Power Density

by Vaclav Smil

  By far the most interesting part of that study is a map of power densities using block land area in the denominator. Some mid-Manhattan blocks with a high density of high-rises show power densities as high as 900 W/m2, which means that a single block demands a year-round average of nearly 18 MW of delivered energy. Other parts of the city where many blocks have power densities in excess of 400 or 500 W/m2 are the financial district, Greenwich Village, the Flatiron, Midtown South, Sutton Place, and the East Side. Manhattan's lowest power densities are in Harlem and East and West Village, and densities in residential boroughs are generally below 25 W/m2, while city blocks in parts of Queens and on Staten Island rate less than 15 W/m2.

  Hong Kong's energy statistics list end uses for specific sectors and detailed land-use data make it easy to reconstruct power densities on an annual basis (Government of Hong Kong 2013). In 2012 the average power density of residential energy use was about 40 W/m2, a high rate reflecting the dominance of the city's crowded high-rise housing estates; the power density of industrial areas was about 20 W/m2, and that of land transportation reached a very high rate of about 50 W/m2, while the overall rate for the city's impervious surfaces (including a large and busy port and airport) was roughly 60 W/m2.

  Power Densities of Buildings

  The order of magnitude does not change as we narrow the spatial focus from the most densely built-up city wards to individual buildings or from areas of heaviest traffic to individual roads or crossroads. Nationwide means of power densities of America's building stock can be calculated from statistics published in the Buildings Energy Data Book, a compilation of the USDOE (2013). Its disaggregated annual totals show the 2010 site use average (that is, with fuel-based electricity not converted to its primary energy equivalent) of 40 W/m2 for commercial buildings (with space heating claiming 27%, cooling 10%, and water heating less than 7%) and just over 16 W/m2 for residential buildings, with about 45% of that rate due to space heating, more than 16% used by water heating, and about 9% by cooling.

  US residential lighting needs less than 6% of all electricity, with a power density of just below 1 W/m2. Commercial indoor lighting claims almost 14% of the total usage (about 5.5 W/m2). Disaggregations by building function for New York City by Howard and co-workers (2012) showed energy use per floor area ranging from just over 20 W/m2 for residential housing (for one to four families) to about 35 W/m2 for multifamily residential housing and almost 70 W/m2 for stores, schools, and hospitals. One of America's best sources for power densities of energy use in a large number of specific buildings is San Francisco's annual Energy Benchmarking Report, which lists the electricity and fuel uses of hundreds of municipal structures (San Francisco Water Power Sewer 2013).

  Modal ranges in the ascending order of densities for 2012 are (all values in W/m2 of floor area and for energy used on-site): parking garages, 2-6 W/m2; warehouses, 5-11 W/m2; schools, 15-22 W/m2; offices, libraries, performance halls, conventions centers, and police and fire stations, 22-35 W/m2; and museums, 35-100 W/m2. As expected, modern offices, schools, and retail space have roughly similar specific energy requirements, on the order of 20-30 W/m2 of floor area, less than half as much as supermarkets (they were even more wasteful in the past due to open-bin freezers) and as little as one-third of the rate for busy restaurants and hospitals.

  I should also note that some studies express demand in terms of primary energy, roughly doubling the usually quoted end-use values. That is, of course, an inevitable consequence of two realities: all modern buildings require large inputs of electricity for lighting, air conditioning, appliances, and electronic devices (some also for heating and water heating), and in most countries (including the United States), most of the delivered electricity comes from thermal generation, with its inherently large conversion losses (the best efficiencies are now around 40%). But, as applied in this book, the power densities of energy use measure only actual on-site consumption.

  But another adjustment is necessary. As I have clearly indicated, the published densities of energy use in buildings refer to requirements per unit of floor space, and hence they equal the power density as defined in this book only for single-story buildings and so must be appropriately enlarged for multistory structures. In any case, published data must make it clear whether the rates refer to a unit of floor area or to a structure's footprint. And comparing the energy performance of buildings simply by referring to their power densities is misleading if such a comparison is intended to illustrate differences in efficiency. Corrections must be made for the average number of heating and cooling days, for the primary sources of used energy, and for the ownership of electricity-consuming appliances and electronic devices; moreover, preferred indoor temperatures and appropriate levels of lighting should also be taken into account.

