by Vaclav Smil
In contrast, the power densities of rooftop installations (whether they are for heat or for electricity) are in a special category as no other energy converters are routinely placed on tops of buildings and they do not claim any new land surface. The same is true of wall-based PV or PV-integrated windows. Moreover, during the periods when rooftop PV modules generate more electricity than can be used by the buildings on whose roofs they are situated, they can send the surplus to the grid. Rooftop thermal and PV solar conversions are thus doubly land-sparing, and as they already have power densities higher than that achievable with the harnessing of any other renewable energy flux, they deserve to be widely promoted and adopted, although the intermittency of the flux continues to pose nontrivial challenges to any system that would raise their contribution to a relatively high level.
Solar Heating
Water heating using rooftop collectors is highly efficient and affordable. With highly selective coatings, the latest designs of flat-plate collectors (typical panels circulating water cover about 2.5 m2 and are less than 8 cm thick) have an absorptivity of 95% (Bosch Thermotechnology 2014; Stiebel Eltron 2014). Evacuated glass tubes have a similarly high absorptivity. They have vacuum surrounding a heat pipe fused to an absorber plate, and they are more efficient, particularly in colder climates and in winter in sunny climates (Silicon Solar 2008). Their efficiencies (when compared for insolation at 1,000 W/m2) differ with the desired temperature: for pools (a water temperature up to 25°C) they have efficiencies of 60%-80%, whereas for domestic water heating (water at 45-60°C), the efficiency figure falls to 40%-75% (Thermomax Industries 2010). Australian studies show that evacuated tubes are about 50% more efficient than flat plates in summer and 80%-130% more efficient in winter (Hills Solar 2008).
Figure 3.1
Rooftop water heating using evacuated tubes. Photo available at Wikimedia.
During the midday hours in such sunny climates as California or Mediterranean Europe, the high absorptivities of flat plates and evacuated tubes translate into power densities of heat collection in excess of 900 W,/m2. During those times water heating may proceed with power densities higher than 700 W,/m2, at rates that are unequaled by any other commercial renewable energy conversion (fig. 3.1). The annual power densities of water heating in sunny climates are much lower but, again, much higher than those of any commercial renewable energy conversion: they can be as high as 110 W,/m2 in Israel or Arizona, while in temperate climates they will generally be no higher than 40-50 W/m2. For example, detailed German data show that by the end of 2012, Germany had 16.5 Mme of solar heating surfaces whose output was about 685 MW, (BSW 2013), and that implies an average power density of 41.5 W,/m2.
Obviously, larger storages extend hot water availability but come at a higher cost. Roof placement is usually available, but shading (total or partial) by nearby trees, buildings, and structures cannot always be avoided. Combined systems can capture irradiance for both space and water heating. The worldwide total of solar heat collectors (dominated by small rooftop heaters) is in the tens of millions. Mauthner and Weiss (2013) estimated that by the end of 2012, solar thermal collectors had an aggregate area of 383 Mme (compared to 125 Mme in 2005), a total capacity of 268 GWt, and an annual output of 225 TWh; that implies a globally averaged power density of 67 Wt/m2.
Power densities between 40 and 100 W/m2 are superior to the power densities of all household-based renewable energy conversions. That is why properly scaled distributed units are a perfect choice for household water heating: in sunny climates they can cover moderate daily needs even without any voluminous hot water storage, and in less sunny climates they can make a significant contribution. Modern water heating systems do not have any extraordinary material requirements, are widely affordable, and can operate reliably for a long time. A rational, systemwide approach to energy use would promote the widespread adoption of distributed rooftop solar water heaters for households and smaller-sized commercial and industrial buildings in any suitable climate. But the promotion of these highpower-density distributed converters has become overshadowed by the rapid (and in some instances questionable) growth of PV-based electricity generation.
Photovoltaics
The conversion of solar radiation to electricity was discovered by Edmund Becquerel in 1839. The first experimental PV cells were made in 1877, but commercialization of the process began only in 1954 with the production of the first silicon solar cells at Bell Laboratories. In 1962 Telstar, the first commercial telecommunications satellite, opened the way to PV-powered space vehicles, but terrestrial applications took off only during the 1990s (Smil 2006). They have been driven by an increasing interest in carbon-free electricity generation, but the rapid diffusion of PV systems began only with the adoption of costly subsidies (in the form of guaranteed long-term feed-in tariffs) in some countries.
