Photovoltaic Theory and Practice John W. Peeples, PhD, P.E. Professor, Electrical and Computer Engineering, The Citadel ELEC 427 Spring 2018 Sources: US DoE, Office of Energy Efficiency and Renewable Energy Energy Systems Engineering, Vanek, Albright, Angenet, Chaptes 9-12
Work, Energy and Power Energy > The ability to do work. Work > Force acting through distance Units of work are same as units of energy In standard units are joule = newton.meter In fundamental metric units a joule is kg m2 s-2 Force=F=m a Work = W = F d=m g h=kg m/s 2 m=kg.m2 s-2 =joule Energy is also power integrated over time E=P t if p is constant. Joule = watt.second 1 kwh=3.6 Mj Good British/Metric Approximations Energy: 1 BTU = 1055 joules Power: 1 hp = 746 w
Forms of Energy Important because we don t make energy, we convert it. Kinetic Energy > moving automobile, moving bullet, E=1/2 m v 2 or E=1/2 I ω 2 (rotational) Gravitational potential > water behind a hydroelectric dam, E=m g h Thermal energy > boiling water, E=3/2 n R T (from ideal gas law) Chemical energy > stored in the C-H bonds of a gallon of gas Nuclear energy > stored in the bonding forces of the nucleus of an atom, E=m c 2 Electrical energy > as represented by current times voltage, E=P t Electromagnetic energy > as associated with photons, E=h f (h is Planck s constant)
The Great Engineering Feats of the 20th Century 20. High Performance Materials 19. Nuclear Technologies 18. Lasers and Fiber Optics 17. Petroleum and Gas Technologies 16. Health Technologies 15. Household Appliances 14. Imaging Technologies 13. Internet 12. Space Exploration 11. Interstate Highways
The Great Engineering Feats of the 20th Century 10. Air Conditioning and Refrigeration 9. Telephone 8. Computers 7. Agricultural Mechanization 6. Radio and Television 5. Electronics 4. Safe and Abundant Water 3. Airplanes 2. Automobiles 1. Electrification
Photovoltaic Theory and Practice The Solar Resource Photovoltaic Technology Implementation Considerations
Solar Resource Topics Why besides abundance, is solar energy appealing. Solar energy is abundant. Insolation, or solar irradiation varies widely Geographically Annually Daily Considerations for collecting solar energy
Solar Energy is Attractive Solar Thermal Energy About 50% of the US energy consumption does not require high temperatures. Hot water heating 4% Space heating 18% Process heat in industry ~20% All Great Solar Thermal Candidates Solar Photovoltaic Self aligned with some high energy use applications. Air conditioning: rapidly increasing developing world Maximum solar flux corresponds to maximum need But, you re right, the big attraction is abundance.
How Much Insolation is There? Short Answer 1368 W/m 2 Earth Intercepts more than 100,000 Terawatts Changes with distance to sun (time of year). But then there is the atmosphere.
The Solar Constant 1368 W/m 2 just outside the Earth s atmosphere This constant varies over time Daily Solar Constant I0 1368{1 0.034cos[2 ( N 3) /365]} N is the Julian date N-3 because January 3 is the current solar perihelion (closest sun approach to Earth) Average Insolation (energy reaching the Earth) will be lower
Reality Average insolation is lower than the adjusted constant Weather Reflection, Absorption and Diffusion Location, location, location These and other considerations affect the journey from watts/m 2 to collected/converted/available watt-hours of energy.
Specific Insolation Averages are deceiving. Wide ranging over time of day, day of year, and geographic location. The good news. Data is available, and variations are consistent over days, seasons and years. Understand the data.
US Daily Insolation, Average Annual Satellite Modeled from 1998-2005 data
European Irradiance (Power)
Sample of Variation in Seasonal Averages Insolation Hours of Direct Sun Solar gain US Summer 1 mega joule = 277.778 watt hours Hours US Winter 26 MJ/m 2 /day = 7222.228 whr/m 2 /day (7222.228 whr/m 2 /day)/11 hrs/day = 656 w/m 2 insolation. 11 MJ/m 2 /day = 3055.558 whr/m 2 /day over 6 hours yields 509 w/m 2 insolation.
