A material or device that is capable of converting the energy contained in photons of light into an electrical voltage and current is said to be photovoltaic. A photon with short enough wavelength and high enough energy can cause an electron in a photovoltaic material to break free of the atom that holds it. If a nearby electric field is provided, those electrons can be swept toward a metallic contact where they can emerge as an electric current. The driving force to power photovoltaics comes from the sun, and it is interesting to note that the surface of the earth receives something like 6000 times as much solar energy as our total energy demand.
Spurred on by the emerging energy crises of the 1970s, the development work supported by the space program began to pay off back on the ground. By the late 1980s, higher efficiencies (Fig.1) and lower costs (Fig.2) brought PVs closer to reality, and they began to find application in many offgrid terrestrial applications such as pocket calculators, off-shore buoys, highway lights, signs and emergency call boxes, rural water pumping, and small home systems. • While the amortized cost of photovoltaic power did drop dramatically in the 1990s, a decade later it is still about double what it needs to be to compete without subsidies in more general situations.1 Best laboratory PV cell efficiencies for various technologies. (From National Center for Photovoltaics, www.gov/ncpv 2003 Figure 8.2 Possible evolution of turn-key PV system prices By 2002, worldwide production of photovoltaics had approached 600 MW per year and was increasing by over 40% per year (by comparison, global wind power sales were 10 times greater).3 World production of photovoltaics is growing rapidly, but the U.
share of the market is decreasing. Based on data from Maycock (2004). Critics of this decline point to the government’s lack of enthusiasm to fund PV R&D. By comparison, Japan’s R&D budget is almost an order of magnitude greater.
Before we can talk about solar power, we need to talk about the sun Need to know how much sunlight is available Can predict where the sun is at any time Insolation : incident solar radiation Want to determine the average daily insolation at a site Want to be able to chose effective locations and panel tilts of solar panels The sun ◦ 1.4 million km in diameter ◦ 3.8 x 1020 MW of radiated electromagnetic energy Blackbodies ◦ Both a perfect emitter and a perfect absorber ◦ Perfect emitter – radiates more energy per unit of surface area than a real object of the same temperature ◦ Perfect absorber – absorbs all radiation, none is reflected Plank’s law – wavelengths emitted by a blackbody depend on temperature 3.1) 5 14400 exp 1 T • λ = wavelength (μm) • Eλ = emissive power per unit area of blackbody (W/m2-μm) • T = absolute temperature (K) Visible light has a wavelength of between 0.7 μm, with ultraviolet values immediately shorter, and infrared immediately longer Source: en.org/wiki/Electromagnetic_radiation The earth as a blackbody Figure 7.1 Area under curve is the total radiant power emitted Total radiant power emitted is given by the Stefan –Boltzman law of radiation E As T 4 (7.2) • E = total blackbody emission rate (W) • σ = Stefan-Boltzmann constant = 5.67x10-8 W/m2-K4 • T = absolute temperature (K) • A = surface area of blackbody (m2) The wavelength at which the emissive power per unit area reaches its maximum point 2898 max (7.3) T • T = absolute temperature (K) • λ = wavelength (μm) • λmax =0.5 μm for the sun , T = 5800 K • λmax = 10.1 μm for the earth (as a blackbody), T = 288 K Figure 7.2 As sunlight passes through the atmosphere, less energy arrives at the earth’s surface • h1 = path length through atmosphere with sun Figure 7.3 directly overhead • h2 = path length through atmosphere to spot on surface • β = altitude angle of the sun h2 1 air mass ratio m = (7.3 Air mass ratio of 1 (―AM1‖) means sun is directly overhead AM0 means no atmosphere AM1.5 is assumed average at the earth’s surface • m increases as the sun appearslower in the sky. • Notice there is a large loss towards the blue end for higher m, which is why the sun appears reddish at sun rise and sun set One revolution every 365.25 days Distance of the earth from the sun 360( n 93) d 1.5) 365 n = day number (Jan. 1 is day 1) d (km) varies from 147x106 km on Jan. 2 to 152x106 km on July 3 (closer in winter, further in summer) Note that the angles in this chapter are in degrees In one day, the earth rotates 360.99˚ The earth sweeps out what is called the ecliptic plane Earth’s spin axis is currently 23.45˚ Equinox – equal day and night, on March 21 and September 21 Winter solstice – North Pole is tilted furthest from the sun Summer solstice – North Pole is tilted closest to the sun Figure 7.5 For solar energy applications, we’ll consider the characteristics of the earth’s orbit to be unchanging