Power Density

by Vaclav Smil

  Manitoba Hydro's high-voltage DC link between the Nelson River power plants and converter stations near Winnipeg was a pioneering application (Manitoba Hydro 2013b). Its first phase, completed in 1973, has two bipole lines (900 kV, 895 km, and 1,000 kV, 937 km) and a capacity of about 4 GW. Two lines of 4,103 towers (spaced 427-488 m apart) claim a ROW of 137 m (about 12,300 ha, of which 10,800 ha are cleared forest) and have a power density of just over 30 W/m2. The power densities for some other major high-voltage DC lines (60-m ROW for a 500-kV link) are close to 50 W/m2 for each of the three lines from the Three Gorges Dam to Shanghai, Changzhou, and Guangdong, each with a capacity of 3 GW and a length of, respectively, 1,060, 890, and 940 km (Kumar, Ma, and Gou 2006). Formerly the world's longest high-voltage DC line, the 1,700-km link from the Inga Dam on the Congo to Kolwezi had an original design capacity of only 560 MW, but with a wide clearance of about 100 m its peak transmission power density is just 3 W/m2 (Clerici 2007). The Xiangjiaba-Shanghai ultrahigh-voltage 800-kV line, now the world's longest DC link, completed in 2010, spans about 2,000 km (ABB 2010).

  The only transmission ROWs that can be attributed to a specific station are those of the lines built to connect it to the existing grid or dedicated high-voltage DC links from large hydro stations to distant cities. The only logical way to calculate the power densities of transmission is to quantify them on a national scale, that is, to divide the nationwide electricity generation by aggregate ROWs. And even that is not a correct solution for small, strongly interconnected countries engaged in vigorous electricity trade. For example, in 2011 Switzerland imported 83 TWh from the EU and exported 81 TWh, while its domestic consumption was only 59 TWh (Pauli 2013). I will present approximate calculations of global and US land claims in the penultimate chapter.

  Examinations of power densities of energy uses on scales ranging from global to local reveal quite a few unexpected (or at least unappreciated) realities. More important, historical perspectives shed light on one of the most important trends in the evolution of human societies, their quest for ever-higher power densities of energy use, be it on a collective level or as individuals.

  In the preface I noted how land, a key concern of classical economics, became a marginal consideration in modern economies driven by concentrated labor and capital deployed in mass production. From a physically fundamental-that is, thermodynamic-perspective, this new pattern of economic organization is nothing but an expression of rising energy use, of deploying new energy conversions on unprecedented scales and with unprecedented intensities. This has resulted in a still continuing upward trend in the typical power densities of energy uses. This trend is an unmistakable but curiously unappreciated reality. Energy publications teem with data, with comparisons and analyses of energy use per capita, per unit of GDP, per unit of capital investment, more recently even per unit of energy (net energy return, or EROI, energy return on investment).

  But energy use per unit of land is rarely investigated, and if so then in its most readily calculated, yet also most misleading, form, as annual energy use prorated over a nation's territory. This quotient may be relevant for Monaco, but its utility breaks down even at Hong Kong's level, as even this circumscribed and densely populated (de facto) city-state contains relatively large areas of steep (and largely deforested) mountain slopes (about two-thirds of its territory) frequented only by hikers and of swampland hosting waterbirds. And calculating such rates for dozens of countries where virtually all the population and all agricultural and industrial activities are concentrated on a small share (less than 10%) of the national territory is an exercise in deliberately introducing errors of one or more orders of magnitude. There are dozens of such nations. The largest ones include most of the countries of North Africa and the Middle East, but also Norway and Finland or Turkmenistan and Mongolia.

  I note these misleading rates in passing as I follow power densities of energy uses from the planetary scale to microprocessors, the smallest massively deployed energy converters in modern civilization. But first, two important clarifications are in order, one definitional, the other one stressing the ever-changing, dynamic nature of energy use. This chapter is called "energy uses" rather than "energy consumption": is this just an idiosyncratic preference? Before I embarked on detailed reviews of the power densities of energy production I sorted out the key terms and provided their correct definitions. In energy studies this effort never ends, and I am not sure which of the pair of terms is misused more often: talking or writing about energy when what is meant is power or referring to energy consumption when what is meant is energy use (I too have been using the term energy consumption).

