by Vaclav Smil
Other space definitions reduce this density: adding front and back clearances around server cabinets cuts the density by roughly two-thirds, adding shared aisles at the end of the row entails a further 25% cut, and including all main aisles and power delivery and cooling units brings the rate down to less than 20% of the rack density value (Brill 2006). The approximate conversion of product (rack) power density to gross computer room density is just 0.018. Moreover, some racks may be empty (held in reserve), while others may be only partially filled, and the centers rarely operate near their full capacity. On the other hand, for every 1 W used by servers up to 0.9 W have typically been needed for the electrical infrastructure that enables the servers, that is, for an uninterruptible power supply, switches, lighting, and, above all (nearly 40% of all power), for cooling (Emerson Network Power 2009).
We have representative data on power densities for data centers housing the servers based on information from 59 facilities in North America and Europe with areas ranging from less than 2,000 m2 to 18,000 m2 (Renaud and Mescall 2011). The centers were designed for a median power density of 730 W/m2, with some smaller centers rated for as much as 1,615 W/m2, but actually used power (gross computer room density) averaged only 437 W/m2, which means that the centers are using less than 60% of their available power. Their median value per rack was only 2,100 W/m2, with the middle 50% ranging from 1,700 to 2,200 W/m2, and the average power density per rack declined with the data center size. Some smaller centers may have overall densities on the order of 2,500 W/m2 (Emerson Network Power 2008).
Coping with less than 500 W/m2 in terms of gross computer room density is not an extraordinary challenge, but removing heat from racks operating with densities of 103 W/m2 (and for rooms whose power density is in excess of 2,000 W/m2) calls for efficient cooling to maintain the temperature between 10°C and 35°C and the relative humidity below 80% (Minas and Ellison 2009; Pflueger 2010). This challenge is perhaps best expressed by the rack power densities in terms of power/volume. A high-rise apartment building in Hong Kong may have a power density twice as high as a server room when both rates are expressed per unit of their footprint area (950 vs. 475 W/m2), but a server rack using 2,100 W/m2 will be rejecting about 1,000 W/m3 of its volume, compared to less than 10 W/m3 of a 38-story apartment building.
Uneven cooling, and hence recurrent hot spots, are a common problem in data centers, with about 10% of racks getting too hot to meet the standards for maximum reliability: every increase of 10°C above 20°C cuts the long-term reliability of hardware by half (Renaud and Mescall 2011). The cooling requirements of data centers have been rising, but 70% of cooling capacity available in a typical computer room is wasted due to bypass airflow. The global electricity demand by data centers doubled between 2000 and 2005 (Koomey 2008), but between 2005 and 2010 (due to recession) it increased by only about 56%, and in the United States it grew by just 36% (Koomey 2011). In aggregate terms, data centers used 1.1%-1.5% of the world's electricity (23-31 GW) in 2010, and the US share was between 1.7% and 2% (7.7-9.8 GW). But between 2011 and 2012 global power requirements rose by 63%, from 24 GW to 38 GW, with 43 GW forecast for 2013 (Computer Weekly 2012). Given a rapid data growth-Intel sees new information load rising from 2 zettabytes (1021 bytes) in 2011 to 8 petabytes in 2015 (Otellini 2012)-further large increases in demand must be expected.
Finally, a few observations on the thermal consequences of energy use in general, and on concentrated heat rejection in particular, are in order. Proceeding from the smallest to the largest scale, it is obvious that the highest power densities of heat rejection are limited to such tiny areas-as small as 101 m2 for microprocessors-that the power fluxes of individual components are too small to have any discernible impact even on a room scale. Keeping a microchip cool may be a challenge, and careful design must be deployed to cool microprocessors in servers that are layered in tall racksbut it is a challenge only in rooms crammed with data processing assemblies where their operation dominates the overall heat balance.
In residential settings, heat rejected by electronic devices represents a negligible addition to a room's thermal background. When I am using a laptop in my living room its operation will add some 60 W of dissipated heat, compared to 400 W coming from recessed ceiling lights, 200 W from a stereo system, 85 W from my metabolism (assuming 1.2 times the basal metabolic rate while sitting)-and, during a summer day, more than 1,500 W of sunlight that is coming in at noon through southwest-facing windows, or, during cold winter evenings, about 1,000 W of hot air that is forced through floor heating vents.
Anthropogenic heat rejection rates that are three orders of magnitude above the peak insolation rates (that is, 106 W/m2) are restricted to areas smaller than 102 m2 (the bottoms of large power plant boilers, the mouths of tall power plants stacks), and those flows that are one to two orders of magnitude higher than noontime irradiance (that is, between104 and 105 W/m2) originate from areas smaller than 100 by 100 m, mainly large cooling towers. Heat rejection by both tall power plant stacks and cooling towers is associated with substantial condensation, often with the formation of clouds, and with some recurrent local fogging and icing, but only rarely with any downwind precipitation anomalies.