  For example, my superinsulated two-story house (2" x 6" frame with fiberglass in the walls, a thick layer of blown insulation in the attic, an exterior Styrofoam wrap around the foundation, triple windows with argon, a 97% efficient natural gas furnace, heat recovery ventilator) will use more energy than an indifferently built house in Vancouver. The two cities have the same latitude (50°N), but during 2013 Winnipeg's mid-continental location had 2.6 times more heating-degree days than Vancouver's much warmer maritime climate (Degree Days 2014). Such differences will always remain, but the historical evidence is clear: better construction, more efficient heating and cooling, fewer electricity-intensive appliances, and less wasteful lighting have brought impressive declines in the average residential power density.

  Many fairly large differences in the power densities of individual buildings are more due to design and operating practices than to disparities in climates and preferred indoor temperatures. European data show that the power densities of single-family house heating in Germany hardly changed between 1918 and 1957 (nearly 30 W/m2 of floor area), but then declined to 18 W/m2 by 1967 and to just 6 W/m2 in 2010. In the UK the drop was from about 66 W/m2 of floor area before 1920 to 23 W/m2 by 2002, and in Italy from 25 W/m2 to about 10 W/m2 between 1950 and 2005 (BPIE 2011). Between 1980 and 2005 the average US decline was 37% for all housing units and 45% for single-family detached houses in the South (USEIA 2009).

  New office buildings are also much more energy-efficient. For example, Canada's most efficient office building, the headquarters of Enermodal Engineering, in Kitchener, Ontario, draws only 8.5 W/m2 of floor area, only a tenth of the country's typical multistory office structure (Enermodal Engineering 2013). The most energy-efficient building in the United States, Seattle's Bullitt Center (with a large PV array, geothermal heating and cooling, and motorized windows), is in a much warmer climate; its demand comes at just 6 W/m2 of floor area (Bullitt Center 2013). The best house designs can result in similarly low rates, but a zero-energy house in any colder climate is a misnomer: the house may not need any external source of energy, but even with an efficient passive design it will require a substantial investment in a rooftop PV array or a geothermal system, or both.

  Finally, it is revealing to add up energy uses per unit of floor area to get the ascending range of power densities of common, as well exceptional, buildings. An energy-efficient single-story house in a mild maritime climate that requires minimum heating and no cooling could average less than 10 W/m2. The two just described superefficient office buildings are both low-rises: Enermodal is only three stories high and the Bullitt Center has just six stories, and hence their average power densities are respectively just 25.5 and 48 W/m2. A modern (post-1990) American detached two-story house will average between 30 and 40 W/m2 of its foundation, and an older (pre-1980) 20-story office building in a climate that requires both heating and cooling will average 800 W/m2. Buildings in Kwai Chung, Hong Kong's largest public housing estate, in New Territories, with 16 towers of 38 floors and almost 25 W/m2 of floor area, will have a power density of roughly 950 W/m2; that is (as already shown) the same as the most energy-intensive city blocks in Manhattan's Midtown (fig. 6.3).

  Figure
6.3

  Kwai Chung housing, Hong Kong. © JEROME FAVRE/epa/Corbis.

  Midprice and luxury hotels have above-average energy needs. The average for US hotels has been 45 W/m2 per unit of floor area, whereas in much colder Ottawa it is 77 W/m2, in London (because of poorly insulated buildings and inefficient heating) as much as 80 W/m2, and in Hong Kong (because of air conditioning) 63 W/m2, but the average in Auckland's moderate climate is only about 30 W/m2 (Deng and Burnett 2000; Su 2012). This means that 10-story buildings will have power densities of up to 800 W/m2 and that the tendency to raise many modern luxury hotels to more than 50 stories creates exceptionally high power densities, particularly in deserts. A 50-story hotel in a hot climate has a power density close to, or in excess of, 2,000 W/m2, and Burj Khalifa, the world's tallest building (828 m, 160 floors), in Dubai, has a base footprint of 8,000 m2 and a peak electricity demand of 50 MW, implying short-term power densities of up to 6,250 W/m2 of its foundation.