  According to the first law of thermodynamics, that is an impossible feat: energy cannot be consumed, it remains conserved. It can be converted to a different form, and all of the conversions eventually end in dissipated heat that provides the feeble thermal backdrop of the known universe. This is not any verbal puritanism, for this critical distinction has important implications for energy use in modern societies: too often people think about energy as if it has been truly consumed, never again to be of any use or consequence. There are two important reasons why that belief is wrong. In the first place, even when we think that we are done with a particular energy conversion (that is, once we conclude that we have derived all useful work in the form of chemical, thermal, electric, kinetic, or electromagnetic energy), those energies have to be dissipated. The power densities of all of our final energy uses are also the power densities of heat rejection. Depending on the intensity and the scale of this heat rejection and on the heat-absorbing medium, such processes can cause significant temperature increases.

  At one end of this heat-release spectrum are microprocessors, whose extraordinarily high power densities pose tremendous challenges for efficient heat dissipation. Among the most obvious objects much higher up on that size spectrum are giant cooling towers, the recipients of concentrated quantities of waste heat from the operation of large thermal electricitygenerating plants. At the opposite end of the spectrum are modern megacities and conurbations. Specific heat rejections (per person, per vehicle) within these areas may be small, but their combined effect helps to create permanent urban heat islands that result in discernible changes in comfort, wind speed, and even precipitation.

  In the second place, there are still too many instances in which the residual heat should not be left to dissipate, where it is unnecessarily wasted because we do not try hard enough to use it. I have already noted how combined-cycle electricity generation uses hot gas discharged by a gas turbine to vaporize water in a heat recovery steam generator and power an attached steam turbine to raise the overall efficiency of fuel use to 60%, roughly 50% above the usual performance of stand-alone gas turbines. And now the most common examples of harnessing "used" energy are hybrid vehicles, whose regenerative braking can recover some of the energy that is normally wasted in slowing a vehicle down by engaging an on-board electric motor as a temporary electricity generator that feeds a storage battery.

  These examples of improving energy conversion efficiencies are also excellent illustrations of the second point I want to stress, the constantly changing levels of energy use. Unlike somatic energy requirements-with nutritional minima and optima delimited by human metabolism, which is itself a function of age, sex, and physical activity-there are no minima or optima for the use of extrasomatic energies. Their harnessing began with the use of draft animals. Preindustrial societies added conversions of water, wind, and biofuels, while affluent modern economies are expressions of large, incessant flows of fossil fuels and primary electricity.

  But at every stage of this evolution there have been enormous differences in the level of use among countries and regions, with average per capita rates rising despite many impressive gains in conversion efficiencies. The quantifications of power densities of energy use in this chapter illustrate these differences and changes, but I am not trying either to forecast the future levels of energy use or to sugge
st optimal rates: the potential for higher conversion efficiencies-or for what I prefer to call a more rational use of energy (which may include avoiding certain conversions altogether)-and hence for reduced power densities of energy use remains large and ubiquitous, but how much of it will be realized will be determined by a complex interplay of social, economic, technical, and environmental factors.

  I will pay attention to both aspects of energy use, as the final, controlled, deliberate conversions of fuels and electricity deployed to produce heat, motion, and light and as unavoidable processes dissipating heat into the environment. This means that I will appraise power densities on a descending scale from the planetary level to megacities and transport corridors to some major industrial process and individual buildings, all the way down to the now numerous indoor energy converters, and that I will also look at the power densities of heat rejection whenever they reach levels that either pose undesirable environmental problems or present great design challenges.

