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Solar Constant ME 432 Fundamentals of Modern Photovoltaics Discussion 2: A Nuclear Fusion Power Plant 9.3(107) Miles Away 26 August 2020 The Sun • Sun’s core: Fusion reaction - the conversion of H to He, T=20,000,000 K • Sun’s surface: Photosphere T=5800K • All life and power on earth comes to us from the sun http://www.solcomhouse.com/thesun.htm (photosynthesis, fossil fuels) Today’s Objectives • Estimate the power density and peak wavelength emitted by a black body at a given temp T • Derive the solar constant and the average solar irradiation at the earth’s surface • Describe 4 ways to directly capture the energy of the sun on earth • List some advantages & challenges for the widescale adoption of solar photovoltaics • Describe the main solar photovoltaic technologies available today, and their relative merits/shortcomings Today’s Objectives • Estimate the power density and peak wavelength emitted by a black body at a given temp T • Derive the solar constant and the average solar irradiation at the earth’s surface • Describe 4 ways to directly capture the energy of the sun on earth • List some advantages & challenges for the widescale adoption of solar photovoltaics • Describe the main solar photovoltaic technologies available today, and their relative merits/shortcomings Planck’s Law of Blackbody Radiation • Hot bodies emit electromagnetic radiation with a spectral distribution that is determined by the temperature • For a “black body”, which is an idealization of a perfect absorber, the spectral distribution is given by Planck’s Law of Blackbody Radiation • As a black body is heated, the total emitted radiation increases and the wavelength of the peak emission decreases • The sun is a very good approximation of a black body at temperature T=5800K hc 1240 (eV-nm) Useful relationship: E = hυ = E (eV) = λ λ (nm) Planck’s Law of Blackbody Radiation • The expression for the unique electromagnetic spectrum that is emitted by a perfect blackbody. • The spectrum depends only on the temperature in terms of frequency … 2hυ 3 1 I (υ,T) = 2 h /kT c e υ −1 in terms of wavelength … 2hc2 1 I (λ,T) = 5 h /kT λ e υ −1 I is the intensity (energy per unit time per unit area of emitter) per unit solid angle per unit frequency/wavelength Planck’s Law of Blackbody Radiation 2 important conseQuences …. 1. Stefan-Boltzmann Law The total power emitted per unit surface area of black body is given by: ∞ P 4 s = Stefan-Boltzmann constant = j = ∫ I (λ,T)dλ ∫ dΩ = σT = 5.67 (10-8) W m-2 K-4 A 0 …. scales as T4 Example: Modeling the sun as a black body at temperature Tsun=5800 K, what is the power per unit area emitted at the sun’s surface? " 5.67(10−8 )W % j T 4 58004 K4 6.42(107 ) W/m2 sun = σ = $ 2 4 '( ) = # m K & That’s 642,000 100W light bulbs per square meter … Planck’s Law of Blackbody Radiation 2 important conseQuences…. 2. Wien Displacement Law As the temperature T increases, the peak of the spectrum shifts to smaller wavelengths b λ = b = 2.898(10-3) m/K peak T Example: Modeling the sun as a black body at temperature Tsun=5800 K, at what wavelength does the solar spectrum peak? −3 b " 2.898(10 ) m/K % −7 λpeak = = $ ' = 5(10 ) m T # 5800 K & … 500 nm wavelength corresponds to visible part of EM spectrum (yellow) Today’s Objectives • Estimate the power density and peak wavelength emitted by a black body at a given temp T • Derive the solar constant and the average solar irradiation at the earth’s surface • Describe 4 ways to directly capture the energy of the sun on earth • List some advantages & challenges for the widescale adoption of solar photovoltaics • Describe the main solar photovoltaic technologies available today, and their relative merits/shortcomings What is the power per unit area received at the surface of the earth from the sun’s electromagnetic radiation? �!"# �$%&'(,*! �!"# P.S. not to scale! ! R $2 This number is known as � sun 2 the solar constant, and $%&'(jea,r*!th = # & jsun =1368 W/m denotes the amount of " D % radiation the earth receives by its cross- section What is the average solar radiation incident on the earth’s surface, not (yet) including effects of atmospheric radiation? �!"# �$%&'(,*! �!"# P.S. not to scale! Given that the energy jearth is being distributed over the entire surface of the earth 2 2 4pRe rather than its cross-section pRe , the average incoming solar radiation is one- fourth of the solar constant: 1 2 That’s 3.42 100W light �$%&'(j,!"