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Solar Energy
C H A P T E R
18 Solar Energy: Photovoltaics Adria E. Brooks Department of Physics, University of Arizona, Tucson, AZ, USA
18.1 INTRODUCTION Photovoltaic (PV) energy is a direct application of the photoelectric effect discovered by Edmund Becquerel in 1839, whereby sunlight energy excites electrons present in metals. PV devices are able to convert sunlight directly into electricity. As such, PV energy is often referred to as solar electric energy to distinguish it from solar thermal energy that uses sunlight energy in the form of heat to produce electricity indirectly.
18.1.1 Solar Resource The driving appeal of solar electric energy is the amount of energy available for conversion into electricity. Given current energy usage and world population, enough solar radiation falls on the Earth’s surface at any given time to provide an average 20 GW of power to every person [1]. Stated another way, given 15 % conversion efficiency of purely dispatchable energy we would only need to cover 1.4 % of the state of Arizona with PV modules to meet the annual energy needs of the entire United States (US energy usage statistics from Ref. [2]). The challenge for the PV industry is determining how to efficiently and economically convert that incident solar energy into usable electricity. The average solar intensity outside the Earth’s atmosphere is 1367 W m22, a figure known as the solar constant. Much of this light is either absorbed or reflected by the atmosphere before reaching the Earth’s surface. The amount of atmosphere through which solar energy
Future Energy. DOI: http://dx.doi.org/10.1016/B978-0-08-099424-6.00018-1
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18. SOLAR ENERGY: PHOTOVOLTAICS
must pass is known as the air mass (AM) and it depends on geographical location and time of day and year. An air mass of zero (AM0) is extraterrestrial radiation, the solar constant, and an air mass of one (AM1) is a path normal to the surface, the shortest possible path to the surface. By industry standards, all PV modules and systems are characterised at AM1.5, 50 % longer than the shortest path length. The solar spectrum represents the intensity of solar radiation at every wavelength for any given AM. Figure 18.1 shows the solar spectrum at AM0 and AM1.5. Materials engineers create PV materials that can convert sunlight into electricity at wavelengths with the most intensity to maximise conversion efficiency. The amount of useful solar energy incident in any particular location is highly dependent on latitude and climate. The equator receives the most annual solar energy and the poles receive the least. Dry climates receive more solar energy than those with cloud cover. The solar resource map in Figure 18.2 shows the average daily insolation and incident solar energy per unit area for the United States. The US Southwest has the highest opportunity for solar electric energy production. The amount of incident irradiance is also dependent on the tilt of the PV module. Average monthly solar insolation incident on three different planes in Tucson, AZ is shown in Figure 18.3 to help understand both the seasonal and PV module tilt differences.
Sunlight intensity / (kW·m–2·µm–1)
2
1.5
1
0.5
0
0
0.5
1 1.5 Wavelength/µm
2
FIGURE 18.1
2.5
Solar spectrum at AM0 (red) and AM1.5 (blue). (The format of the units have been altered from the original [3].)
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18.1 INTRODUCTION
FIGURE 18.2 The United States solar resource map (radiation in units of
W h m22) [4].
Incident solar radiation In Tucson Arizona Average daily solar radiation/kW•h•m–2•d–1 where d refers to day
Normal to ground
At latitude
Dual-axis tracker
12
10 8 6 4 2 0 Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
FIGURE 18.3 Annual insolation at three different orientations for Tucson. Low output in July and August due to summer monsoon clouds. Data from Ref. [5].
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18.1.2 PV Technologies The first PV devices were developed by Bell Laboratories in 1954. The Bell Labs PV modules consisted of many flat silicon material cells and achieved a conversion efficiency of 6 % [6]. Since then, the solar electric industry has developed several more materials and module anatomies. Silicon is still the most common material used in PV modules. Silicon cells are currently achieving conversion efficiencies of 25 %, compared to an efficiency of 13 % in the mid 1970s [7]. Silicon is a relatively expensive material to process. In an effort to lower the cost of solar electric energy, researchers have been developing other PV materials called thin films. Thin film PV materials contain a combination of cadmium, indium, gallium, tellurium, copper and silicon. These materials are much less expensive to manufacture than pure silicon. Some of these materials are found in few geographical locations and are hard to mine. Thin film materials achieve an efficiency of 20.3 %, compared to an efficiency of 6 % in the mid 1970s [7]. The most efficient solar cells are triple-junction cells. As the name suggests, these comprise of three different layers of PV material that are engineered to convert three sections of the solar spectrum. Different PV material conversion efficiencies versus time of development are shown in Figure 18.4. Developers are creating innovative ways to package the PV materials into complete modules for electricity production. The simplest and most common module anatomy for residential systems is a flat-plate module. These modules consist of many cells imbedded within glass and enclosed with a metal frame. Concentrating photovoltaic (CPV) modules make use of mirrors or lenses to concentrate more light on a small amount of PV material. Although more complicated, this module anatomy is cost-effective because metal and glass are less expensive than PV material. Concentrators that focus 1000 3 light on cells can use PV cells no larger than a pen tip. Concentrating technologies are classified as either low concentrating photovoltaics (LCPVs) or high concentrating photovoltaics (HCPVs). LCPV technologies can focus light on any PV material, whereas HCPV technologies use high-quality triple-junction silicon cells to make the most of the large amount of light incident upon them. Most concentrating technologies require the module to be pointed directly at the sun in order to work. CPV modules are often coupled with single-axis or dual-axis trackers for this reason. Single-axis tracking systems are cost-effective with either flat-plate modules or LCPV and dual-axis trackers are only used for HCPV. Large, megawatt-scale solar production sites prefer to use concentrating and tracking technologies to increase their annual energy production. Figure 18.5 shows three different PV systems: a fixed-tilt flat plate, a flat-plate single-axis tracking and a 1000 3 HCPV system.
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Best Research-Cell Efficiencies 50 Multijunction concentrators Three junction (2-terminal, monolithic) Two-junction (2-terminal, monolithic)
48
Single-Junction GaAs
44 40
Single crystal
Single crystal Multicrystalline Thick Si film Silicon Heterostructures (HIT)
Efficiency (%)
20 16 12 8 4 0
NREL (inverted, metamorphic)
Dye-sensitized cells Organic cells (various types) Organic tandem cells inorganic cells Quantum dot cells Varian Varian (216x) (205x) NREL Stanford Kopin (140x) Varian
28 24
Fraunhofer ISE Solar Boeing(metamorphic, Junction Spectrolab 454x) (lattice matched, (lattice matched, Spire 418x) 364x) Semiconductor Boeing-Spectrolab (metamorphic, (metamorphic, 240x) 43.5 % 406x)
NREL (inverted matamorphic, Boeing 325.7x) Sharp Spectrolab (IMM. 1.sun) NREL (inverted. metamorophic. 1.sun)
NREL BoeingSpectrolab
Spectrolab NREL/ Japan Spectrolab Spectrolab Energy NREL NREL Spectrolab (4.0 cm2, 1-sun) SunPower (96x)
FhG-ISE IES-UPM (117x) Radboud (1026x) Alta Univ. Devices FhG-ISE Amonix (232x) (92x)
35.8 % 32.6 %
29.1 % 28.2 % 27.6 % 26.4 %
FhG- Alta Radboud Radboud NREL ISE Devices 25.0 % Univ. Univ. Cu(In, Ga)Se2 Sanyo 23.0 % UNSW UNSW Sanyo Sanyo (14x) UNSW Sanyo Stanford UNSW/ ZSW Georgia Eurosolare 20.4 % Spire FhG-ISE Georgia 20.3 % Georgia Tech UNSW ARCO Sandia NREL ZSW Tech Tech WestingNREL NREL NREL UNSW First Solar Varian NREL NREL national NREL house 17.3 % NREL lab University Sharp Univ. RCA So. Florida No. Carolina AstroPower (large-area) Stuttgart United Solar NREL (small-area) NREL NREL Mobil State Univ. (45 µm thin Boeing ARCO (aSi/ncSi/ncSi) solar kodak Solarex NRELEuro-CIS United Solar film transfer) (CdTe/ClS) IBM 12.5 % Boeing Boeing IBM (CTZSSe) 11.1 % Photon Energy (CTZSSe) AMETEK Sharp 10.1 % United Matsushita Konarka EPFL Kaneka Boeing 8.6 % Solar ARCO EPFL Kodak NREL/Konarka Solarmer United Solar Monosolar 8.3 % (2 µm UCLA Univ. Linz Konarka on glass) Solarex Boeing RCA Heliatek EPFL Groningen EPFL University Heliatek NREL (ZnO/ 4.4 % of Maine PbS-QD) RCA Plextronics University Linz Univ. NREL RCA University Siemens RCA RCA Dresden (ZnO/PbS-QD) RCA RCA Linz IBM (T.J Watson research center)
1975
UNSW
Spire
UNSW
1980
1985
1990
NATIONAL RENEWABLE ENERGY LABORATORY
FIGURE 18.4
Boeing-Spectrolab (metamorphic, 179x)
Emerging PV
Crystalline Si Cells
32
Spectrolab (metamorphic, 299x)
Cu(In, Ga)Se2 CdTe Amorphous Si:H (stabilized) Nano-, micro-, poly-Si Multijunction polycrystalline
Concentrator Thin film crystal
36
Thin film Technologies
Historic PV cell efficiencies in laboratory testing [8].
1995
2000
2005
2010
(Rev. 9-2011)
388
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FIGURE 18.5 Images of a fixed flat-plate system, a single-axis non-concentrating system and a dual-axis HCPV system (left to right).
18.2 ELECTRICAL OPERATING CHARACTERISTICS Regardless of material, all PV devices behave similarly. They can all be modelled electrically as a current source in parallel with a diode. Because PV cells are electrically equivalent, they can all be characterised by the same electrical parameters in order to compare performance. These parameters define the behaviour of current and power changes based on variations in voltage.
