Exergoeconomic Analysis and Benchmark Receiver Technology

Exergoeconomic Analysis and Benchmark Receiver Technology
KTH Energy and
Environmental Technology
Exergoeconomic Analysis and Benchmark
of a Solar Power Tower with Open Air
Receiver Technology
DIPL.-ING. (FH) FELIX
UDO
ERTL
Master of Science Thesis
KTH School of Industrial Engineering and Management
Energy Technology EGI-2012-015MSC
Division of Applied Thermodynamics and Refrigeration
SE-100 44 STOCKHOLM
Master of Science Thesis EGI 2012: 015MSC
Exergoeconomic Analysis and
Benchmark of a Solar Power
Tower with Open Air Receiver
Technology
Felix Udo Ertl
Approved
Examiner
Supervisor
2012-03-20
Prof. Dr. Björn Palm
Prof. Dr. Nabil Kassem
Commissioner
Contact person
Thesis
This thesis has been written in conjunction with the German Aerospace Centre,
Deutsches Zentrum Für Luft- und Raumfahrt e.V. (DLR), at the Institute for Technical
Thermodynamics – Solar research and development, Cologne.
The thesis was examined by the Royal Institute of Technology, Kungliga Tekniska
Högskolan (KTH), Energy and Environmental Technology, Stockholm.
Academic Supervisor:
Prof. Dr. Nabil Kassem
Academic Examiner:
Prof. Dr. Björn Palm
Industrial Supervisors:
Dipl.-Ing. Peter Schwarzbözl
Abstract
Concentrating solar power (CSP) provides a promising answer for the rising energy
demand in emerging and developing countries as well as it can play a significant role for
industrialized countries to provide renewable energy on demand. The highly efficient
storage is the key component for CSP plants. Energy and exergoeconomic analysis are
conducted in this work revealing potential improvements of a young and promising solar
tower technology with open volumetric air receiver (OVR). Weaknesses and potential
improvements are detected in the air cycle and receiver, in particular the absorber
structure. The focus for improvements must further be on the cost reduction of the
heliostat field rather than on improving its efficiency. A benchmark shows higher
operation efficiencies for the parabolic trough system. This is because of the better
performance of transferring heat with the oil cycle, even though this heat transfer cycle
has obvious drawbacks, such as a large receiver area, lower temperatures and its
inertia. In solar operation mode without additional burner the levelized electricity costs
(LEC) are therefore 2.26 €cents lower for the trough system. The OVR tower, however,
has clear advantages with an auxiliary burner due to the good adaptivity into the system.
The LECs are then reduced to 14.48 €cents/kWh, which is 6.5 €cents less as for the
trough system with auxiliary burner. Significant improvements can be expected for the
OVR tower when a gas turbine is deployed.
Keywords: Concentrated solar power, CSP, central receiver, open volumetric air
receiver, power tower, thermal storage, solid bed storage, ceramic receiver, renewable
energy, solar tower Jülich
Acknowledgment
I would like to express my sincerest appreciation to Peter Schwarzbözl, of the
Institute for Technical Thermodynamics, Deutsches Zentrum für Luft- und Raumfahrt.
Without your sound advice, experienced insight and strong support throughout the
duration of this thesis work the accomplishments would not have been possible.
I would like to send my gratitude to Sweden and the KTH that I was able to study
such a valuable course there. Thanks to Prof. Dr. Nabil Kassem, my supervisor in the
department of Energy Technology at KTH. I heartedly thank you for your crucial
support for this thesis work as well as for the freedom which you offered me to
manage and decide on the direction of the project.
I want to thank with all my heart my dear parents, Arthur and Renate Ertl, the best
parents I could have had. You both have always believed in me and given a support
throughout my life. Father, I will always carry you in my heart. I know you will help me
in spirit when I am low.
Abbreviations
AC
Annual costs
CSP
Concentrated solar power
DLR
Deutsches Zentrum Für Luft- und Raumfahrt (German Aerospace Department)
DNI
Direct normal irradiation
ECOSTAR
European Concentrated Solar Thermal Road-Mapping
EES
Engineering equation solver
EIA
Energy Information Administration (US)
ECO
Economizer
HD
Hochdruck (high pressure)
HFLCAL
Heliostat field layout calculator
HRSG
Heat recovery steam generator
HTF
Heat transfer fluid
HTX
Heat exchanger
IAM
Incident angle modifier
IDR
Incident direct radiation
IEA
International Energy Agency
LCC
Life cycle cost
LEC
Levelized electricity cost
LHV
Lower heating value
MD
Mittlerer Druck (medium pressure)
MENA
Middle East and North Africa
ND
Niederdruck (low pressure)
NREL
National Renewable Energy Laboratory
NPV
Net present value
O&M
Operation and maintenance
OVR
Open volumetric receiver
PSA
Plataforma Solar de Almería
PT
Parabolic trough
PV
Photovoltaic
RRM
Revenue requirement method
SEGS
Solar Electric Generating System
SM
Solar multiple
TRR
Total revenue requirement
VDI
Verein Deutscher Ingenieure (Organization of German Engineers)
Contents
1. Introduction
1.1. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3. Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2. State of the Art
2.1. Classification of CSP Technology . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2. Overview of Existing Power Tower Technologies . . . . . . . . . . . . . . . . . . .
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3. Components of the Analyzed Plants
3.1. Parabolic Trough Power Plant . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1. The Solar Field Including Receiver . . . . . . . . . . . . . . . . . . .
3.1.2. Thermal Storage with Molten Salt . . . . . . . . . . . . . . . . . . . .
3.1.3. Power Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2. The Solar Power Tower with Open Volumetric Air Receiver (OVR) Technology
3.2.1. The Heliostat Field . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2. The Open Volumetric Receiver . . . . . . . . . . . . . . . . . . . . . .
3.2.3. The Solid Matter Thermal Storage . . . . . . . . . . . . . . . . . . . .
3.2.4. The Power Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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4. Methodology
4.1. Exergy Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1. Exergy . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2. Exergy Balance . . . . . . . . . . . . . . . . . . . . . . .
4.1.3. Exergy Destruction, Exergy Loss, and Exergetic Efficiency
4.2. Exergoeconomic Analysis . . . . . . . . . . . . . . . . . . . . .
4.2.1. Aggregation Level . . . . . . . . . . . . . . . . . . . . .
4.2.2. Thermoeconomic Variables for Component Evaluation . .
4.3. Thermoeconomic Evaluation . . . . . . . . . . . . . . . . . . . .
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6. Simulation Results and Evaluation
6.1. Exergy Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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5. Modelling and Simulation
5.1. Operation Strategy . . . . . . .
5.1.1. Location . . . . . . . .
5.1.2. Method of Operation . .
5.2. Power Plant Models . . . . . . .
5.2.1. Parabolic Trough Model
5.2.2. Solar Tower . . . . . . .
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i
Contents
6.1.1. Steady State Calculations . . . . . . . . . . . . . . . . . . . . .
6.1.2. Annual Performance Simulations . . . . . . . . . . . . . . . .
6.2. Exergoeconomic Analysis . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1. Cost Calculations . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2. Results and Evaluation of the Exergoeconomic Analysis . . . .
6.2.3. Optimizations and Modifications of the Solar Power Tower Plant
6.2.4. Annual Performance of the Optimized Systems . . . . . . . . .
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7. Discussion
7.1. Simulation in Ebsilon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2. Exergoeconomic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3. Cost Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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8. Conclusion
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9. Outlook
82
Bibliography
83
A. Appendix - Simulation Characteristics
A.1. Control Diagram . . . . . . . . . . . . . . . . . . . . . . . . . .
A.2. Power Plant Specifications . . . . . . . . . . . . . . . . . . . . .
A.3. Ebsilon Models . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.3.1. The Parabolic Trough Scheme of the Andasol Power Plant
A.3.2. The Open Volumetric Receiver Tower Scheme . . . . . .
A.4. Development of the Receiver and Solid Bed Storage for Ebsilon .
A.4.1. The Receiver . . . . . . . . . . . . . . . . . . . . . . . .
A.4.2. The Solid Bed Storage . . . . . . . . . . . . . . . . . . .
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85
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. 113
B. Appendix - Results
123
B.1. Steady State Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
B.2. Annual Performance Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
B.3. Exergoeconomic Results Ordered by Importance . . . . . . . . . . . . . . . . . . . 131
ii
List of Figures
1.1. Outlook of the annual electricity demand and generation in the EUMENA-region according to MED-CSP scenario. [Trieb, 2005] . . . . . . . . . . . . . . . . . . . . .
1.2. The Athene Scenario, predicting cost drop with increased installed capacity and power
generation. [ECOSTAR] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3. The Solar Tower Power Plant in Jülich is the first of its kind. . . . . . . . . . . . . .
3
4
2.1. The main types of concentrating solar power: (a) Solar Fresnel and (b) Parabolic
Trough with a linear receiver concept; (c) Solar Power Tower and (d) Solar Dish with
a central receiver concept [DLR] . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
3.1. Schematic illustration of a parabolic trough power plant with the energy flows over
the areas of the main components. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2. The SEGS power plant located in Kramer Junction in the Mojave desert of California.
[ECOSTAR] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3. (a) The Eurotrough collector (b) Receiver Tube . . . . . . . . . . . . . . . . . . . .
3.4. The solar angles in relation to the surface of the earth. A is the azimuth angle (here
also determined as γ) and θz is the zenith angle. [Powerfromthesun] . . . . . . . . .
3.5. Optical losses at the collector. Location: 30◦ north and 0◦ declination/ Date: September 23th. [Sokrates, 2004] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6. Optical losses at the collector. Location: 10◦ north and 0◦ declination/ Date: September 23th. [Sokrates, 2004] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7. Temperature characteristics of a solid matter storage. . . . . . . . . . . . . . . . . .
3.8. (a) A 100m2 glass-metal-heliostat with facets at the Plataforma Solar dè Almeria.
[Sandia, 2010] (b) A 50m2 SKI stretched-membrane heliostat.[Sandia, 2010] . . . .
3.9. Optical losses occurring in a heliostats’ solar field. . . . . . . . . . . . . . . . . . .
3.10. The receiver cubs are carried by a metal frame. The frame is cooled by the recycled
air flow (blue arrows) in order to withstand the high temperatures. (a) shows the
frontal view of the receiver in Jülich and (b) the three parts, absorber cubs, metal
frame structure and the hopper. Source: DLR . . . . . . . . . . . . . . . . . . . . .
3.11. The volumetric effect causes higher temperatures behind the entrance of the absorber
channels. Source: DLR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.12. Temperature characteristics of a solid matter storage. . . . . . . . . . . . . . . . . .
2
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4.1. The system can interact with its environment to generate work. The exergy of the
system describes the maximum potential work that can be generated until the system
and its environment are in equilibrium. [Bejan, 1996] . . . . . . . . . . . . . . . . .
4.2. The balance of all flows over a control volume at steady state. Tb is the temperature
at which heat transfer occurs.[Bejan, 1996] . . . . . . . . . . . . . . . . . . . . . .
24
5.1. Data flow for the simulation of the open volumetric receiver tower plant . . . . . . .
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iii
List of Figures
5.2.
5.3.
5.4.
5.5.
5.6.
5.7.
The simulation matrix gives an overview of the simulated power plant modifications.
Simplified operation mode of CSP plant with storage and auxiliary burner (solar hybrid).
The Ebsilon scheme for the parabolic trough power plant. . . . . . . . . . . . . . . .
The Ebsilon scheme for the open volumetric receiver tower. . . . . . . . . . . . . . .
The influence of the field losses depending on the incident angle. . . . . . . . . . . .
The receiver cubs are carried by a steel frame. The frame is cooled by the recycled air
flow (blue arrows in figure b) in order to withstand the high temperatures. Figure (a)
shows the Ebsilon model of the receiver split in functional parts. The numbers in the
model show which part they represent in the scheme in figure (b). Figure (b) pictures
the three parts, absorber cubs, metal frame structure and the hopper. . . . . . . . . .
5.8. The surface fitting tool diagram shows the accuracy of the polynomial equation in
comparison with the calculated results of the absorber efficiencies. The number 356
represents the inlet temperature of the absorber in Kelvin. eta is the absorber efficiency, T aus the outlet temperature and Ic the incident concentrated solar energy on
the absorber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.9. The diagram contains values for the K-value and the upper temperature difference
that have been calculated with the EES receiver model for various mass flows. The
polynomial equation calculated with Excel allows to adjust partial characteristics of
the parts in the Ebsilon model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.10. The air blower arrangement in the model is set up with a main blower and a storage
blower in parallel, where as the real system is set up with a receiver blower and a
boiler blower in series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1. Energy and exergy efficiencies of the solar power tower in comparison: (a) Solar
Only, (b) With Auxiliary Burner. The abbreviations are explained in the table 6.1. .
6.2. Energy and exergy efficiencies of the parabolic trough in comparison: (a) Solar
Only, (b) With Auxiliary Burner. The abbreviations are explained in the table 6.1. .
6.3. Energy losses of the main parts of the solar power tower in comparison on a logarithmic scale: (a) Solar Only - Energy Losses and (b) With Auxiliary Burner - Energy
Losses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4. Exergy destructions of the main parts of the solar power tower in comparison on
a logarithmic scale: (a) Solar Only - Exergy Destructions and (b) With Auxiliary
Burner - Exergy Destructions. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5. Energy losses of the main parts of the parabolic trough in comparison on a logarithmic scale: (a) Solar Only - Energy Losses and (b) With Auxiliary Burner - Energy
Losses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6. Exergy destructions of the main parts of the parabolic trough in comparison on a
logarithmic scale: (a) Solar Only - Exergy Destructions and (b) With Auxiliary
Burner - Exergy Destructions. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7. A Sankey diagram of the exergy flow of the air cycle of the solar power tower in
operation mode SE1. Other Sankey diagrams are attached in Appendix B.1. . . . . .
6.8. A Sankey diagram of the exergy flow in the thermal oil cycle in operation mode SE1
under full load. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.9. One day of the solar tower in operation with low solar insulation and an empty storage,
simulated with an auxiliary burner and without. . . . . . . . . . . . . . . . . . . . .
iv
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53
List of Figures
6.10. Comparison of the annual performance of the solar power tower with and without
auxiliary burner. The diagrams show the annual exergy efficiency (equal to the energy
efficiency) and exergy destruction of the main parts. . . . . . . . . . . . . . . . . . .
6.11. Cost distribution over the components of a Rankine cycle in a solar thermal power tower.
6.12. Cost distribution over the parts of the solar power tower (a) and the parabolic trough (c).
6.13. The gas burner configuration in the power plant scheme of the solar power tower (a)
and the parabolic trough (b). The brown pipes represent a gas air mixture, the fuel
pipe is pink and the thermal oil pipe is gray. . . . . . . . . . . . . . . . . . . . . . .
6.14. Overview of the different optimized systems for investigation. . . . . . . . . . . . .
6.15. A comparison of the annual exergy efficiencies of the solar tower and the parabolic
trough with and without a duct burner. . . . . . . . . . . . . . . . . . . . . . . . . .
6.16. The diagram shows the behavior of the power block in the morning of a typical summer. The storage is empty. Two configurations are displayed: The system supported
by a duct burner and the system in solar only mode. . . . . . . . . . . . . . . . . . .
6.18. Exergy efficiencies of operation modes with different HTF recovery factors with the
support of a duct burner. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.17. Overall exergy efficiencies of an annual performance simulation for the different configurations of the solar power tower in solar only operation. . . . . . . . . . . . . . .
6.19. Annual exergy destruction including exergy losses in the main parts of the solar power
tower for the different configurations. . . . . . . . . . . . . . . . . . . . . . . . . .
6.20. The cost rate of the annual exergy destruction C of the different configurations and
main parts in comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.21. The cost importance C+Z (cost rate + cost of components) of the different configurations and main parts in comparison. . . . . . . . . . . . . . . . . . . . . . . . . . .
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A.1.
A.2.
A.3.
A.4.
The logical control scheme for the csp plants simulated in this work. . . . . . . . . . 86
The Ebsilon scheme for the parabolic trough power plant. . . . . . . . . . . . . . . . 93
The Ebsilon scheme for the open volumetric receiver tower. . . . . . . . . . . . . . . 94
The diagram contains values for the K-value and the upper temperature difference
that have been calculated with the EES receiver model for various mass flows. The
polynomial equation calculated with Excel allows to adjust partial characteristics of
the parts in the Ebsilon model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
A.5. The component representing the collecting hopper in the Ebsilon model is considering
the heat losses that occur in the component. The condition under partial load is shown
in the diagram. The polynomial equation is used in the Ebsilon model. . . . . . . . . 112
A.6. The black curve represents the polynomial equation derived from the EES values.
Additionally, this diagram includes a comparison with the polynom of adjustment
suggested by Ebsilon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
B.1. A Sankey diagram of the exergy flow in the heat transfer unit of the solar power tower
in operation mode SE1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.2. A Sankey diagram of the exergy flow in the heat transfer unit of the solar power tower
in operation mode SNE3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.3. A Sankey diagram of the exergy flow in the power block of the solar power tower in
operation mode SE1 under full load. . . . . . . . . . . . . . . . . . . . . . . . . . .
B.4. Solar Only - Energy and exergy efficiencies of the solar power tower in comparison.
124
124
125
126
v
List of Figures
B.5. With Auxiliary Burner - Energy and exergy efficiencies of the solar power tower in
comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.6. Solar Only - Energy losses in comparison on a logarithmic scale. . . . . . . . . . .
B.7. With Auxiliary Burner - Energy losses in comparison on a logarithmic scale. . . . .
B.8. Solar Only - Exergy destruction in comparison on a logarithmic scale. . . . . . . . .
B.9. With Auxiliary Burner - Exergy destruction in comparison on a logarithmic scale. .
B.10. Overall exergy efficiencies of an annual performance simulation for the different configurations of the solar power tower in comparison. . . . . . . . . . . . . . . . . . .
B.11. Exergy destruction including exergy losses in the main parts of the solar power tower
for the different configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.12. The cost rate of exergy destruction C of the different configurations and main parts in
comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.13. The cost importance C+Z (cost rate + cost of components) of the different configurations and main parts in comparison. . . . . . . . . . . . . . . . . . . . . . . . . . .
vi
126
127
127
128
128
130
130
131
131
List of Tables
5.1. Characteristic weather data and geographic data of Seville, which has been used for
simulations. Source: DLR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2. Overview of the operation conditions. . . . . . . . . . . . . . . . . . . . . . . . . .
5.3. Results of the solar field calculations with HFLCAL. . . . . . . . . . . . . . . . . .
5.4. The four parameters show the goodness of fit of the polynomial equation in figure 5.8.
31
32
35
39
6.1. Table of abbreviations for the simulations of all characteristic operations of the solar
power tower. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2. Energy and Exergy analysis of the receiver unit in operation mode SE1. . . . . . . .
6.3. Energy and Exergy analysis of the steam turbine and the condenser unit in operation
mode SE1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4. Annual performance of the solar power tower and the parabolic trough with and without an auxiliary burner. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5. Cost Calculation OVR Solar Power Tower . . . . . . . . . . . . . . . . . . . . . . .
