries solar will be the affordable means of electricity generation now and in the future since it won't require the massive capital investment of a distribution grid. A lot of the equatorial nations also receive the most insolation. A country like Kenya, for example, isn't going to buy anywhere near as many panels per capita as Germany but they will realize greater economic benefits from things such as indoor lighting or refrigeration.

On the environmental cost of PV, I have addressed the energy inputs previously here.
A reference in that post leads to a Dutch study on the various inputs for solar cells. You can check out the Excel spreadsheet they provide.

The land issue is addressed in the original post. I suggested 3.5-7.0 m2 of panels per person, which is relatively limited compared to the resources required to build a car or house.

Anonymous said...

Thanks for the response and the links. Just to clarify, I certainly support solar and think there should be aggressive government incentives to help develop the industry. Guess I'm just quibbling a bit with the core assumption of your otherwise excellent analysis.

My state (Oregon) will be doing its part to help encourage solar. The governor signed a law this week that requires utilities to produce 25% of their power from "new" renewable sources by 2025 ("new" being anything built after 1995). That should give a nice little boost to the solar industry.

Anonymous said...

I found your piece absolutely fascinating and thought-provoking. But I am very worried about your assumptions, particularly, as others have commented, on the 33% growth rate. One always has to be concerned about extrapolations where the timescales of the prediction and the data are significantly different. In the case of solar energy capture, much of the growth has been underpinned by massive subsidies by governments which are not growing to keep up with demand. In the UK, for example, the growth was fuelled by a 50% subsidy which was very recently cut by about a half - not surprisingly growth has slowed substantially. Price elasticity is a bugger, isn't it?
Let us hope that the combination of learning curve and improvements in efficiency are able bring the price down faster than the losses in subsidy.
So I think I'm pretty sceptical about solar making really big inroads since I suspect that as coverage increases, the exponential will start to flatten out.
And that's a shame 'cos I'm committed to the extent of having replaced half of my roof with PVs...
Thanks for giving me so much to think about, though

Anonymous said...

In my opinion in the developing world, LEDs paired with solar panels could provide a cheap, sustainable light source that doesn't need a traditional power grid. In reality, solar power may not provide enough energy for ALL of our energy needs. But it could provide be a large percentage energy source. Coupled with nuclear power, wind power and water power, we could stop global warming. And as an added bonus, the U.S. with lose its dependency on foreign oil.

Anonymous said...

Only the one weak point in your argument that I can see.
That is the assumption that ancillary costs will drop at the same rate as the module costs.
In comparable industries eg computer production this just does not happen.
The price of the electronic gizmos follows Moore's Law, and drops rapidly, but the boxes to put it in, assembly and distribution costs don't.
So I can see the transition being a bit slower and stickier than you project, with ancillary costs making up a more substantial proportion of total costs as module costs drop.
It doesn't invalidate your basic thesis, that PV costs will drop to below grid prices in fairly short order, but it does affect the time scale, and perhaps indicates that technologies such as PV incorporation into roof shingles and so on may be the way to go, as the installation costs are much reduced as you need a roof anyway, although not of course the electronics and so on.
Very interesting blog - thanks.

Anonymous said...

Graphing wind installed capacity against solar PV installed capacity over the sort of time horizon and making the same assumptions as you have made would result in the wind power far exceeding the installed capacity of PV for the foreseeable future, in spite of it's slightly lower growth rate.
The relatively large installed based of wind compared to solar at the present time insures this.
Of course, if your statement about the lower geographical availability of wind as against solar is correct than things would change.
However, things change dramatically if the requirement to generate wind power from towers is relaxed.
Various tether-based proposals would mean that the winds of the jet stream could be utilised, which although it wanders around somewhat would provide much less intermitancy than either ground-based wind or solar power.
It therefore seems entirely possible to me that the present explosive growth of wind-power will continue, with higher altitude winds being utilised as the easier low-level resources are exploited.
So you end up with a tussle for dominance, with the areas of low wind and high solar activity such as the tropics favouring solar, but a much more closely fought battle at more northerly latitudes will better high altitude winds.
I'd be very interested in seeing the graphs of wind vs solar projected into the future, using the methodologies you employed in the original article.

mrshaba said...