18.2.1 Equivalent Circuit All PV cells can be modelled as a current source with a diode and two different sources of resistance. Figure 18.6 shows the equivalent circuit diagram for an ideal PV cell. The amount of current produced by the source is directly related to the amount of illumination incident on the cell. In reality a PV cell could be either a current source or dump, drawing reverse current from a load when not illuminated. The
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18.2 ELECTRICAL OPERATING CHARACTERISTICS
IL
FIGURE 18.6 Equivalent circuit diagram for an ideal PV cell.
I
−
Rs
389
V
+
Rsh
purpose of the diode is to limit the current in one direction so that the PV cells will not use energy when in the shade or at night. A PV cell or module will experience parasitic resistances that limit the amount of power that can be delivered by the device. These resistances define the quality of the electrical connection within cells and between modules. Shunt resistances (Rsh), in parallel with the PV cell, should be maximised to prevent the flow of current through any circuit elements but the diode. Series resistances (Rs) should be minimised so as not to dissipate power generated by the current source before it reaches the load. In the simplest model, series resistances are assumed to be zero and shunt resistances are assumed infinite. The reverse current, also known as dark current, although minimised by the presence of a diode, defines how the output current of a PV device changes with voltage. The governing equation of the equivalent circuit is IðVÞ 5 Isc 2 I0 ½eðqV=kTÞ 2 1
(18.1)
where I0 is the cell saturation current, q is the fundamental charge, k is the Boltzmann constant and T is the operating temperature of the PV device measured in degree Kelvin [9].
18.2.2 Current and Voltage Behaviour As a power device, the quality of a PV electrical circuit is best described using the current and voltage behaviour. An IV curve, shown in Figure 18.7, shows how the current changes as a result of the voltage drop across the load. Information about a PV device can be derived from the overall shape of the IV curve and from four important points along the curve: open-circuit voltage (Voc), short-circuit current (Isc), and voltage and current at maximum power (Vmp, Imp). The open-circuit voltage is the available potential of the PV cell when current is not flowing. The short-circuit current is the maximum current the PV cell can deliver at certain illumination without the presence of a
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18. SOLAR ENERGY: PHOTOVOLTAICS
FIGURE 18.7 IV and PV curves of PV module. Outer dotted square represents the power of an ideal diode and inner dotted square represents the PV maximum power.
Current
Current, Power
Imp, Vmp
Pmp
Power
Voc
Voltage
Small Rs
Isc
Isc
Imp, Vmp Current
Current
Imp, Vmp
Large Rs
Voltage
Large Rsh
Small Rsh
Voc
Voltage
Voc
FIGURE 18.8 IV curves of PV cells showing the effects of series (left) and shunt (right) parasitic resistances.
load. The voltage and current at maximum power is the point along the IV curve where the cell delivers its maximum power (Pmp) given by: Pmp 5 Imp 3 Vmp
(18.2)
The corresponding power and voltage behaviour (PV curve) is also shown in Figure 18.7. An ideal diode provides a constant short-circuit current at all voltage points until the device is in the open-circuit condition, with zero current. The shunt and series resistances can be derived by looking at the overall shape of the IV curve. Shunt resistance can be seen as a deviation of the curve away from the Isc condition. Series resistance is a deviation from the Voc condition. These effects are shown in Figure 18.8. The fill factor (FF) of a PV device is an important parameter that
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18.3 PV PHYSICS
391
characterises how well the cell compares to the performance of an ideal diode. It is defined as: FF 5
Isc 3 Voc Imp 3 Vmp
(18.3)
Increased illumination on the cell results in increased short-circuit current without affecting the open-circuit voltage, providing the same IV curve with larger area. Increased temperature results in significantly decreased open-circuit voltage and a slightly increased shortcircuit current, decreasing the overall area under the curve.
18.3 PV PHYSICS PV materials are manipulated in such a way to have either extraneous free electrons or a lack of electrons. This manipulation causes an intentional polarity within the device which then causes electrons to be attracted from one side of the device to another. An energy barrier exists between the two polarised sides in order to keep the electrons from flowing freely between the two sides and neutralising the material. Electrons can only penetrate the energy barrier when energy is added to excite them. This energy barrier is designed equal to the energy of a photon. An additional trick of PV devices is to capture electrons flowing across the barrier before they neutralise the device on the other side of the barrier. To summarise, the generation of electron flow (current) in a PV device involves (1) the absorption of light, (2) the transport of an excited electron across an energy barrier and (3) the collection of the electron by a circuit to power a load.
18.3.1 Material Band-Gap Energy The electrical properties of atoms are determined by the energy states of the electrons. In a solid with a large number of atoms, electrons of the same energy states form bands, which are organised in levels of ascending energy values. Bands can be either occupied by individual electrons or vacant. The valence band (with energy Ev) is the highest band occupied by an electron. The conduction band (with energy Ec) is the lowest unoccupied band. These two bands are adjacent to one another and the energy barrier between them is known as the band-gap energy (Ebg) of the material. Every material has a unique band-gap energy. Electrons can pass through this energy barrier if they receive enough additional energy by the application of heat, an electric field or illumination.
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Electron
Empty conduction band
Ebg
hν Hole
Band-Gap
FIGURE 18.9 Band-gap energy between valence and conduction bands with photon absorption.
Filled Valence Band
PV materials rely on illumination for added energy to cause electrons to jump the band-gap. When a photon is absorbed by the material and an electron jumps the gap to the conduction band, leaving a vacant hole in the valance band, an electronhole pair is formed (Figure 18.9). (For convenience, holes in PV device physics are considered positively charged carrier particles, when in reality they are simply the absence of an electron.) This requires Ebg of the PV material to be equal to or less than that of an incoming photon (Eγ) given by the relation: Ebg 5 Ev 2 Ec # Eγ 5 hv 5
hc λ
(18.4)
where h is the Planck’s constant, υ is the photon frequency, c is the speed of light and λ is the photon wavelength. Semiconductor materials have band-gap energies between 0.5 and 3.0 eV, well-suited to match the solar spectrum of wavelengths between 0.4 and 2.5 µm. Refer to the solar spectrum in Figure 18.1 to understand the sunlight intensity at these wavelengths. Silicon and gallium arsenide, two semiconductors commonly used as PV materials, have band-gap energies of 1.12 and 1.40 eV, respectively.
18.3.2 Doping and pn Junctions In order to increase the likelihood of electrons crossing the band-gap, it is possible to create materials with a high number of free, unbound electrons and holes. Free electrons only require added energy equal to that of the material Ebg, without the necessary energy to break molecular bonds. The process of adding electrons or holes to a material is known as doping. Silicon, for example, is a Group IV element and must be doped with an acceptor Group III element to gain extra holes or a donor Group V element to gain extra electrons. Common acceptor and donor elements for silicon are Boron and Phosphorus, respectively. Acceptor-doped materials are called p-type materials because their excess holes result in a net positive charge. Alternately, donor-doped materials are called n-type materials due to their net negative charge.
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18.3 PV PHYSICS
hν
++++ – – – – – ++++ – – – – – ++++ – – – – – n ++++ – – – – – ++++ – – – – – ++++ – – – – – ++++ – – – – – ++++ – – – – – ++++ – – – – – ++++ – – – – –
393
p
I
FIGURE 18.10 PV pn junction with electric circuit and current direction shown. Courtesy of Dr. Raymond Kostuk, Department of Electrical and Computer Engineering, University of Arizona.
The excess charges of doping agents effectively lessen the band-gap of their parent material (i.e. silicon). p-type and n-type materials placed next to each other will cause holes and electrons to jump to the other type with the lowered band-gap rather than jumping into their own higher band-gap. PV devices are designed so that the p-type and n-type materials exist between an electrical circuit to capture this flow of charges in the form of electric current. An image of a PV pn junction is shown in Figure 18.10. In Figure 18.10 incoming photons excite free electrons in the n-type material and jump the lowered band-gap into the ptype material. They are picked up by the circuit and carried to the load as electric current before returning across the circuit to the n-type material. By convention, current is in the opposite direction of electron flow.
18.3.3 PV Cell Responsivity A PV device’s ability to effectively convert solar radiation to electric current is described by external quantum efficiency (EQE, ηext) and spectral response (SR). EQE is a measure of how well the PV cell converts incident light to current, including all losses, defined as: ηext 5
Isc Iph
(18.5)
Iph is the maximum possible photocurrent, assuming all photons incident upon the cell create electronhole pairs with an energy greater than the band-gap energy of the PV material. Figure 18.11 shows the ideal and practical EQE relationship expected at all wavelengths. A key design feature of solar cells is that their highest quantum efficiency increases in the most prevalent wavelength of the solar spectrum. Most PV cells have a reduced response in the visible blue and red due to front-surface recombination and back surface passivation of long wavelengths,
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FIGURE 18.11
ηext
Ideal and practical EQE of a PV cell.
Ideal EQE 1 Practical EQE
λG
λ
Responsivity/A·W–1
FIGURE 18.12 Ideal spectral responsivity of a PV cell at all wavelengths until band-gap wavelength (λg). Courtesy of Dr. Kostuk.
Wavelength
λg
respectively. The difference between unity and the maximum plateaued region shown in Figure 18.11 is due to reflected optical losses [3]. The SR of a cell describes the output short-circuit current as a function of the incident photon wavelength, described by: SR 5
Isc λ
(18.6)
All cells have a characteristic SR curve. This unique SR can be related to the EQE by: q SR 5 η (18.7) Eλ ext given the following assumptions: 1. All incident photons with energies exceeding the material band-gap energy produce electronhole pairs. 2. All electronhole pairs are efficiently separated within the pn junction and electrons exit the cell as short-circuit current. Figure 18.12 shows the ideal SR based on the wavelength for a PV device.
