Power density

Making sense of power densities

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Making sense of power densities

A brief recapitulation of power densities representing all major energy conversions and uses precedes some revealing comparisons of supply and demand and the chapter closes with summations of land claims by the global energy systems and by the US provision of fossil, nuclear and renewable energies.

Summing up the findings of strongly quantitative books that contain thousands of numbers as well as a large amount of technical details could be done in ways ranging from an almost perfunctory recital of a few basic generalizations to an excessively elaborate review of all noteworthy conclusions. This book has been rich in numbers and in technical details but neither of these two extreme closing choices is my preference: instead, I will offer a systematic but concise recapitulation of key findings and then make the rates easier to remember as relative values through comparisons of typical power densities of specific production activities and of representative rates of energy use.

I will also use prevailing means, or the most common ranges, of power densities of all modern energy conversions in order to calculate approximate aggregates of spatial claims of energy systems. I will do so first on the global level, an exercise that cannot aspire to any high accuracy but whose order of magnitude quantifications help to set the modern energy provision in a wider context of changing land use. Afterwards I will do the same kind of summation, with a greater degree of accuracy, for the US, and, again, will compare the claims of America’s modern energy system with other major land use categories. But before I present brief recapitulations, comparisons and aggregate accounts, a few deconstructive points are in order.

Higher power density always means lower land claims but it should not be argued that the highest possible power densities are always desirable. Obviously, low power-density solar or wind-driven electricity generation makes sense in many regions that are far from existing grids and yet have abundant sunshine and persistent winds. Well-designed surface coal mines where surface reshaping and replanting closely follows the seam extraction and where landscapes can return to agricultural, forestry or recreational use in less than a generation can be greatly preferable to underground mining with its occupational hazards and often prolonged periods of ground subsidence. Hydrogeneration offers perhaps the best illustration of the less is always better fallacy: according to that simplistic rule run-of-river plants would be then most desirable as the purest examples of this technique have no storage reservoirs and hence claim no additional land beyond the existing river channel, and as other plants in this class (Manitoba’s Nelson River stations being an excellent example) create only mildly expanded river surfaces behind their low dams.

But such stations have obvious disadvantages somewhat akin to those of solar or wind projects: while their generation may not (as is the case with PV and wind) altogether cease it would be always limited by widely fluctuating water flows, particularly in regions with pronounced dry/wet seasons, and the absence of a large reservoir would nullify many advantages of large dams, namely their ability to assure a design level of firm capacity well above that corresponding to the minimum stream flow, to cover rapidly peak power demand, and to create water storages and extended water surfaces that can have other valuable uses beyond electricity generation. Moreover, lower power density may be an asset not only because a larger flooded area enables higher and more regular electricity generation thanks to minimizing seasonal fluctuations of water level (and hence of hydraulic head and power output) but also because it reduces the extent of periodically exposed land, an inevitable consequences of fluctuating river flows that could be eliminated, or greatly, reduced by building a large reservoirs.

Everything else being equal, high power densities would be always preferable but in reality different qualitative considerations invalidate such a simplistic verdict. This means that high power density fossil energies –- which may be also cheaper to transport, easier to store and used on demand –- are not inherently superior: after all, all fossil energies are exhaustible on the civilizational time-scale, while solar radiation and wind will last, when measured on such a times-scale, indefinitely, and properly managed water flows and plants could be harnessed for 103-104 years before another glaciation would. And although many of their uses have been made virtually pollution-free, removing and storing CO2 at scales that would eliminate the gas as a key factor of anthropogenic climate change is a daunting challenge.

Finally, a reminder that capacity (load) factor is a key consideration in a society that is increasingly dependent on incessant (365/24/7) and highly reliable (six nines, available 99.9999% of all time) delivery of electricity. Low power densities combined with low capacity factors offer a distinctly disadvantageous starting point. The most commonly encountered capacity factors go, in the ascending order, from 10-15% for PV generation in mid-latitude locations and 15-22% in the sunniest environments, to 20-35% for wind farms in moderately to very windy regions, 40-60% for large hydrostations, 60-85% for coal-fired electricity generating plants, and about 90% for nuclear reactors.


