Green Energy Course- Renewable Energy Systems Biên sọan: Nguyễn Hữu Phúc Khoa Điện- Điện Tử- Đại Học Bách Khoa TPHCM The Solar Resource • 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 and Blackbody Radiation • 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 The Solar Resource • 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 Plank’s Law • 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) Electromagnetic Spectrum 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 288 K Blackbody Spectrum The earth as a blackbody Figure 7.1 Area under curve is the total radiant power emitted Stefan-Boltzmann Law • Total radiant power emitted is given by the Stefan – Boltzman law of radiation E A 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) Wien’s Displacement Rule • 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 Extraterrestrial Solar Spectrum Figure 7.2 Air Mass Ratio As sunlight passes through the atmosphere, less energy arrives at the earth’s surface Figure 7.3 • h1 = path length through atmosphere with sun directly overhead • h2 = path length through atmosphere to spot on surface • β = altitude angle of the sun Air Mass Ratio 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 Solar Spectrum on Surface M increases as the sun appears lower 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 ECE 333 (398RES) Renewable Energy Systems Lecture 23 The Solar Resource Professor Tom Overbye Department of Electrical and Computer Engineering Announcements • Homework 11 is 7. It is due on Thursday April 30. • Reading: Chapters 7 and 8 • Final exam is on Friday May 8 from 8 to 11am.
Because of the class size we have two rooms, 106B8 Eng. Hall and 163 Everitt. – Last name starting with A through J go to 163, otherwise 106B8. – Final is comprehensive, with more emphasis on solar (since it wasn’t on an earlier exam) – Same procedure except you can bring in one new notesheet and your two previous notesheets.
Another Projection on How Quickly Our Resources will Vanish http://www.com/data/images/archive/2605/26051202.jpg However New Reserves and Sources Often Appear: Uranium Example • Chart shows uranium resources at 59 years at current production levels. • In 2006 worldwide production of uranium ore was about 40,000 tonnes. Economicially viable reserves now at about 5.5 million tonnes, a value that has recently increased because of the increase in price. • There are estimated to be 35 million tonnes than could eventually be mined economically.
• Uranium can be extracted from sea water giving an ultimate potential of about 4.6 billion tonnes, enough for 100,000 years at the current rate of consumption. Solar Spectrum on Surface M increases as the sun appears lower 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 In the News: Solar for Chicago • On 4/22/09 Exelon announced plans to build a solar power plant on Chicago’s South Side. • The $60 million solar power plant will provide a maximum of about 10MW.
Exelon will be relying on loan guarantees from the US DOE as part of the economic stimulus plan • The solar plant will be located in the West Pullman neighborhood • Assuming a 25% capacity factor, a zero percent interest rate, $0.15 electricity, payback time on the plant will be $60,000,000/(0.3 years The Earth’s Orbit • One revolution every 365.25 days • Distance of the earth from the sun 8 360( 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 The Earth’s Orbit • 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 The Earth’s Orbit Figure 7.5 For solar energy applications, we’ll consider the characteristics of the earth’s orbit to be unchanging Solar Declination • 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 The Sun’s Position in the Sky • 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 and Collector Tilt • 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 Figure 7.8 • During solar noon, the sun’s rays are perpendicular to the collector face Altitude Angle βN at Solar Noon • 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 7.2 – Tilt of a PV Module • 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 Example 7.2 – Tilt of a PV Module • 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 Solar Position at Any Time of Day • 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 and Azimuth Angle Altitude Angle Azimuth Angle Figure 7.10 Altitude Angle and Azimuth Angle • 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˚ Altitude Angle and Azimuth Angle 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 (7.3 – Where is the Sun? • 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 40 cos 23.45cos 45 sin 40sin 23.3 – Where is the Sun? • 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) Sun Path Diagrams for Shading Analysis • 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 Sun Path Diagram for Shading Analysis • Trees to the southeast, small building to the southwest • Can estimate the amount of energy lost to shading Figure 7.15 California Solar Shade Control Act • 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.