6.6. Cost Calculation Parabolic Trough . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7. Operation Cost and Total Revenue Requirement of the Solar Power Tower . . . . . .
6.8. Operation Cost and Total Revenue Requirement of the Parabolic Trough . . . . . . .
6.9. Detailed Cost Distribution of the OVR Solar Tower . . . . . . . . . . . . . . . . . .
6.10. LEC of the Power Tower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.11. LEC of the Parabolic Trough . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.12. Solar Tower, Solar Only, @DP: recycling of the air stream: 60%, concentrated solar
irradiation on the receiver: 500kW/m2 , pressure of the water pipe after first economizer: 1.5bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.13. Solar Tower, with Auxiliary Burner, @DP: recycling of the air stream: 60%, concentrated solar irradiation on the receiver: 500kW/m2 , pressure of the water pipe after
first economizer: 1.5bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.14. Parabolic Trough, Solar Only . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.15. Parabolic Trough, with Auxiliary Burner . . . . . . . . . . . . . . . . . . . . . .
67
69
70
A.1. Common specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.2. Solar Parabolic Trough specifications . . . . . . . . . . . . . . . . . . . . . . . . .
A.3. OVR Solar Power Tower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
88
91
43
49
51
52
56
57
59
59
63
64
64
66
B.1. Table of abbreviations for the simulations of all characteristic operations of the solar
power tower. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
B.2. Table of abbreviations for the annual performance simulations of the solar power tower.129
B.3. Solar Only Basis, recycling of the air stream: 60%, concentrated solar irradiation on
the receiver: 500kW/m2 , pressure of the water pipe after first economizer: 1.5bar. . . 132
B.4. Solar only, recycling of the air stream: 80%, concentrated solar irradiation on the
receiver: 500kW/m2 , pressure of the water pipe after first economizer: 1.5bar. . . . . 135
vii
List of Tables
B.5. Solar only, recycling of the air stream: 100%, concentrated solar irradiation on the
receiver: 500kW/m2 , pressure of the water pipe after first economizer: 1.5bar. . . . . 138
B.6. With auxiliary burner, recycling of the air stream: 60%, concentrated solar irradiation on the receiver: 500kW/m2 , pressure of the water pipe after first economizer:
1.5bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
B.7. With auxiliary burner, recycling of the air stream: 80%, concentrated solar irradiation
on the receiver: 500kW/m2 , pressure of the water pipe after first economizer: 1.5bar.
144
B.8. With auxiliary burner, recycling of the air stream: 100%, concentrated solar irradiation on the receiver: 500kW/m2 , pressure of the water pipe after first economizer:
1.5bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
B.9. Solar only, recycling of the air stream: 60%, concentrated solar irradiation on the
receiver: 550kW/m2 , pressure of the water pipe after first economizer: 1.5bar. . . . 150
B.10. Solar only, recycling of the air stream: 60%, concentrated solar irradiation on the
receiver: 600kW/m2 , pressure of the water pipe after first economizer: 1.5bar. . . . 153
B.11. Solar only, recycling of the air stream: 60%, concentrated solar irradiation on the
receiver: 500kW/m2 , pressure of the water pipe after first economizer: 3bar and
135◦ C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
B.12. Solar only, recycling of the air stream: 60%, concentrated solar irradiation on the
receiver: 500kW/m2 , pressure of the water pipe after first economizer: 3bar and
145◦ C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
B.13. Solar only, recycling of the air stream: 60%, concentrated solar irradiation on the
receiver: 500kW/m2 , pressure of the water pipe after first economizer: 3bar and
155◦ C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
1
1. Introduction
1.1. Background
Concentrating Solar Power (CSP) technology is experiencing a revival the recent years driven by an
increasing pressure on authorities due to the threat of global warming and the critical issue of energy
security as well as advanced development achievements in the field of CSP technology.
The Desertec Initiative that gained momentum by the Club of Rome and the DLR is an example of
the extensive potential of solar thermal power plants to meet a main share of the electricity demand in
the near future. A joint-venture between 12 companies founded in 2009, namely the Desertec Industrial Initiative GmbH (DII GmbH), is already elaborating and negotiating the political and economical
framework for an intercontinental grid tabbing the abundantly available renewable sources of energy
in the EUMENA (EUropean, Middle East and North Africa) region. The Desertec Initiative aims to
provide enough energy serving a substantial part of the energy demand of the MENA region and 15%
of Europe’s electricity demand from these energy sources by 2050 [DII]. The major source accounts
to the solar irradiation in the MENA countries, which can be considered as the ”fuel” for CSP plants
(see figure 1.1).
Figure 1.1.: Outlook of the annual electricity demand and generation in the EUMENA-region according
to MED-CSP scenario. [Trieb, 2005]
In 1985, the Solar Electric Generating System I (SEGS I) the first commercial CSP plant, located
in the Mojave desert in California, has been connected to the grid. It has a capacity of 13.8MWel
and is ever since generating electricity. Eight further parabolic trough systems with a larger capacity
followed the years after. All projects have been conducted by Luz International Limited. It was a
2
1.2. Motivation
great opportunity for the technology to prove its reliability and to become further developed.
Besides this early success story, which has been driven by the oil crises of the 70s, the cost of
the electricity generated by any CSP technology is still the major remaining barrier for a widespread
implementation. The electricity cost of solar thermal power plants is lying in the range of 15 - 20
centse/kWh today and is expected to drop to 5-7 centse/kWh according to the learning curve of the
Athene Study in figure 1.2. [ECOSTAR]
Figure 1.2.: The Athene Scenario, predicting cost drop with increased installed capacity and power
generation. [ECOSTAR]
Different ways can be followed in further technical development of CSP projects to induce a fast
and effective cost reductions:
• Upscaling of existing technology can reduce Operation and Maintenance (O&M) costs as well
as the component costs.
• New innovations relating technology and operational concepts.
• Understanding the complexity of the system and prioritizing the main cost drivers for a potential
cost reduction.
In this work all three methods are applied. The potential of cost reduction by upscaling the solar
tower with open air receiver relative to the Andasol parabolic trough power plant is investigated, new
concepts of the power block are examined, and an exergoeconomic analysis enables a prioritized
optimization of the solar tower.
1.2. Motivation
Solar thermal power plants use direct sunlight as an energy source with the aim of producing electricity
with a conventional power plant process. Solar tower power plants are based on the concentration
of direct solar radiation onto a solar receiver at the top of a tower using dual axis tracking mirrors
(heliostats). In the receiver up to 1000-fold concentrated solar energy is absorbed and as heat at a very
3
1. Introduction
high temperature level delivered to a heat transfer fluid (HTF). In the considered procedure ambient
air as heat transfer fluid is heated in a ceramic volumetric receiver to about 700◦ C. The hot air is
conducted to a heat recovery steam generator (HRSG) to drive a steam power process. Alternatively,
the hot air is passed through a fixed-bed storage to store the heat.
Figure 1.3.: The Solar Tower Power Plant in Jülich is the first of its kind.
The development is currently in the demonstration plant stage. This plant is placed in Jülich in
North Rhine-Westphalia in Germany with a capacity of 1.5MW electrical power generation. Kraftanlagen München, which develops this technology in collaboration with DLR, is planning to construct
the first exclusively commercial solar tower with open air receiver in Algeria. The plant will have an
upscaled capacity of presumably 15MW electrical output.
1.3. Objective
The performance and properties of the entire system as well as individual parts in an upscaled plant
are underlying various changes compared to the demonstration plant. In particular these parts and
subsystems that have greater impact on the overall performance should lie in the focus of development. Further, an optimization of the operational conditions of the power plant is stringent.
The objective of this thesis is to identify and analyze optimizing potentials of the upscaled system
and subsystems of a solar thermal power tower. Simulation models are developed to analyze and
optimize the overall system of the air receiver and the steam cycle.
Thereby, the following issues shall be addressed:
• A technical inside of the two concepts: the parabolic trough and the solar tower with open
volumetric receiver
• The maximum possible system efficiency for a 50MW power plant
• Optimal operation in the solar-only or hybrid operation
• Comparison with the parabolic trough system
• Investigation and evaluation of various improvements
4
2. State of the Art
2.1. Classification of CSP Technology
In solar thermal power technology, heat gained from concentrated solar irradiation is supplied to a
thermodynamic cycle process to generate electricity. There are four different types of solar thermal
power technology existing and under development. The solar fresnel, parabolic trough, solar power
tower, and the solar dish concepts are state of the art technology and already widely deployed (see
figure 2.1). All of them are also determined as concentrating solar power, because solar irradiation is
bundled by mirrors on a linear or punctual receiver.
(a)
(b)
(c)
(d)
Figure 2.1.: The main types of concentrating solar power: (a) Solar Fresnel and (b) Parabolic Trough
with a linear receiver concept; (c) Solar Power Tower and (d) Solar Dish with a central
receiver concept [DLR]
The solar tower has a concentration ratio of up to 1000 and the solar dish up to 2000, whereas the
fresnel and the parabolic trough system have a rather low concentration ratio of 40 and 90 respectively.
Higher concentration results in higher temperatures being absorbed at the receiver (see Eq. 2.1).
r
C
Tabs = TSun 4
(2.1)
Cmax
Tabs
TSun
C
Cmax
temperature at absorber
= 5760K, temperature of the sun surface
concentration ratio
= 46200, maximal concentration
[K]
[K]
[-]
[-]
Central receiver systems benefit from a higher concentrating factor with higher temperatures induced into the system. Power towers reach a temperature of 1100◦ C max. From a thermodynamic
5
2. State of the Art
point of view, higher temperatures have a significant advantage due to a greater possible overall efficiency according to the Carnot efficiency [Pitz-Paal, 2008]:
ηc = 1 −
Tmin
Tmax
(2.2)
However a high efficiency does not stringently mean lower electricity production costs, which are
the overall goal in the improvement and adaptivity of these technologies.
2.2. Overview of Existing Power Tower Technologies
As explained above central receiver systems have the highest potential for competitive electricity generation costs. However, none of the existing technologies has been proven as the leading technology
concept yet. An overview of the existing tower concepts is helping project developers to get an understanding about the wide field and the potential.
The concepts can be divided into 7 categories that are defined by the difference of at least one of
its main components, which are the concentrators, the receiver and the thermodynamic cycle. The
following pictures give a short introduction into the different technologies:
6
Pressurized Gas Receiver: The Solar Brayton
Tower concept integrates a pressurized air receiver and a pressurized solid media storage in
a Brayton cycle. The exhaust of the gas turbine
can be used for cogeneration. [Giuliano, 2010]
Pressurized Gas Receiver: The Solar Hybrid
Combined Cycle (SHCC) combines several
solar Brayton cycle towers with one Rankine
cycle. [Giuliano, 2010]
Pressurized Gas Receiver: The CO2 Gas
Tower comprises a cavity receiver with metal
tubes using CO2 as HTF and a Rankine cycle.
[Giuliano, 2010]
Open Volumetric Receiver: The Open Volumetric Receiver Tower is determined by its
receiver that heats up ambient air, which is
sucked through the ceramic receiver structure.
The thermodynamic process is a Rankine cycle.
2.2. Overview of Existing Power Tower Technologies
Direct Steam Receiver: The Direct Steam
Single Tower generates saturated or superheated steam directly in a tube receiver.
Direct Steam Receiver: The Direct Steam
Multiple Tower concept has multiple medium
size towers that are connected together to drive
one steam turbine.
Direct Steam Receiver: The Direct Steam eSolar concept is designed similar the multiple
tower concept, but its unique selling points are
mass produced components. Thus, mirrors and
towers are smaller and the concentrator field is
an uniformly distributed array.
Molten Salt Receiver: The Molten Salt Tower
is one of the earliest concepts with a circular
molten salt receiver. The molten salt is both
storage medium and HTF. [Giuliano, 2010]
Beam Down Concentrator: The Tokyo-Tech
Beam-Down Tower consists of a secondary
concentrator on top of the tower and a molten
salt receiver on ground level.
Beam Down Concentrator: The MultiPurpose Solar Tower is combining the beam
down with the direct steam concept. The
molten salt receiver on ground level functions
as a storage.
7
2. State of the Art
Solid Media Receiver: The Particle Tower;
Solid media particles are exposed to concentrated sunlight in the receiver. The particles heat air for a gas turbine in a direct heat exchanger and act as storage media.
[Giuliano, 2010]
Emerging Technology: Solar Tiles for CSP in
Cities; This concept allows to make use of existing building surfaces to concentrate sunlight
on one receiver. The solar tiles are integrated
in the building and self-powered.
8
Solid Media Receiver: The Graphite Tower;
A graphite block is the receiver and the thermal
storage. Besides the induced solar thermal energy, surplus electricity can be stored in form
of thermal energy.
3. Components of the Analyzed Plants
3.1. Parabolic Trough Power Plant
Parabolic trough power plants consist mainly out of four parts: The solar collector field, the auxiliary
burner, the thermal storage and the power block (see figure 3.1). The parabolic mirrors bundle the
solar irradiation up to 90 fold onto the linear receiver, in which the heat transfer fluid, a thermal oil, is
heated. Heat exchangers transfer the heat to the steam cycle of the power block. A detailed description
of its function is given in the following chapters.
Figure 3.1.: Schematic illustration of a parabolic trough power plant with the energy flows over the
areas of the main components.
This system relies already on a relatively long history of power generation with the first commercial
power plants being built from 1985 to 1991, namely the SEGS power plants I to IX in the US (see
figure 3.2). New power plants of this kind, like Andasol 1,2 and 3 in Spain, are still based on the same
system, because the technology has proven to be commercially ready. Therefore, it serves as a proper
basis for comparison in an exergoeconomic analysis with the solar tower technology.
9
3. Components of the Analyzed Plants
Figure 3.2.: The SEGS power plant located in Kramer Junction in the Mojave desert of California.
[ECOSTAR]
3.1.1. The Solar Field Including Receiver
Direct solar radiation is focused on a linear absorber tube located in the focal line of a parabolic mirror
reflector. The assembly is determined as solar collector. The solar field is arranged in parallel rows of
several solar collectors. Two rows are connected as one loop, through which synthetic thermal oil is
pumped to deliver heat to the steam cycle. The one axis tracking system follows the sun from sunrise
to sunset. A 50MWel power plant using Eurotrough collectors with a dimension of 6m aperture width
and 150m length has an effective field area of ca. 554 000m2 .
(a)
(b)
Figure 3.3.: (a) The Eurotrough collector (b) Receiver Tube
Field Losses
Geometrical losses, optical losses and thermal losses occur at the collector. These losses define the
field efficiency. Losses due to heating up of the collectors are not considered here. (see Eq.3.1).
[Sokrates, 2004]
ηf ield = ηgeo · ηopt · ηtherm
10
(3.1)
3.1. Parabolic Trough Power Plant
3.1.1.1. Geometrical Efficiency ηgeo
The geometrical efficiency is calculated with the quotient of the Incident Direct Radiation (IDR) on
the mirror of the collectors and the actual Direct Normal Irradiation (DNI) (see eq. 3.2).
ηgeo =
IDR
DN I
(3.2)
The DNI is the normal solar irradiance in Watt per square meter on the surface of the earth. The
IDR is the effective useful irradiation per square meter collector surface. There are several geometric
parameters that influence the effective irradiation (eq. 3.3):
IDR = ζCos · ζIAM · ζAV · ζEV · DN I
(3.3)
Losses included in the IDR are depending on the solar angles. The figure 3.4 shows the relation of the
angles for the following interpretations of the losses.
Figure 3.4.: The solar angles in relation to the surface of the earth. A is the azimuth angle (here also
determined as γ ) and θz is the zenith angle. [Powerfromthesun]
Cosine Losses ζCos :
As the solar collector tracking axis is always oriented to the south-north axis, the incident radiation is
not always perpendicular to the solar field. Just the part that is perpendicular can be reflected to the
absorber. The losses are described by the cosine effect:
ζCos = cosθ
(3.4)
Whereas, the angle of incidence θ is given by the equation 3.5 according to [Duffie, 1991]:
cosθ = cosβ · cosθZ + sinβ · sinθZ · cos(γC − γS )
β
θZ
angle of inclination between the collector area and the horizontal (=track angle)
zenith angle of the sun
(3.5)
[◦ ]
[◦ ]
11
3. Components of the Analyzed Plants
γS
γC
[◦ ]
azimuth direction angle of the sun,
γS = 0◦ for south, east positive, west negative
azimuth angle of the collector
[◦ ]
For collectors with an orientation from north to south it is:
γC = 90◦
γC = 270◦
for γS > 0◦
for γS < 0◦
The influence of the cosine effect becomes larger with increasing distance from the equator and it
is at its maximum at solar noon, when the sun is at azimuth γ = 180◦ (see figure 3.5).
Incident Angle Modifier Losses ζIAM :
The IAM incorporates the fact that the solar radiations are not exactly parallel due to the finite distance between earth and sun. So the reflection of the sun onto the receiver is not exactly circular and
its ellipsoidal form variates slightly with a changing incident angle θ. Thus, a part of the reflected
radiation is lost, because the size of the absorber is adjusted to the optimal reflection. An ideal circular reflection occurs for θ = 0. According to [Marco, 1995] the losses related with the IAM are
approximately calculated as follows:
ζIAM = cosθ · (1 + sin3 θ)
(3.6)
Shading Losses ζAV :
Parallel collectors shade each other if the sun is near the horizon. This effect depends on the track
angle (=transversal angle) of the parabolic collectors (see eq. 3.7) [Sokrates, 2004].
!
!
sinγ
A · sinβ tanα
R
R
· 1−
(3.7)
ζAV = 1 − 1 −
cosγ
cosγ
sinβ
sinβ L
A cosβ + tanα
A cosβ + tanα
R
A
L
γ
Distance of collector rows.
Height of collectors
Length of collector rows
relative azimuth of collectors (|γS − γC |)
[m]
[m]
[m]
[◦ ]
Optical End-losses ζEV :
End-losses are considered as the fraction of radiation at the end of a collector that doesn’t hit the
receiver tube. These losses occur at an incident angle θ greater or less than 0◦ , when the radiation
is reflected with an angle to the vertical axis of the collectors. Since collectors are arranged in rows,
the end-losses are diminished by the corresponding neighbor collector. End-losses are determined as
follows [Sokrates, 2004]:
|f · tanθsin|γS − γC ||
ζEV = 1 −
(3.8)
L
12
3.1. Parabolic Trough Power Plant
All optical losses occur related to the position of the sun varying during day and year and to the
distance of the location from the equator. The diagram 3.5 and the diagram 3.6 show the variation of
optical losses at different locations.
Figure 3.5.: Optical losses at the collector. Location: 30◦ north and 0◦ declination/ Date: September
23th. [Sokrates, 2004]
Figure 3.6.: Optical losses at the collector. Location: 10◦ north and 0◦ declination/ Date: September
23th. [Sokrates, 2004]
3.1.1.2. Optical Losses At Mirror And Receiver Tube ηopt
Just a fraction of the incident direct radiation is finally delivering heat to the absorber tube. Optical
losses of the components of the collector are the source of further losses (see eq. 3.9) [Sokrates, 2004].
