Moore’s Law for Solar Power?

Here are two items that were forwarded to me by friends—Mike Stay and Greg Egan. First:

• Ramez Naam, The Moore’s Law of solar energy, Scientific American guest blog, 16 March 2011.

Executive summary: solar cost per watt is dropping on an exponential curve, and will drop below coal by 2020. As usual we see some graphs where the past is fairly wiggly:

while the future is a smooth and mathematically simple, starting tomorrow:

Both these graphs show the price per watt of photovoltaic solar modules (not counting installation), measured in 2009 dollars. Both graphs are logarithmic, so an exponential decline in price per watt would show up as a straight line.

Of course, anyone can draw a curve through points. The question is whether experts can see a way to keep the trend going!

On this, the author writes:

While in the earlier part of this decade prices flattened for a few years, the sharp decline in 2009 made up for that and put the price reduction back on track. Data from 2010 (not included above) shows at least a 30 percent further price reduction, putting solar prices ahead of this trend.

He also writes:

We should always be careful of extrapolating trends out, of course. Natural processes have limits. Phenomena that look exponential eventually level off or become linear at a certain point. Yet physicists and engineers in the solar world are optimistic about their roadmaps for the coming decade. The cheapest solar modules, not yet on the market, have manufacturing costs under $1 per watt, making them contenders – when they reach the market – for breaking the 12 cents per Kwh mark.

The exponential trend in solar watts per dollar has been going on for at least 31 years now. If it continues for another 8-10, which looks extremely likely, we’ll have a power source which is as cheap as coal for electricity, with virtually no carbon emissions. If it continues for 20 years, which is also well within the realm of scientific and technical possibility, then we’ll have a green power source which is half the price of coal for electricity.

What do you think? Is this for real?

By the way, Naam’s blog post has a chart showing efficiencies of various solar cell technologies. It’s unreadably small, but here’s a version you can click to enlarge:

What I want to caution you about is that some of the more efficient solar cells use expensive materials for which the world supply is limited. For more on this see

Photovoltaic solar power, Azimuth Wiki: efficiency and physics of solar cells.

Here’s another article:

• Kevin Bullis, More Power from Rooftop Solar: A startup says technology inspired by RAID hard drives can boost power output by up to 50 percent, Technology Review, 29 April 2011.

Immediately below the headline they tone down the claim slightly, saying “25 to 50 percent”. But that’s still a lot. The idea sounds nice, too:

Solar cells have become more efficient in recent years, but much of the improvement has gone to waste because of the way solar cells are put together in solar panels, the way the panels are wired together, and the way the electricity is converted into AC power for use in homes or on the grid. Typically, the power output from a string of solar cells is limited by the lowest-performing cell. So if a shadow falls on just one cell in a panel, the power output of the whole system drops dramatically. And failure at any point in the string can shut down the whole system.

TenKsolar has opted for a more complex wiring system—inspired by a reliable type of computer memory known as RAID (for “redundant array of independent disks”), in which hard disks are connected in ways that maintain performance even if some fail. TenKsolar’s design allows current to take many different paths through a solar-panel array, thus avoiding bottlenecks at low-performing cells and making it possible to extract far more of the electricity that the cells produce.

20 Responses to Moore’s Law for Solar Power?

  1. Nameless says:

    This is certainly great progress. But we need another 5 years along this trend before PV can start making a dent. Consider that, at $3/watt and assuming ideal conditions (desert climate and extremely expensive electricity, $0.28/kwh on the margin, of inland Southern California, zero installation & equipment costs), each $1 invested up front in residential PV will generate 10 to 15 cents a year in profit.

    And the assumption of zero installation and equipment costs is not quite accurate either. In a typical residential-size PV installation, just the grid-tie inverter and the mounting hardware can add up to $1.5/watt. And installation contractors might easily charge $2..3/watt on top of that.

    I can’t say whether PV will get cheap enough to be employed on a mass scale by utility companies, but there are significant costs beyond the price of the panel itself which might keep PV from widespread adoption in the foreseeable future.