Great article Robert. Amazingly good really. It seems as though some of your earlier posts were rather down on solar. Did you convert to solar in the last few years or have I misinterpreted your earlier posts?

Robert McLeod said...

I've always thought of solar being the eventual winner in the energy lottery, but I am pretty dubious of some of the silly PV concepts designed to liberate technophobic investors from their money. KISS (keep it simple stupid) rules.

Anonymous said...

Great post - very informative. Perhaps for all involved here can we agree on some sort of highly defensible expansion curve for solar. The Hoffman citation for 33% per year is somewhat academic - I wonder if Merrill, GS, or any of the research departments in the banks have commented in an increase in capacity over time.

mrshaba said...

Could you name a few of these silly PV concepts please? What do you think of wide acceptance angle concentrators?

I’ve always found thin film technologies inferior because of the comparatively low efficiencies. In the next 5 years average silicon modules could well get to 20% efficiency. SunPower is already above 19% module efficiency and Suntech is advertising a similar technology being available next year. The triple junction Sharp module you mention comes in at 10% efficiency. Do you have a guess where thin film performance will be in 5 years?

Nuclear engineers aren’t much different than MEs btw. Building and fixing nuclear plants has recently been more limited by welders than engineers. Your personnel shortfall comments talk about the top of the food chain. I’ve always seen more of a personnel shortfall on the installation end of the chain compared to design or manufacturing. The personnel shortfall issue is interesting though. You’ve got to figure that solar energy systems will become easier to install. Once solar subsidies go away there won’t be much stopping a do-it-yourselfer from installing the lion’s share of a system over a few weekends and calling up an electrician to hook up all the hot stuff. We might even see homes pre-prepared for solar with roof anchors and wiring paths etc. The unfinished roof version of the unfinished basement. This sort of development would tend to ease the personnel issue I’m worried about.

But who knows. Everything is growing so fast it's hard to tell. It's fun to extrapolate though.

Robert McLeod said...

anonymous said:
The Hoffman citation for 33% per year is somewhat academic - I wonder if Merrill, GS, or any of the research departments in the banks have commented in an increase in capacity over time.

I'm not sure that the investment banks have been tracking PV that long. The first reference is to a Merrill-Lynch report references SolarBuzz, which is a rather expensive report.

mrshaba said:
Could you name a few of these silly PV concepts please? What do you think of wide acceptance angle concentrators?

I'm not going to 'name names' without backing up my opinions (i.e. with a full post). Wide-angle concentrators are better than tracking optics (on a cost basis) but still suffer in the marginal times (overcast, mornings). As such, caveat emptor applies because if someone is relying on concentrators to boost their cell conversion efficiency, it won't perform as well in the real world as against the Air Mass 1.5 test conditions.

I’ve always found thin film technologies inferior because of the comparatively low efficiencies. In the next 5 years average silicon modules could well get to 20% efficiency. SunPower is already above 19% module efficiency and Suntech is advertising a similar technology being available next year. The triple junction Sharp module you mention comes in at 10% efficiency. Do you have a guess where thin film performance will be in 5 years?

Efficiency isn't the best metric for determining the cost per watt. It has an impact, but it's mostly in terms of the ancillary costs, i.e. the glazing, the frames, etc. It will become more important in time, but I do not see the ancillary costs dominating before PV becomes an important energy source. Thin-films have the potential to greatly reduce both the amount of raw material required and the amount of material processing required.

On the Sunpower monocrystalline cells, well, I am working on electron microscopy techniques for my Ph.D. I do a lot of specimen prep work, which involves polishing, cutting, etc. of semiconductors which is practically identical to what's required for monocrystalline silicon. It's very labour intensive.

Growing thin films via chemical vapour deposition is a lot more straight-forward and allows for vastly higher throughputs. Amorphous silicon has some serious issues but I do think you'll see better and better microcrystalline silicon. I recently saw a paper showing an electron mobility of 450 cm^-2 V^-1 s^-1 for a type of laser annealed microcrystalline silicon. Semiconductor grade Silicon is only about 3x better, so the material continues to improve. See:


and referenes [27] and [28] therein.