Modern civilization energizes its complex metabolism by converting two basic classes of resources into useful energies (mostly heat, light, motion and electricity): renewable flows and finite stores of fuels (mostly fossil minerals and uranium). Except for the geothermal energy, all renewable flows are transformations of solar radiation that reaches the biosphere. Nearly a third of that incoming flux is reflected by the Earth’s clouds and surfaces and nearly all of the rest is reradiated (rapidly or with variable delays), with only a small share driving atmospheric circulation (of which a tiny share can be harnessed as wind energy), the global water cycle (a small part can be converted to hydro-generated electricity) and photosynthesis (the source of biofuels and fossil fuels).

Renewable flows Solar radiation flux is thus many orders of magnitude larger than any of its conversions and even fairly low conversion efficiencies –- to heat (mostly in rooftop water heaters) or to electricity (by photovoltaic cells or by central solar plants) –- can harness it with relatively high power densities, brief maxima on the order of 102 W/m2, annual means on the order of 101 W/m2. Annual power densities for most hydro stations, as well as for wind turbines, are an order of magnitude lower (100 W/m2), exceptionally high phytomass harvests yield power densities around 1 W/m2 and harvests of productive forests and crops can be converted to useful energy with power densities of just 10-1W/m2.

During noon-time hours power densities of solar water heating in sunny climates can surpass 700 W/m2, by far the highest rate of any renewable energy conversion. Annual power densities are an order of magnitude lower, on the order of 100 Wt/m2 in sunny subtropical climates, 40-50 Wt/m2 in cloudy mid-latitudes while the global mean (based on actual performance, not on installed capacity) was 67 Wt/m2 in 2012. Two common biases must be avoided in order to calculate real, comparable, power densities of PV generation: the rates should not be expressed in terms of peak power and the area should not include only the module surfaces. Power densities of PV generation decline by an order of magnitude as we proceed from noon-time maxima to annual averages and from panel areas to total areas of PV projects. Noontime maxima at prevailing efficiencies (10-15%) are 80-150 W/m2 of a module, and modules cover 75-80% of actual PV field and 25-75% of total solar park area. Average capacity factors correlate with irradiance and range from less than 12% to 25%.

Even with today’s still fairly low conversion efficiencies solar PV has by far the highest power density of all practical options for electricity generation based on new renewables. As further cost reductions and further efficiency gains are certain, development of this source should receive commensurate attention. Large ground-mounted PV projects now generate electricity with power densities of between 3-7 We/m2 in less sunny locations and 7-11 We/m2 in sunny regions (all rates for the total plant area, not just for the PV panels). Germany has the largest area of rooftop modules and power density of their PV generation averages 12 W/m2 of roof area covered by solar panels.

Power density of PV-covered walls will be always lower, in most instances less than 5 W/m2. Continuing efficiency gains should soon make power densities above 10 W/m2 common in large-scale PV projects in sunny locations, and it is not unreasonable to expect rates well above 20 W/m2 by the mid-century and, should they turn out be commercially viable, three-dimensional PV converters could push the values far above 50 W/m2. Pioneering central solar power projects have power densities (calculated for their total area) between 4-6 W/m2, similar to those of PV conversions. The largest new design in California desert will average almost 50 W/m2 for the heliostat area and nearly 9 W/m2 for the entire project.

