Product operator formalism

2013-09-03T16:15:17Z

137.122.61.28: I have added that this method is a simplification of the complete theory, the density matrix, which was not clear in the previous article.

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[[File:Energy and fluid flow in a solar turbine power plant.jpg|400px|thumb|Figure 1. Energy and fluid flow in a solar turbine power plant]]
A '''solar turbine power plant''' uses the energy in solar radiation captured by so-called [[Solar thermal collector|solar collector]]s. Solar power is a renewable source of energy. The solar radiant energy reaching the earth's surface is around 1.783*1014 KJ or 1.353kJ/s per square meter. Solar power plants, such as the [[Blythe Solar Power Project]], operate mainly on closed power cycles: [[Rankine cycle]]s (for low temperature ranges) and [[Brayton cycle]]s (for high temperature ranges). Solar plants provide energy ranging from a few kilowatts to a few megawatts. The constraints associated with solar plants are size, space, high capital cost, and the inevitable fluctuations in the daily supply of solar radiant energy.

==Efficiency==
===Concentration ratio===
[[File:Variation of Receiver temperature to Concentration Ratio.jpg|300px|thumb|Figure 2. Receiver temperature as related to concentration ratio]]
The concentration ratio is the ratio of the area of the concentrator to the area of the receiver surface. The amount of solar energy incident on the concentrator is directed towards the receiver, so the ratio is a measure of the energy concentrated towards the receiver.<ref name = sukhatme>{{cite book|title=Solar Energy: Principles of Thermal Collection and Storage|first=Suhas P.|last=Sukhatme|first2=J. K.|last2=Nayak|edition=3|isbn=978-0070142961|year=2008|publisher=McGraw-Hill}}</ref>{{rp|210}}

Higher concentration ratio values can be attained by using large apertures and small receiver. Receiver temperature increases with the increase in concentration ratio, as shown in Figure 2. Concentration ratios vary from 1.5 to 3000 depending on the type of collector, i.e., whether it is a medium- or high-temperature collector. This is an important parameter in determining the efficiency of a solar plant.

<math>{CR}={{aperture\,area\,of\,concentrator}\over{receiver\,surface\,area}} = {Ac\over Ar}</math>

===Optical efficiency===
[[File:Variation of Collector efficiency (%) with Temperature ratio.jpg|300px|thumb|Figure 3. Variation of collector efficiency (%) with temperature ratio]]
The optical efficiency of a solar collector relates the percentage of the solar rays penetrating the transparent cover of the collector (transmission) and the percentage being absorbed.

<math>{\eta_0}={{heat\,energy\,received\,by\,the\,receiver}\over{incident\,radiation\,on\,the\,collector}} = {Qr\over Qc}</math>

Where <math>{Q_c} = {I_c} . {A_c}</math>

<math>{I_c} =</math> incident solar radiation

Therefore, <math>{Q_r} = {\eta_o}.. {I_c} . {A_c}</math>

===Collector efficiency===
There are three types of solar collectors: low (100°C),<ref name=Yahya>{{cite book|title=Turbines, Compressors and Fans|first=S. M.|last=Yahya|edition=3|isbn=978-0070597709|year=2005|publisher=[[Tata McGraw-Hill]]}}</ref>{{rp|699}} medium (300-400°C),<ref name=Yahya />{{rp|701}} and high (400-700°C)<ref name=Yahya />{{rp|706}} temperature collectors. Each type has its own efficiency.

<math>{\eta_c} = {{useful\,heat\,received\,by\,the\,coolant}\over{incident\,radiation\,on\,the\,collector}} = {Qu\over Qc}</math>

<math>{Q_u}={Q_r}-{L}={Q_r}-{Losses}</math>

The losses can be expressed by the overall co-efficient <math>{U}</math> based on receiver area

<math>{L} = {U}.{Ar}.({Tr}-{Ta})</math>

<math>{Q_u}={\eta_0}.{Ic}.{Ac}-{U}.{Ar}.({Tr}-{Ta})</math>

<math>{\eta_c}={\eta_0}-({1\over{cr}}).{{U\,Ta\,}\over{Ic}}.({{Tr}\over{Ta}}-{1})</math>

<math>{\eta_c}=</math> f(CR,TR)

where TR is the receiver temperature ratio. TR increases with the concentration ratio, as shown in Figure 2. Collector efficiency decreases with the temperature ratio, as shown in Figure 3.

