Power density

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Power densities Compared to this fairly high rate, typical power density of wind-driven electricity generation as energy flux prorated per unit of horizontal surface is two orders of magnitude lower because wind turbines must be set apart in order to avoid excessive wake interference. Turbines in wind farms must be set apart at least three, and better five, turbine diameters in the cross wind direction, and at least six and preferably ten diameters in the downwind direction (Hau 2005). Power density of large wind farms with turbines arrayed in a square grid would be then between 2-3 W/m2. Returning to the Vestas 90, spacing these machines in a large wind farm on a regular square grid ten rotor diameters apart would result in power density if 2.37 W/m2 for the rated performance of 3 MW/turbine. American Wind Energy Organization lists the power densities of more than 70 large-scale (what they call industrial) facilities on its website, with the rates ranging from just below 1 Wi/m2 to an exceptionally windy site (Cassia County in Idaho) with 11.1 Wi/m2, and with most densities, as expected, between 2.5-4 Wi/m2 (AWEO 2013).

In reality, turbine configurations in large wind farms include single strings (sometime with discontinuities), parallel strings (often close to a perfect grid spacing), multiple strings that are not uniformly oriented, and clusters laid out in irregular fashion dictated by terrain or micro-scale differences in wind speed. Denholm et al. (2009) studied all of these configurations belonging to 172 existing and proposed US large-scale (with installed capacities greater than 20 MW) wind projects in all windy regions of the nation and their conclusions offer a representative quantification of both typical and extreme land claims of modern wind farms.

Obviously, areas of direct impact –- including land occupied by turbine pads, access and service roads, substations, service buildings and other infrastructure -– make up only a small share of the total land claim. NREL’s wind farm area calculator assumes that it amounts to 0.25 acres per 1,000 kW, that is 1,000 m2/MW or 1,000 W/m2 (NREL 2013). But according to Denholm et al. (2009) direct land claims (permanent and temporary during installations and repairs) average 1 ha/MW of which 0.7 ha/MW are temporary claims during construction and 0.3 ha/MW is permanent land occupation. This last rate translates to power density of 333 W/m2 or three times as much as land-intesive as assumed by the NREL’s area calculator. In any case, direct impacts (structures, roads) are easy to define and to quantify, while indirect land claims are subject to interpretation as the perimeter of a wind farm will vary with turbine size, terrain, existing land use and specific setback regulations.

Denholm et al. (2009) used the land total listed in project applications or associated documentation to find that the average total land claim was 34±22 ha/MW, that is power density of 3±1.7 Wi/m2, with the extreme values more than 15 and less than 0.5 W/m2. Plotting power density as a function of wind farm size does not show any pronounced correlation: most project with overall capacity of less than 100 MW have densities of 2-6 Wi/m2, for larger projects (>300 MW) the density declined a bit but its spread narrows to 2-4 Wi/m2. But all wind power densities cited so far exaggerate the real performance because they all have been calculated with rated capacities that were not corrected for prevailing capacity factors calculated by using actual annual electricity generation totals. These rates vary not only among the sites but also show sometime significant inter-annual fluctuations for the same site.

For many early large-scale wind projects of the late 1980s and 1990s capacity factors were well below 20%. A detailed examination of the actual record of wind generation in the EU, which has the world’s largest concentration of wind power, shows during the five years between 2003 and 2007 the average capacity factor still amounted to less than 21% (Boccard 2009). In 2010 the nationwide means were 25% for the UK, 24% for Spain and Denmark but only 20% for France and 15% for Germany. In the US better siting and better turbine designs have resulted in noticeable long-term gains in average capacity factors. Analysis of 94% of all US projects built between 1983 and 2010 shows average load factor rising from 25% in 1999 to 33% in 2008, then dropping to about 30% in 2009 and 2010 before rebounding to 33% in 2011 (Wiser and Bolinger 2012).