2
· γ · τC · α = IDR · ηopt
q̇A = IDR · δ · ρ · τM
(3.9)
13
3. Components of the Analyzed Plants
δ
ρ
τM
γ
τC
α
Pollution factor; Pollution of the mirrors reduces the reflect-ability in average
about 2%: δ = 0.98
Reflection factor of the mirror; A full reflection is physically not possible: ρ = 0.93
Transmission factor of the mirror; The mirror glass covering the reflecting layer absorbs
a small portion of the incident and reflected radiation: τM = 0.99
Quality factor; It incorporates surface failures, due to manufacturing inaccuracy,
and misalignment of the mirror axis and absorber axis: γ = 0.90
Transmission factor of the cladding tube; Absorption occurs at the glass of the cladding
tube of the absorber: τC = 0.95
Absorption factor of the absorber tube; Radiation on the absorber tube is reflected and
lost. Surface coating, such as black chrome dioxide or a high selective layer of a metal
oxide ceramic basis improves the absorption to approximately α = 0.95.
[-]
[-]
[-]
[-]
[-]
[-]
3.1.1.3. Thermal Losses ηtherm
Additionally to transmission and absorption losses at the receiver tube, thermal losses through convection and subsequent thermal radiation from the absorber tube are significantly influencing the field
performance.
Losses Through Thermal Radiation q̇Em
According to [Kleemann, 1993] a simplifaction (see eq. 3.10) based on the thermal emission law of
a black body can be used to identify the thermal radiation losses of the receiver tube. Manufacturer
of receiver tubes have developed a selective metal-ceramic coating (Cermet) that facilitates a relative
good absorption at a low emission rate.
π·σ·ǫ 4
T − TC4
(3.10)
q̇Em =
C
σ
ǫ
C
T
TC
Boltzmann constant: σ = 5.67 · 10−8
Emission coefficient of the absorber tube; This factor provides the fraction of
the heat emitting related to a black body at same temperature. ǫ = 0.16
Concentration factor of the collector; For Eurotrough collectors is C=90
Mean temperature of the heat transfer fluid
Temperature of the the cladding tube: simplified as TC = Tambient + 37K
W
m2 K 4
[-]
[-]
[K]
[K]
A factor, that has significant influence on the emission and that is not directly related with the receiver tube, is the collector’s concentration factor of the isolation C. The new collector ”Eurotrough”
has reduced the influence of the radiation losses by providing a higher concentration rate of 90 compared to the ”LS2” collector with a concentration rate of 70. Collectors under development aim for
even higher concentration rates, such as the Helio-Trough and the Ultimate-Trough.
Convection Losses q̇Conv
Vacuum is implemented in the annular space between absorber tube and cladding tube so that convection is by approximation avoided. However, convection is occurring at the ends of the receiver, where
14
3.1. Parabolic Trough Power Plant
the cladding tube is mounted with an aluminum connection on the absorber tube (see figure 3.3):
q̇Conv =
U
Tamb
π·U
(T − TA mb)
C
heat loss coefficient; It is an empirically identified coefficient that takes all linear
losses into account in particular convection at the receiver tube and the insulated
pipes: U=2W/m2 K
Ambient temperature
(3.11)
W
m2 K
[K]
Forced convection as well as defocusing of collectors due to wind is not considered in this work.
3.1.2. Thermal Storage with Molten Salt
The ability of storing thermal energy in an efficient way, is seen as the most important asset of CSPplants to all other energy technologies of solar sources 1 . The thermal storage in a solar power plant
allows operation after sun set. It is a puffer during fluctuating sun irradiation caused by passing
clouds, for instance. Furthermore, it offers the advantage of highly dispatchable energy that enables
to generate electricity whenever the demand and thus the tariff of electricity is high. These advantages
add an important economic factor to the CSP plant that should be utilized to an optimal extent.
The three different physical principles of thermal storage:
• Sensible heat storage (SHS): direct and indirect
• Latent heat storage (LHS) using phase change materials (PCM)
• Thermo-chemical heat storage (TCHS) using the principle of chemical reactions
The two types of storages applied in the power plant designs of this work are both storing indirect
sensible heat. Thus, the sensible heat storage is depicted in the following:
A direct system is storing the heat transfer fluid, which is receiving solar heat in the receiver and
generating steam in the boiler, directly in a tank. This is implemented in the ”solar tres” demonstration plant in Andalusia in Spain, for instance, where a storage of 6,250 tons of molten nitrate salt is
delivering heat up to 15 hours. The nitrate salt is stored directly without any heat transfer occurring.
[Sener, 2007]
An indirect system is defined with heat transfer occurring between the fluid or matter that stores
thermal energy and the heat transfer fluid that collects thermal energy in the receiver. The indirect
storage of the parabolic trough plant with thermo oil as heat transfer fluid is a molten nitrate salt
storage. The molten salt is pumped through a heat exchanger between a cold and a hot tank. The
storage has to be operated in a temperature range between 290 and 565◦ C. If the temperature is
reaching a critical low temperature, the salt must be heated to prevent it from freezing. Molten salt
storages have proved to be reliable and high efficient, but they are still expensive and difficult to handle
because of the molten salt characteristics, which are in particular the corrosiveness, the environmental
hazard, and the freezing below 260◦ C.
1
Wind and wave energy is included in this denotation, because solar irradiation on earth causes temperature gradients and
thus wind.
15
3. Components of the Analyzed Plants
3.1.3. Power Block
The power block of the parabolic trough plant model generated for this work is similar to the concept
of the Andasol power plants in Spain. It consists of a single-pressure HTF/ steam generation system,
a Rankine steam turbine/ generator cycle, a dry cooling system and a six-fold feed-water preheater
system. Different to the Andasol design is the dry cooling system. It causes higher investment costs
and a lower overall cycle efficiency, but it allows the power plant to be operated in regions of scarce
water, where solar irradiation is high.
A great asset of this power block is the use of thermal oil delivering the heat to the steam cycle. The
thermal oil has a high heat transfer capacity and thus implies efficient and compact heat exchanger
with low pinch point temperatures. However, due to the temperature limit of the HTF (395◦ C), the
superheated steam entering the steam turbine is of low temperature.
3.2. The Solar Power Tower with Open Volumetric Air Receiver (OVR)
Technology
The plant is determined by its receiver, which contains cubs with an open volumetric ceramic structure. Similar to the parabolic trough technology, the plant comprises concentrators, a receiver, a heat
transfer fluid cycle with an auxiliary burner, a storage and a Rankine cycle power block 3.7.
Figure 3.7.: Temperature characteristics of a solid matter storage.
The innovation of this technology is the receiver that allows the use of ambient air as heat transfer
fluid. When the air is sucked trough the receiver structure high temperatures of up to 800◦ C can
be achieved that allow better performance of the Rankine steam cycle. The recycled air (150◦ C) is
16
3.2. The Solar Power Tower with Open Volumetric Air Receiver (OVR) Technology
leaving the cycle through the receiver to cool down the receiver structure. About 60% of the air
leaving the receiver is recovered, because it gets sucked back in. A ceramic packed bed storage can
be charged by hot air flowing in one direction and discharged in the opposite direction. The storage
and the additional duct burner are compensating fluctuation of the solar irradiation.
After the successful research projects, TSA starting 1993 and Phoebus at the Plataforma Solar
dè Almeria (PSA), to develop and test different open volumetric receiver concepts, Kraftanlagen
München GmbH accomplished to build this concept in Jülich in 2008 in collaboration with the DLR.
The general feedback of the performance of the power plant has been positive.
3.2.1. The Heliostat Field
The mirrors in a solar field for central receiver plant concepts are named Heliostats. It originates from
the Greek word helios for sun and stat for fixed basis. Heliostats are tracking the sun biaxial so that
the reflected sunlight is always fixed to one place independent of the position of the sun. The focus of
all heliostats is the receiver mounted on top of the tower.
(a)
(b)
Figure 3.8.: (a) A 100m2 glass-metal-heliostat with facets at the Plataforma Solar dè Almeria.
[Sandia, 2010] (b) A 50m2 SKI stretched-membrane heliostat.[Sandia, 2010]
There is two different types of heliostats, the glass-metal-heliostats with facets of mirrors and the
metal-membrane-heliostats (see figure 3.8). A common size ranges from 1 to 150m2 . In contrary to
the parabolic mirrors, each heliostat is tracked by its own actuators controlled by a central processing
unit.
3.2.1.1. The Field Efficiency
The field efficiency is the factor that determines the energy of solar radiation that hits the receiver of
the tower. This incident energy on the receiver is defined as follows [Pitz-Paal, 2008]:
Q̇rec = Q̇solar · ηf ield
(3.12a)
with : Q̇solar = DN I · AH · nH
(3.12b)
where AH is the area of one heliostat and nH is the number of all heliostats in a field. The field
efficiency again contains different losses of the field:
17
3. Components of the Analyzed Plants
ηf ield = ρmirror · ηcos · ηb/s · ηtr · ηi
(3.13)
Degree of Reflection ρmirror :
It is the relation of the incident and the reflected solar radiation. The material and the surface quality
of the mirrors is mainly influencing the degree of reflection.
ρmirror =
ρref
ρDN I
(3.14)
Cosine Efficiency ηcos :
The cosine effect of parabolic mirrors described in 3.1.1.1 on page number 11 is similar to the cosine
effect influencing the field efficiency of the heliostats field. The reflected solar radiation is proportional
to the cosine of the angle φ between the perpendicular of the mirror and the incident radiation. Thus,
the effective reflecting area is just the projected area perpendicular to the direction of the incident
radiation, AH,pr .
ηcos =
AH,pr
= cosφ
AH
(3.15)
Therefore, it is best for a field of heliostats on the northern hemisphere to be located mainly in the
north of a solar tower. So that the cosine effect is lowest when the sun is in the south.
Blocking and Shading Losses ηb/s :
Blocking and shading effects occur when reflected solar radiation is not reaching the receiver, because it is blocked by the backside of neighbored heliostats, or when mirrors are partially shaded by
neighbored mirrors, respectively (see figure 3.9.
Figure 3.9.: Optical losses occurring in a heliostats’ solar field.
Transmission Efficiency ηT r :
Absorption and diffusion occurring in the atmosphere between receiver and field degrade the reflected
radiation before it reaches the receiver. The farer the mirrors are located from the receiver the higher
18
3.2. The Solar Power Tower with Open Volumetric Air Receiver (OVR) Technology
are the transmission losses. Thus, these losses are more significant for the tower plant than for the
parabolic trough plant.
Intercept Efficiency 1 ηi :
Not all the reflected solar radiation is reaching the receiver due to optical effects and tracking failures.
Such an optical effect is explained more in detail in section 3.1.1.1 of the parabolic trough field on
page 12, for instance.
3.2.2. The Open Volumetric Receiver
Three parts form the receiver: The absorber cubs with the ceramic channel structure, the steel frame
that holds the absorber cubs, but still allows them to expand and move, and the air collection hopper.
(a)
(b)
Figure 3.10.: The receiver cubs are carried by a metal frame. The frame is cooled by the recycled air
flow (blue arrows) in order to withstand the high temperatures. (a) shows the frontal view
of the receiver in Jülich and (b) the three parts, absorber cubs, metal frame structure and
the hopper. Source: DLR
The open volumetric receiver is classified as an indirect absorbing receiver similar to the tube receiver of the parabolic trough, where thermal solar energy is first absorbed by the receiver material
and then delivered via convection to the HTF.
The concentrated solar radiation hits the ceramic absorber with its channel structure. This structure causes the volumetric effect, which reduces thermal losses. Just a fraction of the irradiation is
absorbed at the surface. The rest of the radiation is trapped in the absorber channels. The ambient
air that is sucked in through this channels is colder at the beginning of the channels and has a greater
cooling effect there. Thus, the highest temperature of the ceramic is not at the entrance but deeper inside (see figure 3.11). So high radiation losses from the surface of the receiver are effectively reduced.
1
The intercept efficiency is also called ”spillage” in the literature.
19
3. Components of the Analyzed Plants
Absorber cubs comprise the partly cylindrical absorber structure, which sits in a ceramic cub and a
cladding tube of steel fixing the ceramic cub. The heated air streams from the absorber through the cub
and the cladding tube into a collection hopper (see figure 3.10). As mentioned above the temperature
in the absorber can reach up to 800◦ C. This requires cooling for the steel cladding tube that carries the
ceramic absorber structure. Cooling is provided by the recycled air stream that comes from the boiler.
[Richter, 2010]
Figure 3.11.: The volumetric effect causes higher temperatures behind the entrance of the absorber
channels. Source: DLR
Losses occur in the receiver heat balance in form of reflection, convection and radiation losses. The
efficiency of the receiver can be calculated as:
ηrec =
Q̇f ield = Q̇solar ηf ield
Q̇f ield − Q̇th,loss
Q̇f ield
=
Q̇rec
Q̇f ield
(3.16)
[W/m2 ]
Further losses in the HTF cycle occur due to the recycled air that is released in the ambient. About
40% of the recycled air stream is not recovered after release.
3.2.3. The Solid Matter Thermal Storage
The indirect storage of the solar tower considered in this thesis is a solid matter storage containing
a ceramic structure. Heat transfer from the working fluid to the solid matter storage occurs on the
surface of the ceramic structure while the HTF is passing through the storage. Thus, the structure
has to be shaped in a way to provide a large contact surface. The air can be blown through the
storage in both directions. The flow directions of charging and discharging are contrarily. In a solid
matter storage the exit temperatures of the HTF are not constant over time in charging and discharging
operation (see figure 3.12). This means, for example in the case of discharging, that as less thermal
energy is still stored as lower is the exit temperature and thus the heat in the HRSG and vice versa.
20
3.2. The Solar Power Tower with Open Volumetric Air Receiver (OVR) Technology
Figure 3.12.: Temperature characteristics of a solid matter storage.
Different factors are affecting this temperature gradation, such as the type of storage, mass flow
of the HTF, current capacity of the storage, number of cycle, etc.. A simplification of this system
characteristic is required to allow the implementation in a simulation software. The solid line in figure
3.12 represents a simplification that is usually shown for the characteristic of a solid matter storage.
In the simulation model of this work, a rather simpler approximation is formulated represented by the
dashed line in figure 3.12. This is because there is no empirical values or no better preliminary design
available. This is:
Charging Tout = Tout + 0.1 ∗ ∆Tn ∗
Q
Q
max
Q
Discharging Tout = Tout − 0.1 ∗ ∆Tn ∗ 1 −
Qmax
∆Tn = Thot,out,nominal − Tcold,out,nominal
(3.17a)
(3.17b)
(3.17c)
A solid matter thermal storage is relatively easy to handle compared to a molten salt storage. There
is no environmental hazard and the operation is secure and reliable. Its drawbacks are a low experience
in power plant operations and the rather new technology is still very expensive. The future potential,
however, is promising for solid matter storages, since it perfectly fits the application in power plants
with gaseous as well as liquid heat transfer fluids.
3.2.4. The Power Block
The power block of the solar tower is in principal similar to the one of the parabolic trough. However,
since the hot air entering the boiler has a higher temperature as the thermo oil of the parabolic trough
system, the Rankine cycle can be much simpler and more efficiently designed. The power block
system that is applied at the Jülich tower had several restrictions due to the small size of just 1.5MWe l
and thus couldn’t be designed in the most efficient way. For larger scale towers, a lot can be derived
from commercial combined cycle power plants, in which the exhaust gas of an upstream gas turbine
reaches similar temperature ranges. In the style of such combined cycle power plants that are further
explained in [Kehlhofer, 1999], the optimal cycle can be determined as a dual-pressure cycle with a
single reheater. The later section will provide more in-depth information on the power block.
21
4. Methodology
4.1. Exergy Analysis
4.1.1. Exergy
The concept of energy, as a tool to develop and optimize thermal systems, is limited. Energy cannot
be destroyed according to the first law of thermodynamics. However, using the idea of energy that is
destroyed or lost is quite commonly accepted, but wrong. In optimization of a thermal system design,
though, it makes sense to think about energy that is potentially available to use.
This idea of destruction can be explained by the second law of thermodynamics, which states that
”in a system, a process that occurs will tend to increase the total entropy of the universe”. When
restoring the total entropy to its initial lower value, additional energy has to be put into the system
again.
Exergy relates to the second law of thermodynamics. Unlike energy, exergy can be destroyed or
lost. The concept of exergy therefore gives a measure about the quality of energy. Electricity with 1kJ
from a power plant compared to a cooling water stream with 1kJ thermal energy in the same power
plant has obviously a greater quality. [Bejan, 1996]
Figure 4.1.: The system can interact with its environment to generate work. The exergy of the system
describes the maximum potential work that can be generated until the system and its
environment are in equilibrium. [Bejan, 1996]
In other words exergy provides information about the maximum amount of work that can be gained
22
4.1. Exergy Analysis
from a process of a system interacting with its environment (see figure 4.1). The final stage of this
process is reached when all properties of the system are in equilibrium with its environment, which is
denoted as the dead state. The environment itself is constant and irreversible.
Exergy includes four components: physical exergy EP H , kinetic exergy EKN , potential exergy EP T ,
and chemical exergy ECH :
E = E P H + E KN + E P T + E CH
(4.1)
It can further be used in a specific version based on a unit-of-mass:
e = eP H + eKN + eP T + eCH
(4.2)
The energy differences of the kinetic and potential conditions of a system compared to its environment
are theoretically equivalent to the work that can be gained from this departure during a process. Thus,
eKN and eP T are as followed:
eKN = 1/2V 2
V
velocity
[m/s]
eP T = gz
g
z
(4.3)
(4.4)
[m2 /s]
[m]
gravity
hight
Whereas the physical exergy is determined by the enthalpy and entropy of a stream of matters
referring to the system environment:
eP H = (h − h0 ) − T0 (s − s0 )
h
h0
s
s0
T0
enthalpy of the system
enthalpy of the environment
entropy of the system
entropy of the environment
temperature of the environment
(4.5)
[J/kg]
[J/kg]
[J/K]
[J/K]
[K]
The chemical exergy considers the departure of the chemical composition of a substance in a system
relative to the one of its environment. This part of the exergy is negligibly small in the applications of
this work. For more information on it see [Bejan, 1996].
The focus in analyzing a thermodynamic system lies on the physical exergy.
23
4. Methodology
Figure 4.2.: The balance of all flows over a control volume at steady state. Tb is the temperature at
which heat transfer occurs.[Bejan, 1996]
4.1.2. Exergy Balance
In system calculations exergy can be applied quite similar than energy. Exergy is transferred through
processes in components. An exergetic balance exists over a control volume or component, respectively. In contrary to the energy concept, though, the exergy sum of all inlet streams of a control
volume is not equivalent to the sum of all outlet streams (see figure 4.2).
