page no.

38 ... compensate for the tilt between the sun and the land. The latitude of Cambridge is 0 = 52°; the intensity of midday sunlight is multiplied by cos 0 ~ 0.6. The precise factor depends on the time of year, and varies between cos(0 + 23°) = 0.26 and cos(0 - 23°) = 0.87.

- In a typical UK location the sun shines during one third of daylight hours. The Highlands get 1100 h sunshine per year - a sunniness of 25%. The best spots in Scotland get 1400 h per year - 32%. Cambridge: 1500 ± 130 h per year - 34%. South coast of England (the sunniest part of the UK): 1700 h per year - 39%. [2rqloc] Cambridge data from [2szckw]. See also figure 6.16.

Biomass: food, biofuel, wood, waste incin'n, landfill gas: 24 kWh/d

Solar heating: 13 kWh/d

Wind: 20 kWh/d

Figure 6.12. Solar biomass, including all forms of biofuel, waste incineration, and food: 24 kWh/d per person.

Figure 6.12. Solar biomass, including all forms of biofuel, waste incineration, and food: 24 kWh/d per person.

19B0

1970 19B0 1990 2000

19B0

1970 19B0 1990 2000

Figure 6.13. Sunniness of Cambridge: the number of hours of sunshine per year, expressed as a fraction of the total number of daylight hours.

Figure 6.14. This figure illustrates the quantitative questions that must be asked of any proposed biofuel. What are the additional energy inputs required for farming and processing? What is the delivered energy? What is the net energy output? Often the additional inputs and losses wipe out most of the energy delivered by the plants.

carbohydrate energy delivered by plants

Energy used or lost in farming and processing delivered energy net energy additional inputs required for farming and processing

38 The average raw power of sunshine per square metre of south-facing roof in Britain is roughly 110 W/m2, and of Hat ground, roughly 100 W/m2. Source: NASA "Surface meteorology and Solar Energy" [5hrxlsj. Surprised that there's so little difference between a tilted roof facing south and a horizontal roof? I was. The difference really is just 10% [6z9epq].

39 ... that would be about 10m2 of panels per person. I estimated the area of south-facing roof per person by taking the area of land covered by buildings per person (48 m2 in England - table I.6), multiplying by 1/4 to get the south-facing fraction, and bumping the area up by 40% to allow for roof tilt. This gives 16 m2 per person. Panels usually come in inconvenient rectangles so some fraction of roof will be left showing; hence 10 m2 of panels.

- The average power delivered by photovoltaic panels...

There's a myth going around that states that solar panels produce almost as much power in cloudy conditions as in sunshine. This is simply not true. On a bright but cloudy day, solar photovoltaic panels and plants do continue to convert some energy, but much less: photovoltaic production falls roughly ten-fold when the sun goes behind clouds (because the intensity of the incoming sunlight falls ten-fold). As figure 6.15 shows, the power delivered by photovoltaic panels is almost exactly proportional to the intensity of the sunlight - at least, if the panels are at 25 °C. To complicate things, the power delivered depends on temperature too - hotter panels have reduced power (typically 0.38% loss in power per °C) - but if you check data from real panels, e.g. at www.solarwarrior.com, you can confirm the main point: output on a cloudy day is far less than on a sunny day. This issue is obfuscated by some solar-panel promoters who discuss how the "efficiency" varies with sunlight. "The panels are more efficient in cloudy conditions," they say; this

 A > J c f 1

0 200 400 600 800 1000 irradiance (W/sq m)

0 200 400 600 800 1000 irradiance (W/sq m)

Figure 6.15. Power produced by the Sanyo HIP-210NKHE1 module as a function of light intensity (at 25 ° C, assuming an output voltage of 40 V). Source: datasheet, www.sanyo-solar.eu.

Anchorage, AK Edinburgh, UK Oslo, NO Dublin, IE Hamburg, DE London, UK Brussels, BE Munich, DE Paris, FR Bern, CH Toulouse, FR New York, NY Seattle, WA Boston, MA Chicago, IL Portland, OR Kansas City, KS Rome, IT Madrid, ES Atlanta, GA Lisbon, PT Algiers, DZ Salt Lake City, UT Denver, CO Athens, GR Tunis, TN Houston, TX Malaga, ES Freetown, SL San Francisco, CA Albuquerque, NM Yaounde, CM Liberia, LR Bangui, CF Limassol, CY Accra, GH Rabat, MA Miami, FL Las Vegas, NV Phoenix, AZ Los Angeles, CA Tarabulus, LY Dakar, SN Abuja, NG Nairobi, KE Cairo, EG Gambia, GM Conakry, GN Addis Abeba, ET Honolulu, HI Ouagadougou, BF Muqdisho, SO Bamako, ML Niamey, NE Al Khur-tum, SD Djibouti, DJ Nouakchott, MR

average sunshine (W/m2)

0 50 100 150 200 250 87

95 99 105 109 112

177 182

190 190

200 204

208 210

215 217 217 219 221 224

255 263 266

Figure 6.16. Average power of sunshine falling on a horizontal surface in selected locations in Europe, North America, and Africa.

photon energy (eV)

photon energy (eV)

photon energy (eV)

photon energy (eV)

may be true, but efficiency should not be confused with delivered power.