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18.4 PV CELL DESIGN
395
18.4 PV CELL DESIGN PV material production is a legacy of the silicon-based microelectronics industry. Materials used for PVs (e.g. Si of 106 purity) do not require the same purity as those used for microelectronics (e.g. Si of 109 purity), and the industry has thus developed less expensive ways to create PV cells. Each material has a unique production technique. In general, the more efficient materials cost more to produce than the less efficient.
18.4.1 Silicon Cell Manufacturing Briefly, the steps to manufacture silicon solar modules include mining quartz, producing silicon from quartz, melting silicon and p-type dopant to produce desired crystalline structure, slicing solidified PV material into wafers, polishing and lapping the wafers, doping wafers with n-type material, applying electrical contacts and finally encapsulating cells with all other materials into a complete module. The commonly used Czochralski (Cz) method of pulling single silicon crystals was first developed by the microelectronics industry. Higher efficiency monocrystalline silicon cells can be grown using the Float Zone production method, but this method is currently too expensive for commercial production of solar cells and is only used in the laboratory. Silicon and the chosen p-type dopant (boron usually) are melted in a large crucible and slowly drawn out of the crucible to cool. The resulting ingot is sawed to form circular wafers. The saws used were the same thickness of the resulting cell, resulting in a loss of 50 % of the silicon material. Square cell profiles allow for better use of space when enclosing cells into a module, requiring an additional loss of material when cutting from a circles to a square. In order to avoid such high losses of silicon, ribbon casting processes for cutting silicon have become popular. This cutting technique also allows for thinner silicon wafers, decreasing the wafer thickness from around 300 µm to less than 100 µm. There are two main processes for multi-crystalline silicon: the slower Bridgman technique and the faster, more controlled block-casting technique. Multi-crystalline silicon is more easily created by pouring molten silicon into a cast of any desired shape (rectangular) and allowing the silicon to cool. As the silicon cools it will solidify from the bottom up and a columnar crystal forms. Less silicon is lost in this process. Although faster and less expensive, the solidification of the multicrystalline silicon introduces grain boundaries and dislocations within the material which lower cell efficiencies [10].
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18.4.2 Texturing and Optical Reflection PV manufacturers employ many techniques to increase the amount of light incident on PV cells. Cell manufacturers will texture the front surface of cells representing inverted pyramids to increase the surface area of the cell and to trap more photons. These pyramids will be lined with an anti-reflection (AR) coating to increase light transfer. Module manufacturers also use coatings that decrease the optical reflection on the surface of the glass. Current AR coatings can decrease the front-surface reflection of glass by 10 %. Some system owners are beginning to use anti-soiling coatings on the front surface of their modules to further increase incident light.
18.4.3 Electrical Contacts The electrical contacts on a PV cell appear as metal grid lines. They do not cover more than 10 % of the front surface. Contacts are required to transport charge carriers (electrons) from the cell to the electrical circuit. Usually the n-type contact and the p-type contact will be placed on opposite sides of the cell (one front and one back). Contacts can introduce series resistance losses and shade small portions of the cell. Some manufacturers are finding ways to print both contact types on the back side of cells to avoid shading losses. Contacts can be applied using photolithography and evaporation, screen printing and laser-grooved buried lines.
18.5 FIELD PERFORMANCE PV systems are designed for ideal performance at standard test conditions (STCs). In the United States STC is defined as operation at 1000 W m22 incident irradiation, 25 C operating cell temperature and 1.5 AMs. Every PV module has nameplate ratings reported for maximum power, current and voltage at STC. Outdoor performance metrics are different from those used for ideal design conditions. No PV device performs ideally under real conditions. PV systems will behave differently based on the climates in which they are performing. Outdoor operating conditions will affect the real-time output and the long-term performance of the system. PVs perform best in cold, dry and sunny conditions.
18.5.1 Power Production Curves The power output of a PV system is proportional to the amount of irradiance incident on the system throughout the day. Daily power
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18.5 FIELD PERFORMANCE
Power output of 2 PV technologies in same location Fixed, Flat-plate Dual-axis tracking, HCPV 20
Power / kW
15
10
5
0 6:00 a.m. 2012-01-12
12:00 p.m.
6:00 p.m.
12:00 a.m. 2012-01-13
6:00 a.m.
12:00 p.m.
6:00 p.m.
FIGURE 18.13 Daily power production for a fixed, flat plate system (20 kWp) and a dual-axis, high concentrating system (10 kWp) on two days one cloudy (left) and one sunny (right).
production curves on two days one sunny and one cloudy are shown in Figure 18.13 for a fixed-tilt system and a dual-axis, concentrating system. The fixed-tilt system is representative of the sun’s apparent path in the sky. The system generates power from sunrise to sunset. The maximum power of the fixed-tilt system is found at solar noon, when the sun is directly overhead. The tracking system curve has a flattened top at maximum power because it is able to maximise incident irradiance all day. On the cloudy day, fluctuations in power show how power production is limited when the modules are in the shadow of a cloud. Shadows on fixed-tilt systems will result in power loss of (8090) %, where concentrating systems will experience a complete power loss. Fixed-tilt systems are able to make use of indirect, diffuse sunlight (accounting for (1020) % of power production) and concentrating systems are only able to use direct sunlight. The power output of a PV system also has a characteristic annual curve, as shown in Figure 18.14 for a fixed-tilt system. Based on the tilt and revolution of the earth, the sun is directly perpendicular to a location’s latitude during the fall and spring equinoxes 20 higher (North for the Northern hemisphere and South for the Southern hemisphere) on the summer solstice and 20 lower on the winter solstice. To maximise annual production, most large fixed-tilt installations are oriented towards the equator at location latitude. In this setup, performance peaks during the summer and fall equinoxes, when the sun is directly perpendicular to the system angle. Although the days are longer in the summer, the angle of the sun during the summer limits PV
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6
4 2 0 1/1/2006
1/1/2007
1/1/2008
1/1/2009
FIGURE 18.14 AC energy (kW h) every day for 4 years, normalised to the system’s STC (kWp) rating. Low points are from cloudy days. The black curve is a prediction based on clear skies, a solar position algorithm, a temperature coefficient of efficiency and 0.5 % degradation per year. Courtesy of Dr. Alexander D. Cronin, Department of Physics, University of Arizona.
performance, just like in the winter. In very hot conditions, like the Southwestern United States, summer performance will be additionally reduced due to hot operating conditions. Like all electronics, PV systems have lower efficiency in the heat than in the cold.
18.5.2 Performance Parameters Several performance parameters are used to compare PV systems of different sizes and technologies. Otherwise, there would be no context for comparing the power production of one system with the power production of a different system in another location. A common performance metric is system AC efficiency (ηac). Like module efficiencies reported by PV manufacturers, system AC efficiency is a measure of how well the PV system converts irradiance to electricity. System AC efficiency will be lower than module efficiency and system DC efficiency because it includes the cumulative efficiencies of every module, wiring resistance and balance of system component. System AC efficiency is calculated as: ηac 5
kW h Hpoa A
(18.8)
using the system AC energy production (kW h), system module surface area (A) and the measured plane of array irradiance during operation (Hpoa). Common system efficiencies for residential systems using crystalline silicon modules are around 15 %. Another common performance metric is final yield (Yf), which normalises the system’s AC energy production based on its STC-rated power production (kWp):
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399
18.5 FIELD PERFORMANCE
Fixed, flat-plate energy production
Dual-axis, HCPV energy production Dual-axis, HCPV final yield
140
12
120
10
100
8
80 6 60 4 40 2
20 0 2012-03-11
Final Yield (kW h/kWp)
Energy production
Fixed, flat-plate final yield
0 2012-03-21
2012-03-31
2012-04-10
2012-04-20
FIGURE 18.15 Daily energy output (solid lines) and final yield (dotted lines) for two systems for several weeks. Notice that Yf for the dual-axis tracker is greater than that of the flat-plate system even though the latter has a higher energy yield.
Yf 5
kW h kWp
(18.9)
Final yield is often reported as an annual metric, averaging all values over an entire year, but can be reported as daily or monthly metrics. Figure 18.15 shows a comparison between AC energy production and the final yield for several systems. The final yield is more indicative of system performance than energy production because it compares systems of different technologies in the same location. The performance ratio metric is able to compare different technologies in different locations. The performance ratio (PR) simply normalises the final yield of a system by the irradiance experienced by the system during rating and during output operation: PR 5 Yf 3
Gpoa Hpoa
(18.10)
where Gpoa is the reference irradiance from the rating standard. PR is often reported as a single value averaged for an entire year of data.
