Power Density

by Vaclav Smil

  Similarly, the power densities of fossil fuel extraction and thermal electricity generation have increased as a result of better mining, drilling, and recovery techniques and the rising efficiencies of boilers, nuclear reactors, steam turbogenerators, and gas turbines. Moreover, some of these innovations (surface coal mining, deep and horizontal drilling, and hydraulic fracturing) made it possible to recover resources that were previously considered uneconomical, including through the surface mining of thick but low-quality coal deposits more than 300 m belowground, the recovery of hydrocarbons in reservoirs deeper than 3 km, and accessing nonconventional resources of oil and natural gas bound in shales.

  This typological detour and the brief notes on assorted caveats were necessary to appreciate that both of the variables used to calculate power densities have a wide range of qualitative attributes. This reality has many counterparts in endeavors aimed at analyzing and understanding other complex phenomena, be they (as I noted when pointing out a quality-free common denominator of food energy densities) studies of human nutrition and average per capita dietary intakes or (to cite very different examples) efforts to understand educational achievements and economic inequality.

  There are, obviously, enormous qualitative differences among PhD degrees from different universities and in different disciplines, or among sources of income measured in the same currency but coming from such qualitatively disparate sources as a comfortable trust fund or three poorly paying part-time jobs. These realities complicate, but never disqualify, the measures we have to use to derive an all-encompassing understanding of complex phenomena. The power density rate is a powerful explanatory variable, but it should be assessed in conjunction with other factors that codetermine the capacities and performances of a specific resource extraction or conversion method or the overall system capability.

  In environmental terms, power density is about claiming space: land use intensity (m2/W) is its obvious inverse. But there are other intensities to consider, above all the intensity of water use (g H20/J) and carbon intensity (g C/J), a marker of the human interference in the global biogeochemical carbon cycle that quantifies the emissions of C02, the dominant anthropogenic greenhouse gas. And even before considering water or carbon, costs might come first to mind. The power density and specific energy production costs of fossil fuels have an obviously significant inverse correlation, but there is no simple general causality.

  Hydroelectric generation, a ubiquitous example of a low-power-density conversion, produces some of the world's cheapest electricity, while liquid metal fast breeders would produce electricity with a much higher power density than rooftop PV cells, but all countries that were initially engaged in operating experimental breeder reactors (the United States, the USSR, and then Russia, France, Japan, and India) found their costs so prohibitive that they stopped (the United States and UK by 1994, France by 2009), curtailed, or suspended further development aimed at commercial application (Cochran et al. 2010). But these two examples are uncharacteristically clear-cut. In most other cases cost considerations are subject to some profound uncertainties.

  All kinds of modern energy conversions have benefited from often generous, and longlasting, subsidies (Gerasimchuk et al. 2012; Laderchi, Olivier, and Trimble 2013; OECD 2013), and a proper accounting of these hidden costs could easily swing around many comparisons of specific energy modes. For example, the most comprehensive comparison of the levelized cost of electricity generation shows that in 2013, US federal tax subsidies could cut the cost of crystalline rooftop PV arrays to as low as $117/MWh (the unsubsidized cost was as high as $204/MWh), making it in many places competitive with coal-fired generation, whose unsubsidized cost ranged from $65 to $146 (Lazard 2013).

  Similarly, a comparison can be turned around by including only one or two ignored externalities: the adoption of fairly high carbon taxes designed to account for the long-range effect of global warming would make coalfired plants-now about $100/MWh, and quite competitive with most forms of renewable electricity generation-instantly uncompetitive. Such shifts would require different margins in different countries, and that is why I will not offer any comparative lists claiming that wind-generated electricity is always cheaper than any thermal generation or that PV is the cheapest alternative. Instead, I will point out a number of technical and environmental realities that should be considered along with power densities.

  This chapter offers a systematic stroll through renewable energies that begins with solar radiation and its three great derivatives-winds, flowing water, and phytomass produced by photosynthesis-and concludes with a brief assessment of geothermal energy, the Earth's most important nonsolar energy flux.

