by Vaclav Smil
Hydro projects built on the middle and upper reaches of rivers have power densities an order of magnitude higher. Itaipu rates 10.4 Wi/m2; Sayano-Sushenskaya, Russia's largest hydroelectric station, on the Yenisei (6.721 GW;), is slightly higher, at 10.8 W,/m2. The Grand Coulee Dam, America's largest project, on the Columbia River (6.809 GWi), comes to about 21 Wi/m2; and China's Sanxia (with a reservoir area of 1,084 km2) has an impressively high rate of 20.8 W;/m2. In contrast, Egypt's Aswan Dam impounds a huge reservoir of 5,250 km2 but has an installed capacity of just 2.1 GW, resulting in a power density two orders of magnitude lower, at a mere 0.4 W/m2. Naturally, the highest rates belong to stations situated in high mountains, whose tall dams impound small but deep reservoirs. The Grand Dixence Dam in the canton of Valois, Switzerland (with the world's tallest gravity dam), has an installed capacity of 2 GW and its lake is just 4.04 km2 (Grand Dixence 2013), implying an extraordinarily high power density of 512 W;/m2, but the station is used for peaking power and generates annually just 2 TWh, that is, an average rate of 228.3 MW but still a very high power density of 56.5 We/m2.
The world's record-holder would be the Nepali Arun III Hydroelectric Project dam. It was originally to be built with World Bank support during the 1990s, and since that time there have been many failed negotiations and delays (Siwakoti 1994). Arun III would essentially be a run-of-river project with just a small, 50-ha reservoir and an installed capacity of 402 MW, resulting in a power density of just over 800 Wi/m2. Goodland (1995) confirmed an expected rise in power density with a higher installed capacity. The average power density of hydroelectric projects with an installed capacity between 2 and 99 MW was just 0.4 Wi/m2; for plants with capacities between 500 and 999 MW it was 1.35 W;/m2, and for the world's largest dams (in excess of 3 GW;) it surpassed 3 W;/m2.
The power densities of actual generation depend on water supply (precipitation) and on competing water uses, above all on flood prevention downstream and withdrawals for irrigation. As a result, capacity factors range from less than 20% during dry years in semiarid or and regions to more than 80% in reliably rainy locations, but commonly are below 50%. For the world's six largest stations these are as follows: as already noted, 50% for Sanxia's and about 80% for Itaipu; Guri (10.2 GW on the Caroni in Venezuela) averages 60%; Tucurui (8.37 GW on the Tocantins in Brazil) averages 57%; the Grand Coulee Dam just 33%; and Sayano-Sushenskaya about 46%. As a result, Sanxia goes from roughly 20 Wi/m2 to just over 10 We/m2 and Sayano-Sushenskaya declines to less than 5 We/m3, but the power density of Itaipu remains high, at 8.3 We/m2, while that of the Grand Coulee Dam drops from 21 W;/m2 to 7 We/m2. McDonald and co-workers (2009) used an average capacity factor of 44% and put the power densities of the most and the least compact US hydroelectric generating projects at about 7.1 and 1.25 We/m2.
Figure 3.5
Power densities of large hydro stations. Graphed are the installed capacities (GWi) and reservoir areas (in m2) of the Sanxia, Itaipu, Grand Coulee, Nurek, Tarbela, Sayano-Sushenskaya, Krasnoyarsk, Tucurui, Gurio, Churchill Falls, Akosombo, and Aswan hydro projects. Carl De Torres Graphic Design.
For the stations with the largest reservoirs, the generation densities are less than 0.6 We/ m2 for Churchill Falls and just 0.06 We/m2 as a 10-year mean (2001-2010) for Akosombo (Volta River Authority 2013). Akosombo, affected by large interannual fluctuations in precipitation, demonstrates the need to use longer-term averages. Even for a single decade the annual extremes can depart ±30% from the mean, and hence in 2007 (with only 3.1 GWh generated) Akosombo's power density would have been merely 0.04 We/m2, a rate lower than that even for low-yielding energy crops. Correcting for actual generation is easy, but (as already noted) there is no obvious or generally acceptable way to correct for the multiple uses of many reservoirs.