18.5.3 Estimating Field Performance As explained, systems in the field will not perform as designed every day of the year. Field power output can be estimated simply by considering the irradiance incident on the system location and angle. This requires knowledge of historical irradiance at the site and a correlation
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of solar angles and system orientation. Once irradiance is known it can be multiplied by the anticipated system efficiency. PV array efficiency is negatively affected by the age and degradation of the array, any soiling or shading present and heat losses in the PV wiring. Each of these conditions causes a derating of the system efficiency and is assigned an individual derate factor based on the percentage of power loss. These values are multiplied to find a single-system derate factor. The National Renewable Energy Laboratory (NREL) created a derate factor calculator as part of their PVWatts tool [5]. The derating conditions and associated factors from NREL PVWatts are given in Table 18.1. The system derate factor can be multiplied by the module nameplate DC efficiency to estimate the system AC efficiency. This method of predicting system performance can be further complicated by understanding how operating temperature affects current and voltage. Translation equations relate field performance to performance under STCs. There are many different translation equations of varying accuracy and complication, but the most basic equation uses temperature coefficients. Temperature coefficients define how the associated parameter changes based on a single-degree increase in temperature. They are usually reported by module manufacturers. The two equations below relate current and voltage at STC to field operation (subscript m): i Gpoa h αIsc ISTC 5 Im 3 3 ðT 2 25 CÞ 3 12 (18.11) Hpoa 100 TABLE 18.1 PV System Derate Factors [5]. Component Derate Factor
PVWatts Default
Derate Factor Range
PV module nameplate DC rating
0.95
0.801.05
Inverter and transformer efficiency
0.92
0.880.98
Mismatch in module operating power
0.98
0.9700.995
Diodes and connections resistance
0.995
0.9900.997
DC wiring resistance
0.98
0.970.99
AC wiring resistance
0.99
0.9800.993
Soiling
0.95
0.3000.995
System availability
0.98
0.0000.995
Shading
1.00
0.001.00
Sun-tracking accuracy
1.00
0.951.00
Age and degradation
1.00
0.701.00
System derate factor
0.77
0.000.99
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18.6 BARRIERS TO GROWTH
β VSTC 5 Vm 3 1 2 Voc 3 ðT 2 25 CÞ 100
401
(18.12)
where αIsc and β Voc are the manufacturer-reported temperature coefficients for short-circuit current and open-circuit voltage, respectively.
18.5.4 Degradation and Failure Modes All PV systems experience degradation due to age. This irreversible damage can be subtle, with minor power losses over many years, or can result from a catastrophic event that significantly reduces the power output in an instant. The specific conditions modules endure when they experience degradation are known as failure modes. Common failure modes experienced by all modules are broken interconnects, broken cells, broken glass, corrosion, delamination and loss of elastomeric properties of encapsulant, encapsulant discoloration, soldier bond failures, hot spots, ground faults, junction box and module connection failures, structural failures, bypass diode failures and arcing. Failure modes like corrosion result in subtle degradation and modes like arcing result in catastrophic damage. Each geographical location will see different modes specific to the type of weathering experienced in the area. All modes have associated characteristic voltage and/or current losses. Most degradation is subtle. PV manufacturers currently guarantee that their modules will perform at least 80 % of their nameplate power rating after 25 years. Slow degradation is best quantified by comparing the system’s nameplate efficiency (η0) to its operating efficiency (ηi) after a certain number of years (N). This is known as the degradation rate (D): η 2 ηi D5 0 =N (18.13) η0 PV materials have different degradation rates. Crystalline silicon usually degrades at a rate of 0.5 % per year, while thin film materials degrade rapidly ( 2.0 %) in the first year of operation and then stabilise to a degradation rate of 0.4 % per year.
18.6 BARRIERS TO GROWTH The PV module industry has experienced exponential growth every year for the last two decades [10]. Module and balance of system technologies have since proven that the hardware is reliable. Now the industry is facing barriers to integrating PV systems with the electric grid. The intermittent nature of PV energy presents problems on grid systems
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designed around dispatchable fossil fuel energy sources. The grid cannot yet tolerate fast fluctuations in voltage that industrial scale PV plants experience when shadowed rapidly by passing clouds. Utility companies managing power on the grid are expected to provide consistent available power to their customers, regardless of changes in supply. Reserve energy is necessary to provide this constant electricity, and energy storage options are not yet financially competitive. Utility-scale PV facilities are just now reaching grid parity with fossil fuel energy sources. The United States Department of Energy Quadrennial Technology Review summarizes five risks that PV energy imposes on utility grid operations [7]: 1. impacts on voltage and current flows, voltage regulation, reactive power flow and system protection, 2. integrating variable and uncertain solar generation into grid operations and planning, 3. unfamiliarity of grid operators with PV system designs and their operating characteristics, 4. inadequate accounting of capacity and energy valuation from variable renewable energy and energy storage technologies in traditional utility rates and costing methods, 5. risk and uncertainty surrounding predicting the availability of solar resource on a small time and spatial scale.
18.6.1 Grid Integration No energy generation plant is available all the time. Conventional generating plants are interrupted by unexpected breakdowns and scheduled maintenance. The amount of time a generator is available is known as the capacity factor. The capacity factor quantifies the amount of time a generator was available to produce energy for a given year versus what it is rated to produce. The capacity factor of fossil fuel generator is between 85 % and 90 % [1]. The solar resource is naturally intermittent, with interruptions at night and due to passing clouds. This causes PV generating facilities to have an additionally lower capacity factor of nearly 20 % [11]. A larger rated solar PV facility must be built to equal a conventional plant. Predicting intermittency of the solar resource is among the challenges we must overcome in order for solar energy to become a large contributor to our energy supply. Utility companies are cautious to adopt solar energy at the industrial scale because cloud cover causes unpredictable fluctuations in irradiance that result in grid instability. Quickly moving clouds can cause solar electric power loss or gain of 20 % per second. Utilities could control the inverters of solar electric
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18.6 BARRIERS TO GROWTH
403
fields to match the tolerable ramp rate as long as incoming cloud cover is predicted. Until solar power intermittency becomes predictable and dispatchable, utilities will continue to overproduce electricity and keep reserves of fossil fuels on hand. Gowrisankaran et al. [12] calculate that having fully dispatchable solar power will result in a PV energy cost of 38 % the current intermittent power source . Intermittency can be mitigated with a combination of energy storage, spinning reserves and demand response. All of these techniques require the ability to forecast the intermittent solar resource in each geographical location utilising solar power. Day-ahead forecasts are useful for pricing within the energy market. Hour-ahead forecasts are necessary for grid operators to manage and schedule spinning reserves. It is vital to store energy in anticipation of when demand exceeds supply, such as at night or during periods of cloudy weather. Stored energy with quick response times can help utilities provide electricity when supply is not available, smooth out intermittent energy variations and readjust seasonal variations in production to match demand load. Energy can be stored as chemical energy (e.g. batteries), electrical energy (e.g. supercapacitors), thermal energy (e.g. steam) and mechanical energy (e.g. pumped hydropower and compressed air storage). Chemical batteries are currently the most common method for storing energy, but they are expensive and unsustainable. Pumped hydropower, which has been used in commercial applications, is more economical and environmentally sustainable. Improvements are being made in all other mentioned energy storage methods.
18.6.2 Expense Historically, the cost of PV energy has been a large barrier to high penetration. The industry has now matured to a point where solar is becoming cost-effective. On average, for every doubling of PV production capacity worldwide, the cost of solar has reduced 20 % [7]. Comparing the levelised cost of energy (LCOE) of different energy production techniques allows for equal comparison of differing technologies. The LCOE is defined as the total lifecycle cost of a facility compared to the amount of energy it is expected to produce. NREL predicts PV energy will cost $0.124 (kW h)21 in locations with a high solar resource by 2016 [13]. In these areas residential solar electric energy has already reached grid parity with conventional energy sources at certain times of the year [7]. In areas with a lower solar resource, energy generated by PVs currently costs twice that produced by fossil fuels. Given continued rapid improvements within the industry, this is expected to become equal to or less than the cost of fossil fuel energy by 2050 [1].
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The cost of PV systems is no longer dominated by the cost of modules as was once the case. Now, the cost of modules is only (1525) % of the total PV system cost. By the end of 2011, crystalline silicon modules cost as low as $1.05 W21 and thin film modules cost $0.85 W21[7]. Other system costs include procurement, balance of systems costs, installation labour and taxes [11]. The industry now recognises the need to improve accompanying power electronics, more thoroughly train installers, and streamline the permitting process in order to decrease costs further. Within the next few decades the industry expects to provide energy at a cost less than fossil fuels without government subsidies or incentives.
References [1] L. Freris, D. Infield, Renewable Energy in Power Systems, Wiley, West Sussex, UK, 2008. [2] U.S. Energy Information Administration, Office of Energy Statistics, U.S. Department of Energy. Monthly Energy Review. December 12, 2012. Washington, DC, U.S. Document No. DOE/EIA-0035(2012/12). p. 92. [3] C. Honsberg, S. Bowden, Photovoltaic Education Network, 2013. ,http://www.pveducation.org. (Accessed 01.05.13). [4] Arizona Solar Center, 2013 ,http://www.azsolarcenter.org/images/articles/az/solmap.gif. (accessed 20.09.13). [5] NREL PVWatts Calculator, 2012. ,http://rredc.nrel.gov/solar/calculators/ pvwatts/version1/. (accessed 20.09.12). [6] J. Perlin. The Silicon Cell Turns 50. National Renewable Energy Laboratory. August 2004. NREL Report No. BR-520-33947. [7] US Department of Energy, Quadrennial Technology Review: Technology Assessments, 2012 (Prepublication copy, accessed 29.06.12). [8] National Renewable Energy Laboratory, U.S. Department of Energy. Best ResearchCell Efficiencies. September 2012. (Most recent version of chart can be found at ,http://www.nrel.gov/ncpv/images/efficiency_chart.jpg/.). [9] J. Nelson, The Physics of Solar Cells, Imperial College Press, London, UK, 2003. [10] A. Luque, S. Hegedus, The Handbook of Photovoltaic Science and Engineering, Wiley, West Sussex, UK, 2003. [11] G.F. Nemet, E. Baker, Demand subsidies versus R&D: comparing the uncertain impacts of policy on a pre-commercial low-carbon energy technology, Energy J. 30 (2009) 4980. [12] G. Gowrisankaran, S.S. Reynolds, M. Samano, Intermittency and the Value of Renewable Energy, NBER Working Paper No. w17086, 2011. [13] M. Woodhouse, et al., An economic analysis of photovoltaics versus traditional energy sources: where are we now and where might we be in the near future?, Proceedings of the IEEE Photovoltaics Specialists Conference, 2011.