A year later Wiser and Bolinger (2013) noted that the rate for 2006-2012 (32.1%) was higher than for 2000-2005 (30.3%) but that the trend has not been either as significant or as consistent as expected, and that the 2012 rate was below the peak of 35% achieved in 2008 and, most importantly, that average capacity factors for projects built after 2005 have been stagnant. The explanation is simple: while better turbine designs boosted capacity factors, locations of many new projects in lower-quality (that is less consistently windy) areas tended to lower it, and in 2012 the average wind resource at the height of 80 m was 15% lower among the projects built in 2012 than among those built in 1998-1999.

This seemingly irrational location choice has been actually very rational because a lower resource quality in locations closer to major markets and readily connected to existing transmission lines is compensated for by the savings on high-voltage transmission lines that would be needed to bring electricity from more windy, but more remote, regions. The same consideration has kept Germany’s capacity factors quite low. The country has EU’s highest wind capacity (about 30% of the total in 2012), much of it in only moderately windy areas and during the first six months of 2013 German wind turbines had capacity factor of only 16%, ranging from 11.8% in May to 21.7% in January (Chabot 2013). This poor European performance has been a major reason why all but one of wind projects rated by Standard & Poor have fallen from investment grade to speculative grade over time (Standard & Poor 2012).

Taking the most recent US mean of 32% would be thus a proper correction factor for American capacities and it would imply –- using the previously established average power density of America’s large wind farms as 3±1.7 W/m2 –- that the power density of the country’s wind-driven electricity generation is only 0.96±0.54 W/m2. McDonald et al. (2009) used a slightly higher capacity factor of 35% when calculating their range of 1.4-1.7 W/m2 for the least and most compact US projects. For the EU the actual power densities should be calculated with average capacity of factor of only about 20% (and 25% for the windier UK and Spain), bringing the rate to just 0.6-0.75 W/m2. This is essentially an order of magnitude less than power densities of solar electricity generation and (and I will show later in this chapter) only about twice as high as the densities of most productive phytomass harvests.

But the comparison must be qualified because of some fundamental differences in the nature of occupancy of the claimed land and the degree of its permanence. Obviously, crops or tree plantations do not allow any other concurrent land use, nor is the area covered by closely-spaced PV cells suitable for any other uses. And while the strips between PV arrays in large solar parks are theoretically available for grazing the coexistence of PV modules and sheep will not be a common occurrence. In contrast, in a large wind farm the land completely excluded from other uses is limited to turbine pads, transmission infrastructures and permanent access roads, and in large US projects these, according to Denholm et al. (2009), will account for less than 1% (3,000 m2/340,000 m2 = 0.88%) of the total area claimed by an average large American wind farm.

Consequently, 99% of land can be devoted to a variety of agricultural (annual or permanent crops), horticultural (flower beds) or silvicultural (tree and shrub nurseries, X-mas tree plantations) uses, or it can be grazed by domestic animals. Clearly, low power densities of wind-driven electricity generation are not of concern (unlike in the case of biofuels or hydro energy) because of a relatively large areas of land are actually claimed or transformed by the conversion but because they indicate the spatial limits of wind exploitation. We can cram PV cells to cover entire roofs or space them densely in large solar farms, we can raise crop or wood yields per unit of land, and we can boost hydro generation by storing more water behind taller dams –- but we cannot increase the density of vertical-axis turbines in order to maximize wind-powered electricity generation within a given area.

In smaller-sized countries with limited wind resources this imperative means that it does not take very long before the continuing exploitation of wind has to move to locations with lower wind quality (speed and frequency). But in nations with large territories many high-quality wind sites that are far away from major urban and industrial areas will remain unexploited until the development of requisite transmission lines connects those relatively high power density locations with large electricity markets. In the US it means building more than a score long-distance lines on a semi-continental scale, and multiple lines connecting the windy Great Plains with the coasts cannot be completed in a matter of years (Smil 2011).

Noise effects Finally, there is one spatial consideration that limits the use of land near large wind turbines: they can overtop crops or grazing animals, but they cannot be sited right next to permanent settlements (as even very large solar parks can) because of the turbine noise. The mechanical component of the noise (from gearboxes) has been reduced by better design, so the concern is about the aerodynamic (whooshing) noise produced by the flow of air around the blades and tall towers. Typical maximum noise levels for human exposure are set at 40 dBA sound intensity (integrated over 20-20,000 Hz band) with wind speed of 8 m/s at 10 m height. This usually means buffer zones of about 350 m for large wind farms: at that distance noise will be 35-45 dB, while a busy office is 60 dB, a quiet bedroom 20 dB; the scale is logarithmic and hence the difference between the power of 40 and 20 dB is 100-fold.

