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Electrical Modelling and Simulation of Solar Power Towers
Electrical Modelling and Simulation of Solar Power Towers Daniel Queluz *, Rui Castro *;** J. Farinha Mendes *** * Instituto Superior Técnico / Technical University of Lisbon (IST/TUL), Portugal (e-mail: [email protected]) ** Centre for Innovation in Electrical and Energy Engineering (Cie3), Portugal (e-mail: [email protected]) *** Instituto Nacional de Engenharia, Tecnologia e Inovação (INETI), IP, Portugal (e-mail: [email protected]) Abstract: Photovoltaic installations seem more adequate to small sized widespread production than to large scale production in power plants. Portugal, namely the southern part, is worldwide known by its sunlight. Therefore, an alternative to use sun power as a source to produce electrical energy in relatively large power plants is the novel technology known as solar power towers. In this paper, an integrated model of the overall production system is presented. Using some available data concerning the solar irradiation in two sites, (one with high irradiation and other with low irradiation) a case study is built. Some simulations of the steady-state behavior of the overall solar power tower system installed in both sites are also presented and some conclusions regarding the electrical performance of such systems are drawn. Keywords: Electrical Energy, Solar Power Towers, Concentrated Solar Power. 1. INTRODUCTION The incorporation of renewable sources in the electricity production has increased in the last years, following the European Union directives based mainly in environmental concerns. Nowadays, a great number of wind generators, gathered in the popular wind farms, are included in the landscape of the European countries. Recent figures indicate that some 4% of the electricity demand is provided by wind power. As far as PhotoVoltaic (PV) power is concerned, the situation is quite different. High investment costs and low production rates lead to high production costs, which explain the scarce dissemination of this renewable source as a form of large scale electrical power production. Under these circumstances, the governments are encouraging the installation of small urban PV units (usually in the roofs of the buildings), typically sized in the range of some kW, in the framework of the so called microgeneration. Portugal is worldwide known as being one of the European countries with more solar radiation along the year. Taking benefit of the national generous feed-in tariffs, large scale PV power plants are being built in Portugal and other European countries. However, the efficiency of the available solar cells technology in the market is still low and therefore this technology is not the best choice for large scale production in large grid connected power plants. This explains why it is required the development and implementation of other solutions, still based on the usage of the sun as primary source of energy, but taking profit of its thermal conversion, to be used in a Rankine cycle. These new solar technologies lay usually under the common designation
of Concentrated Solar Power (CSP). Examples of CSP systems are Parabolic Trough Systems, Parabolic Dish Systems and Power Tower Systems. This paper deals with the later of those innovative methods to produce energy from the sun: the solar power towers. The process of generating electrical energy in a solar power tower can be briefly described as follows. It begins by concentrating the solar radiation in a receiver mounted in the top of a tower. This is achieved through the use of a large field of sun tracking mirrors, called heliostats, forming the collector field. Also, two thermal tanks do exist: one “cold”, that is full of working fluid in the beginning of the process, and another, the “hot” one, which is used to store the working fluid after being heated in the receiver. The heated fluid, usually molten salt, is then pumped to a steam generation system where super-heated steam is produced. The steam activates a conventional turbine working in a Rankine cycle. Electricity is eventually produced in an electrical generator. Finally, the molten salt returns to the “cold” tank and the process reinitiates. The working fluid, molten salt, is a key issue in the process. It is used due to its chemical properties that allow it to stay “hot” for many hours, therefore, storing energy for that period of time. In this way, electricity production can be performed either when it is most needed, namely at peak hours, or even at night. Solar power tower systems already exist either in demonstration or commercial phases. For instance in Spain, the PS10 installation is the first tower in the world commercially delivering electricity as reported by Osuna, R. et al. (2000). It began operation in March, 2007, running a conventional power cycle with a capacity of 11 MW. As can
be seen in Ortega, J.I. (2008) and Martin, J.C. (2007), another Spanish installation, SOLAR TRES, will shortly be the first demonstration plant at commercial scale, based on a molten salt receiver. This technology was successfully tested at the SOLAR TWO experimental plant, which operated for three years in the USA. SOLAR TRES will have an installed capacity of 17 MW with the added capability of 15 hours storage, giving an estimated operating time of 6500 hours / year. A great number of references regarding the project description of existing demonstration and commercial solar power tower projects and technology comparison assessment can be found in the literature, for instance, Mills, D. (2004), Tsoutsos, T. et al. (2003), Romero, M. et al. (2002), Kribus, A. et al. (1998), Buck, R. et al. (2002). However, the literature is scarce in what concerns the electrical behaviour of such systems. In this paper the modelling and the electrical performance simulation of a solar power tower system are assessed. To serve as a case-study for the application of the developed methodologies and simulations, two Portuguese sites were selected based on its different rates of solar radiation. Some conclusions regarding the behaviour of the overall system, from an electrical point of view, are drawn.