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18 Solar Energy: Photovoltaics Adria E. Brooks Department of Physics, University of Arizona, Tucson, AZ, USA
18.1 INTRODUCTION Photovoltaic (PV) energy is a direct application of the photoelectric effect discovered by Edmund Becquerel in 1839, whereby sunlight energy excites electrons present in metals. PV devices are able to convert sunlight directly into electricity. As such, PV energy is often referred to as solar electric energy to distinguish it from solar thermal energy that uses sunlight energy in the form of heat to produce electricity indirectly.
18.1.1 Solar Resource The driving appeal of solar electric energy is the amount of energy available for conversion into electricity. Given current energy usage and world population, enough solar radiation falls on the Earth’s surface at any given time to provide an average 20 GW of power to every person [1]. Stated another way, given 15 % conversion efficiency of purely dispatchable energy we would only need to cover 1.4 % of the state of Arizona with PV modules to meet the annual energy needs of the entire United States (US energy usage statistics from Ref. [2]). The challenge for the PV industry is determining how to efficiently and economically convert that incident solar energy into usable electricity. The average solar intensity outside the Earth’s atmosphere is 1367 W m22, a figure known as the solar constant. Much of this light is either absorbed or reflected by the atmosphere before reaching the Earth’s surface. The amount of atmosphere through which solar energy
Future Energy. DOI: http://dx.doi.org/10.1016/B978-0-08-099424-6.00018-1
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© 2014 Elsevier Ltd. All rights reserved.
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18. SOLAR ENERGY: PHOTOVOLTAICS
must pass is known as the air mass (AM) and it depends on geographical location and time of day and year. An air mass of zero (AM0) is extraterrestrial radiation, the solar constant, and an air mass of one (AM1) is a path normal to the surface, the shortest possible path to the surface. By industry standards, all PV modules and systems are characterised at AM1.5, 50 % longer than the shortest path length. The solar spectrum represents the intensity of solar radiation at every wavelength for any given AM. Figure 18.1 shows the solar spectrum at AM0 and AM1.5. Materials engineers create PV materials that can convert sunlight into electricity at wavelengths with the most intensity to maximise conversion efficiency. The amount of useful solar energy incident in any particular location is highly dependent on latitude and climate. The equator receives the most annual solar energy and the poles receive the least. Dry climates receive more solar energy than those with cloud cover. The solar resource map in Figure 18.2 shows the average daily insolation and incident solar energy per unit area for the United States. The US Southwest has the highest opportunity for solar electric energy production. The amount of incident irradiance is also dependent on the tilt of the PV module. Average monthly solar insolation incident on three different planes in Tucson, AZ is shown in Figure 18.3 to help understand both the seasonal and PV module tilt differences.
Sunlight intensity / (kW·m–2·µm–1)
2
1.5
1
0.5
0
0
0.5
1 1.5 Wavelength/µm
2
FIGURE 18.1
2.5
Solar spectrum at AM0 (red) and AM1.5 (blue). (The format of the units have been altered from the original [3].)
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385
18.1 INTRODUCTION
FIGURE 18.2 The United States solar resource map (radiation in units of
W h m22) [4].
Incident solar radiation In Tucson Arizona Average daily solar radiation/kW•h•m–2•d–1 where d refers to day
Normal to ground
At latitude
Dual-axis tracker
12
10 8 6 4 2 0 Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
FIGURE 18.3 Annual insolation at three different orientations for Tucson. Low output in July and August due to summer monsoon clouds. Data from Ref. [5].
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18.1.2 PV Technologies The first PV devices were developed by Bell Laboratories in 1954. The Bell Labs PV modules consisted of many flat silicon material cells and achieved a conversion efficiency of 6 % [6]. Since then, the solar electric industry has developed several more materials and module anatomies. Silicon is still the most common material used in PV modules. Silicon cells are currently achieving conversion efficiencies of 25 %, compared to an efficiency of 13 % in the mid 1970s [7]. Silicon is a relatively expensive material to process. In an effort to lower the cost of solar electric energy, researchers have been developing other PV materials called thin films. Thin film PV materials contain a combination of cadmium, indium, gallium, tellurium, copper and silicon. These materials are much less expensive to manufacture than pure silicon. Some of these materials are found in few geographical locations and are hard to mine. Thin film materials achieve an efficiency of 20.3 %, compared to an efficiency of 6 % in the mid 1970s [7]. The most efficient solar cells are triple-junction cells. As the name suggests, these comprise of three different layers of PV material that are engineered to convert three sections of the solar spectrum. Different PV material conversion efficiencies versus time of development are shown in Figure 18.4. Developers are creating innovative ways to package the PV materials into complete modules for electricity production. The simplest and most common module anatomy for residential systems is a flat-plate module. These modules consist of many cells imbedded within glass and enclosed with a metal frame. Concentrating photovoltaic (CPV) modules make use of mirrors or lenses to concentrate more light on a small amount of PV material. Although more complicated, this module anatomy is cost-effective because metal and glass are less expensive than PV material. Concentrators that focus 1000 3 light on cells can use PV cells no larger than a pen tip. Concentrating technologies are classified as either low concentrating photovoltaics (LCPVs) or high concentrating photovoltaics (HCPVs). LCPV technologies can focus light on any PV material, whereas HCPV technologies use high-quality triple-junction silicon cells to make the most of the large amount of light incident upon them. Most concentrating technologies require the module to be pointed directly at the sun in order to work. CPV modules are often coupled with single-axis or dual-axis trackers for this reason. Single-axis tracking systems are cost-effective with either flat-plate modules or LCPV and dual-axis trackers are only used for HCPV. Large, megawatt-scale solar production sites prefer to use concentrating and tracking technologies to increase their annual energy production. Figure 18.5 shows three different PV systems: a fixed-tilt flat plate, a flat-plate single-axis tracking and a 1000 3 HCPV system.
VI. RENEWABLES (ENERGY SOURCES)
Best Research-Cell Efficiencies 50 Multijunction concentrators Three junction (2-terminal, monolithic) Two-junction (2-terminal, monolithic)
48
Single-Junction GaAs
44 40
Single crystal
Single crystal Multicrystalline Thick Si film Silicon Heterostructures (HIT)
Efficiency (%)
20 16 12 8 4 0
NREL (inverted, metamorphic)
Dye-sensitized cells Organic cells (various types) Organic tandem cells inorganic cells Quantum dot cells Varian Varian (216x) (205x) NREL Stanford Kopin (140x) Varian
28 24
Fraunhofer ISE Solar Boeing(metamorphic, Junction Spectrolab 454x) (lattice matched, (lattice matched, Spire 418x) 364x) Semiconductor Boeing-Spectrolab (metamorphic, (metamorphic, 240x) 43.5 % 406x)
NREL (inverted matamorphic, Boeing 325.7x) Sharp Spectrolab (IMM. 1.sun) NREL (inverted. metamorophic. 1.sun)
NREL BoeingSpectrolab
Spectrolab NREL/ Japan Spectrolab Spectrolab Energy NREL NREL Spectrolab (4.0 cm2, 1-sun) SunPower (96x)
FhG-ISE IES-UPM (117x) Radboud (1026x) Alta Univ. Devices FhG-ISE Amonix (232x) (92x)
35.8 % 32.6 %
29.1 % 28.2 % 27.6 % 26.4 %
FhG- Alta Radboud Radboud NREL ISE Devices 25.0 % Univ. Univ. Cu(In, Ga)Se2 Sanyo 23.0 % UNSW UNSW Sanyo Sanyo (14x) UNSW Sanyo Stanford UNSW/ ZSW Georgia Eurosolare 20.4 % Spire FhG-ISE Georgia 20.3 % Georgia Tech UNSW ARCO Sandia NREL ZSW Tech Tech WestingNREL NREL NREL UNSW First Solar Varian NREL NREL national NREL house 17.3 % NREL lab University Sharp Univ. RCA So. Florida No. Carolina AstroPower (large-area) Stuttgart United Solar NREL (small-area) NREL NREL Mobil State Univ. (45 µm thin Boeing ARCO (aSi/ncSi/ncSi) solar kodak Solarex NRELEuro-CIS United Solar film transfer) (CdTe/ClS) IBM 12.5 % Boeing Boeing IBM (CTZSSe) 11.1 % Photon Energy (CTZSSe) AMETEK Sharp 10.1 % United Matsushita Konarka EPFL Kaneka Boeing 8.6 % Solar ARCO EPFL Kodak NREL/Konarka Solarmer United Solar Monosolar 8.3 % (2 µm UCLA Univ. Linz Konarka on glass) Solarex Boeing RCA Heliatek EPFL Groningen EPFL University Heliatek NREL (ZnO/ 4.4 % of Maine PbS-QD) RCA Plextronics University Linz Univ. NREL RCA University Siemens RCA RCA Dresden (ZnO/PbS-QD) RCA RCA Linz IBM (T.J Watson research center)
1975
UNSW
Spire
UNSW
1980
1985
1990
NATIONAL RENEWABLE ENERGY LABORATORY
FIGURE 18.4
Boeing-Spectrolab (metamorphic, 179x)
Emerging PV
Crystalline Si Cells
32
Spectrolab (metamorphic, 299x)
Cu(In, Ga)Se2 CdTe Amorphous Si:H (stabilized) Nano-, micro-, poly-Si Multijunction polycrystalline
Concentrator Thin film crystal
36
Thin film Technologies
Historic PV cell efficiencies in laboratory testing [8].
1995
2000
2005
2010
(Rev. 9-2011)
388
18. SOLAR ENERGY: PHOTOVOLTAICS
FIGURE 18.5 Images of a fixed flat-plate system, a single-axis non-concentrating system and a dual-axis HCPV system (left to right).