  Transportation Densities

  Urban traffic is usually a much smaller contributor to urban energy use than domestic demand and industrial processes. For example, disaggregated data for Greater London between 2005 and 2008 show the three shares at, respectively, 15%, 42% and 38%, but urban traffic can reach very high power densities along major heavily traveled roads even when it flows freely, and even higher rates in prolonged traffic jams when drivers keep their engines idling. This is an inevitable consequence of the low efficiency of gasoline engines: they lose about 30% of initial energy input through their radiators and about 40% in exhaust gases.

  Most of the latter flux is redistributed by radiation before it exits a tailpipe: exhaust temperature is less than 70°C, while the gases leaving the cylinder have a temperature of about 800°C. Both radiator heat and exhaust heat are absorbed first by other car structures before they are lost to the atmosphere. The logical way is thus to use a car's footprint rather than just the footprint of a radiator or exhaust system as the denominator in calculating vehicular power densities. Small cars have a footprint of less than 4 m2 (3.8 m2 for the Honda Fit), while large ones go over 5 m2 (5.1 m2 for a Mercedes-Benz S class). With power ratings of, respectively, about 87 kW and 339 kW, the maximum theoretical power densities of energy use by those two vehicles would be 22,900 W,/m2 and 66,500 W,/m2 of their footprint, rates resembling the power densities of heat dissipation in large power plant cooling towers.

  Dissipated heat is diffused along roads, driveways, and parking lots. The maximum short-term rates of that dissipation depend on roadbed widths (3.6 m is the US standard for freeways, 2.7-3.6 m for local roads), speeds, distances between vehicles, and their power rating. Free-flowing car traffic on a freeway (30 cars/km per lane traveling at 80 km/hour) with cars averaging 8 L/100 km (29 mpg in the United States) will have a power density of about 475 W/m2 of paved lane. A mixture of 70% cars and 30% trucks with 1,000 vehicles/km of a single lane in one hour would generate a power density of about 560 W/m2:

  Box 6.2

  Power density of highway traffic

  In a traffic jam, with 125 idling vehicles per kilometer of street lane just 3 m wide and consuming about 1.3 MJ/minute (roughly 21 kW per vehicle), the stationary power density will reach 900 W/m2. These high rates apply only to the lanes. Including the associated road infrastructure in the calculations usually halves those rates and often reduces them even more. Paved shoulders on US interstate highways have minimum width of 3.05 m on the outside and 1.22 m on the inside, while medians have a minimum width of 11 m in rural and 3 m in urban areas. Including these surfaces for a four-lane highway would reduce all of the just calculated rates by at least 57%, and by more than 60% in rural settings, resulting in rates below 250 W/m2 in flowing traffic. Including adjacent land that forms the entire road infrastructure (ditches, embankments, land cut off by approaches, exits, and interchanges) would bring further reductions on the order of 20%40%, to rates well below 200 W/m2 for the entire transportation corridor in flowing high-density traffic.

  Adjusting these calculated short-term peak rates for average annual traffic, with its enormous fluctuations between nearly empty roads in the early morning hours and seemingly endless congestions during rush hours, cuts the rates by an order of magnitude. The next adjustment to make in calculating the long-term power density of urban traffic is to prorate it over the entire area devoted to roads and parking lots, with the former claiming about 30% of all land (35% in many US cities) and the latter at least 20% of the total. Prorating the road transport energy use over the entire city area will cut the density by about two-thirds, to rates below 5 W/m2, compared to the rates derived by having only road infrastructure as the denominator.

  The actual means of urban traffic power densities in Greater London during the years 2005-2008 were 1.65 W/m2 (Iamarino, Beevers, and Grimmond 2012). Recent gasoline consumption data for Los Angeles County, the epitome of high-density traffic, show annual purchases running at a rate of about 72 GW. Even if it assumed that only one-third of all gasoline purchased in the county is actually consumed within its borders, this would prorate to 2 W/m2 for the county's entire area, or 4 W/m2 for its residential and industrial land, and adding diesel fuel (assuming the nationwide proportion of gasoline to diesel use is valid for Los Angeles) would raise this to at least 5.5 W/m2.