==Solar receiver==
[[File:A Heliostat and External receiver.jpg|300px|thumb|Figure 4. A heliostat and external receiver]]
[[File:A cavity of solar radiation receiver.jpg|300px|thumb|Figure 5. A heliostat and external receiver]]
[[File:A tubular collector receiver.jpg|300px|thumb|Figure 6. A tubular collector receiver]]
The receiver absorbs heat transmitted by the collector. Sometimes the receiver is an integral part of the system, for example, in solar ponds and flat plate collectors. Receivers may be stationary or portable.

There are three types of receivers: external, tubular, and cavity.

===External receivers===
A working fluid is provided on the external surface of a vertical body (Figure 4).

Major losses are due to:
* Non-focusing
* [[Thermal conduction|Conduction]], [[convection]], and [[radiation]]
* [[Mirror|Reflection]]

Concentration ratio and fluid temperature attained are 1000 and 500°C, respectively.<ref name=Yahya />{{rp|709}}

===Cavity receivers===
Heat flux enters through the apertures as shown in Figure 5; concentrators transmit the heat flux to the surface of coolant tubes through the apertures. Heat energy is transferred to other parts (where the direct beam is unable to reach) through [[Total internal reflection|internal reflection]]. Overall size is large due to the number of coolant tubes.

===Tubular receivers===
This consists of a row of coaxial tubes. The outer tube receives the radiation, whereas the working fluid enters through the inner tube and leaves through the annular space between the tubes (Figure 6). Concentration ratio and maximum fluid temperature attained are around 1.5 and 200°C, respectively.<ref name=Yahya />{{rp|710}}

==Receiver system==
[[File:Distributed Receiver System.jpg|thumb|Figure 7. Distributed receiver system]]

===Distributed receiver system===
In this system the three collectors (as shown in Figure 7) collect the heat flux and transfer it to receiver from where the coolant takes this energy to the heat exchanger (Path A). The coolant at times serves the purpose of working fluid, as depicted by Path B.

===Central receiver system===
In this system, the solar collectors transmit the heat flux to a receiver which is large in size. External and cavity types of receivers can be employed for this purpose. Example: [[heliostat]]s.

==Net efficiency==
[[File:Variation of Collector efficiencies with Receiver temperature.jpg|300px|thumb|Figure 8. Variation of collector efficiencies with receiver temperature]]
The collector efficiency (ɳc) decreases with increases in receiver temperature. The thermal efficiency (ɳth) increases with increases in the inlet temperature of the working fluid. Therefore, overall plant efficiency (ɳn) varies, as shown in Figure 8. The net efficiency is between 15% and 20%.<ref name=Yahya />{{rp|725}}. The curve is flat at maximum efficiency.

==Solar energy storage==
Since solar radiation is not always available, it becomes necessary to store the energy in some form. [[Solar thermal energy]] storage can be done in:

# Solids: Some rocks absorb heat. The amount of energy stored depends on the mass of the solid material, its specific heat, and the allowable temperature rise.
# Liquids: If the heat is stored below the boiling point of fluids at ambient pressure then some fluids can be used as heat storage media. Some liquids which can be used for this purpose are [[Sodium#Heat transfer|Sodium]], [[Methylcyclopentadienyl manganese tricarbonyl|Hitec]], [[Polychlorinated biphenyl|Therminol]], and oils.
# Latent heat of fusion: In this type of system a solid is heated until it melts. Thus heat is stored in the body at constant temperature in the form of latent heat. Examples LiF (latent heat = 1050 kJ/Kg melting point = 848°C) and LiOH (latent heat = 1080 kJ/Kg melting point =471°C).<ref name=Yahya />{{rp|717}}
# A combination of any of the above approaches can also be used to store solar energy.