As depicted earlier, there is an exergy destruction during the process of interaction in the component. This is because of the total entropy increase during the process (e.g. due to friction). The
balance is correct when the exergy destruction is taken into account. Consequently, one obtains the
exergy destruction and exergy losses by using the exergy balance (equ. 4.6a). [Bejan, 1996] The
following equation shows the exergy balance over a controlled volume in a steady state condition:
0=
X
Ėq,i − Ẇcv +
i
Ėq,i = (1 −
Ėq,i
Ẇcv
Ėi
Ėe
ĖD
ĖL
T0
Tj
24
X
i
T0
)Q̇j
Tj
Ėi −
X
Ėe − ĖD − ĖL
(4.6a)
i
(4.6b)
Ėi = ṁi ei
(4.6c)
Ėe = ṁe ee
(4.6d)
exergy flow of heat transfer
work generated from the process in the control volume
exergy flow at the inlet of the control volume
exergy flow at the outlet of the control volume
exergy destruction
exergy loss
temperature of the environment
temperature where heat transfer occurs
[W]
[W]
[W]
[W]
[W]
[W]
[K]
[K]
4.1. Exergy Analysis
Q̇j
heat transfer
ṁi , ṁe mass flow at the inlet or outlet, respectively
[W]
[kg/s]
4.1.3. Exergy Destruction, Exergy Loss, and Exergetic Efficiency
Exergy destruction ĖD , exergy loss ĖL and exergetic efficiency ε are the values of interest when evaluating a system with an exergy analysis. In the literature exergy destruction is also designated as
availability destruction, the irreversibility, and the lost work. These alternative names emphasize the
important role of the value ĖD in a performance analysis of a system.
Exergy loss is related to heat loss due to the heat transfer and therefore calculated with the following
equation:
Z e
T0
(1 − )q ′ dL
ĖL =
(4.7)
Tj
i
q’
dL
heat transfer rate per unit of length
unit of length
[J/m]
[m]
Both, exergy loss and exergy destruction are explicitly depending on the choice of the system
boundary. This can be seen in the equation 4.7, where the term in brackets becomes ”0” when the
temperature Tj , at which the transfer occurs, is equal T0 . This is the case when the boundary is located outside the considered component in absence of a significant temperature departure. The losses
due to heat transfer are then included in the value of exergy destruction. This is often used in practical
analysis, because q’ as well as Tj are often difficult to determine.
A real understanding about the performance of an entire system, plant, or industry can be obtained
by the exergetic efficiency. It brings the product of a process in relation with the fuel that has been
used for the process (see equ. 4.8). The exergetic efficiency (also called second law efficiency or
rational efficiency) gives more useful information about the performance than any other efficiency,
because of the following reasons: It differs between energy values by considering the maximum work
that can be gained in a system. It further includes energy that has been stored in any way and that is
used in the next component, such as thermal energy that is stored in the first stages of a turbine is still
of use in later stages. [Bejan, 1996]
ε=
ĖP
ĖF
ĖP
ĖD + ĖL
=1−
ĖF
ĖF
product of the process;
The difference between all outgoing and ingoing exergy flows
fuel of the process; all kind of energy input to operate the system
(4.8)
[W]
[W]
Also very useful for the comparison of components in the perspective of one entire system are the
ratios of exergy destruction and exergy loss (see equ. 4.9 and 4.10). As greater the ratio, as greater is
the potential of improving the certain component.
γD =
ĖD
ĖF,tot
(4.9)
25
4. Methodology
γL =
ĖL
ĖF,tot
(4.10)
ĖF,tot fuel of the entire system
[W]
4.2. Exergoeconomic Analysis
The method used to evaluate the power cycles in this work is the exergoeconomic analysis, also
called thermoeconomic analysis. It combines an exergy analysis with an economic analysis with the
objectives of:
• identifying inefficiency costs
• understanding cost formation processes and the flow of costs
• optimizing specific variables in a single component
• and optimizing the overall system
The exergoeconomic balance involves costs that are determined for an exergy stream. It always
exists a balance of exergy cost flows between inlet and outlet flows:
X
(ce Ėe )k + cw,k Ẇk = cq,k Ėq,k +
e
c e , ci
cw,k
cq,k
Żk
X
(ci Ėi )k + Żk
(4.11)
i
specific costs of the outlet and inlet exergy stream
specific costs of the work output
specific costs of the exergy stream related to heat transfer
capital costs of the component k
[e/W]
[e/W]
[e/W]
[e]
The combination of an exergy stream with specific costs results in cost streams:
Ċi = ci Ėi
(4.12)
The exergetic values in these equations are obtained from the exergy analysis. The specific costs
of exergy flows over one component are the same, if no additional exergy is added in the component.
The capital costs Żk are located on the input side of the equation.
4.2.1. Aggregation Level
In order to achieve meaningful results of an exergoeconomic analysis, it is very crucial to apply it
on a component level, even if there is just insufficient information available. It is even advisable to
separate between processes in a component. A too wide aggregation level generates misleading and
too general results. Therefore, it is not possible to consider groups of components in a power plant.
4.2.2. Thermoeconomic Variables for Component Evaluation
Three variables gained from an exergoeconomic analysis allow to draw a conclusion: The cost of
exergy destruction (ĊD,k ), the relative cost difference (rk ) and the exergoeconomic factor (fk ).
26
4.3. Thermoeconomic Evaluation
Cost of Exergy Destruction (CD,k )
It is not possible to determine the exact costs of the exergy destruction. However, it is a very important
value for system improvements. It can be revealed with a thermoeconomic analysis with an adequate
accuracy:
cF,k
cP,k
ĊD,k = cF,k ĖD,k − − > (ĖP,k = f ixed)
(4.13a)
ĊD,k = cP,k ĖD,k − − > (ĖF,k = f ixed)
(4.13b)
specific costs of fuel exergy stream (inlet stream)
specific costs of product exergy stream (outlet stream)
[e/W]
[e/W]
None of the two equations is correct. Equation 4.13a provides a lower assumption (mostly used) and
equation 4.13b a higher assumption. Important to notice is that the effect of exergy destruction on the
performance of the overall system is increasingly higher in components closer to the overall product
stream. That means exergy destructions in a turbine have a greater impact than exergy destructions in
a boiler, for instance.
Relative Cost Difference (rk )
The relative cost difference value gives an understanding about real cost sources in the entire system.
It is calculated as following:
rk =
f F, k(ĖD,k + ĖL,k ) + (ŻkCI + ŻkOM )
(4.14a)
cF,k ĖP,k
or
rk =
ŻkCI
ŻkOM
Ż CI + ŻkOM
1 − ηk
+ k
ηk
cF,k ĖP,k
capital investment costs of the k’th component
operation and maintenance costs of the k’th component
(4.14b)
[e/W]
[e/W]
Exergoeconomic Factor (fk )
The exergoeconomic factor is revealing the relative significance of the performance of a component.
fk =
Żk
Żk + cF,k (ĖD,k + ĖL,k )
(4.15)
4.3. Thermoeconomic Evaluation
In a thermoeconomic analysis, the following values have to be calculated for each component in the
system:
• Exergetic efficiency ηk
27
4. Methodology
• Rates of exergy destruction ĖD,k and exergy loss ĖL,k
• Exergy destruction ratio γD,k and exergy loss ratio γL,k
• Cost rates associated with capital investment ŻkCI , operating and maintenance expenses ŻkOM ,
and their sum Żk
• Cost rate of exergy destruction ĊD,k
• Relative cost difference rk
• Exergoeconomic factor fk
The literature suggests the following methodology for improving cost effectiveness [Bejan, 1996]:
1. Rank in descending order using cost importance (Żk + ĊD,k )
2. Consider design changes for the components showing high costs initially
3. Attention to components with a high rk , especially when (Żk + ĊD,k ) is high
4. fk identifies the major cost sources:
a) fk >>: investigate if it is cost effective to reduce capital costs at the expense of component
costs
b) fk <<: improve component efficiency by increasing capital investment
5. Eliminate sub-processes that increase exergy destruction or loss without contributing the reduction of capital investment or fuel costs.
6. Improve exergetic efficiency of components with relatively low exergetic efficiency or large
values of rate of exergy destruction, destruction ratio, or loss ratio.
28
5. Modelling and Simulation
”Ebsilon” a simulation program for power plants from Evonik provides an advanced modeling surface.
It includes a solar library, which contains all necessary components of a parabolic trough power plant.
With this software a full model of the parabolic trough plant has been built and simulated through out
a year on an hourly basis. This model serves as the basis in a benchmark for the thesis work.
Evonik is at the moment working on the integration of components required for an open volumetric
solar tower. However, solar tower components, such as the heliostats field, the solid bed storage and
the receiver, have not yet been developed for the simulation software. Thus, the entire simulation
work for the open volumetric receiver tower is conducted with a combination of five programs (see
figure A.1).
The heliostat field is designed with the DLR program ”HFLCAL” (Heliostat Field Layout Calculation) and provides the energy of the concentrated incident radiation on the receiver. The receiver
behavior is calculated in an ”EES” (Engineering Equation Solver) model. In ”Matlab”, characteristic
diagrams are formed that are used in Ebsilon to get the efficiency of the absorber relating to the incident energy, the inlet and the outlet temperature. An entire power plant simulation over one year is
accomplished in Ebsilon with the given input of the other programs. The exergoeconomic analysis for
both plant models, the solar tower and the parabolic trough power plant, is carried out in Excel and
EES.
The DLR developed HFLCAL as a tool to design and optimize solar tower plants and their heliostat fields. Given a required receiver capacity (QRec ) for the power plant under nominal conditions,
the solar irradiations (DN I) and a characteristic heat flux on the receiver (qCon ), HFLCAL finds the
optimal tower hight, the aperture area of the receiver as well as the number of heliostats and its arrangement in the field. Furthermore, the program can calculate the field efficiency etaF ield and the
receiver efficiency etaRec throughout a year on a monthly basis. In this study, however, the receiver
efficiency is not analyzed with HFLCAL. The receiver is mapped in Ebsilon in order to get results on
an hourly basis for the exergy analysis and to be able to split up the receiver in its components.
Therefore, a thermodynamic model, which has been developed with EES 1 , is used to elaborate a
characteristic diagram of the absorber part of the receiver. The model integrates the heat balances in
consideration of emission, reflection, convection and conduction losses.
The characteristic diagram, consisting of the power on the absorber QAbs related to the DNI, various outlet and inlet temperatures of the receiver and the absorber efficiency etaAbs , is transformed
into polynomial equations by using the surface fitting tool in Matlab.
1
The thermodynamic model has been elaborated by [Richter, 2010]. Part of this work was to adjust this model to achieve
the required results.
29
5. Modelling and Simulation
Figure 5.1.: Data flow for the simulation of the open volumetric receiver tower plant
Ebsilon is a commercially available simulation software for steady state simulations of thermal
power plants. It offers a comprehensive library of components to generate a power plant model. The
program considers part load conditions with a characteristic performance curve for every component.
An interface in the program using delphi as programming language allows to develop own components that are not part of the component library, such as the absorber and the solid bed storage.The
power plant performance can be simulated in discretized steps on an hourly basis through out a year.
Considering the amount of information for each pipe in the entire power plant, excel is the most
suitable tool to edit and prepare this information for the exergoeconomic analysis in EES. To solve
x-amount of equations with x-amount of variables, EES provides the most practical platform to find
the solution.
A first exergoeconomic analysis has been conducted to identify potential input values and configurations of components that can be changed in order to optimize the entire performance of the power
plant. Thus, the following power plant configurations have been simulated with the above described
programs and methods (see figure 5.2).
30
5.1. Operation Strategy
Figure 5.2.: The simulation matrix gives an overview of the simulated power plant modifications.
5.1. Operation Strategy
5.1.1. Location
For all simulations Seville in Spain has been used as the reference location (see table 5.1.1). DLR
uses this location in many simulations and analysis to be able to classify simulation results. The DNI
data is measured on the ground and thus more meaningful than satellite data from Meteonorm2 , for
instance.
Unit
Location
Latitude
Longitude
Annual DNI
Air Temperature (average/ min / max)
[◦ ] N
[◦ ] E
[kWh/m2 a]
[◦ C]
Value
Seville - Spain
37.4
5.9
2015.1
20.0/ 4.4/ 40.7
Table 5.1.: Characteristic weather data and geographic data of Seville, which has been used for simulations. Source: DLR
2
Meteonorm is a program that provides weather data for many location in the world based on satellite and measured data
31
5. Modelling and Simulation
5.1.2. Method of Operation
Solar Thermal Energy
Q C > QL
0 < QC < QL
QC = 0
Storage empty
full load + charging
full load with burner or part load without burner
full load with burner or no operation without burner
Storage not empty
full load + charging
full load + discharging
full load + discharging
Table 5.2.: Overview of the operation conditions.
For all CSP plants that comprise a thermal storage unit and auxiliary burning, the table above
shows its operating logistic, where QC is the received solar thermal energy and QL is the demand of
the power cycle. In the first scenario the solar thermal energy is greater than the demand and surplus
thermal energy can be stored. Whenever the solar thermal energy is less then required, energy can be
either withdrawn from the thermal storage, or an auxiliary burner can add the required thermal energy,
or the power plant runs on partial load. A more detailed organization chart can be found in Appendix
A.1.
The figure 5.3 shows the general operation strategy throughout a day. In this configuration a CSP
power plant is operated as a base-load power plant. The thermal storage allows to operate the plant
with a higher solar capacity. In the simulations for this work, the plants are operated with the baseload strategy (solar-hybrid) as well as in solar only mode (see table 5.2). The solar-hybrid mode is
used to compare the general performance of the plants and to conduct an exergoeconomic analysis.
Modifications in the power plant, however, can be better analyzed in the solar only mode without
an auxiliary burner. This is because the partial operation of the CSP plants expose the effects of the
optimizations (modifications) more clearly.
Figure 5.3.: Simplified operation mode of CSP plant with storage and auxiliary burner (solar hybrid).
32
5.2. Power Plant Models
5.2. Power Plant Models
Figure 5.4.: The Ebsilon scheme for the parabolic trough power plant.
33
5. Modelling and Simulation
Figure 5.5.: The Ebsilon scheme for the open volumetric receiver tower.
5.2.1. Parabolic Trough Model
The simulation program Ebsilon has been further developed in particular with the focus on parabolic
trough power plants. This allows the user to simply use existing components from the component
34
5.2. Power Plant Models
library with minor adjusting of the partial characteristics of the components. This can all be done with
the interface and functional switches of Ebsilon.
The parabolic trough power plant serves in this work as the reference and the baseline similar to
a benchmark assessment. The model that has been developed in Ebsilon is derived from the existing
power plant Andasol 3 in Spain near Seville. The Ebsilon scheme is shown in figure 5.4. The power
block of the Andasol plant is transferred into the model with a dry cooling system.
The solar field has been designed with a solar multiple (SM) of two. This means that the thermal
energy collected by the receiver is two times higher than the demand of the power block at a nominal
DNI of 850W/m2 . In this way the yield of the solar field is optimized for a thermal storage capacity
of 7.5 hours under full load operations. With the use of switches and control components in the model,
the power plant model can be programmed to automatically switch to the right operation condition
that are described in the section 5.1.2. The model has to be defined for every condition in Ebsilon.
The automatism is required in order to conduct a performance calculation of one entire year.
5.2.2. Solar Tower
The open volumetric receiver tower is a new power plant concept. Many of the components in the
plant have been implemented and realized for the first time at the tower in Jülich. This is why the
integration of such new components have to be arranged in an innovative way. In order to conduct
a comprehensive exergy analysis, the components have to be represented accurately in the Ebsilon
model. The entire model is presented in figure 5.5.
5.2.2.1. The Design of the Solar Field
The solar field of the power tower is designed with a solar multiple of two. Enough to charge the
storage with surplus energy so that the power block can be operated for 7.5 hours from the thermal
energy of the storage. Initial calculations with Ebsilon provide the incident energy that is required in
order to charge the 7.5 hour thermal storage. Approximately 630 MW of thermal energy is required
when the DNI is 850W/m2 and the sun is in the zenith. The diagram 5.6 shows how the efficiency of
the solar field is diverting relating to the position of the sun. The different loss factors that influence
the solar field have been described in chapter 3.2.1.1.
The characteristic data of the location in Seville (see table 5.1.1) have been taken as input parameters for the calculation of the solar field with HFLCAL. The result is presented in the following
table:
The Solar Field
area of one heliostat
tower height
area of the receiver
number of heliostats
total reflective area of the solar field
Unit
[m2 ]
[m]
[m2 ]
[m2 ]
Value
154.92
200
820
4775
739743
Table 5.3.: Results of the solar field calculations with HFLCAL.
35
5. Modelling and Simulation
Figure 5.6.: The influence of the field losses depending on the incident angle.
5.2.2.2. The Integration of the Receiver in Ebsilon
One question to be answered in this work was to find out most effective possible optimizations of the
receiver itself. The receiver can be broken down in several functional parts and it was of interest to
find the components or functional parts that can be improved. Thus, the model should represent these
different functional segments.
Figure 5.7 shows the receiver model in Ebsilon. All yellow parts are components of the receiver
model. The yellow triangle represents the ambient air that is inhaled by the receiver. Number [7] is
the functional area in front of the receiver where ambient air is mixed with the hot released air that
can be recovered. 40% of the released air that cannot be recovered are lost in this cycle represented
by the junction with the open brown pipe.
The main part is the ceramic absorber structure that is integrated in the model with the use of an
Ebsilon Kernel element (number [6]). The heat exchanger component simulates the behavior of the
heat exchange that occurs between the outer surface of the absorber cubs and the recycled cooling
air stream. This functional part has been separated from the absorber part in order to analyze and
understand its effect on the entire efficiency.
The components with the numbers [3], [4] and [5] involve the heat and pressure loss that occurs in
the steel frame of the absorber cubs and in the receiver frame that carries these cubs. [1] and [2] are
describing the characteristics of the hopper and collection pipe of the receiver.
36
5.2. Power Plant Models
(a)
(b)
Figure 5.7.: The receiver cubs are carried by a steel frame. The frame is cooled by the recycled air
flow (blue arrows in figure b) in order to withstand the high temperatures. Figure (a) shows
the Ebsilon model of the receiver split in functional parts. The numbers in the model show
which part they represent in the scheme in figure (b). Figure (b) pictures the three parts,
absorber cubs, metal frame structure and the hopper.
The Kernel element provides an interface to program a new component using Delphi as the pro-
37
5. Modelling and Simulation
gramming code. The code that has been written for the absorber is attached in Appendix A.4.1.1. The
open volumetric receiver is a system with a reaction coupling. This is because the cooled air stream
after the boiler is passing through the receiver and is released into the ambient. A certain percentage
is sucked back in in front of the absorber. Thus, the temperature and the percentage of the recovered
hot air affects the temperature in the receiver, the efficiency of the receiver and the mass flow, which
in turn affects the released air temperature.
This reaction coupling is a challenge for accurate simulations, because it requires many iterations
for many different cases. Ebsilon doesn’t provide an equation solver such as EES and the programming of loops in a Delphi code would slow down the simulations drastically. Therefore, polynomial
equations, describing the varying efficiency under varying conditions, have been developed in order
to implement the receiver in the Ebsilon model. The characteristics of the ceramic absorber have been
described with equations in EES and Matlab to integrate it in the Ebsilon model. EES can find solutions of systems of simultaneous non-linear equations.