18.2 ELECTRICAL OPERATING CHARACTERISTICS Regardless of material, all PV devices behave similarly. They can all be modelled electrically as a current source in parallel with a diode. Because PV cells are electrically equivalent, they can all be characterised by the same electrical parameters in order to compare performance. These parameters define the behaviour of current and power changes based on variations in voltage.
18.2.1 Equivalent Circuit All PV cells can be modelled as a current source with a diode and two different sources of resistance. Figure 18.6 shows the equivalent circuit diagram for an ideal PV cell. The amount of current produced by the source is directly related to the amount of illumination incident on the cell. In reality a PV cell could be either a current source or dump, drawing reverse current from a load when not illuminated. The
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18.2 ELECTRICAL OPERATING CHARACTERISTICS
IL
FIGURE 18.6 Equivalent circuit diagram for an ideal PV cell.
I
−
Rs
389
V
+
Rsh
purpose of the diode is to limit the current in one direction so that the PV cells will not use energy when in the shade or at night. A PV cell or module will experience parasitic resistances that limit the amount of power that can be delivered by the device. These resistances define the quality of the electrical connection within cells and between modules. Shunt resistances (Rsh), in parallel with the PV cell, should be maximised to prevent the flow of current through any circuit elements but the diode. Series resistances (Rs) should be minimised so as not to dissipate power generated by the current source before it reaches the load. In the simplest model, series resistances are assumed to be zero and shunt resistances are assumed infinite. The reverse current, also known as dark current, although minimised by the presence of a diode, defines how the output current of a PV device changes with voltage. The governing equation of the equivalent circuit is IðVÞ 5 Isc 2 I0 ½eðqV=kTÞ 2 1
(18.1)
where I0 is the cell saturation current, q is the fundamental charge, k is the Boltzmann constant and T is the operating temperature of the PV device measured in degree Kelvin [9].
18.2.2 Current and Voltage Behaviour As a power device, the quality of a PV electrical circuit is best described using the current and voltage behaviour. An IV curve, shown in Figure 18.7, shows how the current changes as a result of the voltage drop across the load. Information about a PV device can be derived from the overall shape of the IV curve and from four important points along the curve: open-circuit voltage (Voc), short-circuit current (Isc), and voltage and current at maximum power (Vmp, Imp). The open-circuit voltage is the available potential of the PV cell when current is not flowing. The short-circuit current is the maximum current the PV cell can deliver at certain illumination without the presence of a
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390 Isc
18. SOLAR ENERGY: PHOTOVOLTAICS
FIGURE 18.7 IV and PV curves of PV module. Outer dotted square represents the power of an ideal diode and inner dotted square represents the PV maximum power.
Current
Current, Power
Imp, Vmp
Pmp
Power
Voc
Voltage
Small Rs
Isc
Isc
Imp, Vmp Current
Current
Imp, Vmp
Large Rs
Voltage
Large Rsh
Small Rsh
Voc
Voltage
Voc
FIGURE 18.8 IV curves of PV cells showing the effects of series (left) and shunt (right) parasitic resistances.
load. The voltage and current at maximum power is the point along the IV curve where the cell delivers its maximum power (Pmp) given by: Pmp 5 Imp 3 Vmp
(18.2)
The corresponding power and voltage behaviour (PV curve) is also shown in Figure 18.7. An ideal diode provides a constant short-circuit current at all voltage points until the device is in the open-circuit condition, with zero current. The shunt and series resistances can be derived by looking at the overall shape of the IV curve. Shunt resistance can be seen as a deviation of the curve away from the Isc condition. Series resistance is a deviation from the Voc condition. These effects are shown in Figure 18.8. The fill factor (FF) of a PV device is an important parameter that
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18.3 PV PHYSICS
391
characterises how well the cell compares to the performance of an ideal diode. It is defined as: FF 5
Isc 3 Voc Imp 3 Vmp
(18.3)
Increased illumination on the cell results in increased short-circuit current without affecting the open-circuit voltage, providing the same IV curve with larger area. Increased temperature results in significantly decreased open-circuit voltage and a slightly increased shortcircuit current, decreasing the overall area under the curve.
18.3 PV PHYSICS PV materials are manipulated in such a way to have either extraneous free electrons or a lack of electrons. This manipulation causes an intentional polarity within the device which then causes electrons to be attracted from one side of the device to another. An energy barrier exists between the two polarised sides in order to keep the electrons from flowing freely between the two sides and neutralising the material. Electrons can only penetrate the energy barrier when energy is added to excite them. This energy barrier is designed equal to the energy of a photon. An additional trick of PV devices is to capture electrons flowing across the barrier before they neutralise the device on the other side of the barrier. To summarise, the generation of electron flow (current) in a PV device involves (1) the absorption of light, (2) the transport of an excited electron across an energy barrier and (3) the collection of the electron by a circuit to power a load.
18.3.1 Material Band-Gap Energy The electrical properties of atoms are determined by the energy states of the electrons. In a solid with a large number of atoms, electrons of the same energy states form bands, which are organised in levels of ascending energy values. Bands can be either occupied by individual electrons or vacant. The valence band (with energy Ev) is the highest band occupied by an electron. The conduction band (with energy Ec) is the lowest unoccupied band. These two bands are adjacent to one another and the energy barrier between them is known as the band-gap energy (Ebg) of the material. Every material has a unique band-gap energy. Electrons can pass through this energy barrier if they receive enough additional energy by the application of heat, an electric field or illumination.
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Electron
Empty conduction band
Ebg
hν Hole
Band-Gap
FIGURE 18.9 Band-gap energy between valence and conduction bands with photon absorption.
Filled Valence Band
PV materials rely on illumination for added energy to cause electrons to jump the band-gap. When a photon is absorbed by the material and an electron jumps the gap to the conduction band, leaving a vacant hole in the valance band, an electronhole pair is formed (Figure 18.9). (For convenience, holes in PV device physics are considered positively charged carrier particles, when in reality they are simply the absence of an electron.) This requires Ebg of the PV material to be equal to or less than that of an incoming photon (Eγ) given by the relation: Ebg 5 Ev 2 Ec # Eγ 5 hv 5
hc λ
(18.4)
where h is the Planck’s constant, υ is the photon frequency, c is the speed of light and λ is the photon wavelength. Semiconductor materials have band-gap energies between 0.5 and 3.0 eV, well-suited to match the solar spectrum of wavelengths between 0.4 and 2.5 µm. Refer to the solar spectrum in Figure 18.1 to understand the sunlight intensity at these wavelengths. Silicon and gallium arsenide, two semiconductors commonly used as PV materials, have band-gap energies of 1.12 and 1.40 eV, respectively.
18.3.2 Doping and pn Junctions In order to increase the likelihood of electrons crossing the band-gap, it is possible to create materials with a high number of free, unbound electrons and holes. Free electrons only require added energy equal to that of the material Ebg, without the necessary energy to break molecular bonds. The process of adding electrons or holes to a material is known as doping. Silicon, for example, is a Group IV element and must be doped with an acceptor Group III element to gain extra holes or a donor Group V element to gain extra electrons. Common acceptor and donor elements for silicon are Boron and Phosphorus, respectively. Acceptor-doped materials are called p-type materials because their excess holes result in a net positive charge. Alternately, donor-doped materials are called n-type materials due to their net negative charge.
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18.3 PV PHYSICS
hν
++++ – – – – – ++++ – – – – – ++++ – – – – – n ++++ – – – – – ++++ – – – – – ++++ – – – – – ++++ – – – – – ++++ – – – – – ++++ – – – – – ++++ – – – – –
393
p
I
FIGURE 18.10 PV pn junction with electric circuit and current direction shown. Courtesy of Dr. Raymond Kostuk, Department of Electrical and Computer Engineering, University of Arizona.
The excess charges of doping agents effectively lessen the band-gap of their parent material (i.e. silicon). p-type and n-type materials placed next to each other will cause holes and electrons to jump to the other type with the lowered band-gap rather than jumping into their own higher band-gap. PV devices are designed so that the p-type and n-type materials exist between an electrical circuit to capture this flow of charges in the form of electric current. An image of a PV pn junction is shown in Figure 18.10. In Figure 18.10 incoming photons excite free electrons in the n-type material and jump the lowered band-gap into the ptype material. They are picked up by the circuit and carried to the load as electric current before returning across the circuit to the n-type material. By convention, current is in the opposite direction of electron flow.
18.3.3 PV Cell Responsivity A PV device’s ability to effectively convert solar radiation to electric current is described by external quantum efficiency (EQE, ηext) and spectral response (SR). EQE is a measure of how well the PV cell converts incident light to current, including all losses, defined as: ηext 5
Isc Iph
(18.5)
Iph is the maximum possible photocurrent, assuming all photons incident upon the cell create electronhole pairs with an energy greater than the band-gap energy of the PV material. Figure 18.11 shows the ideal and practical EQE relationship expected at all wavelengths. A key design feature of solar cells is that their highest quantum efficiency increases in the most prevalent wavelength of the solar spectrum. Most PV cells have a reduced response in the visible blue and red due to front-surface recombination and back surface passivation of long wavelengths,
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FIGURE 18.11
ηext
Ideal and practical EQE of a PV cell.
Ideal EQE 1 Practical EQE
λG
λ
Responsivity/A·W–1
FIGURE 18.12 Ideal spectral responsivity of a PV cell at all wavelengths until band-gap wavelength (λg). Courtesy of Dr. Kostuk.
Wavelength
λg
respectively. The difference between unity and the maximum plateaued region shown in Figure 18.11 is due to reflected optical losses [3]. The SR of a cell describes the output short-circuit current as a function of the incident photon wavelength, described by: SR 5
Isc λ
(18.6)
All cells have a characteristic SR curve. This unique SR can be related to the EQE by: q SR 5 η (18.7) Eλ ext given the following assumptions: 1. All incident photons with energies exceeding the material band-gap energy produce electronhole pairs. 2. All electronhole pairs are efficiently separated within the pn junction and electrons exit the cell as short-circuit current. Figure 18.12 shows the ideal SR based on the wavelength for a PV device.