where ω is the hour angle in degrees and ts is the solar time in hours. The solar time, ts, equals 12 h when the sun reaches the highest point in the sky during the day. As far as the declination angle is concerned, it can be calculated by: sin δ = 0,39795 cos[0,98563(N − 173)] (2) In (2) δ is the declination angle and N is the day’s number of the year (since January, 1st). Some other important angles require a definition, namely because they are used to establish the mirrors’ orientation of the collector field that maximize the amount of collected radiation. Those angles are represented in Fig.2 and are as follows: • α is the solar altitude angle defined as the angle between the central ray from the sun and an horizontal plane containing the observer; φ is the local latitude. • θz is the zenith angle, the complement of the solar altitude angle. • A is the azimuth angle that represents the angle, measured clockwise on the horizontal plane, from the northpointing coordinate axis to the projection of the sun’s central ray; A’ is just an auxiliary variable to calculate A.
2. SYSTEM COMPONENTS MODELLING 2.1 Solar Geometry Basics When assessing a solar system like the one under study the definition of the main angles that rule the solar orientation is required. This paragraph follows Stine, W. et al. (2001). To begin with, two angles are of interest: the hour angle, which is used to describe the earth’s rotation about its polar axis, and the angle that takes account of the inclination of the polar axis, the declination angle. Both angles are shown in Fig.1.
Fig.2. Solar altitude, zenith and azimuth angles The above mentioned angles can be calculated by the following equations: Fig.1. Hour and declination angles An expression used to calculate the hour angle from solar is: ω = 15(t s − 12)
(1)
α = sin −1 (sin δ sin φ + cos δ cos ω cos φ)
(3)
θ z = 90º −α
(4)
⎛ − cos δ sin ω ⎞ A' = sin −1 ⎜ ⎟ cos α ⎝ ⎠
(5)
The angle A is evaluated by (6) taking (5) into consideration, through: tan δ ⇒ A = 180º − A' tan φ tan δ cos ω < ⇒ A = 360º + A' tan φ cos ω ≥
(6)
where Pinc is the incident radiation on the heliostats and Pabs is the radiation that reaches the receiver mounted on the top of the tower. 2.3 Receiver System
2.2 Collector Field
The receiver, mounted on the top of the tower, is responsible for the transfer of the energy, collected by the heliostats, to the working fluid. Pacheco, J.E., (editor) (2002) was followed in this paragraph.
The collector field is formed by a large field of two-axis tracking mirrors, called heliostats.
The rate of ‘useful’ energy leaving the absorber (in W) may be written as:
The heliostats will surround the tower and their orientation changes along the day with the sun’s position. In order to be able to determine the orientation of each heliostat along the day, it is useful to look at Fig.3. This figure enables a better understanding of the different variables involved: sun’s position, tower’s position and relative heliostat’s position. Refer to Stine, W. et al. (2001) for more details.
Q useful = m c p (Tout − Tin )
(10)
where m is the mass flow rate of heat transfer fluid (kg/s), cp is the specific heat of heat transfer fluid (J/kg.K) and Tin and Tout are the temperatures (K) of the heat transfer fluid entering and leaving the absorber, respectively. Likewise the collector field, there are losses associated with the energy transfer process. These losses are related with convection, radiation and conduction losses. The efficiency of the receiver system can be determined by: η rec =
Pfluid Pabs
(11)
In (11) Pabs is the radiation that reaches the receiver and Pfluid is the radiation that is transferred to the working fluid. Fig.3. Coordinates defining the reflection of the sun’s rays by a heliostat to a single aim point
2.4 Thermal Storage System
As can be seen in Fig.3, the two axis of the heliostat are controlled by two angles: the heliostat altitude αH and the heliostat azimuth AH. To predict these angles as a function of the sun’s position, the following equations are used.