Your suggestion about building roofs ready for PV is an interesting one, and maybe something Southwest states in the USA should consider. Corrosion, is probably the biggest potential drawback, since that is one of the primary limiting factors in the lifetime of PV system.

mrshaba said...

Thank you for your response. I'll check out the paper and references. My point with efficiency is that it seems to be improving surprisingly quickly. I recognize this translates into ancillary cost reductions but not necessarily the lowest cost per watt.

You mentioned ancillary costs of $2.50/Wp. This would go to $1.50 if you take out the inverter. This leaves roughly 50-75 cents in ancillary costs that can be cut by installing 20% vs 10% efficient panels. This isn't a whole lot... I'll give you that.

But here's what bothers me. Suntech was selling conventional panels for $3/Wp in 2004. Their panels go for $4/Wp currently. The price hike has been driven mainly by inflated raw silicon and wafer costs. When I ponder what the Wp costs would be without the inflation I'm left thinking the 50-75 cents in ancillary cost savings is very significant. Does this reasoning make sense? When I apply the learning curve idea to conventional panels it appears as though grid parity will be reached with or without thin film.

But how long will it take before the inflation goes away? And how will thin film develop? These things I don't know.

This report projects 13% efficiency CdTe modules in 5 years: http://www.nrel.gov/pv/thin_film/docs/first_solar_update2003.pdf

There are clearly applications where size or efficiency matter but 10% efficient panels are plenty good for roofs.

You mentioned it would take 3.5-7 m2 of 10% efficient panels per person to supply all our energy needs. 1.25-5 kWh per person per day isn't high enough. What did you mean with this quote?


Robert McLeod said...

mrshiba said:
But here's what bothers me. Suntech was selling conventional panels for $3/Wp in 2004. Their panels go for $4/Wp currently. The price hike has been driven mainly by inflated raw silicon and wafer costs. When I ponder what the Wp costs would be without the inflation I'm left thinking the 50-75 cents in ancillary cost savings is very significant. Does this reasoning make sense? When I apply the learning curve idea to conventional panels it appears as though grid parity will be reached with or without thin film.

Well you've discovered the difference between price and cost, yes. From what I understand, the Chinese manufacturers can produce amorphous Silicon panels for about $1.0/Wp, with perhaps an efficiency of 7.5 % after the initial photodegradation. Due to worldwide demand, they are selling them for several times that.

For the PV industry to continuously grow at 33 % a year, it will need to realize very healthy profit margins. That will, of course, slow down the rate at which the market price drops, assuming demand doesn't sag.

Thin film does have a couple major steps to take that will greatly reduce its ancillary costs, and those are: application of a thin hardcoat (instead of thick glass glazing), and application onto roofing material as the substrate.

Thin-film PV is currently made backwards: you use the glass as the substrate, apply the transparent conductive oxide, apply your active layers to form junctions, and then finally the back electrode (typically aluminium). However, there's no real need for a ~2.5 mm sheet of glass if you can develop something harder and tougher and apply it via an evaporation process. If you use a roofing material as a substrate so that your panels are now 'dual-use' (absorb sunlight, shed rain) you've now negated the bulk of those efficiency dependent ancillary costs.

I personally do not especially like the toxic panels (CdTe) from a market acceptance perspective. Some of the formation gases in thin-film silicon are just as toxic (e.g. phosphine gas) but not present in the final product.

You mentioned it would take 3.5-7 m2 of 10% efficient panels per person to supply all our energy needs. 1.25-5 kWh per person per day isn't high enough. What did you mean with this quote?

The main difference being that I was giving a world average, and all the countries at the bottom of the list balance the OEDC countries at the top. I am also making the assumption that we could replace our energy consumption with electricity at a 3:1 ratio due to the lower entropy of electricity compared to to fossil fuels.

I consume about 5 kWh a day at home, BTW. About 2/3rds of that is my refrigerator (I rent).

Anonymous said...

I too am concerned with CdTe panels. I can almost see the contaminated groundwater headlines now.

I appreciate your manufacturing explanations for thin-film and your conviction. Thin-film definately wins out in the flexibility of application department.