  The Challenges of Heat Rejection

  Many energy conversions do not require any special arrangements to dissipate heat, just cautious handling of hot light bulbs, toasters, and irons; in many other instances simple arrangements, such as radiator fins, suffice. But even the most efficient large thermal electricity-generating stations reject about 60% of the initial energy input as waste heat, and such large fluxes require appropriate heat-disposal designs. As already noted, cooling towers reject about 50% of all energy used by thermal power plants, and large natural draft units (massive concrete structures up to 100 m in diameter and up to 200 m tall) can handle 20-40 kW;/m2. With a 40% conversion efficiency a 2-GW; plant will reject about 2.5 GWt through its cooling towers, and the actual heat rejection power densities will be close to 80,000 Wt/m2 of the tower footprint. The overall land claim will be larger because the towers must be set well apart to prevent Venturi effect-induced wind loads on their relatively slender walls. Cross-flow cooling towers using mechanical draft units are even more compact, with throughput densities of 100,000-125,000 Wt/m2.

  About 10% of a plant's initial fuel input is rejected through a stack. At a 40% conversion efficiency, this amounts to about 500 MWt for a 2-GW; station. Tall chimneys (scores of the tallest ones have surpassed 300 m) have a top inside diameter of just 3-7 m and a bottom inside diameter of 14-17 m, which means that they reject heat with power densities of 0.7-1 MW,/M2 Of their foundations. The introduction of flue-gas desulfurization changed that because flue gases (120-150°C) must be cooled to saturation temperature before their SO2 reacts with alkaline compounds, and they leave stacks at less than 50°C, producing heat-rejection power densities an order of magnitude lower than they did previously.

  The greatest technical heat rejection challenge takes place on a microscale, thanks to the ever-increasing crowding of microprocessor transistors (fig. 6.4). Intel 4004, the world's first microprocessor, released in 1971, had 2,300 transistors on a 135 mm2 silicon die, and dissipated about 2.5 W,/cm2 (Intel 2013). In 1978 the Intel 8086 contained 29,000 transistors and dissipated 7.6 W,/cm2, almost exactly as much as a small (160 cm2) circular kitchen hot plate rated at 1,200 W.By the beginning of the twentyfirst century Intel's ultra-large-scale integration procedures had crowded 50 million transistors on 130 mm2 of the Xeon Irwindale, whose demand of 115-130 W prorated to up to 100 W,/cm2, equivalent to 1 MW,/m2, and in 2005 the Pentium 4 went above 100 W,/cm2 (Azar 2000; Intel 2005; Joshi 2001).

  Microchips are usually placed in very tight confinement, but to ensure optimum performance, their temperature should be kept below 45°C or else their operation will slow down and eventually cease. The challenge is particularly great when dealing with h
ot spots, whose fluxes can briefly go as high 1,000 W,/cm2; this power density is equal to about 15% of the flux through the Sun's photosphere (64 MW/m2) or through a rocket nozzle (7,000 W,/cm2). Standard operating densities on the order of 100 W,/cm2 are of the same order of magnitude as the heat rejection of hot flue gases through a large stack, and far higher than the heat generated by the US Space Shuttle's reentry into the atmosphere, about 6 W,/cm2 for thermal protection tiles and about 60 W,/cm2 for the leading edge (Harvey 2008). Subsequent microprocessor redesigns reduced the heat flux, in 2006 the Core 2 Duo (65 W) to below 50 Wt/cm2, but by 2010 Intel's Atom was back to the hot-plate power density of 100 W,/m2 (Pant 2011), and the power density at 1-mm2 hot spots can be higher than 300 W/cm2.

  Many ingenious arrangements are needed to manage high heat fluxes (Allan 2011). This challenge becomes even greater when servers and disk storage systems are stacked in data centers in racks. A standard server rack, placed on a raised floor with perforated tiles or grates, has been 2.1 m tall, composed of forty-two units of 48.26-cm (19-inch)-wide slots, but some companies have preferred much taller racks (fifty-seven units by Microsoft) or wider (up to 58.42 cm) enclosures (Miller 2012). The footprint of a standard 42-unit rack is 0.478 m2 for the inside dimensions and 0.65 m2 for the cabinet. The rate of increase in product heat density has slowed since the mid-2000s, but between 1990 and 2010 servers and disk storage systems saw an order of magnitude rise, from just over 2,000 W/m2 to 20,000 W/m2 (Data Clean 2012). Most of the products deployed in large data centers have a rated demand between 8 and 20 kW per rack, and designers are working on servers of 30 kW+.