PV modules and arrays are now mass-produced both for household rooftop installations and for large-scale industrial projects, with modules designed for nominal irradiance, at either 1,000 W/m2 or 800 W/m2, and at an ambient temperature of 20°C or 25°C. Increasing irradiance raises their current and power output but has a much smaller effect on the voltage; increasing the cell temperature brings a significant decline in voltage and also reduces cell output, efficiency, and expected duration. The deployment of PV cells with a conversion efficiency of at least 10% would produce peak power densities of PV modules in the range of 80-100 WP/m2 during a few midday hours; with a 15% conversion efficiency the rate would rise to 120-150 WP/m2. Consequently, approximate calculations of aggregate PV performance should not assume less than 100 WP/m2 for newly installed arrays.
Average annual power densities of PV are calculated by multiplying measured irradiance by the mean efficiency of modular cells adjusted for their specific performance ratio (the difference between their actual and theoretical output). As already noted, the first number is essentially fixed for a given location (with a relatively small interannual variation), while the other two parameters have been steadily increasing through innovation. In 2014 the best research cell efficiencies were as follows: emerging techniques (organic, perovskite, and dye-sensitized cells), 8.6%-17.9%; thin films, 13.4%-23.3%; crystalline silicon cells, 20.4%-27.6%; and multijunction cells, 26.4%-44.7% (NREL 2014). The actual field efficiencies of recently deployed PV cells have been much lower. The conversion efficiency of single crystalline modules, the oldest but still the most efficient PV conversion technique, averages 10%-12%; that of cheaper polycrystalline silicon cells is now close behind, at 10%-11%; string ribbon polycrystalline silicon delivers 7%-8%; and amorphous silicon (vaporized silicon deposited on glass or stainless steel) will convert no more than 5%-7% of irradiance into electricity.
Assuming, again, an average 10% efficiency would result in a fairly representative range of average power densities for the plants operating at the beginning of the second decade of the twenty-first century. Those densities would range from less than 10 We/m2 in cloudy mid-latitudes (Atlantic Europe, the Pacific Northwest) to more than 15 We/m2 in sunnier climates, and would peak at around 25 We/m2 in cloud-free subtropical deserts. These rates are applicable for small modules installed on roofs on the ground; the power densities are lower for large ground-based installations because additional land is required between tilted PV arrays to avoid shading and to provide access for servicing the modules, for roads, for inverter and transformation facilities needed to access the grid, and for service and storage buildings.
Installations with tracking assemblies require even more additional land per PV module to avoid shading. Consequently, anywhere between 25% and 75% of a solar park area will actually be covered by the modules, while for the PV field alone the cell assemblies typically cover 75%-80% of land. But it should be noted that many large solar parks often acquire or lease much larger areas intended to accommodate possible future expansion, and those areas should not be counted when calculating the power densities of actually operating projects. Other projects claim
more land outside their PV array fields to create environmental buffers or to provide corridors for wildlife. The inclusion of those areas in the land denominator is, as with many similar land claims made by other energy installations, arguable.
The general procedure for calculating the power densities of groundbased PV installations is thus quite straightforward: average irradiation (1) is converted from Wh to W, and the result is multiplied by the conversion efficiency (ii) and an appropriate performance factor (p). For the average US insolation of 1,800 kWh/m2, a cell efficiency of 10%, a performance factor of 0.85, and 50% of the ground covered by modules, the result is almost 9 We/m2, while for a cell efficiency of 15% this value would rise to 13.1 We/m2:
Power Densities of Large Ground-Based Projects
The most important correction in calculating actual solar power densities is the adjustment for their relatively low capacity factors. The capacities of new solar projects are always listed in terms of rated peak power (MWP), the performance achievable only by perfect conversion during the time of highest irradiance. As expected, average capacity factors correlate with total irradiance: in places where it is less than 150 W/m2 they will be below 12%, for the insolation between 150 and 200 W/m2 they will range up to 20%, and in the sunniest locations with irradiance in excess of 200 W/m2 they will be up to 25%. Actual performance data show that even in sunny Spain, most plants have capacity factors of less than 20%, and in cloudy temperate climates that indicator will dip below 10%. In addition, only about 85% of a PV panel's DC rating will be transmitted to the grid as AC power: these performance ratios vary, but in the best systems they should always be above 80% and should approach 90%. Several notable examples of large PV plants illustrate actual power densities.
