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Power density (Rev #9, changes)

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The idea

The term power density is used in various ways, but in the work of Vaclav Smil it means the number of usable watts that can be produced per square meter of land (or water) by a given technology, and that is how we will use it here.

Renewables in UK

Renewable forms of energy generally have a much lower power density than fossil fuels. This could have huge impacts on our landscape. For example, consider the plan M (middle) for the United Kingdom on page 215 of David MacKay’s book Without the Hot Air:


In this paper:

• Vaclav Smil, Power density primer: understanding the spatial dimension of the unfolding transition to renewable electricity generation.

Smil writes:

Energy density is easy – power density is confusing.

One look at energy densities of common fuels is enough to understand while we prefer coal over wood and oil over coal: air-dried wood is, at best, 17 MJ/kg, good-quality bituminous coal is 22-25 MJ/kg, and refined oil products are around 42 MJ/kg. And a comparison of volumetric energy densities makes it clear why shipping non-compressed, non-liquefied natural gas would never work while shipping crude oil is cheap: natural gas rates around 35 MJ/m3, crude oil has around 35 GJ/m3 and hence its volumetric energy density is a thousand times (three orders of magnitude) higher. An obvious consequence: without liquefied (or at least compressed) natural gas there can be no intercontinental shipments of that clean fuel.

Power density is a much more complicated variable. Engineers have used power densities as revealing measures of performance for decades – but several specialties have defined them in their own particular ways.


For the past 25 years I have favored a different, and a much broader, measure of power density as perhaps the most universal measure of energy flux: W/m2 of horizontal area of land or water surface rather than per unit of the working surface of a converter.

Here are some of Vaclav Smil’s results:

  • Most large modern coal-fired power plants generate electricity with power densities ranging from 100 to 1,000 W/m2, including the area of the mine, the power plant, etcetera.

  • No other mode of large-scale electricity generation occupies as little space as gas turbines: besides their compactness they do not need fly ash disposal or flue gas desulfurization. Mobile gas turbines generate electricity with power densities higher than 15,000 W/m2 and large (>100 MW) stationary set-ups can easily deliver 4,000-5,000 W/m2. (What about the mining?)

  • The energy density of dry wood (18-21 GJ/ton) is close to that of sub-bituminous coal. But if we were to supply a significant share of a nation’s electricity from wood we would have to establish extensive tree plantations. We could not expect harvests surpassing 20 tons/hectare, with 10 tons/hectare being more typical. Harvesting all above-ground tree mass and feeding it into chippers would allow for 95% recovery of the total field production, but even if the fuel’s average energy density were 19 GJ/ton, the plantation would yield no more than 190 GJ/hectare, resulting in harvest power density of 0.6 W/m2.

  • Photovoltaic panels are fixed in an optimal tilted south-facing position and hence receive more radiation than a unit of horizontal surface, but the average power densities of solar parks are low. Additional land is needed for spacing the panels for servicing, access roads, inverter and transformer facilities and service structures — and only 85% of a panel’s DC rating is transmitted from the park to the grid as AC power. All told, they deliver 4-9 W/m2.

  • Concentrating solar power (CSP) projects use tracking parabolic mirrors in order to reflect and concentrate solar radiation on a central receiver placed in a high tower, for the purposes of powering a steam engine. All facilities included, these deliver at most 10 W/m2.

  • Wind turbines have fairly high power densities when the rate measures the flux of wind’s kinetic energy moving through the working surface: the area swept by blades. This power density is commonly above 400 W/m2 – but power density expressed as electricity generated per land area is much less! At best we can expect a peak power of 6.6 W/m2 and even a relatively high average capacity factor of 30% would bring that down to only about 2 W/m2.

For comparison, incoming Solar radiation reaching the Earth’s surface has a global average power density of 156 W/m2 of which 55 W/m2 is radiated back into the atmosphere as long wave energy.

Of course, power density is of limited value in making decisions regarding power generation, because:

  1. The price of a square meter of land or water varies vastly depending on its location.

  2. Using land for one purpose does not always prevent its use for others: e.g. solar panels on roofs, crops or solar panels between wind turbines.

Nonetheless, Smil’s basic point, that most forms of renewable forms of energy will require us to devote larger areas of the Earth to energy production, seems robust. (A potential exception is breeder reactors). This point is also made by Saul Griffith in his discussion of ‘Renewistan’. Stewart Brand wrote:

The world currently runs on about 16 terawatts (trillion watts) of energy, most of it burning fossil fuels. To level off at 450 ppm of carbon dioxide, we will have to reduce the fossil fuel burning to 3 terawatts and produce all the rest with renewable energy, and we have to do it in 25 years or it’s too late. Currently about half a terrawatt comes from clean hydropower and one terrawatt from clean nuclear. That leaves 11.5 terawatts to generate from new clean sources.

That would mean the following. (Here I’m drawing on notes and extrapolations I’ve written up previously from discussion with Griffith):

“Two terawatts of photovoltaic would require installing 100 square meters of 15-percent-efficient solar cells every second, second after second, for the next 25 years. (That’s about 1,200 square miles of solar cells a year, times 25 equals 30,000 square miles of photovoltaic cells.) Two terawatts of solar thermal? If it’s 30 percent efficient all told, we’ll need 50 square meters of highly reflective mirrors every second. (Some 600 square miles a year, times 25.) Half a terawatt of biofuels? Something like one Olympic swimming pools of genetically engineered algae, installed every second. (About 15,250 square miles a year, times 25.) Two terawatts of wind? That’s a 300-foot-diameter wind turbine every 5 minutes. (Install 105,000 turbines a year in good wind locations, times 25.) Two terawatts of geothermal? Build 3 100-megawatt steam turbines every day — 1,095 a year, times 25. Three terawatts of new nuclear? That’s a 3-reactor, 3-gigawatt plant every week — 52 a year, times 25”.

In other words, the land area dedicated to renewable energy (“Renewistan”) would occupy a space about the size of Australia to keep the carbon dioxide level at 450 ppm. To get to Hansen’s goal of 350 ppm of carbon dioxide, fossil fuel burning would have to be cut to ZERO, which means another 3 terawatts would have to come from renewables, expanding the size of Renewistan further by 26 percent.


Atmosphere, Weather and Climate, R G Barry and R J Chorley, Routledge 2003

category: energy

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