  2. Frederik De Roo says:

    The exponential trend in solar watts per dollar has been going on for at least 31 years now.

    But isn’t a decreasing exponential trend easier to achieve than a decreasing linear trend? In this sense the reference to Moore’s law makes the achievement sound more impressive than it actually is, because a growing exponential trend is much harder to achieve than a growing linear one.

    Btw, is it Azimuth Wiki or Azimuth Library?

    • Think of it another way: can watts-per-dollar *increase* exponentially?

    • John Baez says:

      Frederik wrote:

      But isn’t a decreasing exponential trend easier to achieve than a decreasing linear trend? In this sense the reference to Moore’s law makes the achivement sound more impressive than it actually is…

      I think this achievement is comparable to Moore’s law. Moore’s original law said that “the density of transistors at which the cost per transistor is the lowest” keeps growing exponentially. But if the cost per transistor stayed the same or went up, we wouldn’t be so excited about Moore’s law! In practice, what really matters about Moore’s law is that the price of doing certain things—computing, storing information—keeps dropping exponentially.

      Of course a linearly decreasing cost would be even more exciting, because then the cost would drop to zero in finite time! But that’s not really relevant.

      Azimuth Wiki or Azimuth Library?

      The Azimuth Library is a subset of the Azimuth Wiki: click for some explanations.

  3. Speed says:

    The economics of solar power are complex with the second important variable (after dollars per watt) being areal power density. Even free cells aren’t very useful if it takes an acre to power my house.

    Lawrence Berkeley Labs publishes an annual report,”Tracking the Sun” and they’re up to issue III with data through 2009. It’s hefty.

    The capacity-weighted average installed cost of systems completed in 2009 – in terms of real 2009 dollars per installed watt (DC-STC)4 and prior to receipt of any direct financial incentives or tax credits – was $7.5/Watt, virtually unchanged from 2008, and $0.3/W below the averages in 2006 and 2007. From 1998-2009, capacity-weighted average installed costs declined by about 3.2% (or $0.3/W) per year, on average, starting from $10.8/W in 1998.

    Installed costs lagged wholesale PV module price movements from 2007-2009. Over this period, wholesale PV module prices declined by $1.3/W (based on Navigant Consulting’s Global Power Module Price Index), while total installed costs declined by only $0.2/W. The preliminary 2010 cost data … however, suggests that the drop in wholesale module prices during the preceding years translated into a large reduction in installed costs in 2010.

    (54 page pdf)

  4. Graham says:

    The blog post is only about PV solar power. There is also thermal or concentrated solar power, which is cheaper, though not reducing quickly in price.

  5. Zoran Škoda says:

    What is the meaning of price of photovoltaic cells per watt of power ? I mean say I buy 100 watts of power. What does it mean ? I suppose it is a peak power in some standard “full” insolation conditions ? What are these conditions ? If I know the average insolation at spot y, how can I calculate average production from knowing the factory watt power of the cell array ?

    • Speed says:

      This chart claims to show Average Daily Solar Radiation per Month — ANNUAL. The label is confusing at best. So I guess you multiply that by the efficiency of your solar cells times the number of watts you bought.

    • Nameless says:

      Price per watt is normally quoted in terms of DC power output by the panel under ideal conditions (cloudless sky, panel pointing directly at the sun). Once you account for DC-AC conversion inefficiencies, movement of the sun, clouds, you end up with something like 1000-1500 kWh/year of usable electricity out of a panel assembly that’s rated at 1 kilowatt DC. In ideal conditions, e.g. for a panel on a tracking mount in a tropical desert (Arizona or Libya), you can slightly exceed 2 kWh/year. A fixed-mount panel in Berlin can yield as little as 750 Wh/year.