Solar declination δ – the angle formed between the plane of the equator and the line from the center of the sun to the center of the earth δ varies between +/- 23.45˚ Assuming a sinusoidal relationship, a 365 day year, and n=81 is the spring equinox, the approximation of δ for any day n can be found from 360 23.6) 365 • Another perspective- Solar declination Figure 7.6 Predict where the sun will be in the sky at any time Pick the best tilt angles for photovoltaic (PV) panels Solar noon – sun is directly over the local line of longitude Rule of thumb for the Northern Hemisphere - a south facing collector tilted at an angle equal to the local latitude • During solar noon, the sun’s rays are perpendicular Figure 7.8 to the collector face Find the optimum tilt angle for a south-facing PV module located at in Tucson (latitude 32.1˚) at solar noon on March 1 From Table 7.1, March 1 is day n = 60 The solar declination δ is 360 360 23.3 365 365 The altitude angle is N 90 L = 90 32.6 To make the sun’s rays perpendicular to the panel, we need to tilt the panel by tilt 90 N = 40.4 Altitude angle at solar noon βN – angle between the sun and the local horizon N 90 L (7.7) Zenith – perpendicular axis at a site Figure 7.9 Find the optimum tilt angle for a south-facing PV module located at in Tucson (latitude 32.1˚) at solar noon on March 1 From Table 7.1, March 1 is day n = 60 Described in terms of altitude angle β and azimuth angle of the sun ϕS β and ϕS depend on latitude, day number, and time of day Azimuth angle (ϕS ) convention ◦ positive in the morning when sun is in the east ◦ negative in the evening when sun is in the west ◦ reference in the Northern Hemisphere (for us) is true south Hours are referenced to solar noon Altitude Angle Azimuth Angle Figure 7.10 Hour angle H- the number of degrees the earth must rotate before sun will be over your line of longitude If we consider the earth to rotate at 15˚/hr, then 15 hour angle H hours before solar noon (7.10) hour At 11 AM solar time, H = +15˚ (the earth needs to rotate 1 more hour) At 2 PM solar time, H = -30˚ sin cos L cos cos H sin L sin (7.8) cos sin H sin S (7.9) cos • H = hour angle • L = latitude (degrees) • Test to determine if the angle magnitude is less than or greater than 90˚ with respect to true south- tan if cos H , then S 90, else S 90 (7.11) tan L Find altitude angle β and azimuth angle ϕS at 3 PM solar time in Boulder, CO (L = 40˚) on the summer solstice At the solstice, we know the solar declination δ ˚ = 23.45 Hour angle H is found from (7.10) 15 H -3 h 45 h The altitude angle is found from (7.8) sin cos 40cos 23.45cos 45 sin 40sin 23.8 The sin of the azimuth angle is found from (7.8 Two possible azimuth angles exist S = sin 1 -0.9848 260 or 100 Apply the test (7.517 tan L tan 40 S = 80 (80 west of south) Now we know how to locate the sun in the sky at any time This can also help determine what sites will be in the shade at any time Sketch the azimuth and altitude angles of trees, buildings, and other obstructions Sections of the sun path diagram that are covered indicate times when the site will be in the shade Trees to the southeast, small building to the southwest Can estimate the amount of energy lost to shading Figure 7.15 The shading of solar collectors has been an area of legal and legislative concern (e., a neighbor’s tree is blocking a solar panel) California has the Solar Shade Control Act (1979) to address this issue ◦ No new trees and shrubs can be placed on neighboring property that would cast a shadow greater than 10 percent of a collector absorption area between the hours of 10 am and 2 pm.
◦ Exceptions are made if the tree is on designated timberland, or the tree provides passive cooling with net energy savings exceeding that of the shaded collector ◦ First people were convicted in 2008 because of their redwoods Source: NYTimes, 4/7/08 Most solar work deals only in solar time (ST) Solar time is measured relative to solar noon Two adjustments – ◦ For a longitudinal adjustment related to time zones ◦ For the uneven movement of the earth around the sun Problem with solar time –two places can only have the same solar time is if they are directly north-south of each other Solar time differs 4 minutes for 1˚ of longitude Clock time has 24 1-hour time zones, each spanning 15˚ of longitude Source: http://aa.mil/graphics/TimeZoneMap0802.pdf Time Zone Local Time Meridian Eastern 75˚ Central 90˚ Mountain 105˚ Pacific 120˚ Eastern Alaska 135˚ Alaska and 150˚ Hawaii The earth’s elliptical orbit causes the length of a solar day to vary throughout the year Difference between a 24-h day and a solar day is given by the Equation of Time E E 9.13) 364 n is the day number Combining longitude correction and the Equation of Time we get the following: Solar Time (ST) Clock Time (CT) + 4 min LT Meridian Local Longitude +E (min) degree CT – clock time (7.