Daily Average Insolation (W/m 2 ), Selected Cities Source: F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill. Source: Trewartha & Horn (1980) watt-hours/m 2 /some sunny day Global Direct Diffuse Horizontal Normal Horizontal SC/CHARLESTON 32,54 N/ 80, 2 W 4604 4218 1999 SC/COLUMBIA 33,57 N/ 81, 7 W 4520 4249 1921 SC/GREENVILLE 34,54 N/ 82,13 W 4453 4389 1806
Direct vs Diffuse Radiation Source: F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill.
Solar Radiation Data Given Solar radiation records on an hourly basis Gathered on horizontal surface, as baseline Global insolation Diffuse insolation Can calculate Insolation on surface of any slope nearby Daily, monthly, and annual incident energy Typical values P = 1000 w/m 2 is often used as of maximum insolation, as it roughly adjusts for the albedo (reflection coefficient) of the Earth s surface. Will by much larger than most average values.
Time of Day Considerations Transmittance through the atmosphere Function of sun angle Zenith Angle brings the suns position to zenith (directly overhead) = θ z Θ z + α = 90º What time is it, really? Solar Angle brings the suns position to the horizon = α
Daily Variation - Transmittance Several approaches can be used to determine the transmittance. AM CB AB 1 sec( z ) cos( ) z This construct can be used to find the ratio, m, of the atmospheric path at a given angle to the most direct path (overhead), which can then be used to determine transmittance to within 5% accuracy. Blows up as θz approaches 90º. Use the equation below when the sun approaches the horizon. m 2R 1 H E A ( R E cos ) 2 / H 2 A R E cos H A AM 1 cos( ) 0.50572(96.07995 ) z 1.36364 z m is the ratio of the beam distance through the atmosphere to what it would be directly overhead, and varies about 9:1, consistent with many tables of measured values. Source: F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill.
What time is it, Really? - Solar Time Corrections within time zones Solar time = standard time + 0:04(Long std Long loc ) + ET Corrects for actual location between the 15º time zone boundaries and for the difference between actual and solar time, using the Equation of Time (ET). ET a1 sin( ) b1 cos( ) a2 sin(2 ) b2 cos(2 ) a3 sin(3 ) b3 cos(3 ) a4 sin(4 ) b4 cos(4 ) ET is a fitted solution accommodating the Earth s elliptical orbit of the sun, expressed as a Fourier series. 2 N /365 Degrees. N is the day of year. Coefficients a n and b n are provided. ET yields a decimal result which must be converted to a hour:minute:second format before using in the solar time equation.
Seasonal Variation - Declination Angle between the line of the sun and the plane of the equator. Varies throughout the year per: 23.45 sin[360(284 N) /365)] The maximum solar altitude for a location will be: 90 L max 52 N. Lat. 5 N. Lat. What is the solar altitude The Citadel, (Lat. 32.797) at the winter solstice, December 21? Source: F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill.
Solar Altitude at Winter Solstice Charleston December 21 is N=355, and 360 (284 355) 365 630 3.5 And sin( 3.5 ) 1, so: max 90 L 90 32.797 23.45 33. 753 Zenith Angle brings the suns position to zenith (directly overhead) = θ z Θ z + α = 90º Solar Angle brings the suns position to the horizon = α
Real Data, Fourteen Years Ithaca, NY Transmittance is relatively constant, unlike actual insolation data. On the average, and over the long run!! The tremendous day to day, and hour to hour variation must be considered in the design of Solar Energy Systems. Source: F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill.
Summary To predict the daily energy reaching a solar device, we must: 1. Calculate the hour angle based on the hour of day in solar time. 2. Calculate he solar altitude based on latitude, declination and hour of day. 3. Calculate the solar azimuth from the declination, hour angle and solar altitude. 4. Calculate the angle of incidence from the solar altitude, the solar azimuth, the surface angle and the surface azimuth. Calculations for June 21 at Lat 32 (about Tybee Island, GA) shows that: About 36% of the total available solar flux is collected, due to the time and angular considerations. A lot of solar energy hits the earth. Expected yield can be calculated for specific locations, which includes impact of diffusion components, which are in turn functions of clearness and tilt angle.