Box 3.2
Power density of a PV module
In 2008 Olmedilla de Alarcon (Cuenca, Castile-La Mancha) became temporarily the world's largest solar park, with an installed capacity of 60 MWP. Olmedilla's total area of 283 ha of fixed panels and an annual generation of 85 GWh (or an average power of 9.7 MW) translate to a power density of about 3.4 We/m2 and an average capacity factor of just 16%. Another large plant completed in 2008, the Portuguese Moura (46 MWp of installed capacity, 88 GWh or 10 MW of average power) has a capacity factor of nearly 22%. The plant has both fixed and single-axis tracking panels (covering a total of 130 ha), and its power density is 7.7 We/m2. When it was finished in 2011, Sarnia (Ontario) was the world's largest PV plant; its installed capacity is 97 MWP and its annual generation of 120 GWh comes from 1.3 million panels covering 96.6 ha, while the plant's entire area claims 445.2 ha (Clean Energy 2013c). This prorates to average annual power densities of 14.2 We/m2 for the modules and 3 We/m2 for the total land claim. With an irradiance of about 180 W/m2, this puts Sarnia's average conversion efficiency at less than 8% and its capacity factor at 14%.
Another large project completed in 2011, Germany's Waldpolenz (about 20 km east of Leipzig, on the site of a former Soviet East German air base) has a peak capacity of 52 MW, an annual generation of 52 GWh (5.94 MW), a total panel area of about 110 ha, and a total site of 220 ha (Juwi Solar 2008). These specifications yield a power density of 5.4 W/m2 for the module field, 2.7 We/m2 for the entire plant area, and an annual capacity factor of just 11.4%. Perovo (in western Crimea) has a peak power of 100 MW, generates 132.5 GWh (averaging 15.1 MW) from 200 ha of panels (Clean Energy 2013b), and has a power density of about 7.6 We/m2 and a capacity factor of 15%. Agua Caliente, in 2013 the largest project in North America, on 960 ha in Arizona, has one of the world's highest average annual irradiation rates (2.45 MWh/m2), a capacity of 290 MW, and generates 626.2 GWh/year (Clean Energy 2013a). This yields a high capacity factor of 24.6% and a power density of 7.45 W/m2. The California Valley Solar Ranch (250 MWP, 482 GWh, load factor of 22%) occupies 60 ha and has an operating power density of 9.2 We/m2 (CVSR 2014; fig. 3.2).
Figure 3.2
California Valley solar ranch. © Proehl Studios/Corbis.
Consequently, the largest PV projects now operate with power densities of roughly 3-9 We/m2. Because smaller projects use similar or identical PV cells, it is not at all surprising that their power density range is pretty much the same. McKay's (2013) listing of such projects in Italy (with installed capacities between 1 and 10 MW and a capacity factor about 16%) shows the range of 4-9 We/m2; for projects in Spain (projects rated at 7-23 MW, with load factors between 16% and 23%) the power density range is 4-11 We/m2; for the UK (projects averaging about 5 MW, with an average load factor of about 11%) it is just between 4 and 5 We/m2; and for the ground-based US installations the range is from just 3.8 We/m2 for a two-axis 2.1-MW tracker in Vermont to 11.43 We/m2 for a fixed 250-kW installation in Florida. To minimize capital costs, most of the large PV projects use relatively inefficient, less costly, thin-film Cd-Te cells. In contrast, the highest capacity factors would be around 30% with double-axis tracking in the sunniest locations in the US Southwest (Madaeni, Sioshansi, and Denholm 2012).
Rooftop and Facade PVs
In Germany, the world's leader in harnessing solar radiation for electricity, most PV cells are not massed in large solar parks but rather on rooftops, installed by homeowners and businesses in response to feed-in tariffs guaranteeing high electricity prices for 20 years. In 2011 ground-based PV cell arrays in large solar parks accounted for only 28% of Germany's installed capacity; its largest share, 38%, was in medium-sized installations (10-100 kW,) on the roofs of multifamily dwellings, schools, offices, farms, and small businesses; 23% of all PV modules were larger (more than 100 kWP) units on the roofs of industrial enterprises, and 10% were on the rooftops of private residences (Wirth 2013).