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18.4 PV CELL DESIGN PV material production is a legacy of the silicon-based microelectronics industry. Materials used for PVs (e.g. Si of 106 purity) do not require the same purity as those used for microelectronics (e.g. Si of 109 purity), and the industry has thus developed less expensive ways to create PV cells. Each material has a unique production technique. In general, the more efficient materials cost more to produce than the less efficient.
18.4.1 Silicon Cell Manufacturing Briefly, the steps to manufacture silicon solar modules include mining quartz, producing silicon from quartz, melting silicon and p-type dopant to produce desired crystalline structure, slicing solidified PV material into wafers, polishing and lapping the wafers, doping wafers with n-type material, applying electrical contacts and finally encapsulating cells with all other materials into a complete module. The commonly used Czochralski (Cz) method of pulling single silicon crystals was first developed by the microelectronics industry. Higher efficiency monocrystalline silicon cells can be grown using the Float Zone production method, but this method is currently too expensive for commercial production of solar cells and is only used in the laboratory. Silicon and the chosen p-type dopant (boron usually) are melted in a large crucible and slowly drawn out of the crucible to cool. The resulting ingot is sawed to form circular wafers. The saws used were the same thickness of the resulting cell, resulting in a loss of 50 % of the silicon material. Square cell profiles allow for better use of space when enclosing cells into a module, requiring an additional loss of material when cutting from a circles to a square. In order to avoid such high losses of silicon, ribbon casting processes for cutting silicon have become popular. This cutting technique also allows for thinner silicon wafers, decreasing the wafer thickness from around 300 µm to less than 100 µm. There are two main processes for multi-crystalline silicon: the slower Bridgman technique and the faster, more controlled block-casting technique. Multi-crystalline silicon is more easily created by pouring molten silicon into a cast of any desired shape (rectangular) and allowing the silicon to cool. As the silicon cools it will solidify from the bottom up and a columnar crystal forms. Less silicon is lost in this process. Although faster and less expensive, the solidification of the multicrystalline silicon introduces grain boundaries and dislocations within the material which lower cell efficiencies [10].
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18.4.2 Texturing and Optical Reflection PV manufacturers employ many techniques to increase the amount of light incident on PV cells. Cell manufacturers will texture the front surface of cells representing inverted pyramids to increase the surface area of the cell and to trap more photons. These pyramids will be lined with an anti-reflection (AR) coating to increase light transfer. Module manufacturers also use coatings that decrease the optical reflection on the surface of the glass. Current AR coatings can decrease the front-surface reflection of glass by 10 %. Some system owners are beginning to use anti-soiling coatings on the front surface of their modules to further increase incident light.
18.4.3 Electrical Contacts The electrical contacts on a PV cell appear as metal grid lines. They do not cover more than 10 % of the front surface. Contacts are required to transport charge carriers (electrons) from the cell to the electrical circuit. Usually the n-type contact and the p-type contact will be placed on opposite sides of the cell (one front and one back). Contacts can introduce series resistance losses and shade small portions of the cell. Some manufacturers are finding ways to print both contact types on the back side of cells to avoid shading losses. Contacts can be applied using photolithography and evaporation, screen printing and laser-grooved buried lines.
18.5 FIELD PERFORMANCE PV systems are designed for ideal performance at standard test conditions (STCs). In the United States STC is defined as operation at 1000 W m22 incident irradiation, 25 C operating cell temperature and 1.5 AMs. Every PV module has nameplate ratings reported for maximum power, current and voltage at STC. Outdoor performance metrics are different from those used for ideal design conditions. No PV device performs ideally under real conditions. PV systems will behave differently based on the climates in which they are performing. Outdoor operating conditions will affect the real-time output and the long-term performance of the system. PVs perform best in cold, dry and sunny conditions.
18.5.1 Power Production Curves The power output of a PV system is proportional to the amount of irradiance incident on the system throughout the day. Daily power
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18.5 FIELD PERFORMANCE
Power output of 2 PV technologies in same location Fixed, Flat-plate Dual-axis tracking, HCPV 20
Power / kW
15
10
5
0 6:00 a.m. 2012-01-12
12:00 p.m.
6:00 p.m.
12:00 a.m. 2012-01-13
6:00 a.m.
12:00 p.m.
6:00 p.m.
FIGURE 18.13 Daily power production for a fixed, flat plate system (20 kWp) and a dual-axis, high concentrating system (10 kWp) on two days one cloudy (left) and one sunny (right).
production curves on two days one sunny and one cloudy are shown in Figure 18.13 for a fixed-tilt system and a dual-axis, concentrating system. The fixed-tilt system is representative of the sun’s apparent path in the sky. The system generates power from sunrise to sunset. The maximum power of the fixed-tilt system is found at solar noon, when the sun is directly overhead. The tracking system curve has a flattened top at maximum power because it is able to maximise incident irradiance all day. On the cloudy day, fluctuations in power show how power production is limited when the modules are in the shadow of a cloud. Shadows on fixed-tilt systems will result in power loss of (8090) %, where concentrating systems will experience a complete power loss. Fixed-tilt systems are able to make use of indirect, diffuse sunlight (accounting for (1020) % of power production) and concentrating systems are only able to use direct sunlight. The power output of a PV system also has a characteristic annual curve, as shown in Figure 18.14 for a fixed-tilt system. Based on the tilt and revolution of the earth, the sun is directly perpendicular to a location’s latitude during the fall and spring equinoxes 20 higher (North for the Northern hemisphere and South for the Southern hemisphere) on the summer solstice and 20 lower on the winter solstice. To maximise annual production, most large fixed-tilt installations are oriented towards the equator at location latitude. In this setup, performance peaks during the summer and fall equinoxes, when the sun is directly perpendicular to the system angle. Although the days are longer in the summer, the angle of the sun during the summer limits PV
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6
4 2 0 1/1/2006
1/1/2007
1/1/2008
1/1/2009
FIGURE 18.14 AC energy (kW h) every day for 4 years, normalised to the system’s STC (kWp) rating. Low points are from cloudy days. The black curve is a prediction based on clear skies, a solar position algorithm, a temperature coefficient of efficiency and 0.5 % degradation per year. Courtesy of Dr. Alexander D. Cronin, Department of Physics, University of Arizona.
performance, just like in the winter. In very hot conditions, like the Southwestern United States, summer performance will be additionally reduced due to hot operating conditions. Like all electronics, PV systems have lower efficiency in the heat than in the cold.
18.5.2 Performance Parameters Several performance parameters are used to compare PV systems of different sizes and technologies. Otherwise, there would be no context for comparing the power production of one system with the power production of a different system in another location. A common performance metric is system AC efficiency (ηac). Like module efficiencies reported by PV manufacturers, system AC efficiency is a measure of how well the PV system converts irradiance to electricity. System AC efficiency will be lower than module efficiency and system DC efficiency because it includes the cumulative efficiencies of every module, wiring resistance and balance of system component. System AC efficiency is calculated as: ηac 5
kW h Hpoa A
(18.8)
using the system AC energy production (kW h), system module surface area (A) and the measured plane of array irradiance during operation (Hpoa). Common system efficiencies for residential systems using crystalline silicon modules are around 15 %. Another common performance metric is final yield (Yf), which normalises the system’s AC energy production based on its STC-rated power production (kWp):
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Fixed, flat-plate energy production
Dual-axis, HCPV energy production Dual-axis, HCPV final yield
140
12
120
10
100
8
80 6 60 4 40 2
20 0 2012-03-11
Final Yield (kW h/kWp)
Energy production
Fixed, flat-plate final yield
0 2012-03-21
2012-03-31
2012-04-10
2012-04-20
FIGURE 18.15 Daily energy output (solid lines) and final yield (dotted lines) for two systems for several weeks. Notice that Yf for the dual-axis tracker is greater than that of the flat-plate system even though the latter has a higher energy yield.
Yf 5
kW h kWp
(18.9)
Final yield is often reported as an annual metric, averaging all values over an entire year, but can be reported as daily or monthly metrics. Figure 18.15 shows a comparison between AC energy production and the final yield for several systems. The final yield is more indicative of system performance than energy production because it compares systems of different technologies in the same location. The performance ratio metric is able to compare different technologies in different locations. The performance ratio (PR) simply normalises the final yield of a system by the irradiance experienced by the system during rating and during output operation: PR 5 Yf 3
Gpoa Hpoa
(18.10)
where Gpoa is the reference irradiance from the rating standard. PR is often reported as a single value averaged for an entire year of data.
