Monthly Archives: November 2014

Grains of rice, Japanese swords and solar panels

Even Greenpeace has underestimated the growth of renewables.  In particular, solar has been growing exponentially, and may continue to be so for a while, though likely at a slower percentage rate.

Greenpeace did much better than many at projecting the growth of renewable energy sources in the 2000s.  Their projections were very close to outturn for wind – the 1999 projections were a little below outturn, the 2002 projections a little above.  However even Greenpeace underestimated the growth of solar.  The projections were nevertheless startlingly better than those of the IEA, who have, as I’ve previously noted, consistently underestimated the growth of renewables by a huge margin.  Growth of solar has been exponential, as has that of wind (at least until recently).  Greenpeace appears to have done well by following the logic of exponential growth.

Greenpeace’s projections for wind growth in the 2000s were close to outturn, but they underestimated the growth of solar …


Exponential growth is so powerful that it can confound intuition about how large numbers can become.  The counterintuitive power of exponential growth is illustrated by the process of making a traditional Japanese steel sword.  The supreme combination of strength and flexibility of such a weapon is said to derive from the way an exponential process layers the metal.  As the metal is beaten out and folded repeatedly to forge the sword the number of layers in the metal doubles up each time.  Following this simple process 15 times creates 215 layers, well over 30,000.  This would be impossible in any other way with traditional methods, and the number of layers created would be hard to comprehend without doing the formal calculation.  This property of producing very large numbers from simple repeated doublings may have contributed to previous projections for renewables seeming implausible, because they were so much greater than the then installed base.  This may have contributed to even Greenpeace being a little cautious in its projections for solar.

Nevertheless exponential growth inevitably runs into limits as some stage.  This is captured by the classic fable of grains of rice on a chessboard, where one grain is put on the first square, two on the second, four on the third, eight on the fourth and so on, doubling with each square.  Half way through the chessboard the pile of grains, though very large, is manageable – around 50 tonnes for the 32nd square.  However amounts then quickly begin to go beyond all reasonable physical constraints.  The pile on the final square would contain 263 grains of rice, which is about 230 billion tonnes.  This is about 300 times annual global production, and enough to cover not just a square of the chessboard but the entire land surface of the earth (to a depth of about a millimetre or two).

Extrapolating growth rates for solar PV from the period 2000 to 2013, when cumulative installed capacity doubled every two years, runs into similar limits.  At this growth rate the entire surface of the earth would be covered with solar panels before 2050.  This would provide far more energy than human civilisation would need, if there were room for any people, which there would not be because of all the solar panels.   So are there constraints that imply that renewables are now in second half of the chessboard – or, if you prefer a more conventional model, the linear part of an s-curve for technology adoption?

Looking at solar in particular, as I’ve previously commented, it needs a lot of land, but this is unlikely to be a fundamental constraint.  Some have previously suggested a limit as technologies reach scale, defined as about 1% of world energy supply, after which growth becomes more linear.  However solar manufacture and installation are highly scalable, so there are fewer obstacles to rapid growth than with traditional energy technologies.

Costs are rapidly falling, so that solar is becoming competitive without subsidy, both compared to other low carbon technologies and, increasingly, with high carbon technologies, especially if the cost of emissions is taken into account.  There is no obvious limit to how low the costs of solar cells can go that is likely to bind in the foreseeable future, although the ancillaries may show slower cost falls.  The costs of lithium ion batteries are also falling rapidly, having approximately halved in the last five years and continuing to fall at a similar rate.  As a result daily storage is becoming much more economic, reducing the problem of the peakiness of solar output and easing its integration into the grid, although seasonal storage remains a daunting challenge.

Solar still accounts for only around 1% of world electricity generation so globally there are plenty of opportunities globally in new electricity demand and from scheduled retirement of existing generating plant.  The vexed issues around grid charges, electricity market structures and role of incumbents may slow growth for a while, at least in some jurisdictions, but seem unlikely to form a fundamental barrier globally as long as costs continue to fall.

In short there seem few barriers to solar continuing to grow exponentially for a while, although likely at a slower percentage rate than in the past – each doubling is likely to take longer than two years given the current scale of the industry.  Solar can still continue moving quite a long way up the chessboard before it hits its limits.  How large the industry will become will need to await a future post, but provisionally there does not seem any reason why solar PV should not become a 300-600 GW p.a. or more industry.

Policy has played an important role in the development of solar to date mainly by providing financial incentives.  It will continue to play an important role, but this will be increasingly around removing barriers rather than providing a financial stimulus.

Of course I cannot know if this fairly optimistic view is right.  But it does at least to avoid some issues that might bias projections downwards.  First, it recognises the potential validity of counter-intuitive results.  In a sector such as energy which usually changes quite slowly the numbers resulting from exponential growth can seem implausible.  This can lead to rejection of perfectly sound forecasts, as the intuition of experienced professionals, which is based on long experience of incremental change, works against them.  Second it avoids assuming that all energy technologies have similar characteristics.  Finally, it takes into account a wide range of possibilities and views and considers the drivers towards them, helping to avoid the cognitive glitch of overconfidence in narrow limits to future outcomes.

The rate of growth of renewables is intrinsically uncertain.  But the biases in forecasts are often more towards underestimation than overestimation.  If you’ve been in the energy industries a while it’s quite likely that your intuition is working against you in some ways.  Don’t be afraid to make a projection that doesn’t feel quite right if that’s where the logic takes you.

Adam Whitmore – 25th November 2014


In the calculations of the results from exponential growth I have, for simplicity, assumed very rough and ready rounded values of 40,000 grains of rice = 1litre = 1 kg.  I’ve assumed 10m2/kW (including ancillaries) for the area of solar panels. The land surface of the earth is 1.5 x108 km2.  Solar capacity doubled around every 2 years from 2000 to 2013, growing from 1.25GW in 2000 to 140 GW in 2013 (source:  BP statistical review), reaching a land area of around 1400km2.  217 times its current area takes it past the land surface of the earth, so it would take to 2047 (34 years from 2013) with doubling of installed capacity every 2 years to reach this point.  The source of the story about sword-making is from the 1970s TV documentary The Ascent of Man and accompanying book.

For data on Greenpeace’s historical projections see: See pages 69 and 71