Many jurisdictions simply set standard buffers. Scottish planning policy calls for 2 km between wind farms and the edge of cities and villages, Wales has 500 m recommendation (RegenSW 2012), but in 2013, after Milton Keynes Borough Council wanted to set 1.2 km buffer the UK’s High Court of Justice ruled that local councils cannot impose their own buffer zones for new wind projects (Royal Courts of Justice 2013). The US has has some 25,000 zoning jurisdictions with most setback rules set on the country level (USDOE 2011), and with some buffers being just 150 m from a property line containing a dwelling, other requiring more than 1 km.

What is tolerable and what is objectionable? Large weather variations and often complex landscape specifics require long-term measurements of the noise from wind turbines in order to assess its real impacts; when this is done the measurements may show that urban background noise level (above all road traffic) may dominate at distances beyond 300 m from a wind turbine (Björkman 2004). But this is hardly universal. As with other controversial topics involving complex mental and physical human responses to environmental disturbances, the new field of wind-turbine noise studies spans a wide range from those who see a new, full-blown ‘’wind turbine syndrome’’ of health impacts (Pierpont 2009) to those who dismiss the concern as nothing but ‘’a prime example of a contemporary psychogenic illness” (Chapman 2012, 1).

Such a dismissal is not supported by a great deal of accumulating evidence. There is no need to demonstrate any direct physical effect of noise: noise annoyance can act as a mediator that leads to sleep disturbance and mental distress (Bakker et al. 2012). And there are objective assessments of the effect. Nissenbaum, Aramini and Hanning (2012) studied effects of wind turbine noise on sleep and health at two sites in Maine and demonstrated that participants living within 1.4 km of a wind farm had worse sleep, were sleepier during the day and had worse mental component scores than those living further away. The overall evidence is complex (Roberts and Roberts 2013) but there is no doubt that living too close to large industrial wind turbines can harm human health and that typical symptoms are stress disorder-type diseases acting via indirect pathways (Jeffery, Krogh and Horner 2013). This reality would further dilute the average power density of wind generation located in more populous regions and also in rural areas with relatively high density of population (most notably in many countries in Asia).

At the same time, there are some intriguing possibilities of boosting typical power densities of wind-driven electricity generation. One of them might be to shift away from horizontal-axis turbines that dominate the global market to vertical-axis machines whose denser spacing can raise the output per unit area. Experimental field tests with six 10-m tall and 1.2-m diameter vertical-axis wind turbines with 4.1-m span airfoil blades (modified version of a commercial model by Windspire Energy) that were spaced 1.65 diameters apart with the footprint of 48.6 m2 demonstrated opportunities for raising average power densities by extracting energy from adjacent wakes and from above the wind farm (Dabiri 2011). With three turbines rotating around their central shaft clockwise and the other three counterclockwise, daily mean power densities with winds above 3.8 m/s ranged between 21-47 W/m2 at wind speeds above cut-in speed and 6-30 W/m2 overall during the three months of testing, an order of magnitude above the power density of horizontal-axis wind turbines.

Another option -– one that uses well-developed horizontal-axis turbine designs and that has been already commercially demonstrated in some countries –- is to move away from land and to set up large offshore wind farms. Power density limitations cannot be avoided (offshore wind turbines still have to be spaced appropriately) but stronger and more reliable offshore winds result in higher capacity factors and remove the common environmental concerns associated with land-based wind electricity generation. Denmark was the first country to build a substantial offshore capacity, with 871 MW installed by the end of 2012; in that year Danish offshore farms had capacity factor of 44.9% and a lifetime capacity factor of 39.1% (Energi Styrelsen 2013).