A thermodynamic model in EES has been derived from an existing model developed by the DLR
and it has been further developed for this work. The EES model, which is attached in Appendix
A.4.1.1 listing A.2, provides the efficiencies of the absorber in matrices at different incident concentrated energy on the receiver under varying inlet and outlet temperatures of the absorber and varying
temperatures of the recycled air flow. The surface fitting tool of Matlab can transform this matrices
of efficiencies into polynomial equations. The interface of the surface fitting tool allows to adjust the
parameters of suggested polynomial equations.
A 3D diagram, as the one in figure 5.8, shows the deviation of the polynomial equation to the real
results. The parameters have been adapted as such that keep the deviation low in the middle of the
surface, because these results are more likely to expect and thus more accurate results are wished for
this area. The blue points in the 3D diagram represent the calculated efficiencies of the absorber under
certain varying input conditions. The red surface is representing the optimized polynomial equation
that approximately describes these results in one equation.
38
5.2. Power Plant Models
Figure 5.8.: The surface fitting tool diagram shows the accuracy of the polynomial equation in comparison with the calculated results of the absorber efficiencies. The number 356 represents
the inlet temperature of the absorber in Kelvin. eta is the absorber efficiency, T aus the
outlet temperature and Ic the incident concentrated solar energy on the absorber.
SSE
0.1135
R-square
0.9996
Adjusted R-square
0.9996
RMSE
0.006906
Table 5.4.: The four parameters show the goodness of fit of the polynomial equation in figure 5.8.
The results of the surface fitting tool in Matlab are four polynomial equations. The general efficiency equation is determined as the following:
η:
= p[0] + p[1] ∗ x + p[2] ∗ y + p[3] ∗ x ∗ x + p[4] ∗ x ∗ y + p[5] ∗ y ∗ y + p[6] ∗ x ∗ x ∗ x + p[7] ∗ x ∗ x
∗ y + p[8] ∗ x ∗ y ∗ y + p[9] ∗ y ∗ y ∗ y + p[10] ∗ x ∗ x ∗ x ∗ x + p[11] ∗ x ∗ x ∗ x ∗ y + p[12] ∗ x ∗ x ∗ y
∗ y + p[13] ∗ x ∗ y ∗ y ∗ y + p[14] ∗ y ∗ y ∗ y ∗ y + p[15] ∗ x ∗ x ∗ x ∗ x ∗ x + p[16] ∗ x ∗ x ∗ x ∗ x ∗ y
+ p[17] ∗ x ∗ x ∗ x ∗ y ∗ y + p[18] ∗ x ∗ x ∗ y ∗ y ∗ y + p[19] ∗ x ∗ y ∗ y ∗ y ∗ y + p[20] ∗ y ∗ y ∗ y ∗ y ∗ y
(5.1)
The variables x and y are dependent on the irradiation power on the absorber and the outlet temperature of the absorber, respectively. The variables of the matrix p are determined by the polynomial
equation that is applied. The first function in the absorber code in Appendix A.4.1.1 stores the constants of the correct polynomial equation in the p-Matrix. An evaluation loop (see listing 5.1) is
determining the correct polynomial equation for the occurring inlet temperature of the receiver.
Listing 5.1: Evaluation of the input temperature to choose the right case of the polynomial equations.
1
2
3
4
TB[0]
TB[1]
TB[2]
TB[3]
:=
:=
:=
:=
298;
356.333;
414.667;
473;
5
6
7
{Determine the right temperature interval}
i:=0;
39
5. Modelling and Simulation
pol:=0;
while (i <= 3) do
begin
if (T >= TB[i])then
begin
pol:= i;
end;
i:=i+1;
end;
8
9
10
11
12
13
14
15
16
Moreover, the characteristics of the other components or functional parts (number [1] to [5] in the
receiver model in figure 5.7) in the receiver must be adjusted so that they reflect the results that can
be calculated in EES for varying conditions of the power plant operation. Polynomial equations can
be developed with Excel from the EES results. The relations of the characteristic values, such as
pressure loss and heat loss, are in a direct relation with the input parameters. A polynomial trend
line can be found with excel. Figure 5.9 describes the polynomial equation for the characteristic of
the upper temperature difference and the K value, which determines the heat transfer capability, of
the heat exchanger. The polynomial equations of the other components can be found in Appendix
A.4.1.2.
Figure 5.9.: The diagram contains values for the K-value and the upper temperature difference that
have been calculated with the EES receiver model for various mass flows. The polynomial
equation calculated with Excel allows to adjust partial characteristics of the parts in the
Ebsilon model.
5.2.2.3. The Integration of the Solid Bed Storage in Ebsilon
The solid bed storage is a new technology that has not yet been commercially used, thus Ebsilon has
no component in the library, which would allow a fast and simple integration of the storage component. However, Ebsilon provides interfaces in the software to interact with the simulation model.
Delphi code is used to describe the behavior of the solid bed storage (see Appendix A.4.2).
The nature of a storage is to store thermal energy for the time with lack of solar irradiation. This
means for a discrete simulation process, the software has to remember the energy that is stored in the
40
5.2. Power Plant Models
storage for the next calculation. Another interface of Ebsilon allows this possibility to store information in a global variable. This global variable is used to carry the information of the stored energy
through the entire simulation.
Global variables are defined with an @ symbol in front of the name of the variable. In the Delphi
code in Appendix A.4.2, @model.ES is the global variable that keeps the information of the storage
level. The Delphi script for the storage is not implemented in a Kernel element, as for the absorber. It
is placed in a global script interface of Ebsilon that always runs before the first calculation has been
done in the model. This is necessary because the storage level is one criteria to choose the correct
simulation model (see Appendix A.1).
The arrangement of the air blowers in the model differs from reality (see figure 5.10). In the
actual arrangement there is a receiver air blower and boiler air blower. As described in the section
3.2, the air stream through the storage is controlled by the difference of blowing power of the two
blowers. Two reasons have caused a different arrangement in the model: Firstly, the exergy destruction
caused by the storage due to the blower system is difficult to determine and secondly, Ebsilon had
convergence problems caused by the two blowers in series. However, a smaller inaccuracy remains in
the simulation, when the storage is discharged. This is because there is a different pressure resistance
in the storage than in the receiver.
Figure 5.10.: The air blower arrangement in the model is set up with a main blower and a storage
blower in parallel, where as the real system is set up with a receiver blower and a boiler
blower in series.
41
6. Simulation Results and Evaluation
6.1. Exergy Analysis
The exergy analysis is divided into two parts. The first part shows the characteristics of typical operation modes of the solar power tower plant. These are steady state simulations showing the effects of
part load conditions and other operation strategies. In the second part annual performance simulations
show the behavior of the power plant over an entire year and allow a full exergoeconomic analysis
following Tsatsaroni’s method. The results show possibilities to optimize either components or operation strategies of the plant. These modified models are included in the exergy analysis. However, the
exergoeconomic analysis that leads to these modifications is described in the section thereafter.
The parabolic trough power plant serves as a basis for comparison throughout the analysis.
6.1.1. Steady State Calculations
In these simulations four values are of interest: The energy and exergy efficiency, the energy losses,
and the exergy destruction.
The efficiencies provide an understanding how an exergy analysis differs from an energy analysis.
The figures 6.1 and 6.2 show that both efficiencies can be absolutely different from each other and
this difference varies for every operation mode.
(a)
(b)
Figure 6.1.: Energy and exergy efficiencies of the solar power tower in comparison: (a) Solar Only,
(b) With Auxiliary Burner. The abbreviations are explained in the table 6.1.
42
6.1. Exergy Analysis
(a)
(b)
Figure 6.2.: Energy and exergy efficiencies of the parabolic trough in comparison: (a) Solar Only,
(b) With Auxiliary Burner. The abbreviations are explained in the table 6.1.
Table 6.1.: Table of abbreviations for the simulations of all characteristic operations of the solar power
tower.
Abbreviation
Initialize
SE1
SE2
SNE2
SNE3
100%DNI
80%DNI
60%DNI
40%DNI
20%DNI
Explanation
The solar irradiation is set to operate the power plant exactly under full load without any excess thermal energy to
charge the storage
=Storage Empty 1: The storage of the plant is empty. It
can be charged but not discharged
=Storage Empty 2: The storage of the plant is empty. It
can be charged but not discharged
=Storage Not Empty 2: The storage of the plant is NOT
empty or full, respectively. It cannot be charged but discharged
=Storage Not Empty 3: The storage of the plant is NOT
empty or full, respectively. It cannot be charged but discharged
100% of the solar irradiation at the design point
(=850W/m2 )
80% of the solar irradiation at the design point
(=850W/m2 )
60% of the solar irradiation at the design point
(=850W/m2 )
40% of the solar irradiation at the design point
(=850W/m2 )
20% of the solar irradiation at the design point
(=850W/m2 )
Input
DNI=500W/m2
DNI=850W/m2 , storage
level = 0MW
DNI=300W/m2 , storage
level = 0MW
DNI=300W/m2 , storage
level = 900MW
DNI=0W/m2 ,
level = 900MW
storage
DNI=850W/m2 ,
level = 0MW
DNI=680W/m2 ,
level = 0MW
DNI=510W/m2 ,
level = 0MW
DNI=340W/m2 ,
level = 0MW
DNI=170W/m2 ,
level = 0MW
storage
storage
storage
storage
storage
Regarding equation 4.8, the exergy efficiency is calculated as the energy efficiency, namely exergy
of the product over the exergy of the fuel. So the difference depends on the exergy definition of the
product or fuel, respectively. The exergy content of solar radiation is still a topic of scientists that
43
6. Simulation Results and Evaluation
hasn’t been developed to a common comprehension. It has to be noted that in this work the exergy of
solar radiation is considered to be equal to its energy level as well as energy and exergy of the gas for
the auxiliary burner and of the electricity are equal.
This can be seen in the results, where energy and exergy efficiency is equal in the operation mode
Initialize, 40%DNI and 20%DNI. In the Initialize phase the concentrated solar radiation on the receiver is exactly the amount that is needed for full load operations and in the part load phases 40%DNI
and 20%DNI no energy can be discharged from the storage so that in all cases the energy and exergy
of fuel and product are the same, namely electricity (product) and solar radiation (fuel).
The difference between exergy and energy becomes clear in all operation modes when excess thermal energy is either stored or discharged. This is clearly the case in the mode SE1, 100%DNI and
80%DNI, where the storage is empty and the irradiation is greater than necessary for the Rankine
cycle to operate under full load conditions. In these cases the charged thermal energy is a part of the
product and thermal energy has a lower exergy than energy level (see 4.6b). There is no difference in
an energy point of view. When the stored thermal energy is used to run the Rankine cycle in SNE3,
the exergy efficiency is now greater than the energy efficiency, because the fuel (thermal energy) has
a much lower ”quality level” than the product (electricity) of this operation mode. The energy efficiency doesn’t consider this point, which can be seen when comparing the energy efficiency of SE1
(charging) and SNE3 (discharging). Both efficiencies are quite the same compared to the difference
of the exergy efficiency. The smaller difference relies mainly on the fact that the air stream is fully
recycled when the receiver is not in use in SNE3.
This means that the storage is the only component in the entire plant that induces the differences
between energy and exergy overall efficiencies.
Additional valuable information that can be drawn from these diagrams is that the auxiliary burner
allows to operate the Rankine cycle always under full load condition, which makes the entire system
more efficient. In the diagram (b) the auxiliary burner is used in conditions of low solar irradiation,
thus there is no part load operation and the efficiencies don’t decrease. The efficiency increases with
less solar irradiation due to the fact that a higher share of the air stream is recycled and not lost when
leaving the receiver.
It is also apparent that the parabolic trough system has higher efficiencies in general than the solar
tower system despite the fact that the solar tower operates with higher temperatures and a smaller
receiver area.
However, an exergy analysis just gives hints for improvements. It is not possible to draw the
conclusion whether it is economically better to operate the plant with or without an auxiliary burner,
for instance. A plant operating with high efficiencies can still generate electricity more expensively.
A closer look at the energy losses and exergy destructions (including the exergy losses) of the
main parts gives some hints of the weaknesses of the system and further explanations concerning the
differences of the parabolic trough and the solar tower plant.
The figures 6.3, 6.4 and 6.5, 6.6 present the results of the different operation modes for the main
parts Heliostat Field, Receiver, Storage, HRSG (Heat Recovery Steam Generator), Turbine + Condenser, Generator and the Auxiliary Burner.
44
6.1. Exergy Analysis
(a)
(b)
Figure 6.3.: Energy losses of the main parts of the solar power tower in comparison on a logarithmic
scale: (a) Solar Only - Energy Losses and (b) With Auxiliary Burner - Energy Losses.
45
6. Simulation Results and Evaluation
(a)
(b)
Figure 6.4.: Exergy destructions of the main parts of the solar power tower in comparison on a logarithmic scale: (a) Solar Only - Exergy Destructions and (b) With Auxiliary Burner Exergy Destructions.
46
6.1. Exergy Analysis
(a)
(b)
Figure 6.5.: Energy losses of the main parts of the parabolic trough in comparison on a logarithmic
scale: (a) Solar Only - Energy Losses and (b) With Auxiliary Burner - Energy Losses.
47
6. Simulation Results and Evaluation
(a)
(b)
Figure 6.6.: Exergy destructions of the main parts of the parabolic trough in comparison on a logarithmic scale: (a) Solar Only - Exergy Destructions and (b) With Auxiliary Burner Exergy Destructions.
The first two diagrams for each plant are showing energy losses, the two others show exergy destructions each with Solar Only and With Auxiliary Burner operations. These diagrams tell a few
things about the system and its characteristics and allow to draw some conclusions of difference in
performance of both plants:
First the solar field: The energy loss and exergy destruction are significantly bigger than the ones of
the power block for both plants. The value of exergy destruction or energy loss is the same, because
48
6.1. Exergy Analysis
Table 6.2.: Energy and Exergy analysis of the receiver unit in operation mode SE1.
Absorber
Recycled Air
Collection
hopper
+
pipe
Energy
Loss
Fraction Exergy
Destr.
[kW]
86207
46353
4301
[%]
18.54%
9.97%
0.92%
[kW]
211138
16774
1820
Fraction Exergy
Destr.
Ratio
[%]
[%]
44.31% 33.58%
3.52%
2.67%
0.38%
0.55%
Exergy
Loss
[kW]
Fraction Exergy
Loss
Ratio
[%]
[%]
14990
3073
38.66%
7.93%
2.38%
0.49%
exergy fuel and product of the heliostat field is solar irradiation, which is considered to be the same as
its energy level. Not for the collector field in the parabolic trough system, here, the collector transfers
the solar radiation into heat in the receiver tubes.
The generator shows also no difference between exergy and energy destruction and loss, respectively, because the exergy of mechanical work (fuel) and the exergy of electricity (product) are regarding Tsatsaronis determined to be equal to their energy level.
The stored energy in the thermal storage is not changing its energy form. Fuel and product are
thermal energy. The exergy destruction is a little bit less than the energy loss, since the thermal
energy lost in the storage has a lower exergy level. The exergy destruction caused by the blower,
which is included in the storage system, is significantly smaller and is not adding up as much.
When energy is transferred to another energy medium, the first law of thermodynamics says that
energy is conserved. Regarding this law there is an energy balance. The second law of thermodynamics, though, considers the entropy level and this level can only increase resulting in exergy destruction.
This effect can clearly be seen in the heat recovery steam generator (HRSG), where the exergy destruction is much greater than the energy loss.
In the receiver concentrated solar radiation is absorbed and transformed into thermal energy. It
requires an even closer look in this case to understand the receiver unit. From an energy analysis point
of view one could think of the radiation losses of the absorber and the loss of the recycled air stream
as its main weaknesses. These two losses are in fact the reason for its high energy losses (see table
6.2).
The table opposes the energy losses and its fraction of the entire system to the exergy destruction
and losses, respectively, and the fraction and ratio of the entire plant. This means for example that
44.31% of the exergy destruction in the entire power plant is destroyed in the absorber. The ratio is
defined as the exergy losses or destruction over the fuel of the system (heat from the sun or the storage,
respectively).
The energy losses due to the recycled air are about half of the radiation and heat losses of the
absorber. Considering the exergy analysis side (table 6.2), however, the major part of the exergy destruction occurs in the absorber structure. This is where concentrated solar radiation is transformed
into hot air, which causes an entropy increase. The Sankey diagram in figure 6.7 shows the exergy
flow of the air stream in operation mode SE1. The exergy destruction in the Sankey diagram is the
sum of the exergy destruction in table 6.2. The rectangles stand for processes occurring in the system
that cause an exergy change in the flow. The yellow stream in the diagram represents the exergy flow
of the concentrated solar radiation. The stream colored in gray is the exergy flow of the hot air cycle.
Heat losses and exergy destructions are illustrated as arrows leaving the processes. Looking at the
49
6. Simulation Results and Evaluation
exergy analysis and the Sankey diagram it becomes obvious that the recycled air stream and its losses
are relatively small in comparison to the exergy destruction in the absorber (hatched arrow). Thus, the
weakness of the receiver is largely in the absorption of the solar radiation and in the energy transformation due to the lower ”quality” of the hot air and the low heat transfer coefficient of air.
The low heat transfer coefficient of air becomes also apparent when comparing the solar field and
absorber of both plants. The parabolic trough system shows much better performance for the collectors, despite the fact of lower temperatures and a very large receiver area. This is explained with the
better heat transfer coefficient and heat capacity of the thermal oil ”therminol” compared to the very
low heat transfer capability and heat capacity of air. Due to this a lot more volume has to be pumped
through the system for the solar tower and the exergy destruction is very much higher in the absorber
of the solar tower.
Figure 6.7.: A Sankey diagram of the exergy flow of the air cycle of the solar power tower in operation
mode SE1. Other Sankey diagrams are attached in Appendix B.1.
50
6.1. Exergy Analysis
Figure 6.8.: A Sankey diagram of the exergy flow in the thermal oil cycle in operation mode SE1 under
full load.
The advantage of an exergy analysis becomes also apparent in the turbine and condenser part. The
energy losses of this part in the plant are much higher than its exergy destruction (figure 6.4 and figure
6.3). These high energy losses are delusive, because the main part of these energy losses are due to the
heat loss in the cooling towers (see table 6.3). The energy losses in the turbine are rather negligible
in comparison. The exergy loss takes still a major part in the exergy analysis, but it appears not as
dominant anymore. A lot of energy is lost to the ambient, but the saturated water and wet steam after
the last turbine step has a relatively low exergy level in comparison to the ambient air. The potential
of withdrawing work from this level is rather small and cooling the wet steam back to liquid phase is a
necessity for the cycle. Therefore, a potential for improvement can rather be found in the last turbine
step and in reducing the electricity consumption of the compressor for the dry cooling towers.
Table 6.3.: Energy and Exergy analysis of the steam turbine and the condenser unit in operation mode
SE1.
Turbine
Turbine˙1
Turbine˙2
Turbine˙3
Condenser +
Cooling
Comp. Cooling Tower
Energy
Loss
Fraction Exergy
Destr.
[kW]
15
34
18
38
87423
[%]
0.00%
0.01%
0.00%
0.01%
18.80%
[kW]
446
1158
788
2676
1048
0.23%
1048
Fraction Exergy
Destr.