Most of the planet’s large wind energy potential is at high altitudes where engineering challenges and economic realities preclude any imminent commercial conversions. Electricity generation by ground-based wind turbines has typical power densities on the order of 100 W/m2 in terms of installed capacity and 10-1W/m2 for actual annual production. Large (3-4 MW) turbines set in a square grid would have power densities of mostly 2-3 Wi/m2, and the actual range for America’s large wind farms is roughly 1-11 Wi/m2 with most projects rating between 2.5-4 Wi/m2. Annual capacity factors of wind generation have been rising but recent nationwide means have been just between 15% (Germany) to 25% (UK) in Europe, and the US maximum reached 33%. Appropriate adjustments would then lower actual average operating power densities to less than 0.75 W/m2 in Europe and to about 1 W/m2 in the US, and order of magnitude below the PV generation.

Although power densities of large hydro projects span four orders of magnitude, from 10-1 to 102 W/m2, most of the world’s hydroelectricity originates in plants whose installed capacities and large reservoirs translate to rates of 101-101 W/m2. Average power densities of hydro projects with capacities of less than 100 MW are below 0.5 Wi/m2, the mean is nearly 1.5 Wi/m2 for stations up to 1 GW and it surpasses 3 Wi/m2 for the projects in excess of 3 GW. This correlation of rising densities with rising capacities continues, as the projects with the world’s largest installed capacities (China’s Three Gorges, Brazil’s Itaipu, US Grand Coulee, all above 6 GW) have power densities between 10-20 Wi/m2. As expected, the highest power densities, some in excess of 500 Wi/m2, belong to some Alpine stations with high generating heads and small reservoirs.

Power densities of actual generation are considerably lower because typical capacity factors of hydro stations are usually less than 60%, and often less than 50%, and some are used even less, primarily just for peaking power. and whose capacity factors are often less than 50%. When the numerator is actually generated electricity (rather than installed capacity) this means that their typical power densities are thus roughly halved, with most of the rates falling to less than 10 W/m2 for the largest stations, below 3 W/m2 for medium-sized projects and less than 1 W/m2 for the stations with the largest reservoirs and low capacity factors. Hydrogeneration is thus highly space-demanding, with many smaller projects having power densities of just around 1 We/m2 or less (similar to those of phytomass harvests in temperate climates) but with the global mean pushed up by higher power densities (>5 We/m2) or the largest stations that supply most of the world’s hydroelectricity.

Photosynthesis is an inherently low-efficiency conversion and power densities of phytomass harvests are highly correlated with temperature and precipitation prevailing during the growing season and with the availability of macro- and micronutrients. Dense plantings of fast-growing trees harvested in short rotations have very high yields in small experimental plots but will not perform at that level during large-scale cultivation with moderate fertilization and without irrigation. Realistic yields in most temperate environments are 5-15 t/ha (power densities of 0.3-0.9 W/m2) and 20-25 t/ha in the subtropics and tropics (power densities of 1.2-1.5 W/m2).

Modern commercial version of charcoal-making (in Brazil, to supply the country’s blast furnaces) is much less wasteful than were the traditional methods but its power density is still no higher than about 0.6 W/m2; higher tree plantation yields and increased charcoaling efficiency could raise it close to 1 W/m2. Converting a rich harvest of tropical trees (20 t/ha or 1.2 W/m2) by three different methods –- by combustion of woody phytomass (efficiency of roughly 90%), by wood gasification and subsequent combustion in engines or turbines (overall efficiency of 35-40%), and by production methanol (efficiency of 70%) –- would result in power densities of, respectively, 1.1 W/m2, about 1 W/m2 and around 0.8 W/m2, and the density would be less than 0.5 W/m2 if wood-based gas were to be used for electricity generation. When converting wood harvests from temperate forests (10 t/ha, 0.6 W/m2) all of these values would be roughly halved.

Production of liquid biofuels from crops is done with even lower power densities. Although the yields of sugar cane and grain corn, the two most important feedstock crops, have been rising (as have been the efficiencies of their fermentation), power density of producing ethanol from the US corn yielding 10 t/ha is no higher than 0.25 W/m2. In Asia, where average corn yields are much lower, power density of ethanol production would be just above 0.1 W/m2. In contrast, power density of ethanol production from high-yielding Brazilian sugar cane is nearly twice as high as that of US corn-based alcohol, about 0.4 W/m2 for five years of harvests before the perennial grass is replanted.