Other concentrated heat rejection processes (ranging from hot plates and car exhausts to tall power plant stacks) are limited to relatively small areas: as the power density of anthropogenic energy conversions increases, the spatial extent of the more intensive heat rejection fluxes declines at a considerably faster rate. As a result, heat-rejection phenomena that constitute a significant share of solar inputs (101 W/m2) are limited to areas no larger than 101 m2, to large cities, extensive industrial regions, and busy transportation corridors. As already noted, energy use in buildings, industries, and transport helps turn large cities into urban heat islands. Other factors contribute to this phenomenon: impervious surfaces have a higher thermal capacity than does vegetation, and their heating generates stronger convective flows; many buildings and most parking lots and roads have a lower albedo than many natural surfaces; and the restricted sky view in canyon-like streets reduces radiative cooling and sensible heat loss is larger than latent heat flux (Stewart 2011).
As a result, urban heat islands commonly average 2°C more than the surrounding countryside, and peak differences may be temporarily (especially during the night) as much as 8°C higher. Urban heat islands can explain only a negligible fraction of global temperature rise during the twentieth century (Peterson and Owen 2005), but they have a number of well-documented impacts, including statistically significant (local and downwind) increases in cloudiness, precipitation, and thunderstorms and reductions in relative humidity, wind speed, and horizontal insolation as a result of shading. They also promote the formation of photochemical smog, contribute to premature mortality during summer heat waves (Wong, Paddon, and Jimenez 2013), and increase energy use for air conditioning.
A brief recapitulation of power densities representing all major energy conversions and uses precedes some revealing comparisons of supply and demand. The chapter closes with summations of land claims by the global energy systems and by the US provision of fossil, nuclear, and renewable energies.
My recapitulation will avoid both a perfunctory recital of a few basic generalizations and an elaborate account of all noteworthy conclusions. Instead, I will offer a systematic but concise review of key findings, and then present comparisons of the typical power densities of specific production activities and major energy uses. I will also use representative power density means to calculate approximate aggregates of the spatial claims of energy systems, first on a global level (to set energy provision in a wider context of changing land use), then, with a greater degree of accuracy, for the United States. But before I do so, some analytical points are in order.
Higher power densities mean lower land claims, but the highest possible densities are not always most desirable. Well-designed surface coal mines, with surfaces reshaped and land returned to agricultural, fo
restry, or recreational use in less than a generation, are preferable to underground mining with its occupational hazards and often prolonged periods of ground subsidence. And while run-of-river plants would be the most desirable choice (as they do not claim any additional land), they have obvious disadvantages: unlike PV-based solar and wind generation of electricity, they may not cease to operate altogether, but their capacities may be periodically limited in all regions with widely fluctuating water flows; in contrast, spaceintensive large reservoirs ensure a predictable capacity far above that corresponding to the minimum stream flow.
And, most fundamentally, qualitative differences invalidate any simplistic verdicts about superiority. High-power-density fossil energies-which are also cheaper to transport, easier to store, and can be used on demandare preferable but not inherently superior because, unlike solar radiation and its conversions, they are exhaustible on the civilizational time scale of 103 years. And while many conversions of fossil fuels are now virtually pollution-free, removing and storing CO2 at scales that would eliminate the gas as a key factor of anthropogenic climate change (a necessity largely eliminated with renewable sources of energy) remains an extraordinary challenge. At the same time, thermal electricity generation has unrivaled availability, a key consideration in societies dependent on an incessant and highly reliable (99.9999% of all time) supply. The most commonly encountered capacity factors range from 10% to 15% for PV-based electricity generation in mid-latitude locations and 15%-25% in the sunniest environments to 20%-35% for wind farms in moderately to very windy regions, 40%-60% for large hydro stations, 60%-85% for coal-fired electricity-generating plants, and about 90% for nuclear reactors.
Recapitulations
Modern civilization energizes its complex metabolism by converting two basic kinds of resources into useful energies: renewable flows, and finite stores of fossil fuels and uranium. Except for geothermal and tidal energies, all renewable flows are transformations of a tiny fragment 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 the rest is reradiated, with only a small share driving atmospheric circulation (of which a small share can be harnessed as wind energy), the global water cycle (with river flows partially convertible to hydro-generated electricity), and photosynthesis, the source of biofuels and fossil fuels (after 105-10$ years of heat and pressure processing).