      • Zoran Škoda says:

        Again, what is the “ideal conditions”, I do not need description of a sunny day but quantity. A manufacturer sells its product world wide. Sunny day in California is not the sunny day in Berlin, one in Spring noty the same as summer. It is not problem to estimate local data of average power per square meter. The problem is at which etalon of insolation a cell of factory 1 watt gives 1 watt. I want precise number of the standard reference insolation. Then I rescale linearly to actual insolation, what will be a good approximation.

        Speed your answer has noithing to do with question. I understand how to look at power per square meter; I was interested in manufacturers labels per watt which are independent from which surface area realizes this power in their standard conditions.

        • Speed says:

          I suggest that you contact one or more of the manufacturers at this link.

        • Nameless says:

          Conditions used to measure Pmax are called Standard Test Conditions (STC): irradiance of 1000 W/m2, AM1.5 spectrum (that is, spectrum of sunlight that passed through 1.5 thicknesses of the atmosphere), cell temperature 25°C.

          There’s a second number that is reported (but usually in fine print) called NOCT (nominal operating cell temperature). Since solar panels tend to get hot during operation, and they tend to lose efficiency above room temperature, and the assumption of 1000 W/m2 insolation at sea level is a best-case scenario, NOCT is more realistic. NOCT power rating can be 20-30% lower than STC power rating.

        • John Baez says:

          Thanks for that information, Nameless! For more:

          •, Nominal Operating Cell Temperature.

          Standard operating conditions, The Encyclopedia of Alternative Energy and Sustainable Living.

          I hadn’t known about this “Encyclopedia” – it’s being created by David Darling, who has also done other nice things.

        • Zoran Škoda says:

          Thank you, Nameless, this is what I was looking for! Speed, I guess this is independent from a particular manufacturer. Of course, scaling away from the standard conditions, reported by Nameless to other conditions is undoubtfully nonlinear (probably relative efficiency decreasing slightly with insolation and temperature), but for the estimates, one could rescale it linearly to the average actual insolation, I guess.

  6. Web Hub Tel says:

    Lots of interesting “green math” in understanding the amount of disorder in PV materials and how it affects the electrical characteristics. That has been my keen interest recently and no one else is looking at it in any new ways.

  7. Phil Henshaw says:

    Well… It’s a bit “out of the box”, but don’t the trends shown depend on there being no thermodynamic limit to solar energy conversion, as well as having all the technologies used to make solar cells and the prosperity of the economy largely relying on fossil fuels? What would happen if instead of asking if the trend will continue you started asking when the effect of all the things that will certainly prevent it from continuing will come into effect?

    The one thing that seems remotely possible to extend arbitrarily far, might depend on other things that obviously can’t, is the idea.

  8. […] John Baez: What To Do?, Moore’s Law for Solar Power? […]

  9. john says:

    If PV’s historical 30-yr price and efficiency improvement slopes remain about the same for the next 30 years, the median U.S. raw-cost of PV electricity will be roughly $0.035/kwh by 2035. In “DC nameplate” costs, that’s roughly $0.20/watt for panels, $0.20/watt for micro-inversion, and $0.50/watt for the remaining parts, installation, permits, and project management (total installed cost $0.90/watt). This assumes that panel prices will continue to halve in price every 8 years and commodity panel efficiency will continue to improve 3% per year (15% eff today to 30% eff in 2035).

    PV is the future, along with all the other renewables: wind, hydro, geo-thermal, etc… California is projecting 30% renewable electricity by 2020, and Germany is on slope for 95% renewable by 2050. By 2070, the industrialized world should be well over 80% renewable.

    The bad news is that we still have a massive transportation problem, especially in the developing world. I don’t see how the earth can deliver 110-120M b/d of affordable oil by 2040. My hope is that market signals will push far greater investments into storage and PV mobility, reducing the 2040 estimated 1B I.C. vehicles and apps to perhaps 500M or less.

  10. […] Revisiting Simon-Ehrlich 3) A note on the Simon-Ehrlich Bet 4) Moore’s Law for Solar Power? 5) What is the future of solar power? 6) Moore’s Law in […]

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