Ratio
[%]
[%]
0.09%
0.07%
0.24%
0.18%
0.17%
0.13%
0.56%
0.43%
0.00%
0.00%
Exergy
Loss
[kW]
Fraction Exergy
Loss
Ratio
[%]
[%]
12555
2.64%
2.00%
51
6. Simulation Results and Evaluation
The energy losses and the exergy destructions of the Rankine cycle remain relatively high under
part load conditions in the solar only operation phases 40%DNI and 20%DNI (see figure 6.4 and
figure 6.3) and the electricity generation drops. The overall efficiency decreases to less than 5%.
An auxiliary burner supports to deliver hot air to the boiler. It allows to continue operating the
plant under moderate overall efficiency. The energy losses of the auxiliary burner are acceptable. The
exergy destruction, however, is as high as the exergy destruction of the heliostat field. This raises the
question whether using a fossil burner to generate electricity in this way is a waste of valuable energy.
However, this seems to be an even greater problem for the parabolic trough, where the energy loss of
the auxiliary burner is even greater than the one of the collector field (see figure 6.5).
6.1.2. Annual Performance Simulations
The annual performance exergy analysis sheds light on the effect of an auxiliary burner. The plant with
burner generates more than twice as much electricity as without (see table 6.4). The main advantage,
though, is the dispatchability of the power plant with burner.
Table 6.4.: Annual performance of the solar power tower and the parabolic trough with and without an
auxiliary burner.
Solar Input
Gas for
Burner
[h/a]
3432
8749
Average
Power
Generation
[MW]
47.15
49.21
[GWh/a]
1490.67
1490.67
[GWh/a]
0
434.54
3781
8737
44.11
49.85
1490.67
1490.67
0
1601.39
Electricity Parasitics
Production
Running
hours
Power Tower
Solar Only
Auxiliary Burner
[GWh/a]
161.82
430.54
[GWh/a]
19.50
36.47
Parabolic Trough
Solar Only
Auxiliary Burner
166.79
435.58
11.01
28.37
The efficiency of the plant is twice as good with burner as without (see figure 6.10). As mentioned
in the section above, the burner allows the Rankine Cycle to run under full load operation improving
its efficiency and can make use of insulation with lower energy on the receiver, which would otherwise
be untapped (see figure 6.9).
The exergy destruction in the power block is greater in the operation with a burner due to more
operating hours. The burner is also needed to bring the temperature in the boiler up to its design
temperature in the evening hours when only the storage is used to run the plant. The storage has
losses, thus the discharging temperature is lower than the charging temperature.
The simulation in Ebsilon is a discrete simulation. It can be expected that the burner would show
an even better effect in a dynamic simulation when considering the inertia of the power block. The
burner can help to keep the power block in a more stable operation and reduces losses due to the
inertia of the acceleration of the turbines, for instance.
52
6.1. Exergy Analysis
Figure 6.9.: One day of the solar tower in operation with low solar insulation and an empty storage,
simulated with an auxiliary burner and without.
53
6. Simulation Results and Evaluation
(a)
(b)
Figure 6.10.: Comparison of the annual performance of the solar power tower with and without auxiliary burner. The diagrams show the annual exergy efficiency (equal to the energy efficiency) and exergy destruction of the main parts.
6.2. Exergoeconomic Analysis
The overall goal of the design of a power plant is not to find the most efficient system from a technical
standpoint, but to find the system with the lowest levelized costs of electricity. The levlelized costs of
electricity can be reduced with technical optimizations in a cost effective way. The entire power plant
is a complex system that provides a multitude of components and processes that can be improved.
Thus, investments and efforts for optimization is not necessarily reasonable. In order to find the
most promising potentials for an optimization of the power plant an exergoeconomic analysis helps
to evaluate the possibilities and takes both the cost flow and the exergy flow through the entire power
plant into account.
6.2.1. Cost Calculations
6.2.1.1. Common Approach for Cost Estimation
As there is no concrete cost information about components available for this work, high uncertainties
have to be acknowledged. The common method to elaborate detailed costs of a power plant in this
case is described by Tsatsaronis [Bejan, 1996]. The method is called Revenue Requirement Method
(RRM), chapter 7 in the book [Bejan, 1996].
The general approach comprises the determination of the following factors:
1. The total capital investment of the system;
2. The Total Revenue Requirement (TRR);
3. The Levelized Electricity Cost (LEC).
54
6.2. Exergoeconomic Analysis
6.2.1.2. Estimation of the Total Capital Investment of the OVR Solar Tower
The focus in this chapter is narrowed down on the development of the costs for the solar power tower.
Results of the parabolic trough system have been calculated the same way and thus are just provided
and not further explicated.
Solar Field:
Many of the cost calculations can be derived from the [ECOSTAR] study. This is also the case for
the solar field. Tsatsaronis [Bejan, 1996] offers an equation that considers a scaling factor when the
system is of a different size as the one that provides the information of costs:
CP E,Y = CP E,W
CP E,Y
CP E,W
XY
XW
α
XY
XW
α
purchase cost of the required equipment size or capacity
given purchase cost of the same equipment item at a different size or capacity
size or capacity of the required equipment
size or capacity of the given equipment size or capacity
scaling exponent
(6.1)
[e]
[e]
The cost of the solar field in [ECOSTAR] is given for a 10MWel OVR solar power tower with a
field size of 104,600m2 (=15.69MIOe) and for 50MWel system with 5 towers with a field size of
524,400m2 (=72.37MIOe). These two inputs allow to find the costs of the solar field for the single
solar tower for this work under consideration that the 5 tower concept needs less heliostats as the
single tower concept. The scaling factor α can be calculated with equation 6.1. The cost reduction are
as following: The 10MWel power plant has specific costs of 150e/m2 and the multi tower concept
has 138e/m2 . Using a scaling factor α of -0.052, leads to 135e/m2 for the heliostats of the analyzed
OVR Solar Tower. This means that the purchase costs of the entire field of a size of 763,700m2 are
103.35MIOe.
Receiver:
The same procedure applies for the investment cost of the open volumetric receiver, since the costs
are given for the same power plant concepts. Using equation 6.1 with a scaling factor of -0.068, the
specific cost of the receiver is 102.3e/kWth and 28.57MIOe entirely for a solar thermal capacity of
279MW at the design point and an area of 820m2 .
Solid Bed Storage:
The same counts for the storage, too. [ECOSTAR] provides the costs of both storages of the
10MWel solar tower and 50MWel multi tower concept. The scaling exponent is 0.93 and the specific costs of the storage result in 51.2e/kWhth . A storage with the capacity of 900MWth has then a
purchase cost of 46.11MIOe.
Tower and Land:
The cost of the 200m tower has been estimated to be 3.5MIOe using an assumed scaling factor of
0.73 and the investment cost for a 92m tower with 2MIOe. The land costs of 6MIOe derive from
the assumption of the specific land costs of 2e/m2 in [ECOSTAR] and the total area size of 3km2 .
Power Block:
55
6. Simulation Results and Evaluation
[ECOSTAR] also provides the information about the costs of the power block. The entire costs have
to be split up over the main components for a detailed exergoeconomic analysis. The distribution of the
costs over the parts in a Rankine cycle (see figure 6.11) has been derived from the cost calculation that
has been used in [Runkel, 2007] on page 71 for a power block of a coal power plant. The distribution
can be used, because the steam turbine and the boiler of a solar power tower is equally complex
as the one in a coal power plant. This is not the case for a parabolic trough power plant, though.
The calculated costs for the 50MWel steam turbine of 8.48MIOe are confirmed to be accurate by
DLR’s experience. The rest divides as following: 11.37MIOe for the heat recovery steam generator
including the air blowers and pumps, 9.57MIOe for the dry cooling system and 3.48MIOe for the
generator. The generators of the solar tower and of the parabolic trough systems are the same. All
capital expenditures are listed in table 6.5.
Figure 6.11.: Cost distribution over the components of a Rankine cycle in a solar thermal power tower.
Table 6.5.: Cost Calculation OVR Solar Power Tower
Solar Field
Receiver
Storage
Tower
Land
HRSG
Turbine
Cooling System
Generator
Sum Total Equipment Cost
Indirect Cost
Total Investment Cost
56
Spec. Costs
135.32
102.32
51.23
17,600
2.00
81.89
162.91
109.52
69.60
Unit
[e/m2 ]
[e/kWth ]
[e/kWhth ]
[e/m]
[e/m2 ]
[e/kWth ]
[e/kWmech ]
[e/kWth ]
[e/kWel ]
Capital Investment [e]
103,349,705
28,569,838
46,109,599
3,511,806
6,110,045
11,370,690
8,484,789
9,574,542
3,480,000
220,561,013
20
5,293.46
[%]
[e/kWel ]
44,112,203
264,673,215
6.2. Exergoeconomic Analysis
Table 6.6.: Cost Calculation Parabolic Trough
Solar Field
Storage
Land
HRSG
Turbine
Cooling System
Generator
Sum Total Equipment Cost
Indirect Cost
Total Investment Cost
Spec. Costs
275.00
44.19
2.00
89.91
267.26
141.74
69.60
Unit
[e/m2 ]
[e/kWhth ]
[e/m2 ]
[e/kWth ]
[e/kWmech ]
[e/kWth ]
[e/kWel ]
Capital Investment [e]
136,857,600
40,000,000
3,483,648
11,600,000
13,920,000
11,000,000
3,480,000
220,341,248
20
5,288.19
[%]
[e/kWel ]
44,068,250
264,409,498
20% of the fixed investment costs are estimated as indirect costs given by the [ECOSTAR] study.
Indirect costs imply costs for engineering and supervision, the entire construction as well as contingencies.
For an accurate exergoeconomic analysis, detailed costs of every component have to be available in
order to find weaknesses and potential for optimization. Costs have to be allocated to every component in the model. Thus, the costs of the power block have to be split up more detailed and costs that
are directly related to some components have to be included. This is the case for the receiver and the
height of the tower. The tower is not considered in the thermodynamic flow through the system, but
the height of the tower is determined by the size of the receiver and so are the costs. The results will
be provided in the next chapter, since direct costs and operation and maintenance costs have to be
included as well (see table 6.9 in the following chapter).
6.2.1.3. The Total Revenue Requirement
The Total Revenue Requirement is defined as follows:
T RR = CRF ∗ T CI + AC
(6.2)
Besides the total capital investment costs, cost evaluations always require a consideration of the
time value of money. It can also be described as the earning power of money, which means that a
dollar in hand today is more worth than a dollar in future considering the income that can be generated
with other investments with the present dollar. Therefore, the present value (P) of an investment at a
particular time in future is determined. These present costs have to be levelized over a certain period
in time, usually one year, using the Annuity. The Annuity (A) is a series of annual transactions of
equal amount of money. The Total Revenue Requirement (TRR) method uses the Capital Recovery
Factor (CRF) to determine the levelized cost value [Bejan, 1996]:
CRF =
ief f (1 + ief f )n
A
=
P
(1 + ief f )n − 1
(6.3)
ief f is the annual dept interest rate of 8% [ECOSTAR] and n is the life time (depreciation period)
considered for the project with 30 years. CRF is then 0.0888. CRF is multiplied with the Total
Investment Costs to find the Total Revenue Requirement of the capital investment.
57
6. Simulation Results and Evaluation
(a)
(b)
Figure 6.12.: Cost distribution over the parts of the solar power tower (a) and the parabolic trough (c).
58
6.2. Exergoeconomic Analysis
Annual Costs (AC) are the second part of the Total Revenue Requirement. The ACs are listed in the
tables 6.7 and 6.8. The Operation and Maintenance cost comprise labour costs, water costs for mirror
cleaning and for the power block, maintenance and replacement costs.
Table 6.7.: Operation Cost and Total Revenue Requirement of the Solar Power Tower
Annual O&M Cost
Annual Insurance Cost
Annual Fuel Cost
Sum Annual Cost
Spec. Costs
17,551.86
1.00
8.73
78,418.30
Unit
[e/GWha ]
[%]
[e/GJ]
[e/GWha ]
Total Revenue Requirement
Annual Cost [e/a]
6,916,540
2,205,610
21,779,604
30,901,754
57,058,729
Table 6.8.: Operation Cost and Total Revenue Requirement of the Parabolic Trough
Annual O&M Cost
Annual Insurance Cost
Annual Fuel Cost
Sum Annual Cost
Total Revenue Requirement
Spec. Costs
17,162.01
1.00
8.73
150,470.61
Unit
[e/GWha ]
[%]
[e/GJ]
[e/GWha ]
Annual Cost [e/a]
6,762,914
2,203,412
50,328,578
59,294,905
85,425,817
The annual fuel cost stand out in the tables above. One has to notice that the power plants in these
simulations have been operated under full load conditions every hour in the year. This is why the
costs for the fuel of the auxiliary gas burner outweigh the annual operation cost by far. It is also not
surprising that the amount of gas used for the power tower is less than the half of the amount used for
the parabolic trough plant. The air cycle of the power tower allows a duct burner configuration, which
blows the combusted hot gas directly into the air cycle of the plant and in principle directly into the
boiler comparably to a conventional thermal power plant. The parabolic trough system, though, has
a thermal oil cycle that delivers the heat to the boiler. The combusted hot gas leaving the burner is
passed through a heat exchanger to deliver the heat to the thermal oil cycle with a significant loss. The
colder but still hot gas leaving the heat exchanger is released to the environment (see figure 6.13).
59
6. Simulation Results and Evaluation
(a)
(b)
Figure 6.13.: The gas burner configuration in the power plant scheme of the solar power tower (a) and
the parabolic trough (b). The brown pipes represent a gas air mixture, the fuel pipe is
pink and the thermal oil pipe is gray.
Levelized capital cost distributed over each component
For the exergoeconomic calculation the TRR is too global. The capital costs have to be allocated to
each component or part of interest of the power plant. It is determined as the levelized capital costs of
a component (Zk ). The capital cost including the indirect costs of a specific component are levelized
to one year and operation & maintenance costs are added except the fuel cost for the auxiliary burner.
Zk = T RRk − f uelcost
(6.4)
The results are given in table 6.9. In the following, it is explained how the capital costs for specific
components, which are not yet sufficiently determined, have been revealed.
For this work the solar field, the receiver and the storage don’t have to be split up more in detail
anymore. If the results reveal that these parts of the power plant must be optimized, it will require a
new study just focusing on these parts. [Uhlenbruck, 2001] provides relations that allow to distribute
the capital costs over the components of a Rankine cycle properly. The following equation allows to
adapt the cost of the steam turbine parts with the factor K so that the sum is similar to the estimated
turbine costs above:
60
6.2. Exergoeconomic Analysis
0.7
CST = KST · fT · fh · PST
CST
KST
PST
(6.5)
capital cost of the steam turbine/ -stage
factor to adapt the sum to the general cost
mechanical power of the steam turbine/- stage
fT = 1 + 5 · e
T
[e]
[-]
[kW]
in −Tref ·K
10.42·K
(6.6a)
and
fh = 1 +
Tin
Tref
his,ST
0.05
1 − ηis,ST
3
(6.6b)
inlet temperature of the turbine/ -stage
determined reference temperature
the isentropic efficiency of the steam turbine/ -stage
[K]
[K]
[-]
With KST = 3788 and Tref = 914K the sum of all stages are adjusted to the estimated capital
investment cost of 8.485 Mioefor the tower concept. The same approach is used to estimate the
component costs of the parabolic trough system.
The capital costs for the generator are for both power plants the same. It has been estimated by the
DLR that they are 12% of the power block. This means in numbers 4.176 Mioeincluding the indirect
costs.
Following the stream of the Rankine Cycle, the next subsystem of interest is the dry cooling system, which is also similar for both power plants. [Runkel, 2007] has developed a derivative from
detailed cost information given by [Maulbetsch, 2002] and [Lees, 1995] to find a proper estimation
for dry cooling systems. The derivative is given in equation 6.7:
CDC = 36.9M ioEuro ·
CDC
Q̇Cond
IT D
Q̇Cond · 20K
287M Wth · IT D
!0.89
capital costs of the dry cooler of interest
thermal heat capacity of the condenser of interest
chosen initial temperature difference of the condenser of interest, here 20 K
(6.7)
[Mio e]
[ M Wth ]
[K]
Pumps in the cycle that are also not considered in the global perspective in figure 6.12 are calculated
following [Uhlenbruck, 2001]’s example:
0.71
Cpump = Kpump · fη · Ppump
(6.8)
The factor Kpump can be found by the ratio of the components in a Rankine cycle that is given by
[Uhlenbruck, 2001] and is then used for all pumps and compressors in the plants. Kpump is 1210 and
the isentropic efficiency fη is 0.8.
61
6. Simulation Results and Evaluation
An exergoeconomic optimization requires a detailed resolution of the component costs. This is
also the case for the HRSG. The distribution of the costs can be achieved with [Uhlenbruck, 2001]’s
approach, too.
CHT X = KHT X · fp,i · fT,Steam,i · fT,Gas,i ·
Q̇i
∆Tln,i
!0.8
(6.9)
As in all cost equations of [Uhlenbruck, 2001], the K factor allows to adjust the sum of all HRSG
components to the power block costs that are known from [ECOSTAR]. KHT X is 10283. The three
f-factors fp,i , fT,Steam,i and fT,Gas,i consider the dependency of the costs from the water/steam pressure as well as from the temperature of the heat transfer fluid and water/steam leaving the specific
component. However, the costs of a heat exchanger are predominantly dependent on the area of the
heat exchanger. The area is represented by the relation of the heat that is transfered in the heat exchanger and the mean logarithmic temperature difference. The rest of the equations that are needed to
calculate the f-factors can be found in the attachment chapter 6 of [Runkel, 2007].
The last component that requires a closer cost consideration is the auxiliary gas burner. The costs
of the combustion chamber are neglected, but the air preheater for the tower is calculated with this
relation
CairHT X = 0.63 · KairHT X ·
Q̇a irHT X
k · ∆Tln,airHT X
!0.6
(6.10)
where KairHT X is 10283. k is the heat transfer coefficient indicated with 0.018kW/m2 . The
levelized capital costs are low compared to the fuel costs. These are not involved in the levelized
costs, though, because they are considered separately in the analysis like the parasitics.
62
6.2. Exergoeconomic Analysis
Table 6.9.: Detailed Cost Distribution of the OVR Solar Tower
OVR Solar Power Tower
Components/ Parts
Solar field incl. land
Receiver incl. tower
Turbine 1-2
Turbine 3-4
Turbine 6-8
Condenser incl. cooling tower
Generator
Superheater2-MD1
Superheater1-MD
Superheater2-HD2
Superheater1-HD
Evaporator-HD
Superheater-ND3
ECO-HD
Evaporator-ND
ECO-ND
ECO-condensate
Pump
Pump˙ND
Pump˙HD
Compressor˙2 (main comp)
Compressor˙storage
Storage
Duct burner
Sum
Zk [The/a]
15,244
3,735
343
615
882
2,076
698
140
108
238
460
798
34
626
241
14
159
2
2
55
254
145
5,323
10
32,201
Solar Parabolic Trough
Components/ Parts
Solar collector field incl. land
Turbine 1
Turbine 2
Condenser incl. cooling tower
Generator
Superheater 1
Evaporator
Eco
Reheater
Feed water preheater HP 2
Feed water preheater HP1
Feed water preheater LP3
Feed water preheater LP2
Feed water preheater LP1
Pump feed water
Pump condensate
Pump˙1 oil
Pump˙2 oil
Storage
Duct burner
Sum
Zk [The/a]
18,693
1,150
2,060
1,613
803
168
505
181
213
256
386
82
162
206
78
11
210
159
5,810
215
32,960
6.2.1.4. Levelized Electricity Cost, LEC
The Levelized Electricity Cost is the most interesting value for a comparison of different power plant
concepts. It involves all cost parameters and the actual net electricity production (Enet ) (equation
6.11).