Cellulosic ethanol, produced by enzymatic hydrolysis of wood or rapidly growing, high-yielding grass species, is yet to be commercialized on a large scale but its power densities would be on the order of 0.4 W/m2, similar to those of sugar cane-based Brazilian ethanol. Production of biodiesel from oil seeds is limited by inherently low yields of commercial oil crops. Even for relatively high-yielding Dutch rapeseed power density is only 0.18 W/m2 and the EU’s biodiesel mean is only 0.12 W/m2. Finally, small-scale biogas generation, used to convert biomass wastes, is rather inefficient and even the best commercial conversion (German biogas production using corn silage as feedstock) translates to power densities of about 0.6 W/m2 for the gas and 0.2 W/m2 for using that gas to generate electricity. All of these rates show inherent limits on power densities of energy supply based on phytomass: even an unlikely early doubling of commercial performance would keep power densities of wood-based electricity generation, and ethanol, biodiesel and biogas production below 1 W/m2.

Geothermal power plants have widely variable power densities, with large projects rating between 100-800 Wi/m2 of directly affected land. These values go down an order of magnitude, mostly to 50-80 We/m2, when actual generation is prorated over all affected land of accurately assessed projects in the US. Iceland and New Zealand. Simple quantitative comparison thus puts power densities of geothermal electricity generation at the same level as Alpine stations, an order of magnitude above typical PV performance in the Atlantic Europe (5 We/m2) or in more sunny US (8-10 We/m2), and also an order of magnitude higher than the densities for the best large wind farms. Supplies of geothermal heat for individual houses has similar densities, commonly between 40-100 Wt/m2.

Fossil fuels Compared to sprawling land claims of phytomass energies and hydrogenation reservoirs, extraction of the richest deposits of fossil fuels is almost punctiform –- but, at the same time, power densities of fossil fuel extraction show even wider ranges than do the conversions of renewable energy flows. Specific rates of coal mining depend on the depth, thickness and quality of coal seams. Permanent structures of large underground mines (machinery, maintenance, storage and office buildings, parking lots, facilities to process raw coal and load it for shipment) occupy relatively small areas (on the order of 1 ha for annual output of 1 Mt) and much more land is taken by the on-site disposal of rocks separated from coal and by tailing ponds that receive small-particle waste. Even so, the largest underground mines producing high-quality coal from thick seams will have power densities in excess of 10,000 W/m2 while the rates for smaller operations extracting lower-quality fuel from thinner seams (hence generating with more waste) will be often in excess of 2,000 W/m2 and usually no less than 1,000 W/m2.

The ratio between variable and fixed land claims is much larger for surface mining because large volumes of overburden must be stripped away and repositioned in order to get access to coal. The highest ratios of overburden to coal seam are now nearly 7, and the deepest surface mines go below 300 m. Many destructive and unsightly mountaintop removals in central Appalachia produce coal with power densities of just 200 W/m2 and some go well below 100 W/m2, while the operating densities of the largest surface mines that extract the thickest seams (102 m), be it in Wyoming’s Powder River basin or Australia’s Latrobe Valley, are more than 10,000 and even higher than 15,000 W/m2.

This means that the lowest power densities of coal extraction are comparable to those of PV electricity generation while the highest rate are as good, or better, than hydrocarbon production in major oil and gas fields. But most surface mines do not belong to either of these extreme categories whose power densities are two orders of magnitude apart: their operating power densities are typically between 1,000-5,000 W/m2. These rate do not change significantly even in the case of dedicated railroad shipments (typically a link built solely to move coal from a large mine to a power plant) because land disturbed by surface mining over a lifetime of an operation greatly surpasses rights-of-way of a rail line.