But costs and technical challenges (above all building long-lasting structures in corrosive environment and putting in place new long-distance high-voltage transmission lines) have moderated initial expectations concerning the offshore wind revolution. In 2012 the US still did not have a single offshore wind farm (although the first ones were planned already during the 1990s), Germany found that its offshore aspirations had become ‘’dramatically problematic’’ (Dohmen and Jung 2011), and analyses done in both the UK and Germany showed that just connecting an offshore wind farm to the land grid costs more than building an equivalent capacity in gas turbines that can be located virtually anywhere. Even so, the European Wind Energy Association envisages great advances not just for near-shore installations in shallow water but for deep-water turbines far offshore (EWEA 2013).

Water power and hydrogeneration

Energy flux of water turning a turbine (P) depends on the rate of water flow (Q, in m3/s) and on the hydraulic head (h, in m), the distance through which the eater falls before impacting the blades and the actually delivered power will be also a function of the turbine efficiency (η); water density and acceleration of gravity remain identical (ρ = 1 g/cm3, that is 1,000 kg/m3, and g = 9.81 m/s2). A large, highly efficient (87%) turbine working under the head of 118 m and receiving water flow 700 m3/s will generate about 700 MW of electricity:

Power of a water turbine
P = ηρQgh

= 0.87 x 1,000 x 700 x 9.81 x 118

= 704. 97 MW
These are actually specifications for each of the 20 turbines installed in Itaipu, still the world’s largest hydrostation in terms of annual electricity generation, located on the Paraná River between Brazil and Paraguay. China’s Sanxia (Three Gorges, completed in 2009) has a 60% higher installed capacity (22.5 GW compared to Itaipu’s 14 GW) but a much lower capacity factor (about 50% compared to Itaipu’s rate of close to 80%) and hence it typically delivers only about 85% of Itaipu’s power (CTGC 2013; Chincold 2013). With little difference in high efficiency of modern turbines and with ρ and g constant, power densities of modern hydroelectricity generation will range widely along the continuum governed by the extremes of Q and h. At one extreme are the projects that rely on massive water flows with small generating heads created by low dams. Yacyretá project on the Paraná between Paraguay and Argentina is an excellent example of this category: its hydraulic head is just 22 m but the low dam createa a reservoir of 1,600 km2 which supplies enough water to installed capacity of 3.1 GW and annual generation of 20 TWh (that is 2.29 GW and a high load factor of nearly 75%).

The other extreme is represented by plants that let relatively small mass of water fall from great heights created by tall dams whose construction was pioneered in the Alps. The world’s tallest dam is 300-m Nurek on the Vakhsh in Tajikistan, built during the Soviet era and operating since 1980; an even taller dam upstream on the same river has been under considerations for decades, but so far the Rogun project with its 335-m dam has no financing. In some cases of high-head mountain stations there may be no reservoir at all: these river-run projects merely divert part of a mountain water flow into a steeply falling conduit (underground tunnel or aboveground pipes) that leads it to turbines located far below.

And there is yet another kind of river-run stations (streaming systems), exemplified by Manitoba Hydro’s Limestone project on the Nelson River, where a low dam (hydraulic head 27.6 m) creates virtually no reservoir but the flow (regulated by three dams upstream) suffices to support install capacity of 1.34 GW (Manitoba Hydro 2013). But, not surprisingly, for the world’s largest hydroelectric projects both Q and h are substantial. Rated heads determine the type of turbine uses: Francis turbines can work with both low and high heads (10-300 m), Pelton and Turgo impulse designs are used for high heads (> 100 m) and Kaplan machines, with adjustable guide vanes, are installed at projects with low to medium heads (2-70 m). Rated speeds can be up to 1,500 rom for Francis and Pelton turbines, half that rate for Kaplan machines, and maximum unit ratings can be in excess of 500 MW. Plant structures (dam including spillway, powerhouse and for some projects also ship locks or fish ladders) and associated infrastructures (switchyard, access roads) make almost always very small claims compared to land submerged by a reservoir.