The thermal storage system is composed by two thermal tanks, a “cold” one and a “hot” one, and the working fluid, which is a mixture of 60% sodium nitrate (NaNO3) and 40% potassium nitrate (KNO3). Therefore, it can be considered as a salt. This salt has a nominal working temperature of 565º. Due to its chemical properties, it can be stored with a high efficiency: it can stay “hot” for about one day, if properly stored.
sin α H =
R z + sin α 2 cos θ i
R + cos α sin A sin AH = e 2 cos θ i cos α H cos 2θi = Rz sin α + Re cos α sin A + Rn cos α cos A
(7)
(8)
In (7) and (8), Rz, Re and Rn are the components along the z, e and n axis, respectively, of a unit vector pointing from the reflector toward the aim point (R), and θi is the incidence angle of the sun’s rays on the heliostat. Although the mirrors are sun-tracking, there is always some power lost in the collector field. These losses are represented by an efficiency given by: η field =
Pabs Pinc
(9)
Some salt’s characteristics change as a function of the temperature. When assessing a system like the one under consideration, at least two of those characteristics must be taken into account: the salt density (ρ) and specific heat (cp) (T is the salt temperature), as reported by Pacheco, J.E., (editor) (2002): ρ = 2090 − 0,636T c p = 1443 + 0,172T
(12)
At the beginning of a typical day the salt is in the “cold” tank at 290º. When the sun rises and enough energy reaches the receiver, the salt is pumped and heated to a temperature of 565º. After being heated, the salt is stored in the “hot” tank and ready to be used on the steam generation system. Then, it returns to the “cold” tank and the cycle is reinitiated.
2.5 Electric Power Generation System The electric power generation system is essentially composed by two components: the steam generation system (SGS) and the turbine/generator system. Sonntag, R. et al. (2003) was an important input in this topic. The main objective of the SGS is to create super-heated steam using the “hot” salt that passes through the heat exchangers levels. In order to maximize the efficiency of the system, three different heat exchangers are normally used: preheater, vaporizer and superheater. The amount of super-heated steam generated depends on the temperature and mass flow rate of the salt that passes through the steam generator: m w (h2 − h1 ) = m h c p (Tc − Td ) = Q pre m w (h3 − h2 ) = m h c p (Tb − Tc ) = Q eva
(13)
In (16) Ppmec are the mechanical losses, Ppel are the electrical losses on the generator and on the transformer and Paux are the losses associated with the auxiliary services of the power plant. 3. CASE-STUDY RESULTS AND DISCUSSION Based on the models presented in the previous section and on the results of Pacheco, J.E., (editor) (2002), a dedicated solar power tower system simulator was conceived and implemented. Details of this tool can be found in Queluz, D. (2007). The main parameters of the simulator are presented in Appendix A. Data regarding the solar irradiation in two Portuguese cities, site A, located in the southern part and site B, located in the northern part, are available. For testing purposes, 3 days in the winter and 3 days in the summer were selected. Fig.4 and Fig.5 show the solar irradiation for the above mentioned seasonal periods for the two sites.
m w (h4 − h3 ) = m h c p (Ta − Tb ) = Q sup
where m w and m h are the mass flow rates of engine working fluid (water) and heat-transfer fluid (salt), respectively, h represents enthalpies, T represents temperatures and cp is the heat-transfer fluid specific heat. In order to provide mechanical power to the generator, a steam turbine is used in the turbine/generator electrical generation system. The turbine operates under the wellknown Rankine cycle. We recall that a Rankine cycle is composed by the steam generator, the turbine, the condenser and the pump.
Fig.4. Radiation diagrams for site A in 3 days of the summer (left) and in 3 days of winter (right)
A simplified model for the four states of the Rankine cycle is given by: wT = h1 − h2 qout = h3 − h2
(14)
wP = h3 − h4 qin = h1 − h4
Fig.5. Radiation diagrams for site B in 3 days of the summer (left) and in 3 days of winter (right)
In (14) wT is the specific work provided by the turbine, qout is the energy transferred on the condenser, wP is the specific work provided to the pump and qin is the amount of energy transferred on the steam generator system.
Three operating modes of the solar tower power plant were selected for performance evaluation purposes.
It is also important to quantify the mechanical power of the turbine:
• Network charge synchronization operation mode
Pmec = m w (wT − wP
)
(15)
Finally, the electrical power available at the generator terminals is given by: Pel = Pmec − Ppmec − Ppel − Paux
(16)
• Nominal power operation mode • Continuous power operation mode
3.1 Nominal Power Operation Mode In this operation mode, the plant is generating power since it has enough “hot” salt stored to activate the SGS. The turbine is thereafter regulated to its nominal power and produces energy until there is no more “hot” salt available. The power output for this operation mode is shown in Fig.6 and Fig.7.
the off-peak hours. The obtained results are shown in Fig.10 and Fig.11.
Fig.6. Power output for the plant located at site A; 3 summer days (left) and in 3 winter days (right); nominal power operation mode
Fig.7. Power output for the plant located at site B; 3 summer days (left) and in 3 winter days (right); nominal power operation mode 3.2. Continuous Power Operation Mode In this case, the purpose is to operate the system as continuously as possible during the three days. So, by managing the “hot” salt stored and by reducing the power output, it is intended to generate power without interruptions. The results for this operation mode can be found in Fig.8 and Fig.9.