18.5.3 Estimating Field Performance As explained, systems in the field will not perform as designed every day of the year. Field power output can be estimated simply by considering the irradiance incident on the system location and angle. This requires knowledge of historical irradiance at the site and a correlation
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of solar angles and system orientation. Once irradiance is known it can be multiplied by the anticipated system efficiency. PV array efficiency is negatively affected by the age and degradation of the array, any soiling or shading present and heat losses in the PV wiring. Each of these conditions causes a derating of the system efficiency and is assigned an individual derate factor based on the percentage of power loss. These values are multiplied to find a single-system derate factor. The National Renewable Energy Laboratory (NREL) created a derate factor calculator as part of their PVWatts tool [5]. The derating conditions and associated factors from NREL PVWatts are given in Table 18.1. The system derate factor can be multiplied by the module nameplate DC efficiency to estimate the system AC efficiency. This method of predicting system performance can be further complicated by understanding how operating temperature affects current and voltage. Translation equations relate field performance to performance under STCs. There are many different translation equations of varying accuracy and complication, but the most basic equation uses temperature coefficients. Temperature coefficients define how the associated parameter changes based on a single-degree increase in temperature. They are usually reported by module manufacturers. The two equations below relate current and voltage at STC to field operation (subscript m): i Gpoa h αIsc ISTC 5 Im 3 3 ðT 2 25 CÞ 3 12 (18.11) Hpoa 100 TABLE 18.1 PV System Derate Factors [5]. Component Derate Factor
PVWatts Default
Derate Factor Range
PV module nameplate DC rating
0.95
0.801.05
Inverter and transformer efficiency
0.92
0.880.98
Mismatch in module operating power
0.98
0.9700.995
Diodes and connections resistance
0.995
0.9900.997
DC wiring resistance
0.98
0.970.99
AC wiring resistance
0.99
0.9800.993
Soiling
0.95
0.3000.995
System availability
0.98
0.0000.995
Shading
1.00
0.001.00
Sun-tracking accuracy
1.00
0.951.00
Age and degradation
1.00
0.701.00
System derate factor
0.77
0.000.99
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18.6 BARRIERS TO GROWTH
β VSTC 5 Vm 3 1 2 Voc 3 ðT 2 25 CÞ 100
401
(18.12)
where αIsc and β Voc are the manufacturer-reported temperature coefficients for short-circuit current and open-circuit voltage, respectively.
18.5.4 Degradation and Failure Modes All PV systems experience degradation due to age. This irreversible damage can be subtle, with minor power losses over many years, or can result from a catastrophic event that significantly reduces the power output in an instant. The specific conditions modules endure when they experience degradation are known as failure modes. Common failure modes experienced by all modules are broken interconnects, broken cells, broken glass, corrosion, delamination and loss of elastomeric properties of encapsulant, encapsulant discoloration, soldier bond failures, hot spots, ground faults, junction box and module connection failures, structural failures, bypass diode failures and arcing. Failure modes like corrosion result in subtle degradation and modes like arcing result in catastrophic damage. Each geographical location will see different modes specific to the type of weathering experienced in the area. All modes have associated characteristic voltage and/or current losses. Most degradation is subtle. PV manufacturers currently guarantee that their modules will perform at least 80 % of their nameplate power rating after 25 years. Slow degradation is best quantified by comparing the system’s nameplate efficiency (η0) to its operating efficiency (ηi) after a certain number of years (N). This is known as the degradation rate (D): η 2 ηi D5 0 =N (18.13) η0 PV materials have different degradation rates. Crystalline silicon usually degrades at a rate of 0.5 % per year, while thin film materials degrade rapidly ( 2.0 %) in the first year of operation and then stabilise to a degradation rate of 0.4 % per year.
18.6 BARRIERS TO GROWTH The PV module industry has experienced exponential growth every year for the last two decades [10]. Module and balance of system technologies have since proven that the hardware is reliable. Now the industry is facing barriers to integrating PV systems with the electric grid. The intermittent nature of PV energy presents problems on grid systems
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designed around dispatchable fossil fuel energy sources. The grid cannot yet tolerate fast fluctuations in voltage that industrial scale PV plants experience when shadowed rapidly by passing clouds. Utility companies managing power on the grid are expected to provide consistent available power to their customers, regardless of changes in supply. Reserve energy is necessary to provide this constant electricity, and energy storage options are not yet financially competitive. Utility-scale PV facilities are just now reaching grid parity with fossil fuel energy sources. The United States Department of Energy Quadrennial Technology Review summarizes five risks that PV energy imposes on utility grid operations [7]: 1. impacts on voltage and current flows, voltage regulation, reactive power flow and system protection, 2. integrating variable and uncertain solar generation into grid operations and planning, 3. unfamiliarity of grid operators with PV system designs and their operating characteristics, 4. inadequate accounting of capacity and energy valuation from variable renewable energy and energy storage technologies in traditional utility rates and costing methods, 5. risk and uncertainty surrounding predicting the availability of solar resource on a small time and spatial scale.
18.6.1 Grid Integration No energy generation plant is available all the time. Conventional generating plants are interrupted by unexpected breakdowns and scheduled maintenance. The amount of time a generator is available is known as the capacity factor. The capacity factor quantifies the amount of time a generator was available to produce energy for a given year versus what it is rated to produce. The capacity factor of fossil fuel generator is between 85 % and 90 % [1]. The solar resource is naturally intermittent, with interruptions at night and due to passing clouds. This causes PV generating facilities to have an additionally lower capacity factor of nearly 20 % [11]. A larger rated solar PV facility must be built to equal a conventional plant. Predicting intermittency of the solar resource is among the challenges we must overcome in order for solar energy to become a large contributor to our energy supply. Utility companies are cautious to adopt solar energy at the industrial scale because cloud cover causes unpredictable fluctuations in irradiance that result in grid instability. Quickly moving clouds can cause solar electric power loss or gain of 20 % per second. Utilities could control the inverters of solar electric
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403
fields to match the tolerable ramp rate as long as incoming cloud cover is predicted. Until solar power intermittency becomes predictable and dispatchable, utilities will continue to overproduce electricity and keep reserves of fossil fuels on hand. Gowrisankaran et al. [12] calculate that having fully dispatchable solar power will result in a PV energy cost of 38 % the current intermittent power source . Intermittency can be mitigated with a combination of energy storage, spinning reserves and demand response. All of these techniques require the ability to forecast the intermittent solar resource in each geographical location utilising solar power. Day-ahead forecasts are useful for pricing within the energy market. Hour-ahead forecasts are necessary for grid operators to manage and schedule spinning reserves. It is vital to store energy in anticipation of when demand exceeds supply, such as at night or during periods of cloudy weather. Stored energy with quick response times can help utilities provide electricity when supply is not available, smooth out intermittent energy variations and readjust seasonal variations in production to match demand load. Energy can be stored as chemical energy (e.g. batteries), electrical energy (e.g. supercapacitors), thermal energy (e.g. steam) and mechanical energy (e.g. pumped hydropower and compressed air storage). Chemical batteries are currently the most common method for storing energy, but they are expensive and unsustainable. Pumped hydropower, which has been used in commercial applications, is more economical and environmentally sustainable. Improvements are being made in all other mentioned energy storage methods.
18.6.2 Expense Historically, the cost of PV energy has been a large barrier to high penetration. The industry has now matured to a point where solar is becoming cost-effective. On average, for every doubling of PV production capacity worldwide, the cost of solar has reduced 20 % [7]. Comparing the levelised cost of energy (LCOE) of different energy production techniques allows for equal comparison of differing technologies. The LCOE is defined as the total lifecycle cost of a facility compared to the amount of energy it is expected to produce. NREL predicts PV energy will cost $0.124 (kW h)21 in locations with a high solar resource by 2016 [13]. In these areas residential solar electric energy has already reached grid parity with conventional energy sources at certain times of the year [7]. In areas with a lower solar resource, energy generated by PVs currently costs twice that produced by fossil fuels. Given continued rapid improvements within the industry, this is expected to become equal to or less than the cost of fossil fuel energy by 2050 [1].
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The cost of PV systems is no longer dominated by the cost of modules as was once the case. Now, the cost of modules is only (1525) % of the total PV system cost. By the end of 2011, crystalline silicon modules cost as low as $1.05 W21 and thin film modules cost $0.85 W21[7]. Other system costs include procurement, balance of systems costs, installation labour and taxes [11]. The industry now recognises the need to improve accompanying power electronics, more thoroughly train installers, and streamline the permitting process in order to decrease costs further. Within the next few decades the industry expects to provide energy at a cost less than fossil fuels without government subsidies or incentives.
References [1] L. Freris, D. Infield, Renewable Energy in Power Systems, Wiley, West Sussex, UK, 2008. [2] U.S. Energy Information Administration, Office of Energy Statistics, U.S. Department of Energy. Monthly Energy Review. December 12, 2012. Washington, DC, U.S. Document No. DOE/EIA-0035(2012/12). p. 92. [3] C. Honsberg, S. Bowden, Photovoltaic Education Network, 2013. ,http://www.pveducation.org. (Accessed 01.05.13). [4] Arizona Solar Center, 2013 ,http://www.azsolarcenter.org/images/articles/az/solmap.gif. (accessed 20.09.13). [5] NREL PVWatts Calculator, 2012. ,http://rredc.nrel.gov/solar/calculators/ pvwatts/version1/. (accessed 20.09.12). [6] J. Perlin. The Silicon Cell Turns 50. National Renewable Energy Laboratory. August 2004. NREL Report No. BR-520-33947. [7] US Department of Energy, Quadrennial Technology Review: Technology Assessments, 2012 (Prepublication copy, accessed 29.06.12). [8] National Renewable Energy Laboratory, U.S. Department of Energy. Best ResearchCell Efficiencies. September 2012. (Most recent version of chart can be found at ,http://www.nrel.gov/ncpv/images/efficiency_chart.jpg/.). [9] J. Nelson, The Physics of Solar Cells, Imperial College Press, London, UK, 2003. [10] A. Luque, S. Hegedus, The Handbook of Photovoltaic Science and Engineering, Wiley, West Sussex, UK, 2003. [11] G.F. Nemet, E. Baker, Demand subsidies versus R&D: comparing the uncertain impacts of policy on a pre-commercial low-carbon energy technology, Energy J. 30 (2009) 4980. [12] G. Gowrisankaran, S.S. Reynolds, M. Samano, Intermittency and the Value of Renewable Energy, NBER Working Paper No. w17086, 2011. [13] M. Woodhouse, et al., An economic analysis of photovoltaics versus traditional energy sources: where are we now and where might we be in the near future?, Proceedings of the IEEE Photovoltaics Specialists Conference, 2011.
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