  When classified by their origin, renewable energy flows belong to just three categories. By far the most important is solar radiation (direct and diffuse) and its diverse transformations, manifested as wind (generated by pressure differences resulting from the differential heating of the Earth's surfaces), a vertical temperature gradient in the ocean (created by the heating of the surface layer above the isothermal deep water), ocean currents (resulting, again, from differential heating of the liquid mass), the kinetic energy of streams (created by the Sun-driven water cycle of evaporation, precipitation, and runoff), and plant mass (phytomass, created through photosynthesis).

  The second category of renewable energy flows is energized by the decay of radioactive elements in the Earth's crust and by the flow of basal heat from the planet's hot interior, and manifests as an omnipresent but low temperature gradient and, particularly along tectonic plate boundaries, as high-temperature-gradient flows of hot water and steam that can be used for space heating or electricity generation. The last category of renewable flows also has only a single entry, as the gravitational interplay of the Earth and its orbiting satellite creates tides that are highly predictable but that reach impressively high differentials only in a few regions.

  I will concentrate on major land-based fluxes whose conversions have been indispensable in the past, that are increasingly exploited today, and that have the greatest practical promise for future innovations. These flows include the conversion of solar radiation into heat (the most common application is to heat water) and electricity (done mainly by photovoltaic [PV] cells or by concentrating solar radiation to heat a working medium in a standard thermal power plant); phytomass (used for millennia as the dominant source of heat and light in the form of fuelwood, charcoal, and lamp oils, and more recently also converted to liquid fuels, above all to ethanol and biodiesel); hydro energy (a leading source of mechanical energy during the preindustrial era, produced by waterwheels, and now a major global supplier of electricity generated by water turbines); and wind (converted in the past into mechanical energy by windmills, and today into electricity by wind turbines).

  Despite its large aggregate global potential, geothermal power must be classed in a less consequential category, and although the commercial exploitation of ocean currents, ocean thermal differences, and tidal energy has some tireless proponents, these energy sources will not be considered here: they are the least promising renewable energy alternatives, their power densities (per unit of ocean surface) are inherently low, and their land claims (for associated infrastructures) would be minimal. My systematic review will clearly establish a hierarchy of renewable energies based on their average, as well as peak, power densities. These findings are used later in the book when I contrast the typical power densities of modern ways of energy production with the prevailing, and changing, power densities of energy use in high-energy urban societies.

  Solar Radiation and Its Conversions to Heat and Electricity

  The Sun is situated in a spiral arm of our galaxy, with its closest neighboring star, u Centauri, 4.3 light-years away. Our star is a dwarf (size class V) belonging to a rather common spectral group (G2), whose radius (696.7 Mm) is more than 100 times that of the Earth, and it keeps the planet orbiting at a mean distance of 149.6 Gm (Mullan 2010). Hydrogen makes up about 91% of
the Sun's huge mass, and its energy is produced in its core mostly by the fusion of protons, forming helium, which consumes about 4.4 t of its mass every second. The Stefan-Boltzmann equation states that the radiant flux (F) must be proportional to the fourth power of temperature (box 3.1).

  Box 3.1

  Radiant flux

  This means that the Sun's isotropic radiation is 63.2 MW for every square meter of its photosphere.

  This granulated layer radiates along a wide spectrum whose wavelengths range from less than 0.1 nm (y rays) to more than 1 m (infrared radiation). The peak radiation-dictated by Wien's displacement law, Xmax = 0.002898/T (K)-is at about 500 nm, close to the lower limit of green light (491 nm), and about two-fifths of all energy is radiated in visible wavelengths between 400 nm (deep violet) and 700 nm (dark red). Ultraviolet radiation carries about 8% of all solar energy, infrared the rest (53%). Visible wavelengths energize photosynthesis (it proceeds mainly by the means of blue and red light, with green reflected) and are sensed by organisms ranging from bacteria to humans: our vision is most sensitive to green (491-575 nm) and yellow (5 76-585 nm) light, with the maximum visibility at 556 nm. But the heating of the biosphere is done mostly by infrared radiation at wavelengths shorter than 2 pm.