Fig.8. Power output for the plant located at site A; 3 summer days (left) and in 3 winter days (right); continuous power operation mode
Fig.9. Power output for the plant located at site B; 3 summer days (left) and in 3 winter days (right); continuous power operation mode 3.3 Network Load Curve Synchronization Operation Mode In this operation mode, the plant is operated so that it tries to follow the load curve of the network. Therefore, the objective is to produce more energy during the peak hours and less in
Fig.10. Power output for the plant located at site A; 3 summer days (left) and in 3 winter days (right); network load curve synchronization operation mode
Fig.11. Power output for the plant located at site B; 3 summer days (left) and in 3 winter days (right); network load curve synchronization operation mode 3.4 Discussion of the Results Some conclusions may be drawn from the analysis of the results presented. • Nominal power operation mode – In summer, about 115 MWh are produced per day, in each location. However, in winter days, much less energy is produced at site B than in site A, due to its lower solar radiation levels: for instance, site B only reaches 24.5 MWh against the 47.25 MWh of site A. • Continuous power operation mode – In summer, at site A, the plant worked continuously at 3.5 MW (for a plant nominal power of 10.5 MW) since 9 a.m. until the end of the third day. As far as site B is concerned, the operation was similar, the only difference being that operation started one hour later. In winter days, different results were obtained. Both plants located at site A and site B, could only be operated at 1 MW. However, in site A the plant started operation on the first day, whereas in site B the SGS was turned on at 10 a.m. of the second day. So, less energy was generated in site B again, as expected. • Network load curve synchronization operation mode – In summer days, the site A plant could be operated accordingly to the network demands, without any interruptions, whereas, in site B, an interruption from 4 a.m. until 9 a.m. of the second day was detected. In the winter, site B was, again, the worst result, producing energy only for a few hours on the night of the second day. Site A plant, however, produced energy in some periods of time but was able to synchronise with the network peak hours.
4. CONCLUSIONS This paper showed that the solar power towers can perform an important role in the future of solar technologies. The use of molten salt as the working fluid that can store energy for hours, enable this technology to produce electricity after the sunset, which is a significant advantage because electrical energy can be produced in pace with the load diagram. When compared to the conventional photovoltaic systems the energy from solar power towers is cheaper. The main reason for that can be found in the sun-tracking mirrors usage that increases the production a lot. However, when compared to other renewable technologies that are more developed, such as wind and small hydro systems, the solar power tower is not yet competitive. This happens essentially for two main reasons: the high price of the collector field (the heliostats are responsible for almost 50% of the initial investment) and the relatively low global efficiency of the system. This figure is about 18%, but can be improved to about 23% if, instead of using a single turbine in the Rankine cycle, a re-heated turbine is used.
Pacheco, J.E. (editor) (2002). Final test and evaluation results from the Solar Two project, Sandia National Laboratories. Queluz, D. (2007). Central de torre solar para produção de energia eléctrica: modelação e simulação do sistema em regime permanente, MSc Thesis, Technical University of Lisbon (in Portuguese). Romero, M., Buck, R., Pacheco, J.E. (2002). An update on solar central receiver systems, projects, and technologies, Transactions of the ASME, Vol. 124. Sonntag, R., Borgnakke, C., Van Wylen, G.J. (2003). Fundamentals of Thermodynamics, John Wiley & Sons, Sixth Edition. Stine, W., Geyer, M. (2001). Power from the Sun, online book available at http://www.powerfromthesun.net Tsoutsos, T., Gekas, V., Marketaki, K. (2003). Technical and economical evaluation of solar thermal power generation, Renewable Energy 28.
Appendix A. SIMULATOR PARAMETERS
REFERENCES Buck, R., Bräuning, T., Denk, T., Pfänder, M., Schwarzbözl, P. (2002). Solar-hybrid gas turbine-based power tower systems (REFOS), Journal of Solar Energy Engineering, Vol. 124, Issue 1. Kribus, A., Zaibel, R., Carey, D., Segal, A., Karni, J. (1998). A solar-driven combined cycle power plant, Solar Energy Vol. 62, No. 2. Martin, J.C. (2007). Solar Tres: First commercial molten salt central receiver plant, NREL CSP Technology Workshop, Denver. Mills, D. (2004). Advances in solar thermal electricity technology, Solar Energy 76. Ortega, J.I., Burgaleta, J.I., Téllez, F.M. (2008). Central receiver system solar power plant using molten salt as heat transfer fluid, Journal of Solar Energy Engineering, Vol. 130, Issue 2. Osuna, R., Fernández, V., Romero, M., Marcos, M.J. (2000). PS10: A 10 MW solar tower power plant for southern Spain, in “Energy 2000 – The beginning of a new millennium”, Peter Catania (editor), ENERGEX'2000 – Proceedings of the 8th International Energy Forum, Las Vegas.