Your numbers make a little more sense now. But you did state that all energy and not just electricity could be replaced. Did you mean just electricity? Would it not be more reasonable to extrapolate where electricity use per capita is headed and use that to figure for solar area requirements?

Anonymous said...

Here's some solar ready home info.


Krassen Dimitrov said...

Interesting... but flawed:

1. Even though PV technology is akin to semiconductor, the same scaling effects do not apply. When people talk about the scaling in semiconductors it is in the context of an Integrated Circuit: size of a transistor  transistor density. The cost of processing a sq. cm. of silicon has been surprisingly constant. You can't expect that to change in such drastic measures...
2. The historic data on the learning curve has nothing to do with decreasing production costs per sq.cm. due to technological innovation as you imply. The two major drivers have been: (i) improved efficiency  lower price per Wp (not per sq. cm), and (ii) the growth in semiconductor fab capacity has created slack in older generation foundries, which cannot process at the current node. PVs have been a good way for them to extend their economic life by utilizing the already sunken cost. None of these two factors will keep up with more significant instalment.
3. Vapour Deposition is not an answer, I don’t know where you got that from… It is quite expensive actually. The big rage now is with baking thin films of nanoparticles (NanoSolar), however this is not just silicon, it is CGS (copper-gallium-silicon), which of course is not scalable (worldwide gallium production is only a few tons).
4. With respect to your PV electricity cost simulation: if the discount rrate was 1% over the central bank rate, that’s too low, it won’t excite too many investors with such returns. Also, I don’t see cleaning costs in your models.
5. I am totally confused by your estimates of 3.5 sq.m. per person of solar panels.

You reference 18TW for human use, divided by 6B people, this equals 3kW per person. 3.5 sq.m with 300W constant insolation and 10% efficiency gives only 105W per person. And that’s for peak output. You have capacity factor, which for baseload (which solar is) is very low.

Anonymous said...

I'm a long-time reader, first-time poster. Could Robert respond to "dr. Krassen Dimitrov"? I'm just really, really curious...and pretty damn unfamiliar with science and technology. I try to keep up as best I can, though. :)

Cyril R said...

Perhaps I can clarify a few points that KD made:

The cost of processing a sq. cm. of silicon has been surprisingly constant. You can't expect that to change in such drastic measures...

That's for traditional flat plates. You mean ingots, right?

First, as you said their efficiency kept going up. Double the efficiency at the same area costs means twice the energy. Given the fact that electricty cost is inversely proportional to the energy harvested, that means half the cost per unit of energy.

Of course, you have a valid point in implying that the limits of efficiency of traditional flat plates silicon PV are in sight, so novel approaches are needed to further reduce cost. You are wrong to think this isn't happening: Sliver cells and String Ribbon are just two of the approaches that could plausibly reduce the cost per square meter quite drastically.

Second, there's manufacturing improvements. Non cell related costs have gone down a lot due to improved manufacturing and technology, and larger scale production. Don't underestimate those cost, they are big and subject to continuous improvement.

Here is where thinfilms often have an advantage. I am skeptical about rare earth thinfilms (CIGS, CdTe etc) being able to keep on growing exponentially long enough. As you mentioned also, there are huge uncertainties with the availability of rare earths. Some people argue that the percentage of rare earth cost of the total cost is so low that prices could go up a lot, and in that way stimulate new exploration and exploitation of previously uneconomical deposits. But this is very speculative, and even if true it will take a long time to get the capacity up and running. Will the mining capacity be able to grow exponentially?

But silicon thinfilms show a lot of promise. Manufacturing investment is much lower, especially with new manufacturing processes like roll-to-roll production, printing technologies etc.

Installation can be made very easy, for example one could buy rolls of thinfilm "carpet" with an adhesive underneath and just stick it on your roof. I think United Ovonics has such a product. Other approaches are to make the modules very large in order to reduce overhead costs. For new build, or roofs that require heavy refurbishment, Building Integrated PhotoVoltaics (BIPV) is promising.

As for inverters, mass production really does wonders. Car inverters cost 40 cents per Watt according to the engineer-poet. That's less than half of the cost of solar inverters.