These rooftop PV modules come in sizes from roughly 0.5 m2 to 3 m2. Most modules have 36 cells in series, with a maximum power voltage of 15 V and a maximum power current of 3 A.Changing irradiance affects their current and power output, but the voltage varies very little, facilitating battery charging. In 2012 Germany had nearly 1.1 million solar installations serving 5.2 million households. But the trend has been toward large units: in the year 2000, projects with more than 500 kWp accounted for just over 10% of new capacity, whereas in 2012 they accounted for nearly half of a much larger annual addition (Fraunhofer ISE 2012). The shift toward larger projects has been the principal reason for rising performance; load factors have also been rising, slowly but steadily. The average irradiance of 1,055 kWh/m2 of flat surface is boosted to about 1,200 kWh/m2 by appropriate tilting (30-40 degrees) of the panels, and with a performance ratio of 0.85, the effective annual radiation input is about 1,020 kWh/m2 (Wirth 2013). That implies an average exploitable flux of about 116 W/m2.
With an average 11% efficiency, that amounts to an annual electricity generation of about 112 kWh/m2 and an average power density of more than 12 We/m2 of roof area covered by modules-and all that without making any land claims. Using an average PV generation full load of nearly 970 hours (Fraunhofer ISE 2012) and the exploitable flux of 116 W/m2 confirms this density (970 x 116 = 112.5 kWh/m2). In more sunny locations the power densities of rooftop PV installations will be proportionately higher. McKay's (2013) maxima for US rooftop installations are 20.69 We/m2 for a 390-kW project in Hawaii and 17 We/m2 for an 830-kW installation in California.
The practical maximum capacity of a roof-based PV module is easy to calculate for a particular house or a commercial or industrial enterprise, but nationwide estimates are not that easy to quantify. Many roofs are obviously either poorly suited or entirely unsuitable for such installations because of excessive pitch (greater than 40 degrees; on the other hand, the slope should be at least 15 degrees for self-cleaning), suboptimal orientation, or shading by surrounding buildings or trees, and many roofs are unavailable because of the presence of heating, air conditioning, and ventilation equipment. Denholm and Margolis (2008b) cite Navigant Consulting data that assume 22% availability of roof area for residential buildings in cool climates and 27% in warm and and climates (the difference owing to reduced t
ree shading), while for commercial buildings the means are 60% in warm climates and 65% in cooler climates.
A German study (based on sampling of countryside, village, and suburban homes in Bavaria) assumed that 80% of the area of all sloping south-facing roofs of houses and 50% of the area of flat roofs of industrial buildings were available for PV installations (Lodl et al. 2010). This resulted in a PV potential of 8.7 kW, for suburban houses with an average footprint of 116 m2 and 12.5 kWP for village houses with a built area of 167 m2. Based on that sample, the Bavarian PV rooftop potential was put at 25.3 GW, the nationwide total was estimated at 161 GWP, and the authors cite two other estimates of total German rooftop PV potential at 53-116 GWP and at 130 GWP. For comparison, German rooftop capacity was nearly 18 GWP in 2011, or one-third of the lowest potential estimate.
Although differences in house sizes and in residential and industrial population densities mean that national rates are not readily transferable, it is interesting to note that the German mean amounts to 75 WP/m2 of building footprint, and so, at least in countries with similar residential/ industrial patterns, that rate might be used to approximate a national rooftop PV potential by using a much more readily available total of built-up area. An even more interesting recent study considered the degree to which the loss of nuclear generation in post-Fukushima Japan could be replaced by rooftop PV-based electricity generation in Tokyo (Stoll, Smith, and Deinert 2013).
The study used data from 34 years of solar irradiance for the Tokyo metropolitan area (averaging 154 W/m2). A satellite-based analysis of the area available for rooftop greening in the city (flat and free of obstruction) found a total of 50.69 km2 (assumed to be available for PV panels) and an adjusted total of 10.03 km2 for sloped house roofs. The suitable rooftop area of Tokyo's 23 wards was put at 64.28 km2, and the total was 204.05 km2 for Kanto, the region surrounding the city that is supplied by the Tokyo Electric Power Corporation (TEPCO): that area could support 43.1 GWp of PV capacity, and if its generation were coupled with the region's existing pumped storage of 7.28 GW, the combined system could provide 4.8 GW 91% of the time. But this was a theoretical exercise that assumed an unrealistically high installation coverage.