Pumped Storage
There is yet another challenge in calculating the power densities of water power: how to treat pumped hydroelectric storage (PHES) projects. These stations (the first ones were built in the Swiss and Italian Alps during the 1890s) use cheaper, off-peak (that is, usually nighttime) electricity to pump water from a lower-lying reservoir to a higher reservoir built on adjacent elevated land (fig. 3.6). They can fill it typically in five to six hours, creating hydraulic heads of more than 300 m, with the record difference nearly 700 m (690 m at Chaira in southwestern Bulgaria). During hours of peak demand they serve as a rapidly deployable reserve to provide a virtually instant additional supply for brief periods of time.
PHES projects use reversible pumps or turbines that can switch from pumping to generating mode in just six to ten minutes and that can usually reach full-capacity generation in a just a few minutes, while turbines synchronized to the grid and spinning on air can go from standby to full load almost instantly. For example, the largest British PHES, Dinorwig, in northern Wales, completed in 1984, with an installed capacity of 1.728 GW, can reach maximum power in just 16 seconds (First Hydro Company 2013). The maximum power of PHES projects is the product of the mass of released water, the generating head, and g (a constant, the acceleration of gravity at 9.81 m/s').
Figure 3.6
Upper reservoir of Ronkausen pumped storage in Germany. (0 Hans Blossey/ imagebroker/Corbis.
For example, Dinorwig can release 7 Mm' over a five-hour period to turn its six reversible Francis turbines receiving water from the upper reservoir that is 500 m above the lower storage (First Hydro Company 2013). This translates into a theoretical maximum power of about 1.9 GW, and the plant's actual rated capacity, taking into consideration a roughly 90% conversion efficiency by its large turbines, is about 1.7 GW), and its output is 8.6 GWh.
The same equation can be used to calculate the cost of water pumping. Because it takes 6.5 hours to fill the reservoir, the pumping flow rate is 299.1 m3/s, and because of frictional drag the effective pumping height is 530 m and the efficiency is, once again, about 90%: these specifics result in a pumping cost of 11.2 GWh and an overall efficiency of 77%. PHES operators are willing to lose a substantial share of electricity in order to generate electricity almost instantly at the time of peak demand:
Box 3.5
Power of Dinorwig pumped storage plant
Box 3.6
Energy cost of water pumping
PHES stations are also generally expensive to build, but they remain the only means to store electricity (by converting it to potential power) on a multi-megawatt to gigawatt scale. In 2010 the worldwide capacity of PHES reached 120.7 GW, with Europe having slightly more than a third of the total, Japan a fifth, and the United States nearly a fifth (USEIA 2013b). This means that the worldwide pumped storage capacity was equal to about 13% of all installed hydropower, but the comparison is misleading, for two major reasons. First, hydroelectric power-generating stations and PHES represent two very different modes of generation: hydropower stations generally produce as much electricity as precipitation and water storage will allow, whereas pumped storages generate according to peak demand.
Second, PHES is always a net energy loser, with the most efficient projects consuming about 20% more electricity than they generate. In 2010 the global electricity cost of running PHES facilities amounted to about 22 TWh, and in the United States pumped storages consumed about 5.5 TWh more electricity than they produced (USEIA 2013b). This reality makes it difficult to compare the PHES's performance with other modes of electricity generation. In any case, a project with an installed capacity of 1 GWe, a reservoir area of about 800 ha, and a load factor of 13% will have an annually averaged power density of just 16 We/m2. In contrast, here are the specifics for a few top projects that show peak power densities up to about 50 times higher.
The Bath County pumped storage station in Virginia, completed in 1985, remains the world's largest pumped storage facility, with 3 GW of installed capacity (Dominion 2013), followed by two 2.4-GW stations in China. The Bath County pumped storage project has an elevation difference of 385 m, the upper reservoir covers 1.07 km2, and the lower reservoir covers 2.25 km2 (Domi
nion 2013). This gives the project a peak power density of just over 900 We/m2, an impressively high rate that could be sustained for only a few hours a day, and hence it is not comparable with the power densities of conventional hydroelectricity stations, which have much higher capacity factors. China's largest pumped storage plant in Guangdong has a head of 535 m, an upper reservoir of 1.2 km2, and a lower reservoir of 1.6 km2 (Chincold 2013). The station uses nighttime electricity from the Dayawan nuclear station to provide peak power to Hong Kong and Guangzhou with a maximum power density of nearly 860 We/m2.