A bit further in the future, there's a lot more intersting stuff coming up. Infrared nano-antennas potentially up to 80% efficiency. Amorphous diamond as a semiconductor in stead of silicon promises up to 50% efficiency at lower production costs per square meter. Silicon nano-crystals of up to 30% effiency while using a tiny fraction of the raw silicon.

Vapour Deposition is not an answer, I don’t know where you got that from… It is quite expensive actually.

Depends on the type of CVD and the type of material that has to be deposited and onto what material. Some processes are already very cheap. Just look at how cheap low e coatings are for insulated windows. Ten years ago they were really expensive. I think that saying CVD is expensive is a blanket statement that has no value without a good reference. This is an industry that is developing fast, with innovations in manufacturing following quickly one after another (just look up low e coatings development for an example).

With respect to your PV electricity cost simulation: if the discount rrate was 1% over the central bank rate, that’s too low, it won’t excite too many investors with such returns. Also, I don’t see cleaning costs in your models.

I could think of a model in which the government stimulated PV installations by allowing PV owners to get most of their loan from them. The government is able to borrow money very cheaply from private investors. However, the extra demand for loans means the govt has to provide sligthly higher interest for private entities in order to attract the extra money. And the banks aren't going to be happy about all this of course; they'll cry that it's unfair competition, and they may have a good point. But it's definately doable; it's a strategic policy which may very well be enough justification.

Also, cleaning costs are very low for large systems. The Springerville generation station has a few mills or something like that in cleaning costs. In fact the total variable costs are under one cent per kWh. Of course, a smaller system is going to have higher costs per kWh. A 5 kW system could require 15 minutes of cleaning every month to keep it close to optimal in output, according to a friend of mine which has a similar installation. Let's take 50 bucks an hour including materials. (all you need is a bucket of water and a long cleaning pole so you don't have to get up the roof). That's 150 bucks of cleaning per year. In a good solar location you'd get 10000 kWh per year from this installation which is 1.5 cents per kWh. If the solar system gets cheaper, it will actually make sense to devote less time to cleaning. Cleaning only 10 minutes six times a year means just 0.5 cents per kWh. That would have to be compared to the loss in output, if any. Of course, a location with less sunshine is going to be more expensive, but even at half the above production, still not exactly a showstopper. For now, I don't suggest solar panels in areas that get less than 20 percent capacity factor, unless for off-grid and remote applications of course.

You reference 18TW for human use, divided by 6B people, this equals 3kW per person. 3.5 sq.m with 300W constant insolation and 10% efficiency gives only 105W per person. And that’s for peak output. You have capacity factor, which for baseload (which solar is) is very low.

You are confusing peak figures with average figures. You already calculated constant insolation, so you already have average output - not peak.

However, the way to do these macro scale calculations is to look at energy, not power. The world uses about 18000 billion kWhs per year. If your figure of 18 TW is correct then that implies a capacity factor of 11 or 12 percent, very reasonable I think.

But let's do our own calculations. Using a reasonable solar insolation figure of 2000 kWh/square meter per year and 10 percent efficiency that's 200 kWh net. That's 90 billion square meters or 90000 square kilometers. The world is about 149 million square kilometers of land area; about 0.06 percent of the world's land area. Even at half the insolation I used that's still just 0.12 percent of the world's land area.

Whoa. This post has gotten way too long!

Cyril R said...

Oh, and that's 90 billion divided by 6 billion people (it's probably closer to 7 billion actually) means 10 square meters per person. For the low insolation case there's half the energy available, so double the area becomes 20 square meters per person.

This doens't include storage losses. But even then the area is just not big. My house is pretty big at more than 200 square meters, and much more still if you count the backyard. And the agricultural land I use (by consuming food) has to be many times that figure. So solar land area won't be the bottleneck at all.

Cyril R said...

Whoops, 15 and 30 square meters, respectively.

Alexander Forstner said...

Would you happen to have a copy of report you referenced "Solar Wave - Apr-07 Edition" that you could share. The link is broken and I have been unable to find any reference to it elsewhere on the net.


Robert McLeod said...

Lynch report:


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