Variable
Description
Value
Atotal
Total heliostats area
80 000 m2
η field
Collector field efficiency
0.7
Pmax
Maximum radiation supported by the receiver
42.2 MW
ηrec
Receiver efficiency
0.9
m salt ,max
Maximum mass flow rate of salt passing through the receiver
85 kg/s
cp
Salt specific heat
1540.18 J/kgºC
msalt ,total
Mass of salt available
1 400 000 kg
ηthermal
Thermal efficiency
≅1
msalt ,SGS m w ,max
Mass of “hot” salt needed to activate the SGS Maximum mass flow rate of steam in the Rankine cycle
wT
Turbine specific work
1 102.6 kJ/kg
Pelec ,max
Plant nominal power
10.5 MW
457 254.12 kg 10.5 kg/s
of Concentrated Solar Power (CSP). Examples of CSP systems are Parabolic Trough Systems, Parabolic Dish Systems and Power Tower Systems. This paper deals with the later of those innovative methods to produce energy from the sun: the solar power towers. The process of generating electrical energy in a solar power tower can be briefly described as follows. It begins by concentrating the solar radiation in a receiver mounted in the top of a tower. This is achieved through the use of a large field of sun tracking mirrors, called heliostats, forming the collector field. Also, two thermal tanks do exist: one “cold”, that is full of working fluid in the beginning of the process, and another, the “hot” one, which is used to store the working fluid after being heated in the receiver. The heated fluid, usually molten salt, is then pumped to a steam generation system where super-heated steam is produced. The steam activates a conventional turbine working in a Rankine cycle. Electricity is eventually produced in an electrical generator. Finally, the molten salt returns to the “cold” tank and the process reinitiates. The working fluid, molten salt, is a key issue in the process. It is used due to its chemical properties that allow it to stay “hot” for many hours, therefore, storing energy for that period of time. In this way, electricity production can be performed either when it is most needed, namely at peak hours, or even at night. Solar power tower systems already exist either in demonstration or commercial phases. For instance in Spain, the PS10 installation is the first tower in the world commercially delivering electricity as reported by Osuna, R. et al. (2000). It began operation in March, 2007, running a conventional power cycle with a capacity of 11 MW. As can
be seen in Ortega, J.I. (2008) and Martin, J.C. (2007), another Spanish installation, SOLAR TRES, will shortly be the first demonstration plant at commercial scale, based on a molten salt receiver. This technology was successfully tested at the SOLAR TWO experimental plant, which operated for three years in the USA. SOLAR TRES will have an installed capacity of 17 MW with the added capability of 15 hours storage, giving an estimated operating time of 6500 hours / year. A great number of references regarding the project description of existing demonstration and commercial solar power tower projects and technology comparison assessment can be found in the literature, for instance, Mills, D. (2004), Tsoutsos, T. et al. (2003), Romero, M. et al. (2002), Kribus, A. et al. (1998), Buck, R. et al. (2002). However, the literature is scarce in what concerns the electrical behaviour of such systems. In this paper the modelling and the electrical performance simulation of a solar power tower system are assessed. To serve as a case-study for the application of the developed methodologies and simulations, two Portuguese sites were selected based on its different rates of solar radiation. Some conclusions regarding the behaviour of the overall system, from an electrical point of view, are drawn.
where ω is the hour angle in degrees and ts is the solar time in hours. The solar time, ts, equals 12 h when the sun reaches the highest point in the sky during the day. As far as the declination angle is concerned, it can be calculated by: sin δ = 0,39795 cos[0,98563(N − 173)] (2) In (2) δ is the declination angle and N is the day’s number of the year (since January, 1st). Some other important angles require a definition, namely because they are used to establish the mirrors’ orientation of the collector field that maximize the amount of collected radiation. Those angles are represented in Fig.2 and are as follows: • α is the solar altitude angle defined as the angle between the central ray from the sun and an horizontal plane containing the observer; φ is the local latitude. • θz is the zenith angle, the complement of the solar altitude angle. • A is the azimuth angle that represents the angle, measured clockwise on the horizontal plane, from the northpointing coordinate axis to the projection of the sun’s central ray; A’ is just an auxiliary variable to calculate A.