China's second 2.4-GW station, Huizhou, is also in Guangdong province. In 2012 the country had 24 PHES stations with a total capacity of 16.95 GW. Japan's Okutataragi station (1.93 GW) in southern Honshu prefecture and the Ludington pumped storage facility in Michigan (1.872 GW delivered within 30 minutes after startup) complete the world's top five pumped storage facilities. Germany, which would benefit from a higher PHES capacity to accommodate its rising solar and wind electricity generation, had 6.7 GW installed in 2012 (about 5% of total capacity), and despite a common belief that the country's PHES potential is largely exhausted, Steffen (2012) shows that another 4.7 GW could be realized in the coming years. Similarly, more projects are planned for several other EU countries, the United States, and Japan (Deane, Gallach6ir, and McKeogh 2010).
Phytomass for Traditional and Modern Uses
In most of Europe, in North America, and in Japan, traditional phytomass fuels-dominated by wood and charcoal, but also including large amounts of crop residues and in some societies also dried dung-were the dominant source of thermal energy until the late nineteenth century. In the rest of the world (including populous China, India, Indonesia, and Brazil), they retained that place for most of the twentieth century. There were only two great exceptions to the dependence on wood in the early modern (15001800) world, England-Wales and the Netherlands. England was the first country that accomplished its transition to coal, while the Dutch relied heavily on peat. Warde (2007) suggests that the most likely time when energy from coal combustion surpassed that from the burning of wood was around 1620, and that by 1650 coal provided two-thirds of all primary energy. The Dutch golden age of the seventeenth century was fueled by peat: its per capita consumption was higher than India's average energy supply in the year 2000 (de Zeeuw 1978; Smil 2010b).
In the United States, coal (and the still relatively small flow of crude oil) began to supply more than half of all primary energy by the mid-1880s. In Japan the tipping point came a generation later, while in the USSR it was delayed until the early 1930s and in China until the mid-1960s (Smil 2010b). At the beginning of the twentieth century traditional phytomass fuels provided half of the total primary energy supply; by its end their global harvest had actually doubled as hundreds of millions of poor villagers and many people in smaller towns throughout Asia, Africa, and Latin America continued to rely on phytomass for cooking and heating, but in relative terms those fuels became a marginal part of the total supply, providing no more than 12% by 2010 (Smil 2010b).
In the poorest parts of the world household fuel is still gathered mostly by families, much of it in a way unchanged for millennia, not by cutting trees but by collecting fallen and dry branches of small trees and shrubs. This often requires lengthy walks to the nearest sources of woody phytomass, making it a time-consuming chore that is usually done by women and children. At the same time, in many tropical countries a surprisingly large share of woody phytomass does not come from forests but from roadside and backyard trees and from small groves. And while the increasing availability of kerosene, LPG, and electricity reduced the dependence on crop residues, the burning of cereal straws is still a common practice in many rural areas, particularly in Asia.
In modern countries virtually all phytomass for energy conversions comes from three major sources. The first one is woody phytomass explicitly destined for energy conversions (combustion, gasification), with an increasing share coming from tree plantations of fast-growing species. The second one is a diverse group of residual phytomass that includes those tree parts that do not become merchantable timber or pulp for making paper (bark, chips, wood shavings, sawdust) and crop residues (a category dominated by cereal straws and sugar cane bagasse). The third one, the latest addition to the two well-established sources, is the cultivation of annual or perennial field crops that are converted to liquid biofuels (mostly ethanol and biodiesel) or are gasified.
The power density of phytomass energy use is always very low, an inevitable consequence of the inherently poor efficiency of the conversion chain that starts with solar radiation and ends with actually harvested phytomass. The photosynthetic conversion of select wavelengths of solar radiation to the chemical energy of new phytomass is a remarkable transformation, the foundation of all heterotrophic life and hence also of all human societies and civilizations (Smil 2013a), but one with inherently low efficiency because only a small part of solar energy that is initially converted to new chemical bonds in those plant tissues ends up as harvestable phytomass.