LEC =
T RR
Enet
(6.11)
63
6. Simulation Results and Evaluation
Table 6.10.: LEC of the Power Tower
Total Revenue Requirement
Burner in Operation
Gross Electricity Production
Parasitics
Net Electricity Production
Levelized Electricity Cost
[e/a]
[%/a]
[GWh/a]
[GWh/a]
[GWh/a]
[e/kWh]
Solar Only
35,279,125
0%
161.82
19.50
142.31
0.2479
With Gas Burner
57,058,729
59%
430.54
36.47
394.06
0.1448
Table 6.11.: LEC of the Parabolic Trough
Total Revenue Requirement
Burner in Operation
Gross Electricity Production
Parasitics
Net Electricity Production
Levelized Electricity Cost
[e/a]
[%/a]
[GWh/a]
[GWh/a]
[GWh/a]
[e/kWh]
Solar Only
35,097,238
0%
166.79
11.01
155.78
0.2253
With Gas Burner
85,425,817
67%
435.58
28.37
407.21
0.2098
Looking at the tables above, the difference in performance of the basic systems becomes clear. The
auxiliary burner is improving the performance of the systems and decreases the LEC. In the ”Solar Only” operation mode both plants divert just 2.3 ecents/kWh, but the solar tower provides much
cheaper electricity with the support of the gas burner as the parabolic trough with a difference of about
6.5 ecents/kWh.
This improvement derives from the better ability of the OVR solar tower to operate in a hybrid
mode mainly due to two properties: The solar tower is equipped with a duct burner. The duct burner
injects the heat with the exhaust gas directly into the boiler and the HTF cycle. This is not the case for
the parabolic trough, which requires a heat exchanger to deliver the heat first to the thermo oil cycle,
which then goes to the boiler. This makes the entire system comparatively inert.
Especially in the morning, when the oil from the collector field is recycled again, the entire oil in
the cycle has to be heated up. This doesn’t count for the solar tower, where the plant is easily switched
back to solar mode when the receiver reaches the required temperature. In this analysis the two plants
have been simulated to operate on a base load mode, so this characteristic cannot be seen in the results.
Due to the low efficiency of the auxiliary burner in the parabolic trough, the portion of the burner
running is much higher than in the solar tower system. Therefore, the burner for the parabolic trough
plant is rather an ”auxiliary” burner compared to the duct burner that has an effective performance
improvement for the solar tower.
The parasitics in the solar tower are higher. In both systems are the cooling tower fans the major
source of electricity consumption. However, the demand for the blowers in the air cycle is higher in
the solar tower than the demand for the oil pumps in the thermo oil cycle of the parabolic trough. A
lot more volume has to be pumped due to its lower heat transfer coefficient and the lower density.
64
6.2. Exergoeconomic Analysis
The reason for the lower gross electricity production of the solar tower originates also from convergence problems in the simulation structure of the solar tower system. Due to the embedding of
several scripts for the storage and the receiver, the system has comparatively more stability problems
and some hours in the annual performance simulation were clearly wrong and had to be taken out of
the results. The influence of the failure can be seen when comparing the gross electricity production
in the mode ”With Gas Burner”. As the system is supported with the burner in both cases the result of
the annual electricity generation can be expected to be similar.
6.2.2. Results and Evaluation of the Exergoeconomic Analysis
The thermoeconomic analysis is conducted as described in chapter 4.3 following the steps of [Bejan, 1996].
Two different systems have been simulated as basis systems for the Solar Power Tower: ”Solar Only”
looking at the system without any auxiliary burner and ”With Auxiliary Burner”. The results are provided in appendix B.3 prepared as described in chapter 4.
The three values [(CD +CL )+Z] (cost influence), r (relative cost difference) and f (exergoeconomic
factor) are in particular of interest for the optimization of the power plants. The following tables are a
section of the results in the appendix just focusing on these values. Numbers of [(CD + CL ) + Z] that
are marked red show high initial costs and thus have to be considered in the optimization as well as
parts that have red values for r. The value f tells what to do with the specific component that should be
changed, either investing more in the component for a higher efficiency (colored in blue) or reducing
the investment cost and excepting efficiency losses (colored in green).
Especially the high cost influence [(C˙D+C˙L)+Z] of the solar field and the absorber stick out in
these tables. Already before these analysis, it was a common understanding that the solar field and
the absorber have the highest potential for improvement. The exergoeconomic results strengthen this
assumption in particular, as the weight of importance is stronger than expected. Thus, it is of high
importance for an optimization to consider these two parts.
Since sun radiation is a free energy source the f-factor is ”1” stating that a cost reduction of the field
is more important than to improve the efficiency. In this work, however, the solar field is excluded as
the focus of this work is on the thermodynamic parts of the plant.
The receiver has been split up in its main parts. Besides the high cost importance the relative cost
influence factor r also shows that the ceramic absorber structure is the crucial part of the receiver and
thus needs to be in focus for optimizations. The exergoeconomic factor f=0.2938 is low, which means
that the improvement should focus on a better efficiency accepting higher investments to reach it. This
counts for the operation in ”Solar Only” mode as well as for the operation ”With Gas Burner”.
Secondly, the air mixing unit shows the highest relative cost difference with r=2.122 in the system.
The ”cold” air that is recycled to the absorber is released back to ambient. This recycled air has still a
high temperature and thus is very valuable for the system. This fact has been clear from the beginning.
The results just emphasize the importance to find a good balance of the air that is recovered after it
has been released to the ambient. The f-factor, however, reveals the fact that higher investments are
not worth to take into account for an improvement of the efficiency.
65
6. Simulation Results and Evaluation
Table 6.12.: Solar Tower, Solar Only, @DP: recycling of the air stream: 60%, concentrated solar
irradiation on the receiver: 500kW/m2 , pressure of the water pipe after first economizer:
1.5bar.
Solar field
Absorber
Condenser+Dry Cooler
Air mixing unit in absorber
Storage discharging
Storage charging
Turbine 6-8
Steam generator HP
HTX in absorber
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
Pipes and hoppers
HTX superheater HP 2 (HTX 34)
HTX reheater 2 (HTX12)
HTX reheater 1 (HTX23)
Compressor storage
Pump HP
Dearator
HTX superheater LP
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
66
C˙D+C˙L
[e/a]
0
8981000
4488000
3964000
73700
64634
1274000
750862
1438000
715343
421216
539536
899273
475793
163059
233680
143697
352785
109924
172492
190111
150978
83403
84734
38142
50023
41154
10997
14879
5309
876.8
611.8
13.74
0
0
0
0
Z
[e/a]
15240000
3736000
2581000
0
2661500
2661500
1096000
797822
0
626361
764361
460299
0
158858
426680
254086
241081
0
237644
139861
107578
145048
54746
0
33682
0
0
13994
0
0
2088
1690
0
0
0
9883
0
(C˙D+C˙L)+Z
[e/a]
15240000
12717000
7069000
3964000
2735200
2726134
2370000
1548684
1438000
1341704
1185577
999835
899273
634651
589739
487766
384778
352785
347568
312353
297689
296026
138149
84734
71824
50023
41154
24991
14879
5309
2964.8
2301.8
13.74
0
0
0
0
r
[-]
0
1.98
0
2.12
0.41
0.45
0.24
0.24
1.70
0.40
0.20
0.28
1.051
0.99
0.23
0.44
0.33
1.02
0.33
0.37
0.38
0.50
0.47
1.03
0.44
1.00
1.00
0.8
1.00
1
0.95
0.97
1
0
0
0
0
f
[-]
1
0.2938
0.3651
1
0.97
0.98
0.46
0.52
1
0.47
0.64
0.46
1
0.25
0.72
0.52
0.63
1
0.68
0.45
0.36
0.49
0.40
1
0.47
1
1
0.56
1
1
0.70
0.73
1
0
0
0
0
6.2. Exergoeconomic Analysis
Table 6.13.: Solar Tower, with Auxiliary Burner, @DP: recycling of the air stream: 60%, concentrated solar irradiation on the receiver: 500kW/m2 , pressure of the water pipe after first
economizer: 1.5bar.
Solar field
Absorber
Condenser+Dry Cooler
Mixing unit/ burner (Mixer2)
Turbine 6-8
Air mixing unit in absorber
Storage charging
Storage discharging
Steam generator HP
Generator
Eco HP
HTX superheater HP 1 (HTX 45)
Turbine 3-4
HTX in absorber
HTX preheater
Compressor HRSG
Turbine 1-2
Steam generator LP
HTX reheater 1 (HTX23)
HTX reheater 2 (HTX12)
HTX superheater HP 2 (HTX 34)
Pipes and hoppers
Mixing unit/ bypass of receiver (Mixer1)
Compressor storage
Pump HP
Air preheater for burner (HTX)
Water injection superheater (Mixer25)
Dearator
Water injection reheater (Mixer22)
HTX superheater LP
Eco LP
Duct burner
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
C˙D+C˙L
[e/a]
0
8684000
8217000
3848000
2583000
3300000
349710
-300034
1534000
1543000
1448000
1122000
811257
1287000
1052000
410369
312267
276670
395030
362150
236251
332608
247978
102690
153954
178713
152694
129778
110603
75346
21546
24295
10590
4614
1581
1234
2075
Z
[e/a]
1.52E+07
3.74E+06
2.08E+06
0.00E+00
8.82E+05
0.00E+00
2.66E+06
2.66E+06
7.98E+05
6.98E+05
6.26E+05
4.60E+05
6.15E+05
0.00E+00
1.59E+05
2.54E+05
3.43E+05
2.41E+05
1.08E+05
1.40E+05
2.38E+05
0.00E+00
0.00E+00
1.45E+05
5.47E+04
9.88E+03
0.00E+00
0.00E+00
0.00E+00
3.37E+04
1.40E+04
0.00E+00
0.00E+00
0.00E+00
2.09E+03
1.69E+03
0.00E+00
(C˙D+C˙L)+Z
[e/a]
1.52E+07
1.24E+07
1.03E+07
3.85E+06
3.46E+06
3.30E+06
3.01E+06
2.36E+06
2.33E+06
2.24E+06
2.07E+06
1.58E+06
1.43E+06
1.29E+06
1.21E+06
6.64E+05
6.55E+05
5.18E+05
5.03E+05
5.02E+05
4.74E+05
3.33E+05
2.48E+05
2.48E+05
2.09E+05
1.89E+05
1.53E+05
1.30E+05
1.11E+05
1.09E+05
3.55E+04
2.43E+04
1.06E+04
4.61E+03
3.67E+03
2.92E+03
2.08E+03
r
[-]
0.00
1.85
0.00
1.04
0.17
2.12
0.55
0.35
0.17
1.04
0.30
0.21
0.13
1.70
0.95
0.53
0.13
0.23
0.31
0.28
0.21
1.02
1.01
0.63
0.42
0.00
1.00
1.03
1.00
0.33
0.57
0.00
1.00
1.00
0.68
0.73
1.00
f
[-]
1.00
0.30
0.20
1.00
0.25
1.00
0.88
1.13
0.34
1.00
0.30
0.29
0.43
1.00
0.13
0.38
0.52
0.47
0.21
0.28
0.50
1.00
1.00
0.59
0.26
0.05
1.00
1.00
1.00
0.31
0.39
1.00
1.00
1.00
0.57
0.58
1.00
67
6. Simulation Results and Evaluation
Two optimizations have been drawn from these findings for further analysis: Increasing the incident
radiation flux on the receiver (q = 550kW/m2 and q = 600kW/m2 ) and recovering more air that
has been released back into the cycle (80% and 100%). Recycling 100% air of the air released to the
ambient in front of the receiver means that the receiver must be covered by a glass. How this would
be managed is not important now. The aim is just to analyze a potential improvement of the system.
Another strategy has been developed with the preheater of the Rankine cycle. Firstly, the preheater
raises attention due to its rather high r (r=0.95) at a higher priority position on the ordered list and
secondly, the preheater has the capacity to reduce the final temperature of the air that is recycled back
to the receiver. The f-factor (f=0.25 and f=0.13) shows the possibility to improve the efficiency by
investing more capital into this component or arrangement.
The way to reduce the HTF output temperature is to increase the water output temperature. In
order to achieve this, the pressure in the water pipe has to be increased to avoid steam generation in
the preheater. Steam at this point in the Rankine cycle is a problem for the high and low pressure
pumps down the stream. Steam is compressible and the pumps wouldn’t be able to reach the required
pressures for the boiler streams. Thus, three more operation modes have been considered for the optimization analysis, namely the water outlet temperature at 135◦ C, 145◦ C and 155◦ C applying a 3 bar
pressure in the water pipe.
Comparing the results of the exergoeconomic analysis of the parabolic trough power plant (see table 6.14) with the one of the solar tower, the factor r says that there is little to optimize in the trough
system. The cost importance factor gives a hint of potential cost reduction in the collector field and
the two oil pumps in the HTF cycle stick out as the most potential part for an efficiency improvement.
However, the analysis shows that the parabolic trough system is more advanced than the solar tower.
The main weakness of the parabolic trough system becomes apparent when looking at the auxiliary
burner in table 6.15. It has an even higher cost importance than the collector field, which reflects the
very high costs of energy coming from the burner. As the heat has to be delivered to the thermo oil
cycle by the use of a gas/oil heat exchanger, much of the heat is lost to the ambient. This configuration
is not supporting a hybrid power plant. Even when the waste heat is recovered from the stack, the
burner will always waste a lot of valuable energy in order to heat up the entire oil cycle. Thus, its
purpose is to support the collector field and the storage for stable operation conditions.
68
6.2. Exergoeconomic Analysis
Table 6.14.: Parabolic Trough, Solar Only
Solar Field
Storage Discharging
Storage Charging
Turbine2
Turbine1
Condenser
Evaporator
Generator
Pump Oil
Preheater HP 1
Reheater
Pipes to PP
Pipes to SF
Preheater HP 2
Economizer
HTX Superheater
Preheater LP 1
HTX Burner
Preheater LP 2
Pump feed water HP
Dearater
Preheater LP 3
Pump Oil Discharging
Mixer HTF after boiler
Mixer Preheater
Pump feed water LP
Mixer after Charging
Mixer after Discharging
Duct Burner
Mixer Burner/Discharging
C˙D+C˙L
[e/a]
0
832128
633936
1413000
527864
0
778340
31675
417217
224771
325585
470169
453545
107797
181496
186110
103193
0
44522
81777
125099
23452
36450
48064
18258
5018
1883
297.7
0
0
Z
[e/a]
18690000
2905000
2905000
2060000
1150000
1613000
505178
802818
209870
386375
213291
0
0
255876
181086
167627
205932
215408
161688
78420
0
81640
53445
0
0
10979
0
0
0
0
(C˙D+C˙L)+Z
[e/a]
18690000
3737128
3538936
3473000
1677864
1613000
1283518
834493
627087
611146
538876
470169
453545
363673
362582
353737
309125
215408
206210
160197
125099
105092
89895
48064
18258
15997
1883
297.7
0
0
r
[-]
0.00
0.38
0.27
0.24
0.24
0.00
0.21
0.09
1.82
0.33
0.15
1.01
1.01
0.20
0.11
0.11
0.74
0.00
0.62
0.46
1.03
0.34
2.23
1.00
1.06
0.90
1.00
1.00
0.00
0.00
f
[-]
1.00
0.78
0.82
0.59
0.69
0.00
0.39
0.96
0.33
0.63
0.40
1.00
1.00
0.70
0.50
0.47
0.67
0.00
0.78
0.49
1.00
0.78
0.59
1.00
1.00
0.69
1.00
1.00
0.00
0.00
69
6. Simulation Results and Evaluation
Table 6.15.: Parabolic Trough, with Auxiliary Burner
Auxiliary Burner
Solar Field
HTX Burner
Turbine2
Evaporator
Storage Charging
Storage Discharging
Turbine1
Pump Oil
Reheater
Condenser
Preheater HP 1
HTX Superheater
Economizer
Generator
Pipes to SF
Preheater LP 1
Pipes to PP
Preheater HP 2
Dearater
Preheater LP 2
Pump feed water HP
Mixer HTF after boiler
Preheater LP 3
Pump Oil Discharging
Mixer Preheater
Pump feed water LP
Mixer after Charging
Mixer after Discharging
Mixer Burner/Discharging
C˙D+C˙L
[e/a]
36370000
0
8885000
5977000
3129000
497166
446581
2121000
1655000
1413000
0
923523
809236
777281
93593
768995
516278
692419
430298
455779
187528
204633
249248
116052
99883
101449
23406
4018
1036
0
Z
[e/a]
0
18690000
215408
2060000
505178
2905000
2905000
1150000
209870
213291
1613000
386375
167627
181086
802818
0
205932
0
255876
0
161688
78420
0
81640
53445
0
10979
0
0
0
(C˙D+C˙L)+Z
[e/a]
36370000
18690000
9100408
8037000
3634178
3402166
3351581
3271000
1864870
1626291
1613000
1309898
976863
958367
896411
768995
722210
692419
686174
455779
349216
283053
249248
197692
153328
101449
34385
4018
1036
0
r
[-]
0.83
0.00
0.25
0.13
0.09
0.33
0.17
0.12
1.52
0.10
0.00
0.17
0.07
0.07
0.05
1.01
0.39
1.01
0.09
1.03
0.25
0.23
1.00
0.15
1.46
1.10
0.50
1.00
1.00
1.00
f
[-]
0.00
1.00
0.02
0.26
0.14
0.85
0.87
0.35
0.11
0.13
0.00
0.30
0.17
0.19
0.90
1.00
0.29
1.00
0.37
1.00
0.46
0.28
1.00
0.41
0.35
1.00
0.32
1.00
1.00
1.00
6.2.3. Optimizations and Modifications of the Solar Power Tower Plant
The investigations of the exergoeconomic results presented in the chapter above lead to the following
changes in the system that are possibly improving the entire system performance (figure 6.14).
70
6.2. Exergoeconomic Analysis
Figure 6.14.: Overview of the different optimized systems for investigation.
The following diagrams in this chapter present the most important factors of the thermoeconomic
analysis of the optimized systems.
An annual simulation regarding chapter 5 is conducted for every power plant configuration. The
annual efficiency is calculated with the equation 4.8. The overall annual exergy efficiency here is equal
the energy efficiency, because the energy of the solar irradiation (fuel) and the electricity (product) is
considered to consist of 100% exergy with the absence of anergy.