39 Typical solar panels have an efficiency of about 10%; expensive ones perform at 20%. See figure 6.18. Sources: Turkenburg (2000), Sunpower www. sunpowercorp.com, Sanyo www.sanyo-solar.eu, Suntech.

- A device with efficiency greater than 30°% would be quite remarkable. This is a quote from Hopfield and Gollub (1978), who were writing about panels without concentrating mirrors or lenses. The theoretical limit for a standard "single-junction" solar panel without concentrators, the Shockley-Queisser limit, says that at most 31% of the energy in sunlight can be converted to electricity (Shockley and Queisser, 1961). (The main reason for this limit is that a standard solar material has a property called its band-gap, which defines a particular energy of photon that that material converts most efficiently. Sunlight contains photons with many energies; photons with energy below the band-gap are not used at all; photons with energy greater than the band-gap may be captured, but all their energy in excess of the band-gap is lost. Concentrators (lenses or mirrors) can both reduce the cost (per watt) of photovoltaic systems, and increase their efficiency. The Shockley-Queisser limit for solar panels with concentrators is 41% efficiency. The only way to beat the Shockley-Queisser limit is to make fancy photovoltaic devices that split the light into different wavelengths, processing each wavelength-range with its own personalized band-gap. These are called multiple-junction photovoltaics. Recently multiple-junction photovoltaics with optical concentrators have been reported to be about 40% efficient. [2tl7t6], www.spectrolab.com. In July 2007, the University of Delaware reported 42.8% efficiency with 20-times concentration [6hobq2], [2lsx6t]. In August 2008, NREL reported 40.8% efficiency with 326-times concentration [62ccou]. Strangely, both these results were called world efficiency records. What multiple-junction devices are available on the market? Uni-solar sell a thin-film triple-junction 58 W(peak) panel with an area of 1 m2. That implies an efficiency, in full sunlight, of only 5.8%.

40 Figure 6.5: Solar PV data. Data and photograph kindly provided by Jonathan Kimmitt.

- Heliodynamics - www.hdsolar.com. See figure 6.19.

A similar system is made by Arontis www.arontis.se.

Figure 6.17. Part of Shockley and Queisser's explanation for the 31% limit of the efficiency of simple photovoltaics.

Left: the spectrum of midday sunlight. The vertical axis shows the power density in W/ m2 per eV of spectral interval. The visible part of the spectrum is indicated by the coloured section. Right: the energy captured by a photovoltaic device with a single band-gap at 1.1 eV is shown by the tomato-shaded area. Photons with energy less than the band-gap are lost. Some of the energy of photons above the band-gap is lost; for example half of the energy of every 2.2 eV photon is lost. Further losses are incurred because of inevitable radiation from recombining charges in the photovoltaic material.

y re est lk is i koc eiu iml Sh uQ

I amorphous silicon

| multi-crystalline silicon n

■I single crystal silicon .o —I Sunpower WHT —I Sanyo HIP Suntech poly-crystalline'

thin-film triple junction uj -el lpi irT

Figure 6.18. Efficiencies of solar photovoltaic modules available for sale today. In the text I assume that roof-top photovoltaics are 20% efficient, and that country-covering photovoltaics would be 10% efficient. In a location where the average power density of incoming sunlight is 100 W/m2, 20%-efficient panels deliver 20 W/m2.

41 The Solarpark in Muhlhausen, Bavaria. On average this 25-hectare farm is expected to deliver 0.7MW (17000 kWh per day).

New York's Stillwell Avenue subway station has integrated amorphous silicon thin-film photovoltaics in its roof canopy, delivering 4 W/ m2 (Fies et al., 2007).

The Nellis solar power plant in Nevada was completed in December, 2007, on 140 acres, and is expected to generate 30 GWh per year. That's 6 W/m2 [5hzs5y].

Serpa Solar Power Plant, Portugal (PV), "the world's most powerful solar power plant," [39z5m5] [2uk8q8] has sun-tracking panels occupying 60 hectares, i.e., 600 000 m2 or expected to generate 20 GWh per year, i.e., 2.3 MW on average. That's a power per unit area of 3.8 W/m2.

41 The solar power capacity required to deliver 50 kWh/d per person in the UK is more than 100 times all the photovoltaics in the whole world. To deliver 50 kWh/d per person in the UK would require 125 GW average power, which requires 1250 GW of capacity. At the end of 2007, world installed photo-voltaics amounted to 10 GW peak; the build rate is roughly 2 GW per year.

- ... paving 5% of this country with solar panels seems beyond the bounds of plausibilit . My main reason for feeling such a panelling of the country would be implausible is that Brits like using their countryside for farming and recreation rather than solar-panel husbandry. Another concern might be price. This isn't a book about economics, but here are a few figures. Going by the price-tag of the Bavarian solar farm, to deliver 50kWh/d per person would cost €91 000 per person; if that power station lasted 20 years without further expenditure, the wholesale cost of the electricity would be €0.25 per kWh. Further reading: David Carlson, BP solar [2ahecp].