Renewable Flows
Solar radiation flux is so large that even fairly low conversion efficienciesto heat (mostly in rooftop water heaters) or to electricity (by PV cells or by central solar plants)-can harness it with relatively high power densities. For heat, the maxima are on the order of 102 W/m2; for PV-based electricity generation, they reach 101 W/m2. Power densities for most hydro stations are an order of magnitude lower (100 W/m2), large-scale harnessing of wind does not go above 10° W/m2, exceptionally high phytomass harvests yield power densities a bit above 1 W/m2, and harvests of wood and crops can be converted to useful energies with power densities of just 10-1 W/m2.
During noontime hours the 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 on the order of 100 W,/m2 in sunny subtropical climates and 40-50 W,/m2 in cloudy mid-latitudes, while the global mean (based on actual performance) was 67 W,/m2 in 2012. Two common biases must be avoided in order to calculate comparable power densities of PV-based electricity generation: the rates should not be expressed in terms of peak power and the area should not include only module surfaces. The power densities of PV-based electricity generation decline by an order of magnitude as we proceed from noontime maxima to annual averages and from panel areas to total areas of PV projects. Noontime maxima at prevailing efficiencies (10%-15%) are 80150 W/m2 of a module, and modules cover 75%-80% of an actual PV field and 25%-75% of a total solar park area. 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 renewable flows. As further cost reductions and further efficiency gains are certain, the development of this source should receive commensurate attention. Large ground-mounted PV projects now generate electricity with power densities of between 3 and 7 We/m2 in less sunny locations and 7-11 We/m2 in sunny regions (all rates are for the total plant area). Germany has the largest area of rooftop modules, and the power density of their PV-based electricity generation averages 12 W/m2 of roof area covered by solar panels. The power density of PV panel-covered walls will be always lower, in most instances less than 5 W/m2.
Continuing efficiency gains should soon raise 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 mid-century; 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 and 6 W/m2, similar to those of PV conversions. The largest new design in the California desert averages 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 spacing power densities on the order of 100 W/m2 in terms of installed capacity and 10-1 W/m2 for actual annual production. Large (3-4 MW) turbines set in a square grid have power densities of mostly 2-3 W,/m2, and the actual range for America's large wind farms is roughly 1-11 W,/m2, with most projects between 2.5 and 4 W,/m2. The annual capacity factors of wind generation have been rising, with recent nationwide means between 15% (Germany) and 25% (UK) in Europe, and the US maximum reached 33%. Average operating power densities are thus less than 0.75 W/m2 in Europe and about 1 W/m2 in the United States, an order of magnitude below that of PV-based electricity generation. When only the tower footprints and access roads are counted, the power densities of wind generation rise by an order of magnitude, but that is an erroneous value to use in making comparisons with other modes of electricity generation because it does not convey the fundamental spacing requirements that limit the power densities of wind turbines.
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 comes from plants whose installed capacities and large reservoirs translate to rates of 101 W,/m2. The average power densities of hydro projects with capacities of less than 100 MW are below 0.5 W,/m2; the mean is nearly 1.5 W;/m2 for stations up to 1 GW, and it surpasses 3 W,/m2 for 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 Dam, Brazil's Itaipu, the Grand Coulee Dam in the United States, all above 6 GW) have power densities between 10 and 20 W,/m2. As expected, the highest power densities, some in excess of 500 W,/m2, belong to some alpine stations with high heads and small reservoirs.
The power densities of actual electricity generation are considerably lower because the typical capacity factors of hydro stations are usually less than 60%, and often less than 500/6--and even less when used just for peaking power. Actual operating power densities are thus roughly halved, with most of the rates falling to less than 10 We/m2 for the largest stations, less than 3 We/m2 for medium-sized projects, and less than 1 We/m2 for stations with the largest reservoirs and low capacity factors. Hydroelectric generation 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 (above 5 We/m2) for the largest stations that supply most of the world's hydroelectricit
y.
Figure 7.1
Power densities of phytomass and biofuel production. Carl De Torres Graphic Design.
Photosynthesis has an inherently low efficiency, and the power densities of phytomass harvests are highly correlated with temperature and precipitation during the growing season and with the availability of macro - and micronutrients (fig. 7.1). Dense plantings of fast-growing trees harvested in short rotations have very high yields in small experimental plots but will not perform that well in large plantations with no or only 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).
The modern commercial version of charcoal making (in Brazil, to supply blast furnaces) is much less wasteful than traditional methods were 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 the combustion of woody phytomass (an efficiency of roughly 90%), by wood gasification and subsequent combustion in engines or turbines (an overall efficiency of 35%-40%), and by the production of methanol (an 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. For wood harvests from temperate forests (10 t/ha, 0.6 W/m2), all of these values would be roughly halved.