Power densities of large hydro projects Dams built in the lower reaches of major rivers create large, and even enormous and relatively shallow reservoirs. Akosombo (on the Volta in Ghana) covers 8,502 km2, Churchill Falls (on the Churchill River in Labrador) reaches almost 7,000 km2, Kuybyshev (on the Volga) has maximum extent of 6,500 km2: Akosombo is thus nearly as large as Puerto Rico (about 8,900 km2) and Kuybyshev is larger than Brunei (nearly 5,300 km2). Power densities of these projects (leaving aside comparatively minor areas required for dams, associated structures, transformers and HV connectors, and approach roads) are almost invariably less than 1 W/m2: Akosomobo, with installed capacity of 912 MW and the head of 68.9 m (Volta River Authority 2013) rates just 0.11 W/m2 and Churchill Falls rate less than 0.8 W/m2.

Hydro projects built on the middle and upper reaches have power densities an order of magnitude higher. Itaipu rates 10.4 Wi/m2, Sayano-Sushenskaya, Russia’s largest hydrostation on the Yenisei (6.721 GWi) is slightly higher at 10.8 Wi/m2, Grand Coulee, America’s largest project ion the Columbia (6.809 GWi) comes to abut 21 Wi/m2 and Sanxia (with reservoir area of 1,084 km2) has an impressively high rate of 20.8 Wi/m2. In contrast, Egypt’s Aswan dam creates a huge reservoir of 5,250 km2 but it has installed capacity of just 2.1 GW, resulting in power density of 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. Grand Dixence in Valois, Switzerland (with the world’s tallest gravity dam) has 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 it generates annually just 2 TWh, that is an average rate of 228.3 MW but still a very high power density of 56.5 W/m2.

The world’s record holder would be the Nepali Arun-III: it was to be built originally with the World Bank’s support during the 1990s and since that time there have been many failed negotiations and delays (Siwakoti 1994). Arun would be essentially a run-of-river project with just a small 50 ha reservoir and installed capacity of 402 MW resulting in power density of just over 800 W/m2. Goodland (1995) confirmed an expected rise of power density with higher installed capacity. Average power density of hydro projects with installed capacity between 2-99 MW was just 0.4 W/m2, for plants with capacities between 500-999 MW it was 1.35 W/m2 and for the world’s largest dams (in excess of 3 GWi) it surpassed 3 W/m2.

All of the hydrogenation power densities that I have cited so far have been calculated by using installed capacities in the numerator but actual generation will prorate to capacities that are only a fraction of those totals. Its level is a function of water supply (determined by precipitation that is fairly predictable in some regions, highly fluctuating in others) as well as of competing water uses (flood prevention downstream of a dam may maximize reservoir volume and reduce power generation, and requirements for irrigation, industrial and municipal water supplies may divert water from a reservoir). As a result, capacity factors of hydro stations can range from less than 20% during dry years in semi-arid or arid regions to more than 80% in reliably rainy locations, but they are commonly below 50%.

Load factors for the world’s six largest stations indicate a considerable range of actual performances: as already noted, Sanxia’s average load is about 50% and Itaipu’s about 80%; Guri (10.2 GW on the Caroní in Venezuela) averages 60%; Tucuruí (8.37 GW on the Tocantins in Brazil) 57%; Grand Coulee just 33%; and Sayano-Sushenskaya about 46%. Consequently, when the power densities are corrected for actual generation they are commonly halved: Sanxia goes from nearly 36 to less than 18 W/m2, Sayano-Sushenskaya from 10.8 to 4.8 W/m3 but Itaipu remains high at 8.3 W/m2 while Grand Coulee declines from 21 to 7 W/m2. McDonald et al. (2009) use average capacity factor of 44% and put the power densities of the most and the least compact US hydro projects at about 7.1 and 1.25 W/m2.

For the stations with the largest reservoirs the densities calculated with actual generation totals are less than 0.6 W/m2 for Churchill Falls and just 0.06 W/m2 as a 10-year mean (2001-2010) for Akosombo (Volta River Authority 2013). That hydrostation, affected by large inter-annual fluctuations in precipitation, demonstrates the need to use longer-term averages: even for a single decade the extremes of annual generation 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 W/m2 lower (as I will show) than even for low-yielding crops. Correcting for actual generation is easy as long as annual output data are available, but (as already noted in the first chapter) there is no obvious or generally acceptable way to correct for multiple uses of many reservoirs. Similarly, there is no reliable way to base those power densities on life cycle analysis because reservoirs will have very different longevities that can be only inaccurately estimated.

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