2. SYSTEM COMPONENTS MODELLING 2.1 Solar Geometry Basics When assessing a solar system like the one under study the definition of the main angles that rule the solar orientation is required. This paragraph follows Stine, W. et al. (2001). To begin with, two angles are of interest: the hour angle, which is used to describe the earth’s rotation about its polar axis, and the angle that takes account of the inclination of the polar axis, the declination angle. Both angles are shown in Fig.1.
Fig.2. Solar altitude, zenith and azimuth angles The above mentioned angles can be calculated by the following equations: Fig.1. Hour and declination angles An expression used to calculate the hour angle from solar is: ω = 15(t s − 12)
(1)
α = sin −1 (sin δ sin φ + cos δ cos ω cos φ)
(3)
θ z = 90º −α
(4)
⎛ − cos δ sin ω ⎞ A' = sin −1 ⎜ ⎟ cos α ⎝ ⎠
(5)
The angle A is evaluated by (6) taking (5) into consideration, through: tan δ ⇒ A = 180º − A' tan φ tan δ cos ω < ⇒ A = 360º + A' tan φ cos ω ≥
(6)
where Pinc is the incident radiation on the heliostats and Pabs is the radiation that reaches the receiver mounted on the top of the tower. 2.3 Receiver System
2.2 Collector Field
The receiver, mounted on the top of the tower, is responsible for the transfer of the energy, collected by the heliostats, to the working fluid. Pacheco, J.E., (editor) (2002) was followed in this paragraph.
The collector field is formed by a large field of two-axis tracking mirrors, called heliostats.
The rate of ‘useful’ energy leaving the absorber (in W) may be written as:
The heliostats will surround the tower and their orientation changes along the day with the sun’s position. In order to be able to determine the orientation of each heliostat along the day, it is useful to look at Fig.3. This figure enables a better understanding of the different variables involved: sun’s position, tower’s position and relative heliostat’s position. Refer to Stine, W. et al. (2001) for more details.
Q useful = m c p (Tout − Tin )
(10)
where m is the mass flow rate of heat transfer fluid (kg/s), cp is the specific heat of heat transfer fluid (J/kg.K) and Tin and Tout are the temperatures (K) of the heat transfer fluid entering and leaving the absorber, respectively. Likewise the collector field, there are losses associated with the energy transfer process. These losses are related with convection, radiation and conduction losses. The efficiency of the receiver system can be determined by: η rec =
Pfluid Pabs
(11)
In (11) Pabs is the radiation that reaches the receiver and Pfluid is the radiation that is transferred to the working fluid. Fig.3. Coordinates defining the reflection of the sun’s rays by a heliostat to a single aim point
2.4 Thermal Storage System
As can be seen in Fig.3, the two axis of the heliostat are controlled by two angles: the heliostat altitude αH and the heliostat azimuth AH. To predict these angles as a function of the sun’s position, the following equations are used.
The thermal storage system is composed by two thermal tanks, a “cold” one and a “hot” one, and the working fluid, which is a mixture of 60% sodium nitrate (NaNO3) and 40% potassium nitrate (KNO3). Therefore, it can be considered as a salt. This salt has a nominal working temperature of 565º. Due to its chemical properties, it can be stored with a high efficiency: it can stay “hot” for about one day, if properly stored.
sin α H =
R z + sin α 2 cos θ i
R + cos α sin A sin AH = e 2 cos θ i cos α H cos 2θi = Rz sin α + Re cos α sin A + Rn cos α cos A
(7)
(8)
In (7) and (8), Rz, Re and Rn are the components along the z, e and n axis, respectively, of a unit vector pointing from the reflector toward the aim point (R), and θi is the incidence angle of the sun’s rays on the heliostat. Although the mirrors are sun-tracking, there is always some power lost in the collector field. These losses are represented by an efficiency given by: η field =
Pabs Pinc
(9)
Some salt’s characteristics change as a function of the temperature. When assessing a system like the one under consideration, at least two of those characteristics must be taken into account: the salt density (ρ) and specific heat (cp) (T is the salt temperature), as reported by Pacheco, J.E., (editor) (2002): ρ = 2090 − 0,636T c p = 1443 + 0,172T
(12)
At the beginning of a typical day the salt is in the “cold” tank at 290º. When the sun rises and enough energy reaches the receiver, the salt is pumped and heated to a temperature of 565º. After being heated, the salt is stored in the “hot” tank and ready to be used on the steam generation system. Then, it returns to the “cold” tank and the cycle is reinitiated.