From Solar Radiation to Phytomass
Cannell (1989) offered a representative sequence of efficiencies and conversion losses leading from the insolation to actual wood yield, and I have updated some of his multipliers and recalculated all the steps in terms of power densities for a location with 115 W/m2 of annual irradiance (typical for the forests in southern Sweden) and with all progressive rates expressed in W/m2 (rounded to the nearest 0.1).
Conversion of the power density of 0.6 W/m2 back to annual phytomass yields (assuming an energy density of 19 GJ/t and a specific density of 500 kg/m3) roughly 10 t/ ha in terms of dry matter. This would be a fairly representative mean for a growing (nonclimax) forest on fairly good soils and receiving adequate precipitation. Indeed, Luyssaert and co-workers (2009) found that the best available model of the net primary productivity (NPP) of European forests (for EU-25) produces an annual mean of 520 ± 75 g C/ m2, that is (assuming that wood is 50% C), 10.4 ± 0.75 t/ha. Another set of estimates puts the mean annual NPP of EU-25 cropland at 646-846 g C/m2, or roughly 13-17 t/ha (Ciais et al. 2010). Most of the world's terrestrial plants have yields, and hence production power densities, of the same order of magnitude. The NPP (with all values in dry matter) of tropical ecosystems is on the order of 20 t/ha, the means for temperate and boreal forests and woodlands are around 10 t/ha, and the world's cultivated land has a very similar mean.
Box 3.7
Power densities of a photosynthetic progression
The global terrestrial NPP is between 110 and 115 Gt/year (Ito 2011; Zhao et al. 2005). If we assume (conservatively) 18 GJ/t, this is at least 2 ZJ, or nearly 63 TW. Prorated over the Earth's ice-free surfaces the average photosynthetic power density would be just 0.4 W/m2, but a more accurate rate results from also leaving out both hot and cold deserts, which raises the mean power density to about 0.6 W/m2 (11 t/ha). During periods of most rapid growth, NPP additions could amount to 200 kg/ha a day for the inherently more efficient C4 plants and up to 150 kg/day for C3 species. But NPP does not measure actual phytomass harvest; it is a construct of the gross productivity adjusted for respiration. NPP excludes heterotrophic consumption (all preharvest losses to bacterial and fungal infestations, to insects, birds, rodents, and other mammals), as well as losses to inclement weather (wind damage, flooding, drought).
The rate that adjusts for all losses is net ecosystemic production (NEP), and if there are no weather-induced preharvest losses and if the entire aboveground growth is harvested (such as with whole-tree utilization for wood chips or with a forage or silage crop), then the NEP should be identical to the actual harvest. But more often our harvests do not include all the aboveground phytomass. When trees are grown for stemwood (for sawnwood or pulp), the actually harvested net stem growth is only about 20% of NPP and 40% of NEP (Pretzsch 2009). And for cereal crops, which are by far the largest category of agricultural products, the harvested grain is typically no more than 40%-45% of t
he aboveground phytomass (the rest being cut straw and the remaining stubble). The power density of actual phytomass harvests has changed with time as a result of changes in harvesting methods as well as in the degree of phytomass utilization.
Harvests, Yields, and Power Densities
Studies in tropical and subtropical forests show annual production rates as low as 5-6 t/ha and as much as 12-15 t/ha, whereas in temperate forests the rates are mostly less than 5 t/ha (Bala et al. 2010; Clark et al. 2002; Liu et al. 2003; Odiwe and Muoghalu 2003). Converted by using an average of 18 MJ/kg, these rates would translate to 90-270 GJ/ha in the tropics and subtropics and mostly to less than 80 GJ/ha elsewhere, or between roughly 0.25 and 0.85 W/m2. Many litterfall studies also show the composition of the fallen phytomass: leaves (or needles) typically account for 65%-75% of the total mass, reproductive parts (flowers, seeds, nuts) for 5%-10%, and coarse woody debris for only 15%-25% of the total, or as little as 750 kg and as much as 3.75 t/ha a year. Only the last part of litterfall, coarse woody debris, is usually collected, and the annual power densities of collectable woody phytomass would be no higher than 0.04-0.20 W/m2.