43 People in Britain throw away about 300g of food per day Source: Ventour (2008).

- Figure 6.10. In the USA, Miscanthus grown without nitrogen fertilizer yields about 24t/ha/y of dry matter. In Britain, yields of 12-16 t/ha/y are reported. Dry Miscanthus has a net calorific value of 17MJ/kg, so the British yield corresponds to a power density of 0.75 W/m2. Sources: Heaton et al. (2004) and [6kqq77]. The estimated yield is obtained only after three years of undisturbed growing.

- The most efficient plants are about 2%o efficient; but the delivered power per unit area is about 0.5 W/m2. At low light intensities, the best British plants are 2.4% efficient in well-fertilized fields (Monteith, 1977) but at higher light intensities, their conversion efficiency drops. According to Turkenburg (2000) and Schiermeier et al. (2008), the conversion efficiency of solar to biomass energy is less than 1%.

Here are a few sources to back up my estimate of 0.5 W/m2 for vegetable power in the UK. The Royal Commission on Environmental Pollution's estimate of the potential delivered power density from energy crops in Britain is 0.2 W/m2 (Royal Commission on Environmental Pollution, 2004). On page 43 of the Royal Society's biofuels document (Royal Society working group on biofuels, 2008), Miscanthus tops the list, delivering about 0.8 W/m2 of chemical power.

Figure 6.19. A combined-heat-and-power photovoltaic unit from Heliodynamics. A reflector area of 32 m2 (a bit larger than the side of a double-decker bus) delivers up to 10 kW of heat and 1.5 kW of electrical power. In a sun-belt country, one of these one-ton devices could deliver about 60 kWh/d of heat and 9 kWh/d of electricity. These powers correspond to average fluxes of 80 W/m2 of heat and 12 W/m2 of electricity (that's per square metre of device surface); these fluxes are similar to the fluxes delivered by standard solar heating panels and solar photovoltaic panels, but Heliodynamics's concentrating design delivers power at a lower cost, because most of the material is simple flat glass. For comparison, the total power consumption of the average European person is 125 kWh/d.

In the World Energy Assessment published by the UNDP, Rogner (2000) writes: "Assuming a 45% conversion efficiency to electricity and yields of 15 oven dry tons per hectare per year, 2 km2 of plantation would be needed per megawatt of electricity of installed capacity running 4,000 hours a year." That is a power per unit area of 0.23W(e)/m2. (1W(e) means 1 watt of electrical power.)

Energy for Sustainable Development Ltd (2003) estimates that short-rotation coppices can deliver over 10 tons of dry wood per hectare per year, which corresponds to a power density of 0.57 W/m2. (Dry wood has a calorific value of 5 kWh per kg.)

According to Archer and Barber (2004), the instantaneous efficiency of a healthy leaf in optimal conditions can approach 5%, but the long-term energy-storage efficiency of modern crops is 0.5-1%. Archer and Barber suggest that by genetic modification, it might be possible to improve the storage efficiency of plants, especially C4 plants, which have already naturally evolved a more efficient photosynthetic pathway. C4 plants are mainly found in the tropics and thrive in high temperatures; they don't grow at temperatures below 10 ° C. Some examples of C4 plants are sugarcane, maize, sorghum, finger millet, and switchgrass. Zhu et al. (2008) calculate that the theoretical limit for the conversion efficiency of solar energy to biomass is 4.6% for C3 photosynthesis at 30 °C and today's 380 ppm atmospheric CO2 concentration, and 6% for C4 photosynthesis. They say that the highest solar energy conversion efficiencies reported for C3 and C4 crops are 2.4% and 3.7% respectively; and, citing Boyer (1982), that the average conversion efficiencies of major crops in the US are 3 or 4 times lower than those record efficiencies (that is, about 1% efficient). One reason that plants don't achieve the theoretical limit is that they have insufficient capacity to use all the incoming radiation of bright sunlight. Both these papers (Zhu et al., 2008; Boyer, 1982) discuss prospects for genetic engineering of more-efficient plants.

43 Figure 6.1 . The numbers in this figure are drawn from Rogner (2000) (net energy yields of wood, rape, sugarcane, and tropical plantations); Bayer Crop Science (2003) (rape to biodiesel); Francis et al. (2005) and Asselbergs et al. (2006) (jatropha); Mabee et al. (2006) (sugarcane, Brazil); Schmer et al. (2008) (switchgrass, marginal cropland in USA); Shapouri et al. (1995) (corn to ethanol); Royal Commission on Environmental Pollution (2004); Royal Society working group on biofuels (2008); Energy for Sustainable Development Ltd (2003); Archer and Barber (2004); Boyer (1982); Monteith (1977).

44 Even just setting fire to dried wood in a good wood boiler loses 20% of the heat up the chimney. Sources: Royal Society working group on biofuels (2008); Royal Commission on Environmental Pollution (2004).

### 7 Heating and cooling

This chapter explores how much power we spend controlling the temperature of our surroundings - at home and at work - and on warming or cooling our food, drink, laundry, and dirty dishes.