2.5 Electric Power Generation System The electric power generation system is essentially composed by two components: the steam generation system (SGS) and the turbine/generator system. Sonntag, R. et al. (2003) was an important input in this topic. The main objective of the SGS is to create super-heated steam using the “hot” salt that passes through the heat exchangers levels. In order to maximize the efficiency of the system, three different heat exchangers are normally used: preheater, vaporizer and superheater. The amount of super-heated steam generated depends on the temperature and mass flow rate of the salt that passes through the steam generator: m w (h2 − h1 ) = m h c p (Tc − Td ) = Q pre m w (h3 − h2 ) = m h c p (Tb − Tc ) = Q eva
(13)
In (16) Ppmec are the mechanical losses, Ppel are the electrical losses on the generator and on the transformer and Paux are the losses associated with the auxiliary services of the power plant. 3. CASE-STUDY RESULTS AND DISCUSSION Based on the models presented in the previous section and on the results of Pacheco, J.E., (editor) (2002), a dedicated solar power tower system simulator was conceived and implemented. Details of this tool can be found in Queluz, D. (2007). The main parameters of the simulator are presented in Appendix A. Data regarding the solar irradiation in two Portuguese cities, site A, located in the southern part and site B, located in the northern part, are available. For testing purposes, 3 days in the winter and 3 days in the summer were selected. Fig.4 and Fig.5 show the solar irradiation for the above mentioned seasonal periods for the two sites.
m w (h4 − h3 ) = m h c p (Ta − Tb ) = Q sup
where m w and m h are the mass flow rates of engine working fluid (water) and heat-transfer fluid (salt), respectively, h represents enthalpies, T represents temperatures and cp is the heat-transfer fluid specific heat. In order to provide mechanical power to the generator, a steam turbine is used in the turbine/generator electrical generation system. The turbine operates under the wellknown Rankine cycle. We recall that a Rankine cycle is composed by the steam generator, the turbine, the condenser and the pump.
Fig.4. Radiation diagrams for site A in 3 days of the summer (left) and in 3 days of winter (right)
A simplified model for the four states of the Rankine cycle is given by: wT = h1 − h2 qout = h3 − h2
(14)
wP = h3 − h4 qin = h1 − h4
Fig.5. Radiation diagrams for site B in 3 days of the summer (left) and in 3 days of winter (right)
In (14) wT is the specific work provided by the turbine, qout is the energy transferred on the condenser, wP is the specific work provided to the pump and qin is the amount of energy transferred on the steam generator system.
Three operating modes of the solar tower power plant were selected for performance evaluation purposes.
It is also important to quantify the mechanical power of the turbine:
• Network charge synchronization operation mode
Pmec = m w (wT − wP
)
(15)
Finally, the electrical power available at the generator terminals is given by: Pel = Pmec − Ppmec − Ppel − Paux
(16)
• Nominal power operation mode • Continuous power operation mode
3.1 Nominal Power Operation Mode In this operation mode, the plant is generating power since it has enough “hot” salt stored to activate the SGS. The turbine is thereafter regulated to its nominal power and produces energy until there is no more “hot” salt available. The power output for this operation mode is shown in Fig.6 and Fig.7.
the off-peak hours. The obtained results are shown in Fig.10 and Fig.11.
Fig.6. Power output for the plant located at site A; 3 summer days (left) and in 3 winter days (right); nominal power operation mode
Fig.7. Power output for the plant located at site B; 3 summer days (left) and in 3 winter days (right); nominal power operation mode 3.2. Continuous Power Operation Mode In this case, the purpose is to operate the system as continuously as possible during the three days. So, by managing the “hot” salt stored and by reducing the power output, it is intended to generate power without interruptions. The results for this operation mode can be found in Fig.8 and Fig.9.
Fig.8. Power output for the plant located at site A; 3 summer days (left) and in 3 winter days (right); continuous power operation mode
Fig.9. Power output for the plant located at site B; 3 summer days (left) and in 3 winter days (right); continuous power operation mode 3.3 Network Load Curve Synchronization Operation Mode In this operation mode, the plant is operated so that it tries to follow the load curve of the network. Therefore, the objective is to produce more energy during the peak hours and less in
Fig.10. Power output for the plant located at site A; 3 summer days (left) and in 3 winter days (right); network load curve synchronization operation mode
Fig.11. Power output for the plant located at site B; 3 summer days (left) and in 3 winter days (right); network load curve synchronization operation mode 3.4 Discussion of the Results Some conclusions may be drawn from the analysis of the results presented. • Nominal power operation mode – In summer, about 115 MWh are produced per day, in each location. However, in winter days, much less energy is produced at site B than in site A, due to its lower solar radiation levels: for instance, site B only reaches 24.5 MWh against the 47.25 MWh of site A. • Continuous power operation mode – In summer, at site A, the plant worked continuously at 3.5 MW (for a plant nominal power of 10.5 MW) since 9 a.m. until the end of the third day. As far as site B is concerned, the operation was similar, the only difference being that operation started one hour later. In winter days, different results were obtained. Both plants located at site A and site B, could only be operated at 1 MW. However, in site A the plant started operation on the first day, whereas in site B the SGS was turned on at 10 a.m. of the second day. So, less energy was generated in site B again, as expected. • Network load curve synchronization operation mode – In summer days, the site A plant could be operated accordingly to the network demands, without any interruptions, whereas, in site B, an interruption from 4 a.m. until 9 a.m. of the second day was detected. In the winter, site B was, again, the worst result, producing energy only for a few hours on the night of the second day. Site A plant, however, produced energy in some periods of time but was able to synchronise with the network peak hours.