&+ = 342 W/m 4 earth bulbs per square meter … Today’s Objectives • Estimate the power density and peak wavelength emitted by a black body at a given temp T • Derive the solar constant and the average solar irradiation at the earth’s surface • Describe 4 ways to directly capture the energy of the sun on earth • List some advantages & challenges for the widescale adoption of solar photovoltaics • Describe the main solar photovoltaic technologies available today, and their relative merits/shortcomings Estimated US Energy Use in 2018: ~101.2 Quads Source: Lawrence Livermore National Laboratory (2019). Estimated US Energy Use in 2018: ~101.2 Quads Overall Efficiency of US Energy Consumption: ~ 32.3% Source: Lawrence Livermore National Laboratory (2019). Estimated US Energy Use in 2018: ~101.2 Quads Overall Efficiency of US Energy Consumption: ~ 32.3% Source: Lawrence Livermore National Laboratory (2019). Estimated US Energy Use in 2018: ~101.2 Quads fuel Overall Efficiency of US Energy Consumption:heat ~ 42% useful energy Source: Lawrence Livermore National Laboratory (2019). The Solar Resource large potential for direct conversion processes Entire Human Energy Use (mid to late 20th century): 4x1014 kWh/year Theoretical Potential for Various Renewable Energy Sources: Source Theoretical Potential (kWh/year) Hydro 4.1x1014 Biomass 8.1x1014 Wind 1.7x1015 Ocean 2.1x1015 Solar 1.1x1018 Source: United Nations World Energy Assessment: Energy and the Challenge of Sustainability http://www.undp.org/energy/activities/wea/drafts-frame.html 4 Ways to Capture Solar Energy Approach Energy In Energy Out 4 Ways to Capture Solar Energy Approach Energy In Energy Out Photosynthesis Sunlight (EM Energy) Chemical Energy 4 Ways to Capture Solar Energy Approach Energy In Energy Out Photosynthesis Sunlight (EM Energy) Chemical Energy Solar Thermal Sunlight (EM Energy) Heat Energy 4 Ways to Capture Solar Energy Approach Energy In Energy Out Photosynthesis Sunlight (EM Energy) Chemical Energy Solar Thermal Sunlight (EM Energy) Heat Energy Photovoltaics Sunlight (EM Energy) Electrical Energy 4 Ways to Capture Solar Energy Approach Energy In Energy Out Worldwide Conversion Rate (circa end of 2015) Photosynthesis Sunlight (EM Chemical 100-500 TW Energy) Energy Solar Sunlight (EM Heat Energy 4.5 GW Thermal/CSP Energy) Photovoltaics Sunlight (EM Electrical 233 GW Energy) Energy Photocatalysis* Sunlight (EM Chemical NA Energy) Energy 1. Photosynthesis • conversion of carbon dioxide (CO2) and water (H2O) into sugars in tHe presence of sunligHt • overall reaction: sunlight 6CO2 + 6H2O → C6H12O6 + 6O2 energy stored in the chemical bonds of sugar molecules • takes place in the chloroplasts of plant, algae, and cytoplankton cells Picture Credit: http://www.desmids.nl/maand/english/0602_febeng_ frame.html 1. Photosynthesis http://oceancolor.gsfc.nasa.gov/SeaWiFS/BACKGROUND/Gallery/index.html 1. Photosynthesis How efficient are plants are converting incident sunlight to chemical energy? Main sources of loss: - Plants only absorb 400-700 nm wavelengths (45% of incident sunlight) - Some light waves do not strike the right part of the cell (chloroplasts) - Some of the absorbed light is used by the leafs for respiration, or used by the plants to grow roots, etc. NET EFFICIENCY IS AROUND 1-2% (sugarcane: 8%) http://library.thinkquest.org/3715/ 2. Concentrated Solar Power The use of optics, mirrors, etc to concentrate a large amount of solar radiation on to a small area. It is most often used for heating water (either for direct use or to run a heat engine). • The conversion of sunlight to heat is Parabolic trough quite efficient (~60-80%), but then a heat engine is still needed for electricity generation (net efficiency around 15%) • Five years ago, CSP was cost competitive with PV, today solar PV is less expensive • Currently: ~ 2.2GW of Concentrated Solar Power (CSP) solar thermal electricity generation available worldwide; another 17-18 GW under Picture Credit. development http://nenmore.blogspot.com/2010/12/doe-backs- 145-bil-az-solar-power-plant.html 2. Solar Thermal (CSP) http://www.lpdaniel.com/SEGS.html 2. Solar Thermal (CSP) • 354 MW installed capacity (second largest today) • Hybrid generation plant, using sunlight during daytime and natural gas at night • 936,384 mirrors covering around 6.5 km2 • Sunlight reflected from mirrors is ~80 more intense than ordinary sunlight, and heats s synthetic oil or a molten salt in the central tube to 400 °C. SEGS, or Solar Energy Generating Systems. Mojave Desert, CA. • The synthetic oil transfers its heat to water, which boils and drives the Rankine cycle steam turbine, thereby generating electricity. 2. Solar Thermal (CSP) Ivanpah Solar Electric Generating System (in Mojave desert, CA) – 392 MW capacity; current largest • example of a solar thermal tower, in which mirrors focus sunlight into a large reservoir that heats water Heliostat mirrors focus sunlight on receivers in tower, generate steam, and drive steam turbines; world’s first fully solar powered turbine 3. Photovoltaics How a PV cell works: 4. Photocatalysis* the acceleration of a photoreaction in the presence of a catalyst, resulting in storing chemical energy in a fuel. Example: water splitting 2H2O → 2H2 +O2 Sunlight, TiO2 • In this example, TiO2 is the catalyst that accelerates the reaction.
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