  Once the radiation leaves the Sun's photosphere it travels virtually unimpeded through space, and its power density at the top of the Earth's atmosphere is easily calculated by dividing the star's total energy flux (3.845 x 1026 W) by the area of the sphere whose radius is equal to the planet's mean orbital distance of 149.6 Gm. This rate-1,367 W/m2-is known as the solar constant, although the rate has both short-term and longer-term deviations (de Toma et al. 2004; Foukal 2006). The mean value of satellite observations is 1,366 W/m2, with brief declines of 0.2-0.3 W/m2 (caused by the passage of large sunspots across the Sun) and periodic undulations (caused by the 11-year solar cycle), with the peaks as high as 1366.9 W/m2.

  Although the Earth is a rotational ellipsoid rather than a perfect sphere, dividing the solar constant by four (the difference between the area of a circle and of a sphere of the same radius) yields a fairly accurate mean of the solar radiation (341.5 W/m2) that would reach the rotating planet if it were a perfect absorber (black body) and had no atmosphere. In reality, the Earth's atmosphere absorbs about 16%, and hence even without any clouds the annual mean irradiance would be no more than 287 W/m2. Clouds absorb another 3%, reducing the mean to about 278 W/m2. But the atmosphere is also a reflector of incoming radiation; long-term satellite measurements have confirmed that the Earth's albedo (the share of the reflected radiation) averages almost exactly 30%, with obvious seasonal fluctuations between the northern and southern hemispheres.

  The Earth's atmosphere reflects 6% of the incoming radiation, clouds reflect 20%, and continental surfaces and water account for the remaining 4%. This means that about 55% of incoming radiation could be absorbed by an average square meter of a perfectly nonreflecting horizontal ground surface, the rate that translates to about 188 W/m2. Actual irradiance is subject to daily and seasonal variations that can be perfectly predicted for any site on the Earth as the planet rotates on a tilted axis; it is also subject to the much less predictable mesoscale influences of cloud-bearing cyclonic systems, and to highly unpredictable local cloudiness. The values for the total annual global irradiance are, obviously, a function of latitude and cloudiness. Below I cite just a few representative rates calculated from daily measurements (Ineichen 2011; NASA 2013).

  Annual Irradiance

  The rate for Berlin, representative of populated northern hemisphere midlatitudes influenced by regular cyclonic flows, is just 116 W/m2 (an annual energy total of 1.016 MWh/m2); the rate for Dublin, within the same zone, is only about 100 W/m2. London is very close to Berlin (110 W/m2), while Paris gets around 125 W/m2. Murcia, in Spain, representative of sunny Mediterranean locations, receives 196 W/m2, similar to Athens and a bit more than Rome, at about 175 W/m2. The southern states of America's Great Plains experience the same range of average irradiance (Tulsa in Oklahoma receives about 180 W/m2, San Antonio in Texas about 200 W/m2).

  At 266 W/m2 (2.328 MWh/m2 in a year), Tamanrasset in southern Algeria indicates the maxima receivable in the planet's sunniest climates of the and subtropical belt. The only larger city with a slightly higher long-term rate is Nouakchott, the capital of Mauritania, which receives 273 W/m2, while the Saudi capital, Riyadh, receives slightly less, about 251 W/m2. The largest relatively heavily populated regions with average rates above 200 W/m2 are in the US Southwest (with Los Angeles and Phoenix receiving 225 W/m2) and Egypt's Delta (Cairo at 237 W/m2). In contrast, frequent cloudiness keeps the rate for such tropical megacities as Singapore and Bangkok well below 200 W/m2.

  Differences in monthly insolation averages depend on latitude and cloudiness: in Oslo the difference between January and June is 16-fold; in Riyadh it is only twofold. These differences are reflected by actual PV electricity generation: in 2012 the German output was 4 TWh in May and just 0.35 TWh in January, an order of magnitude disparity (BSW Solar 2013). The annual variability of irradiance is significantly larger in cloudy climates and in mountainous regions: fluctuations of total irradiance are as high as 7% in Berlin and Zurich, 2% in Murcia and Tamanrasset. Naturally, monthly differences can be much larger. For example, in January 2013 the Czech Republic averaged 50% less sunlight than in January 2012 (Novinky 2013). During cloud-free days the highest daily global irradiance is a perfectly predictable function of a calendar day and latitude; naturally, daily minima in the northern hemisphere occur during the winter solstice and maxima occur six months later. Theoretical expectations of noontime maxima are as high as 1,065 W/m2 (the solar constant minus atmospheric absorption and reflection).

