What’s the best way of harvesting the energy of the sun?

This is another post inspired by my current first year physics course, The Physics of Sustainable Energy (PHY123). Calculations are all rough, order of magnitude estimates – if you don’t believe them, try doing them for yourself.

We could get all the energy we need from the sun, in principle. Even from our cloudy UK skies an average of 100 W arrives at the surface per square meter. Each person in the UK uses energy at an average rate of 3.4 kW, so if we each could harvest the sun from a mere 34 square meters with 100% efficiency, that would do the job. For all 63 million of us, that’s just a bit more than 2,000 square kilometres out of the UK’s total area of 242,900 km2 – less than 1%. What would it take to turn that “in principle” into “in practise”? Here are the problems we have to overcome, in some combination: we need higher efficiencies (to reduce the land area needed), lower costs, the ability to deploy at scale and the ability to store the energy for when the sun isn’t shining.

There are at least four different technological approaches we could use. The most traditional is to use the ability of plants to convert the sun’s energy into fuel molecules; this is cheap, deployable at scale, and provides the energy in easily storable form, but it’s not very efficient and so needs a lot of land. The most technologically sophisticated is the solar cell. These achieve high efficiencies (though still not generally more than about 20-25%), but they cost too much, they are only available at scales that are still orders of magnitude too small, and produce energy in the hard-to-store form of electricity. Other methods include concentrating the sun’s rays to the extent that they can be used to heat up a working fluid directly, a technology already in use in sunny places like California and Spain, while in the future, the prospect of copying nature by using sunshine to synthesise fuel molecules directly – solar fuels – is attractive. How do these technologies compare and what are their future prospects?

We can get a useful baseline by thinking about the most traditional of these technologies – growing firewood. Traditional methods of sustainably managing a wood for fuel – a coppiced hardwood – would give you an annual harvest of between 5 and 10 tonnes of wood a year per hectare. At an energy yield of about 15 GJ/tonne, this corresponds to an average power yield of perhaps 0.25 W/m2. The energy arrives in conveniently storable form (though to convert it into the most useful form – electricity – you have to factor in conversion losses of perhaps 60-70% after you’ve taken your woodchips to your local communal thermal power station). In round numbers, this corresponds to a conversion efficiency to electricity of 0.1%. To meet one person’s energy needs, you’d need about 30,000 m2 – 3 hectares. For one person this doesn’t sound too bad a deal – the woodland would cost perhaps £30,000 up front, and it would need a certain amount of time and labour to manage it. But, on the positive side, the woodland would have other wildlife and ecosystem value as well. The problem, of course, is that for all 63 million people to be so supplied would take more than 7 times the total area of the UK, even leaving aside the need to have some land to live in and grow food on.

With solar cells of 20% efficiency, you’d need much less land area – a still large, but more manageable 11,000 square kilometres in total, 170 square meters per person (for comparison, about 3,500 km2 of the UK is covered with buildings) . The trouble with this is that we can’t at the moment make anything like enough of them. The total annual world production of solar cells has been growing fast, but it is still only a few hundred square kilometres a year. The energy arrives in the form of electricity, which is flexible and useful, but not easily storable in large enough quantities to smooth out the obvious differences between night and day, summer and winter. The solar thermal technologies operate at roughly similar efficiencies to photovoltaics, and don’t have significant advantages in cost or scalability.

Can we make biofuels more efficient, so their land demands are more reasonable? For first generation biofuels, such as rapeseed for biodiesel and maize to produce bioethanol, the selling point is not so much efficiency, as the ability to produce directly a liquid fuel that can conveniently substitute for fossil fuels. On the other hand, the use of more intensive agricultural methods means that one needs to carefully account for energy inputs into process. One estimate of the energy return from rapeseed for biodiesel gives 0.15 W/m2. This in the same ball park as the traditional woodland, though in that case to deliver the energy in convenient liquid form you would have to use the Fischer-Tropsch process to convert solid fuel to liquids, which would lose a further factor of 2 or 3 in conversion losses. Another estimate, for the net energy yield from bioethanol derived from maize (corn) grown in the US midwest, is 0.05 W/m2; this is a biofuel that wouldn’t survive in a rational world. Bioethanol derived from sugar cane in Brazil, on the other hand, yields a much more respectable 0.3 W/m2, though of course Brazil is more than twice as sunny as the UK.