Early oil field development was marked by drilling too many wells in close proximity in predatory quest for maximized output; modern development optimizes production, with 5-30 wells/km2 and with as few as 2-3/km2 as several directional or horizontal wells can be drilled from a single pad. A relatively small number of giant oil reservoirs produces disproportionate amount of oil but their life-long power densities cannot be accurately calculated: the largest ones are still producing and there are no firm numbers on the ultimate mass of oil they will produce. Data from North American oil fields show long-term cumulative power densities of about 2,500 W/m2 for more than 80 years in California, about 1,100 W/m2 for 50 years in Alberta, with both rates calculated for land occupied by wells.

Annual statistics on producing wells and national and regional oil output make it possible to trace gradual decline of power densities (assuming, liberally, 2 ha/well). Between 1972 and 2012 they declined from about 40,000 W/m2 to 23,000 W/m2 in Saudi Arabia, and from almost 25,000 W/m2 to less than 9,000 W/m2 in the Middle East. Very low US and global rates (100 and 650 W/m2) are biased by the inclusion of thousands of America’s old wells kept in marginal production that is justified by recent high oil prices. The span is thus between 102 W/m2 for mature fields that have been producing for generations to 104 W/m2 for the world’s most productive reservoirs, with the value near the lower end of 103 W/m2 being modal or typical.

The two most important ways of non-conventional oil production are horizontal drilling and hydraulic fracturing of oil-bearing shales in the US, and extraction of oil from Alberta’s sands. Production from oil shales is characterized by rapid, hyperbolic declines and this means that, unlike in conventional oil fields where well flows can be regulated md kept fairly steady or gradually declining, power densities during the first year of extraction will be much higher than just a few years later. For North Dakota’s Bakken shale, now the largest oil shale producing region, power densities decline from about 4,000 W/m2 in the first year to the mean of 1,600 W/m2 for the first five years and less than 1,000 W/m2 for ten years of extraction.

Production of oil from Alberta’s oil sands began with surface mining of sands and their processing to extract bitumen followed by the fuel’s upgrading before sending it to a refinery. Not surprisingly, power densities of these operations are similar to those of surface coal mining, ranging from roughly 2,000 to 4,000 W/m2. In contrast, in situ recovery, the dominant way of future production, has power densities of 7,000-16,000 W/m2 and averages about 10,000 W/m2. These high densities drop significantly with the inclusion of land required to produce natural gas use for bitumen extraction and steam generation: power densities of surface mining are lowered to about 2,300 W/m2 and those of in situ extraction to less than 3,200 W/m2.

Not surprisingly, transportation and processing of crude oil have fairly high throughput power densities. Crude oil pipelines need construction corridors of 15-30 m wide and rights-of-way are typically 15 m for buried lines. Average US throughput power density is nearly 700 W/m2, with major trunk lines rating well above 1,000 W/m2. Pumping of crude oil into large tankers in major export facilities has very high throughput power densities of 104-105 W/m2. As is the case with oil fields, a disproportionate amount of liquid fuels comes from a relatively small number of large refineries whose processing power densities are mostly between 4,000 and 8,000 W/m2.

As expected, power densities of natural gas and crude oil extraction are similar, with most operations rating between103-104 W/m2: 2,300 W/m2 for all of Alberta’s extraction to nearly 50,000 W/m2 for Groningen, the Dutch super-giant field. And gas flows from hydraulically fractured horizontal wells show the same rapid production decline as oil production from shales, from power densities of 103 W/m2 in the first year to low 102 W/m2 just a few years later. Processing of natural gas before it is sent through pipelines is done with high throughput densities of 104 W/m2, and power densities of long-distance pipeline transportation rage from 102-103 W/m2. Rising trade in LNG involves high power density operations: gas liquefaction proceeds at high 103 W/m2 while power densities of re-gasification can be well into 104 W/m2.

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