==Solar turbines==
The performance of the coolants, working fluid, and steam or gas turbines together determine the efficiency of the plant.

===Coolants and working fluids===
A coolant absorbs energy in the receiver and transfers the energy to the working fluid in the heat exchanger. Example water/steam, liquid metals, molten salts, gases and oils.

Water can be used as coolants in low and medium temperature solar power plants.

The maximum temperature deployed in an oil type of coolant is 250°C.<ref name=Yahya />{{rp|717}} Oil can be dangerous because it is inflammable. It is also relatively costly.

Gases that can be used as coolants are air, helium, argon, and carbon dioxide. They can be used for high temperature ranges (Tmax=800°C).<ref name=Yahya />{{rp|717}}

Molten salts are also used for high temperature regions. They have high specific heat.

Molten metals (sodium or aluminium) can also be used as coolants. Since their density is high they require a smaller receiver.

steam, freon, or helium are some of gases used as working fluids.

===Steam turbines===
[[Steam turbine]]s operate on a [[Rankine cycle]].<ref name = cengel>{{cite book|title=Thermodynamics: An Engineering Approach |first=Yunus|last=Çengel|last2=Boles|first2=Michael|edition=7|year=2011|publisher=[[McGraw-Hill]]|isbn=978-0073529325}}</ref> Steam can be generated by a receiver directly from the solar heat flux, which eliminates the need for a heat exchanger. However, some plants deploy molten salts to attain higher temperatures, which eliminates the need for steam boilers. Values of pressure and temperature in solar plants are 50-100 bar and 400-500°C, respectively. Both impulse and reaction stages can be used. For small values of power, impulse stages are preferable.

===Gas turbine===
[[Gas turbine]]s operate on a [[Brayton cycle]], that is, with inlet temperatures around 500-800°C.<ref name = cengel /> A conventional gas turbine power plant uses a combustion chamber, but here the combustion chamber is the receiver/heat exchanger. However, using a gas solar turbine power plants with stored thermal energy is quite difficult because the power plant operates at a high temperature range and it is quite difficult to store heat energy at this high temperature. Gas turbines use fewer stages, do not require feed water heaters or condensers and have a low cooling requirement.

==Advantages and disadvantages==

===Advantages===
* Being a renewable form of energy, the fuel is free and surplus
* No fuel storage, processing or handling equipment is required
* Being an alternative form of energy saves of oil/petrol/diesel resources
* Less environmental pollution
* Can be operated in remote areas or places which are unfit for habitation

===Disadvantages===
* Reliable power generation (dependence on weather)
* Large amount of area required for its establishment
* High capital cost
* Overall efficiency is low

==See also==
* [[Concentrated solar power]]
* [[List of concentrating solar thermal power companies]]
* [[List of solar thermal power stations]]

== References ==
{{reflist}}

==Further reading==
* {{cite book|series=Solar Thermal Central Receiver Systems|volume=3|title=Performance Evaluation Standards for Solar Central Receivers|editor-last=Carasso|editor-first=Meir|editor2-last=Becker|editor2-first=Manfred|isbn=9783540532705|year=1990|publisher=[[Springer Science+Business Media|Springer-Verlag]]}}
* {{cite book|title=Solar Power Plants: Fundamentals, Technology, Systems, Economics|first=Carl-Jochen|last=Winter|first2=Rudolf L.|last2=Sizmann|isbn=978-0387188973|year=1991|publisher=Springer-Verlag}}
* {{cite journal|url=http://www.wired.com/science/planetearth/news/2005/11/69528|title=Huge Solar Plants Bloom in Desert|work=[[Wired (magazine)|Wired]]|first=Will|last=Wade|date=15 November 2005|accessdate=20 May 2012}}

{{Solar energy}}
{{Renewable energy by country}}

[[Category:Solar power stations]]
[[Category:Solar thermal energy]]

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Product operator formalism