  Indeed, the highest recorded maxima in subtropical cloud-free deserts come within a small fraction of 1% of that value. For example, the noontime May and June hourly maxima from Saudi Arabia are 1,059 W/m2 for Dhahran on the Gulf coast and 1,056 W/m2 for Riyadh in the interior (Stewart, Dudel, and Levitt 1993). Irradiance delimits the range of power densities that can be harnessed as heat or converted by PV cells to electricity. There is an order of magnitude difference between annual averages of less than 100 W/m2 in cloudy temperate mid-latitudes and the just noted maxima above 1,000 W/m2 available for one to three hours a day during the sunniest spells in the great subtropical desert belt that extends from the Atlantic coast of Mauritania to North China and that has its (much more circumscribed) western hemisphere counterparts in the US Southwest and northwestern Mexico, and in the southern hemisphere it prevails throughout large parts of Australia and in a narrow strip along the coast of South America.

  Conversions of Solar Radiation

  Life's evolution and the biosphere's dynamics are determined by the levels and variations of irradiance. Irradiance energizes photosynthesis and warms the atmosphere, waters, rocks, and soils (creating pressure differences and hence powering the global air circulation, and evaporating moisture and hence powering the global water cycle), as well as bodies of organisms (critical to keep optimal temperatures for enzymatic reactions) and surfaces of buildings (every aboveground structure that shelters is solar heated). Direct solar radiation has also been used for millennia to evaporate salt along seashores, to dry crops, to sunbake clay bricks, and to dry clothes. In cold climates the best design tries to maximize solar gain in passive solar buildings-and, taking some ancient lessons, to minimize it in hot environments (Athienitis 2002; Mehani and Settou 2012).

  Not long after modern indoor plumbing became available, solar radiation began to be used to heat water in simple rooftop collectors. This practice has become increasingly more efficient and is now quite common in many sunny countries (Mauthner and Weiss 2013). Improvements in plant productivity aside, the most important active step in harnessing irradiance has been the development of solar electricity generation, primarily based on the PV effect but also using concentrated solar power to run steam turbines. These conversions have power densiti
es higher than those of any other means of harnessing renewable energy flows; moreover, PV efficiencies have been gradually improving, and further significant gains are certain.

  The power densities of solar conversions have several unique attributes: they belong to two distinct categories; calculations for nearly all of them are done for tilted rather than for horizontal surfaces; and some of them refer to active (adjustable) areas rather than to fixed level surfaces. Most tilted panels on roofs on large solar farms are fixed in one position: optimal angles from horizontal are easily calculated (Boxwell 2012). The best fullyear angle for my latitude (Winnipeg is 50°N, the same as London or Prague) is 41.1 degrees, and that position will capture about 70% of radiation compared to a tracker; for Tokyo (35°N) it is 29.7 degrees; and, obviously, fixed panels should remain horizontal at the equator. Panels are usually adjusted according to season (twice or four times a year), while full tracking has so far been reserved for some commercial installations.

  The two distinct categories are land-based systems (large-scale PV plants and concentrated solar power harnessing-irradiance with a field of heliostats) and rooftop installations (both for solar heating and for PV electricity generation). In the future a third category might become important as vertical surfaces-mostly suitably oriented building walls-can be either clad in PV panels or glazed with PV glass unit windows (Pythagoras Solar 2014). With land-based systems, solar power densities are both similar to and different from those of wind-powered electricity generation. PV arrays, much like wind turbines and their associated access roads and structure, will not completely cover the land claimed by the project, but their degree of coverage will be much greater, and in most cases the PV arrays will be fenced.