  A Brief Historical Perspective

  I open this segment with a brief look at the power densities of human metabolism. No energy conversion is obviously more important for our survival than food digestion, and as the evolution of human societies led first to higher densities of sedentary farming populations and then to even higher concentrations of anthropomass in cities, the power densities of human metabolism moved from negligible to substantial, and in many places still rising, values. The calculation of population-wide metabolic rates is a complex task that must take into account the age and sex structure of the societies studied and then apply appropriate activity adjustments to age - and sex-specific basal metabolic rates (Smil 2008). But to get fairly representative rates, it is much easier just to use data from metabolic models (Hall 2009) or from food intake surveys, which indicate that in affluent countries, the daily per capita means of food intake are mostly between 8.3 and 10 MJ (2,000-2,400 kcal/day).

  In premodern societies these rates were considerably higher for adults because greater physical exertions (at least 15 MJ/day) were necessary to secure enough food and to energize the mining, transport, construction, and artisanal manufacturing that provided shelter and some material comforts. On the other hand, the smaller body sizes of most preindustrial populations and the common use of child labor tended to reduce average population-wide food requirements. Most people in premodern societies had barely adequate diets and owned little beyond often inadequate clothing and a small number of indispensable household items (Smil 2013b).

  The population densities of foragers (hunters and gatherers) were as low as 1 person/10 km2 of exploited land in marginal (arid, Arctic) environments and as high as 1/km2 in coastal ecosystems where most food came from the ocean. The latter rate translates, even with heavy exertions in fishing and boat building, to a vanishingly low metabolic power density of 0.1 mW/m2. Shifting cultivation raised the population densities to 20-30/km2 (up to 4 mW/m2), and traditional farming easily tripled or even quintupled those values, going from 100 people/km2 of arable land in dynastic Egypt to 150 people/km2 in medieval England and 400 people/km2 (a metabolic power density of up to 45 mW/m2) in intensively cultivated China in the late nineteenth century (Smil 2013a; fig. 6.1).

  Even at the outset of the early modern era, populations were overwhelmingly rural: in 1500, cities contained perhaps no more than 4% of all people, and just 5% a century later (Klein Goldewijk, Beusen, and Janssen 2010). The largest cities of the ancient and medieval world had high population densities within their often massive protective walls. In 300 CE, imperial Rome housed about one million people in an area of just 15 km2 enclosed by the Aurelian walls, the population density of nearly 67,000 people/km2 (Smil 2010c) implying a metabolic power density of 7 W/m2, a rate comparable to that of modern capitals.

  The combination of post-1850 industrialization and rapid post-1950 population growth resulted in extensive urbanization: by 1900 15% of the global population lived in cities, by the year 2000 the share was about 47%. Using historical estimates of the total built-up area occupied by cities-10,000 km2 in 1500, 47,000 km2 in 1900, and 538,000 km2 in the year 2000 (Klein Goldewijk, Beusen, and Janssen 2010)-results in the rise of average worldwide urban metabolic power densities from about 0.2 W/m2 in 1500 to 0.5 W/m2 in 1900 and to almost 0.6 W/m2 by the year 2000. The urban share of the global population reached 50% in 2007; by the middle of the twenty-first century it is expected to approach 70% (UN 2012).

  Extrasomatic Energies

  In preindustrial societies these energies came overwhelmingly either from working animals or from the combustion of biofuels. My reconstruction of energy use in imperial Rome around 300 CE came up with about 100 MW of food energy (human metabolic power), less than 5 MW of feed energy (to sustain donkeys and horses engaged in urban transport), and at least 300 MW of wood and charcoal for cooking requirements, heating (including numerous baths with hot water pools), and artisanal manufacturing (Smil 2010c). This prorates to a power density of 25 W/m2 within the Aurelian walls, a high rate reflecting the high population density during the later imperial era and the low efficiency of biofuel combustion.

  Not surprisingly, as long as cities remained densely populated (confined by walls), and as long as animate energies and the combustion of biofuels remained the only energy inputs, the highest power densities of urban energy use remained very similar. Galloway, Keene, and Murphy (1996) put London's wood consumption at the beginning of the fourteenth century at about 25 GJ/capita, implying an annual power of about 63 MW for the town's 80,000 inhabitants; adding their metabolism and the (relatively unimportant) feed for horses raises the total to less than 75 MW, and prorated over the area of some 1.8 km2 that yields an overall power density of London's energy use in 1300 of roughly 40 W/m2.