Solar Photovoltaic Technologies Muehlhausen, Germany, 10 MW Courtesy of SunPower Corporation. Reprinted with permission.
Solar Technology Topics Photovoltaics: History of Photovoltaic (PV) development How PV cells work Types of PV cells Extra at no charge Solar thermal applications
Optoelectronic Devices Light Emitting Diodes Photodiodes Solar Cells Photodectectors It all starts with E=hν
History of PV Cells 1839: Becquerel discovers photovoltaic effect in electrochemical cells Two Nobel Prizes, Planck, 1918 and Einstein, 1921 explained the photoelectric effect. 1954: Chapin, Fuller & Pearson develop first efficient solar cell Late 1950s: first non-laboratory use of PV cells Telephone relay station in rural Georgia Power for NASA s Vanguard I satellite 1973: Grad student Peeples, et al
Realms of Operation No battery Reverse current LEDs Photodetectors Solar Cells
Optoelectronic Effect Photons of frequency E g /h add to generation current The result is a family of reverse bias curves
Light Emitting Diodes First Quadrant Carriers injected across the junction must recombine Recombination in indirect band gap materials generates heat Si Ge Recombination in direct band gap materials generates light (and some heat) GaAs GaP Ternary and quaternary compounds Luminosity (brightness) and Color bands are important
Light Emitting Diodes Brighter LEDs enable tailight and traffic light arrays Colors important for displays and for communications
Designer Light Emitters Energy varies near linearly with stoichiometry Energy determines emitted frequency Stoichiometry dictates color Color dictates application Red, Yellow, Green traffic lights Red, Blue, Green color displays Red tail lights IR, other non-visibles communications E g(ev) hv hc / 1.24 / ( m) red 680nm 0.68 m E g(ev) 1.24 / 0.68 1.82eV GaA 0.68 P 0.32 or Al 0.32 Ga 0.68 As (fig. 3-6)
Photodetectors 3 rd quadrant operation (Fig 8-3) P-Intrinsic-N Impinging photons generate EHPs, changing I o I r reflects the shift in the 3 rd quadrant characteristic
Photoconductivity Effect of photon excitement Equilibrium, Constant Fermi Level Photo-generated charge carriers disrupt equilibruim creating an open circuit voltage (V oc )
Solar Cells
Photovoltaic Overview How PV cells work: incoming photon breaks bond electron is free to roam lattice vacancy left by electron is also able to move in lattice Structure of PV cell controls movement of electrons & vacancies so as to create useful current in an external circuit Silicon n-type region doped with Phosphorus (5 valence electrons) p-type region doped with Boron (3 valence electrons) Difference in concentration across p-n junction causes permanent electric field from n to p
Cross section of PV cell Source: F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill.
Solar Cell Construction
Current as a function of voltage in ideal PV cell for values between V = 0 and V = V OC Source: F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill.
Solar Cell Fill Factor Maximum Power Figure of Merit V oc Bandgap Dependent I sc Area and Process Dependent Notice that this is 4 th Quadrant Operation (chart flipped around for instructional purposes)
Solar Cell Fill Factor Maximum Power Figure of Merit V oc Bandgap Dependent I sc Area and Process Dependent Ratio of this area If I sc =100mA and V oc =0.8V, Then Pmax=(0.8)(100)(.7) =56mW if the fill factor is 70%. To this area
Current and power as a function of voltage for PV cell Source: F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill.
Solar Cell Technologies Crystalline Silicon Thin-film Amorphous Silicon Amorphous Silicon Germanium Polycrystalline Cadmium Telluride Polycrystalline Copper Indium Gallium diselenide (CuIn 1-x Ga x Se 2 ), or CIGS
Effect of Material Choice on Efficiency Basic Si Types Monocrystalline: <25% (but expensive) Multicrystalline: <20% (lower cost offsets lower efficiency) Amorphous: <13% (up from ~4% in 1978) Other emerging materials: Gallium Arsenide, Cadmium Telluride, Copper Indium Gallium Diselenide (CIGS)
Solar Thermal Systems For large-scale, centralized solar energy generation systems: Resemble fossil fuel combustion, except different means of heating working fluid Possible to have hybrid solar/gas systems Capital costs dominate system. In order of cost: 1. Collector System 2. Power conversion system 3. Receiver system 4. Transport-storage system Land, structure, & control costs are small, but not negligible Examples of decentralized applications: Domestic hot water (DHW) generation Solar cooking, etc.