What are the ultimate limits on the efficiency of biofuel production? The first obvious point to make is that leaves are green, not black – they don’t absorb light across the whole spectrum. Different varieties of chlorophyll absorb red light and blue light, leaving the green light unabsorbed – this puts a fundamental upper limit of 43% on the efficiency of photosynthesis. But the actually achievable efficiencies are much lower; further energy losses take place during the photochemistry of photosynthesis and in the synthesis of the carbohydrates that are its ultimate products. Efficiencies are further lowered in most plants by a back-reaction called photorespiration. In certain plants, adapted for hot, dry conditions, a physiological mechanism suppresses this reaction; these so-called C4 plants can achieve a maximum efficiency of about 6%, compared to the 4.6% possible for normal, or C3 plants. There’s an obvious advantage to using C4 plants as biofuels – such plants include sugar cane, maize and the tropical grass miscanthus. It’s probably also possible to genetically modify normal C3 plants so they use the more efficient C4 mechanism (this is the aim of the Bill and Melinda Gates supported C4 Rice project).

These figures, on the face of it, should encourage us to be optimistic about biofuels – they suggest that our baseline energy yield, from traditional firewood, could be improved by a factor of 20 or so. But as the discussion of maize bioethanol makes clear, actual net yields fall far below these theoretical maxima. Many other factors limit plant growth in practise, and the energy inputs in intensive farming and processing aren’t negligible.

To return to photovoltaics, one can see that the key issues to be solved are cost, scale and storage. I don’t include efficiency here; silicon is quite close to being the ideal single semiconductor to make a solar cell from, in terms of the match of its band-gap to the solar spectrum, and commonly available silicon solar cells are already close to their theoretical efficiency limit. To improve on this level of efficiency one needs complex compound semiconductor nanostructures which necessarily will greatly increase cost and reduce scalability. Roughly speaking, we’d need to increase the annual production of solar cells by a factor of 100 or so for them to approach the point of being able to supply most of our energy needs (this would ramp production up to the point at which a year’s output would yield capacity to generate 5% of our current world needs). To do this in 20 years would require annual compound growth rates of 25%, which is by no means completely ridiculous – recent years have actually seen higher rates of growth. But I doubt that these growth rates can be sustained with current technologies – instead, we’ll need new designs of cells, not significantly worse in efficiency and lifetime than silicon, that can be made by very large scale, low-cost, reel-to-reel processes. A variety of promising new technologies promising this are on the horizon, with the organo-metallic perovskites introduced by Oxford’s Henry Snaith being the most topical.

But this still leaves the problem of storage. There are at least three separate issues for a solar-dominated energy economy – the need for seasonal storage to get us through our cold, dark winters, the need for smoothing energy needs over day and night, and the need for energy for transport. I believe that current battery technologies are inadequate for these tasks by orders of magnitude and are unlikely to improve fast enough to solve these problems fully (to justify this statement would require another long post, of course). The lesson of our current fossil fueled world, on the other hand, is that flammable liquids are an enormously effective way of storing and transporting energy, hence the attractiveness of current liquid biofuels, despite the inefficiency of their production.

The easiest fuel to produce from electricity is hydrogen, easily generated from water by hydrolysis. But hydrogen, as a gas, has a very low energy density and is difficult to store and transport. One attractive option is to use the hydrogen, together with nitrogen, to make ammonia, using the Haber-Bosch process. This is an easily liquified gas that can be burned in a gas turbine – to generate electricity from the stored fuel – or a modified diesel engine, without producing carbon dioxide. But ammonia is toxic and less convenient than hydrocarbon fuels, as it has to be stored under pressure. Methanol is much more attractive as a liquid fuel, as it can be used in minimally modified petrol engines. It can be made from hydrogen and carbon dioxide; a zero-emission methanol economy would extract carbon dioxide from the atmosphere, though that separation in itself needs both energy and new technology. An intermediate technology would use carbon dioxide that would otherwise be released into the atmosphere, for example from a gas-fired power station or a cement works.

These ways of of producing liquid fuels from the sun look to be roundabout and indirect, and it’s tempting to ask whether we can design a synthetic chemistry that does the same as plants do – absorb light in a photocatalyst that directly converts water and carbon dioxide into fuel. This is the idea behind the field of “solar fuels”. It’s a fascinating research field, but we’re at a very early stage, and I’m not convinced that we are anywhere close to the conversion efficiencies that can be achieved by the less elegant alternative of using a solar cell to make electricity and using that to produce hydrogen from water by electrolysis. Or, for that matter, the efficiencies that can in principle be obtained by what are potentially the most effective biofuel systems – using algae in tanks, with added carbon dioxide, to make algal biofuels.

I am optimistic in the long run about solar energy – the order of magnitude calculations I began with make it clear that it does have the potential to provide plentiful, entirely sustainable energy to the whole world. But there’s a lot of technology to be done to get there, and some interesting choices to be made on the way.

The estimates of the maximum efficiencies for plant photosynthesis come from Zhu et al., Current Opinion in Biotechnology 2008, 19:153–159, and for net energy returns on biofuels from H.S. Kheshgi et al, Annu. Rev. Energy Environ. 2000. 25:199–244