  Initially, industrialization brought a counterintuitive shift in the power densities of energy use: in large European cities they began to decline during the early and middle decades of the nineteenth century even as the inputs of coal (for households, industries, and transportation) were rising, and as (starting in the early 1880s) coal-fired power plants (all originally situated in cities) created a new large fuel demand. This is easily explained by the rapid spatial growth of modern cities. For example, London's area expanded more than tenfold during the nineteenth century, from about 24 to 280 km2 (Demographia 2014). Paris expanded at a slower rate, from 34 km2 in the early eighteenth century to just over 100 km2 two centuries later (with its population growing from 600,000 in 1700 to 2.7 million in 1900). A study by Kim and Barles (2012) makes it possible to follow the city's rising, and changing, energy demand.

  By 1800 the city's average per capita demand for all extrasomatic energies was almost 30 GJ/capita, with wood dominant; coal began to supply more than half of the city's energy demand by 1860, and even as the population expanded nearly fivefold during the nineteenth century, the average per capita energy use remained at about 25 GJ, reflecting the higher efficiencies of modern conversions. These shifts translate to almost 500 MW of wood and charcoal in 1800 and 2.1 GW (mostly coal) in 1900, and prorate to power densities of nearly 15 and 20 W/m2. The addition of metabolic energies would raise these rates only slightly, to, respectively, 16 and 23 W/m2, as expanding fuel use relegated somatic energies to totals lower than the inherent errors in estimating extrasomatic inputs.

  Fuel, and later also electricity, requirements for the most energy-intensive and spatially concentrated industrial processes brought unprecedented power densities, as exemplified by contrasting one of the most advanced large-scale manufacturing enterprises of the early nineteenth century with the signature facility of the most important branch of early twentiethcentury manufacturing. The Merrimack Manufacturing Company, America's first large and fully integrated clothing producer (mainly of calico fabrics), opened in 1823 in Lowell, Massachusetts (Malone 2009). The plant occupied about 10 ha and drew about 2 MW of water power from a large (10-m) drop in the Merrimack River. The plant operated with a power density of about 20 W/m2 when pro
rated over its entire area, and about 50 W/m2 when prorated over its actual floor space.

  Almost exactly a century later, in 1928, Henry Ford's River Rouge plant began to produce cars on about 3.6 km2 of land west of Detroit in a completely integrated complex where all essential inputs (coke, steel, glass) and components (steel plates, forgings, engines) were made on-site. During its peak production the plant employed more than 100,000 people and produced a car every 50 seconds (The Henry Ford 2013; fig. 6.2). The primary energy inputs at the River Rouge plant-dominated by coal to make about 1.5 Mt coke/year and to generate electricity in a plant with an installed capacity of 375 MW, - amounted to nearly 3.5 GW, resulting in a power density in excess of 1,000 W/m2 when prorated over the entire site and about 2,500 W/m2 when 1.42 Mme of floor space is used as the denominator. Consequently, the two great phases of modern industrialization, set a century apart, had roughly a 50-fold difference in their operating power density.

  Operating power densities on the order of 103 W/m2 became common in large metallurgical enterprises as well as in new large refineries producing a wider range of liquid fuels and gases with higher efficiency. Pennsylvania's Homestead Steel Works, bought in 1883 by Andrew Carnegie and expanded to become the largest component of his eponymous steel company, are among the best illustrations of these high operating power densities. The complex required about 300 PJ of coke, coal, and natural gas for some 6 Mt of finished steel products (Carnegie Steel Company 2012). The works occupied about a 112-ha site on the southern bank of the Monongahela east of Pittsburgh, and their operating power density of about 2,000 W/m2 remained characteristic of large iron and steel mills for most of the twentieth century.