4. CONCLUSIONS This paper showed that the solar power towers can perform an important role in the future of solar technologies. The use of molten salt as the working fluid that can store energy for hours, enable this technology to produce electricity after the sunset, which is a significant advantage because electrical energy can be produced in pace with the load diagram. When compared to the conventional photovoltaic systems the energy from solar power towers is cheaper. The main reason for that can be found in the sun-tracking mirrors usage that increases the production a lot. However, when compared to other renewable technologies that are more developed, such as wind and small hydro systems, the solar power tower is not yet competitive. This happens essentially for two main reasons: the high price of the collector field (the heliostats are responsible for almost 50% of the initial investment) and the relatively low global efficiency of the system. This figure is about 18%, but can be improved to about 23% if, instead of using a single turbine in the Rankine cycle, a re-heated turbine is used.
Pacheco, J.E. (editor) (2002). Final test and evaluation results from the Solar Two project, Sandia National Laboratories. Queluz, D. (2007). Central de torre solar para produção de energia eléctrica: modelação e simulação do sistema em regime permanente, MSc Thesis, Technical University of Lisbon (in Portuguese). Romero, M., Buck, R., Pacheco, J.E. (2002). An update on solar central receiver systems, projects, and technologies, Transactions of the ASME, Vol. 124. Sonntag, R., Borgnakke, C., Van Wylen, G.J. (2003). Fundamentals of Thermodynamics, John Wiley & Sons, Sixth Edition. Stine, W., Geyer, M. (2001). Power from the Sun, online book available at http://www.powerfromthesun.net Tsoutsos, T., Gekas, V., Marketaki, K. (2003). Technical and economical evaluation of solar thermal power generation, Renewable Energy 28.
Appendix A. SIMULATOR PARAMETERS
REFERENCES Buck, R., Bräuning, T., Denk, T., Pfänder, M., Schwarzbözl, P. (2002). Solar-hybrid gas turbine-based power tower systems (REFOS), Journal of Solar Energy Engineering, Vol. 124, Issue 1. Kribus, A., Zaibel, R., Carey, D., Segal, A., Karni, J. (1998). A solar-driven combined cycle power plant, Solar Energy Vol. 62, No. 2. Martin, J.C. (2007). Solar Tres: First commercial molten salt central receiver plant, NREL CSP Technology Workshop, Denver. Mills, D. (2004). Advances in solar thermal electricity technology, Solar Energy 76. Ortega, J.I., Burgaleta, J.I., Téllez, F.M. (2008). Central receiver system solar power plant using molten salt as heat transfer fluid, Journal of Solar Energy Engineering, Vol. 130, Issue 2. Osuna, R., Fernández, V., Romero, M., Marcos, M.J. (2000). PS10: A 10 MW solar tower power plant for southern Spain, in “Energy 2000 – The beginning of a new millennium”, Peter Catania (editor), ENERGEX'2000 – Proceedings of the 8th International Energy Forum, Las Vegas.
Variable
Description
Value
Atotal
Total heliostats area
80 000 m2
η field
Collector field efficiency
0.7
Pmax
Maximum radiation supported by the receiver
42.2 MW
ηrec
Receiver efficiency
0.9
m salt ,max
Maximum mass flow rate of salt passing through the receiver
85 kg/s
cp
Salt specific heat
1540.18 J/kgºC
msalt ,total
Mass of salt available
1 400 000 kg
ηthermal
Thermal efficiency
≅1
msalt ,SGS m w ,max
Mass of “hot” salt needed to activate the SGS Maximum mass flow rate of steam in the Rankine cycle
wT
Turbine specific work
1 102.6 kJ/kg
Pelec ,max
Plant nominal power
10.5 MW
457 254.12 kg 10.5 kg/s