Large-Scale Solar Thermal Application Mojave Desert, CA Source: NREL Pix Service. Picture No.00036. Reprinted with permission.
Low-Cost Application of Solar Thermal Solar Cooking in Box Oven Parametric testing of solar box oven by Engineers for a Sustainable World course at Cornell, 2004-2005
The Solar Photovoltaic Business 2.6 MW, 18,000 Thin Film Laminates, Boeing SC Photo credit: SCANA Corporation
The Solar Photovoltaic Business Installations and Costs Utilization Component Costs and Payback Production Incentives and Change
PV Panel Installation and Cost per MWatt Worldwide, 1975 to 2010 Sources: Energy Information Administration; Renewable Energy World; BP Energy Statistics; Solar Energy Industries Association Source: F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill.
PV Panel Installation and Cost per MW Worldwide, 2000 to 2010 Sources: Energy Information Administration; Renewable Energy World; BP Energy Statistics; Solar Energy Industries Association Source: F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill.
Share of World Cumulative Installed PV Capacity 2010, Total = 40.0 GW Sources: BP Energy Statistics Source: F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill.
2.24kW PV System Output and Load, June 15, 2011 Grid-connected household array in Ithaca, New York Source: F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill.
2.2 kw Array Output by Month Ithaca, New York, July 2010 to June 2011 Source: F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill.
Table 10-6. Components of cost per watt and total cost for 80 MW solar farm (2010 prices in U.S. dollars) Source: F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill.
Table 10-4. Cost components and rebate for representative solar PV system (2010 dollar costs) Source: F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill.
Payback Years for PV systems versus productivity (kwh/kw/year) retail electric rates ($/kwh), and discount rate Source: F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill.
Economic Break-Even Considertions Cost based case Cost and environmental benefit case Source: F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill.
U.S. PV Installation 2000 to 2010 Demand aided by federal and state incentives Sources: Energy Information Administration; Renewable Energy World; BP Energy Statistics; Solar Energy Industries Association Source: F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill.
US Production? Since 2010 Solyndra Suspended operation in September 2011 Over $500M in government backed debt Evergreen Solar Traded on NASDAQ from 1994 Shut down US production in March 2011 Shifted production to JV in China Uni-Solar
The PV Industry in 2001 Worldwide photovoltaic (PV) industry Major producers (2001) Japan 42% EU 25% USA 24% Major exporters (2001) Japan 42% of output USA 67% of output Major installations (2001) Japan 100 MW (grid-connect) Germany 75 MW (grid-connect) USA 32 MW (grid-connect + off grid) Developing world 120-130 MW (off grid) Also significant solar domestic hot water DHW industry worldwide; solar energy not in significant use in industry
The PV Industry in 2013 US National Renewable Energy Lab The 2013 Renewable Energy Data Book, pp 62-67
Summary Photovoltaic Energy Conversion is compelling Immediately applicable in some areas, AZ, CA and even NJ for example. For some, payback requires consideration of environmental savings. I look forward to watching this intriguing theatre for 3 more decades Sources F. Vanek, L. Albright and L. Angenent (2012) Energy Systems Engineering: Evaluation and Implementation, 2 nd Ed., McGraw-Hill. B. Streetman, S. Banerjee, Solid State Electronic Devices, 6 th Ed. PearsonPrentice Hall www.pveducation.org www.nrel.gov http://nobelprize.org/nobel_prizes/physics/laureates/1903/becquerel-bio.html http://en.wikipedia.org/wiki/calvin_souther_fuller http://www.motherjones.com/blue-marble/2012/06/uni-solar-energy-economy-greenville-biello