Figure 6.15.: A comparison of the annual exergy efficiencies of the solar tower and the parabolic trough
with and without a duct burner.
The graph shows how much the trough power plant differs from the solar tower. The annual perspective reveals this fact more than the perspective of the peak efficiency. Referring to the results
71
6. Simulation Results and Evaluation
Figure 6.16.: The diagram shows the behavior of the power block in the morning of a typical summer.
The storage is empty. Two configurations are displayed: The system supported by a duct
burner and the system in solar only mode.
in figure 6.15, the annual simulations prove the fact that with the support of a duct burner the plant
operates by a twofold more efficient. This can be derived from the following reasons:
• The steam turbine requires stable and optimal steam parameters in order to be run efficiently.
The duct burner can be started quickly in the event of clouds passing over the solar field, for
instance.
• The Rankine cycle is very inert. This means that it requires valuable hours in the morning to
be started (see figure 6.16). The diagram shows that it takes 1 to 2 hours to start generating
electricity! The configuration with a duct burner allows to harness these valuable sun hours in
the morning.
• A similar situation appears in the evening when thermal energy is drawn from the storage. The
duct burner helps to run the Rankine cycle under full load and to make the best out of the
degrading heat coming from the storage.
• As the simulations in Ebsilon are not dynamic, another drawback is not reflected in the results:
The starting phase of the entire system takes a significant share of the parasitics.
One has to note that the annual simulations are run under full load operation of the power plant. 1
Under real conditions it is more common for such a plant to be run under half load operation during
the night hours. This would reduce the overall efficiency, but it would increase the dispatchability of
the power plant improving the value of the power plant for the national grid as a plant covering the
medium load.
1
The power generation of the system with duct burner fluctuates in the diagram caused by convergence problems due to
the complexity of the model.
72
6.2. Exergoeconomic Analysis
Other configurations of the plant system have a rather small impact compared to the improvement
of the efficiency with the application of a duct burner. However, the improvements are still significant,
which can be seen in diagram 6.17. In total an improvement of ca. 1 to 1.5% are possible under solar
only operation.
An understanding of the power block can be gained through the analysis of the increased feed-water
pressure and the possibility of an increased temperature after the preheater. The exergoeconomic analysis suggests to increase the investment (f is large and r is small) for a higher efficiency. Originally
1.5bar and 135◦ C are intended for the feed water leaving the preheater.
With higher pressures higher temperatures can be applied, because the feed-water shall not boil in
the dearator. However, as closer the water reaches saturated water properties as better is the performance of the preheater and this can be seen in the following diagram. The system with saturated water
(155◦ C) shows the higher overall performance. An improvement of ca. 0.4% is achieved due to the
higher temperature that can be reached compared to the system with 1.5 bar.
A drawback of such a high pressure in the feed-water pipe is the more complicated refilling of water
into the Rankine cycle. The dearator is usually just slightly run above atmospheric pressure in order
to allow a simple refilling without pressure losses. However, a reduced pinch point temperature in the
heat exchanger means more energy can be harnessed from the HTF cycle.
The exergoeconomic analysis has shown that the optimization of the receiver could be most beneficial. Therefore, changes of two factors and its effect have been analyzed in this work, namely to
increase the recovery rate of the recycled HTF stream (in the table 6.12 determined as ”Air mixing
unit in absorber”) and to increase the concentration rate on the receiver resulting in an higher incident
radiation flux (q). The latter one is increased from 500kW/m2 to 600kW/m2 , while remaining the
solar field size and the absorber temperature constant. The effect is presented in figure 6.17. The
receiver area is ca. 20% smaller and thus radiation losses are reduced. More significant, though, for
the LEC in this case could be the reduction of the investment cost coming along with a smaller receiver.
Most effective is here to increase the recovery rate of the hot air released to the atmosphere in front
of the receiver. Full recovery is just possible when the receiver is covered. The effects of a cover in
front of the receiver, such as losses caused by reflection and savings due to the prevention of radiation losses, are here neglected. However, inexpensive changes can be worth it. An idea could be to
increase the angle of inclination on the receiver surface. Maybe a cap on top of the receiver could also
help to prevent larger air circulation and exchanges with the ambient. Since the factor f of the part
”Air mixing unit in absorber” is 1 in the exergoeconomic analysis, the investment of this component
shall not increase for this improvement (see chapter 6.2.2).
73
6. Simulation Results and Evaluation
Figure 6.18.: Exergy efficiencies of operation modes with different HTF recovery factors with the support of a duct burner.
Figure 6.17.: Overall exergy efficiencies of an annual performance simulation for the different configurations of the solar power tower in solar only operation.
The improvement, which can be achieved with a higher recovery rate, becomes less important
when the system is hybridized with a duct burner (see figure 6.18). The theoretical maximum of the
improvement lies in the range of 0.5%.
The changes undertaken on the tower system haven’t shown much of an improvement except for
the support with a duct burner.
74
6.2. Exergoeconomic Analysis
The following graphs are presenting the most important values of the exergoeconomic analysis
comparing all configurations of the solar tower plant. Here again figure 6.19 shows that most exergy
is destroyed in the solar field and the receiver. When relating only to these exergy destructions, this
could lead to a mistake to only draw attention to the receiver and the solar field for optimizations
of the power plant. The cost rate of exergy destruction is showing that this is not the case. Exergy
destroyed in the power block is more valuable (figure 6.20).
This is even more apparent when the plant is hybridized with a gas burner. Finally, the factor that is
involving all aspects, exergy destruction and its cost rate as well as the capital investment costs of the
components, is giving clear hints where optimization should take place (figure 6.21). A reduction of
these factor compared to the original basis configuration is a sign for a successful optimization.
Figure 6.19.: Annual exergy destruction including exergy losses in the main parts of the solar power
tower for the different configurations.
75
6. Simulation Results and Evaluation
Figure 6.20.: The cost rate of the annual exergy destruction C of the different configurations and main
parts in comparison.
Figure 6.21.: The cost importance C+Z (cost rate + cost of components) of the different configurations
and main parts in comparison.
Parts that are rather not significant can be neglected for further optimizations, such as the generator,
the storage system and the auxiliary burner (duct burner). The solar field has not been changed in the
different configurations. The results of the analysis (r=1) suggest that cost reduction is stringent for
lower LEC. As the optimization of the turbine is mainly possible with lowering the back pressure, it is
very site depending. Water cooling would improve the performance, but this is out of the scope of this
work cause the goal is to reduce the overall water consumption with the dry cooling systems. To put it
76
6.2. Exergoeconomic Analysis
in a nutshell, two parts should mainly be considered for further improvements regarding this analysis:
• Capital cost reduction of the solar field.
• Improvement of the receiver efficiency.
Many studies have been done for cost reduction of the solar field of a solar tower power plant, such
as the Sandia Labs study ”Cost Reduction of Heliostats”. One idea remains that could potentially
increase the receiver efficiency, when looking at the Carnot equation (2.2). The absorber temperature
can be increased for a greater efficiency.
6.2.4. Annual Performance of the Optimized Systems
The following table compares the LECs of the optimized systems. Besides the lower LECs for the
hybrid system, the amount of electricity generated through out the year is more than twice of the
solar only systems. This results strengthen again how important it is for the open volumetric solar
tower to be operated in hybrid mode. Although, there is a relatively good improvement achieved in
this simulations with the hybrid system, it is not yet enough to be competitive to commercial power
plants. Wind power has achieved costs as little as 8ecents/kWh and power generated by gas turbines
reaches LECs down to 6ecents/kWh. 2
2
Source: Sarasin Solar Study 2011
77
6. Simulation Results and Evaluation
Solar Only
Total Revenue Requirement
Gross Electricity Production
Parasitics
Net Electricity Production
Levelized Electricity Cost
Solar Only
Total Revenue Requirement
Gross Electricity Production
Parasitics
Net Electricity Production
Levelized Electricity Cost
Solar Only
Total Revenue Requirement
Gross Electricity Production
Parasitics
Net Electricity Production
Levelized Electricity Cost
With Duct Burner
Total Revenue Requirement
Gross Electricity Production
Parasitics
Net Electricity Production
Levelized Electricity Cost
78
[e/a]
[GWh/a]
[GWh/a]
[GWh/a]
[e/kWh]
60% Recovery
35,279,125
161.82
19.50
142.31
0.2479
80% Recovery
35,279,125
169
20.68
148.21
0.2380
100% Recovery
35,279,125
177
22.94
154.53
0.2283
[e/a]
[GWh/a]
[GWh/a]
[GWh/a]
[e/kWh]
q = 500kW/m2
35,279,125
161.82
19.50
142.31
0.2479
q = 550kW/m2
35,279,125
165
20.00
145.23
0.2429
q = 600kW/m2
35,279,125
168
20.38
147.46
0.2392
[e/a]
[GWh/a]
[GWh/a]
[GWh/a]
[e/kWh]
3bar/135◦ C
35,279,125
155.21
19
136.69
0.2581
3bar/145◦ C
35,279,125
155.15
19
136.63
0.2582
3bar/155◦ C
35,279,125
167.46
20
147.03
0.2399
[e/a]
[GWh/a]
[GWh/a]
[GWh/a]
[e/kWh]
60% Recovery
57,058,729
430.54
36.47
394.06
0.1448
80% Recovery
56,351,599
430.36
37.29
393.07
0.1434
100% Recovery
55,732,467
430.67
37.48
393.19
0.1417
7. Discussion
The results achieved in this work have to be considered as very sensitive. Many factors influence the
simulation and can cause wrong results or misleading understanding. It is therefore important to give
an inside in the problems of the tools applied for this work.
7.1. Simulation in Ebsilon
Ebsilon is a very strong tool for power plant simulations delivering very detailed informations about
each part involved in the plant, but this makes it also very complex and unstable when new components are integrated by the user. This was the case here with the solar tower power plant. Components
like the storage and receiver were not provided by the program and have been integrated with kernel
scripts.
These kernel scripts are reacting with the rest of the system and cause unstable operation of the
annual performance simulation with the result of convergence problems and some undefined peaks.
The simulation becomes too complex and time intensive that a limit of simulation steps per hour has
to be applied. Sometimes this limit has been reached and wrong results (even peaks) have been given
out for these specific hours. These peaks had to be taken out of the annual performance calculation
and thus some hours are missing with an effect on the annual performance calculations.
7.2. Exergoeconomic Analysis
Limits of the exergoeconomic analysis are reached. Such limits are for example reached whenever
larger changes of the system are possible. When relying strongly on the suggestion of the analysis
these changes remain hidden.
It cannot be derived from the analysis of the solar only mode that a duct burner would have such
an improvement on the system, for instance. Also, when analyzing the system with a duct burner,
it doesn’t seem to be apparent to apply a gas turbine instead of a gas burner, but experiences with
combined cycles show that this can affect the system very positively. However the solar share would
most likely drop dramatically with such an arrangement.
Another problem coming with the perspective of exergy is the question mark that remains related
to the treatment of solar radiation. Can solar radiation be considered as 100% exergy? Obviously
not, because it is not possible to use a 100% of the terrestrial solar radiation. There are direct and
diffuse radiations, for instance, and it is not possible to make use out of the diffuse light for CSP.
Also concentrated solar radiation is more valuable than normal radiation. Scientists are still analyzing
this topic. Interesting articles are for example the one of S.X. Chu, L.H. Liu (Analysis of terrestrial
solar radiation exergy, 2009) and the one of Yves Candau (On the exergy of radiation, 2003). In this
thesis work the terrestrial solar radiation has been considered to contain a 100% exergy, because of
79
7. Discussion
simplifications. This is definitely wrong, but this is one of the reasons why the benchmark with the
parabolic trough has been undertaken. When seeing the results of the parabolic trough as the basis,
the mistake can be neglected. However, the results shall not be taken out of the context.
The main reason why such an exergoeconomic analysis has not been established in the daily work
of power plant developers is its complexity. As described in chapter 4.2.1, it is crucial for an exergoeconomic analysis to pay attention to every component. It is not possible to group components in order
to get a better understanding and to minimize the complexity. It is therefore very time intensive and
difficult to derive conclusions out of the large amount of results.
7.3. Cost Calculations
The most critical part of the exergoeconomic analysis and the performance calculation is the cost
calculation, as its influence is very strong on the results. The cost estimations, however, are very
vague. This problem counts also for developer companies to get reliable offers from suppliers, but
it becomes even more difficult for research institutes that work together with companies of the entire
branch, such as the DLR. Companies that know real costs are very careful with this knowledge. This
is why cost estimations are often just based on such very vague estimates.
Therefore, the real LECs can differ very significantly from the results presented in this work. This
is even more the case for the solar tower system than for the parabolic trough, as more information is
available for this system. The parabolic trough system as a basis for comparison helps here just for
a few components, because many parts are completely different to the ones used in the solar power
tower.
80
8. Conclusion
The technical inside provided in this thesis follows the construction of the two concepts, the parabolic
trough and the solar tower, in Ebsilon. These models can be used for further design considerations
and operation simulations for the power plant that is under development for Algeria.
The parabolic trough system is serving as the basis in order to draw conclusions from the results.
The comparison also shows that the solar tower has a much higher potential for lower electricity costs,
especially under hybrid operation mode with LECs down to ca. 14ecents/kWh.
Several improvements in the system are investigated with the help of an exergoeconomic analysis.
All these adopted systems are compared with each other applying an exergy analysis and an exergoeconomic analysis as well as an annual performance analysis to calculate the levelized electricity costs.
The results show that the suggested improvements have a positive impact on the overall performance
and thus reduce the LECs.
However, none of the optimizations has shown an improvement like the additional gas burner in the
solar tower. It is therefore also recommended to look further into the potential of a combined cycle
solar tower.
The results of the exergoeconomic analysis substantiate the presumption that the receiver and the
solar field are the parts with the highest potential for optimizations. The focus for technical improvements should lie on the receiver and here in particular on the absorber elements. About 43% of the
exergy destruction occurs in the absorber, for instance. Higher receiver efficiencies are worth higher
investments. The optimization of the solar field, however, should mainly be cost reduction of its
components.
81
9. Outlook
The exergoeconomic analysis has shown that the most critical parts are still the receiver and the solar
field. The analyis could further be applied for the improvement of the solar field and the storage
relation and for the hybridization with a gas turbine. The results could help to find the optimized sizes
of the solar field, the storage and the turbine. Especially in this combined cycle configuration the
analysis can help to find the optimal solar share for the system. However, it would be most critical to
apply better cost estimations for the components.
The development stage of the tower technology is still in the early stages that remind on the early
stages of the wind turbines 20 years ago when the first demonstration turbine was built, the ”Grovian”.
Many turbines have been erected since then and the improvement came along. It seems that science
has shown that the OVR technology can work reliably and that it has significant advantages that are
strongly needed in a new EUMENA power park, such as dispatchability offered by the storage and a
very good potential of hybridization. The next step, following the example of the wind turbines, is to
erect plants of several Giga Watts of overall capacity. Just this way, significant cost improvements can
be achieved. When a market is existing suppliers will develop systems optimized for this technology
and the costs can be decreased with quantity, when mass production lines are in place.
82
Bibliography
[Trieb, 2005]
Trieb, F., Concentrating Solar Power for the Mediterranean Region (MED-CSP
2005), Final Report, German Aerospace Center (DLR), Institute of Technical Thermodynamics, 2005
[ECOSTAR]
R. Pitz-Paal, J. Dersch, B. Milow, European Concentrated Solar Thermal RoadMapping (ECOSTAR), German Aerospace Center (DLR), Institute of Technical
Thermodynamics, Cologne, 2005
[DII]
Dii GmbH, Joint venture DII established and ready to take up work, Press release
- Munich, Germany, October 30, 2009
[Powerfromthesun] Powerfromthesun, The Sun’s Possition, http://www.powerfromthesun.net, accessed at the 23th of June, 2010
[Bejan, 1996]
A. Bejan, G. Tsatsaronis, M. Moran, Thermal Design and Optimization, published
1996 by Wiley, ISBN 0-471-58467-3
[Pitz-Paal, 2008] R. Pitz-Paal Lecture notes ”Solartechnik”, RWTH Aachen, 2008
[Sokrates, 2004]
Franz Trieb, Stefan Kronshage, Volker Quaschning, Jürgen Dersch, Hansjörg
Lerchenmüller, Gabriel Morin, and Andreas Häberle, SOKRATES-Projekt, Solarthermische Kraftwerkstechnologie fà 41 r den Schutz des Erdklimas, German
Aerospace Center (DLR), Institute of Technical Thermodynamics, Stuttgart, and
Fraunhofer Institute for Solar Energy Systems, Freiburg, and PSE, Freiburg, 2005
[Duffie, 1991]
Duffie, J.A. und William A. Beckman, Solar Engineering of Thermal Processes.
Second Edition., published by John Wiley and Sons, Inc. New York., 1991
[Marco, 1995]
Marco, A., Integrierte Konzepte zum Einsatz der Solarenergie in der Kraftwerkstechnik., published by VDI-Verlag, Düsseldorf, 1995
[Kleemann, 1993] Kleemann, M., M. Meliss, Regenerative Energiequellen, published by Springer
Verlag, Berlin, October 30, 1993
[Sener, 2007]
Martin, J. Solar Tres, Sener Ingenieriá y Sistemas, published at the NREL CSP
technology workshop, Denver, March 07, 2007
[Sandia, 2010]
Sandia
National
Laboratories
Photo
database,
http://www.energylan.sandia.gov/photo/, accessed at the 16th of August,
2010
[Giuliano, 2010]
S. Giuliano, R. Buck, S. Eguiguren, Analysis of Solar Thermal Power Plants with
Thermal Energy Storage and Solar-Hybrid Operation Strategy, German Aerospace
Center (DLR), Institute of Technical Thermodynamics, Solar Research, Stuttgart,
2010
83
Bibliography
[Ardanuc, 2010]
S. Ardanuc, A. Lal, S. Jones, SELF-POWERED, WIRELESS, THIN-PROFILE SOLAR TILES (STILES) FOR CONCENTRATED SOLAR POWER HARVESTING,
Solar Paces 2010, Perpignan, 2010
[Richter, 2010]
T. Richter, Entwicklung eines Modells zur Ertragssimulation fà 41 r ein solares Turmkraftwerk und Implementierung in eine Software zur technischwirtschaftlichen Bewertung von regenerativen Kraftwerksanlagen, German
Aerospace Center (DLR), Institute of Technical Thermodynamics, Solar Research,
Köln, 2010
[Kehlhofer, 1999] Kehlhofer, R., Bachmann, R., Nielsen, H., Warner, J., Combined-Cycle Gas &
Steam Turbine Power Plants, 2. edition, PennWell Publishing Company, Tulsa,
1999
[Stine, 1985]
Stine, W., Harrigranm, R., Solar Energy Fundamentals and Design, John Wiley &
Sons. Inc., 1985.
[Runkel, 2007]
Runkel, F. Solarthermische War̈meeinkopplung aus Parabolrinnenkollektoren bei
einem kohlegefeuerten Dampfkraftwerk in China, Technical University Berlin, Institute of Energy Engineering, Berlin, December 2007.
[Uhlenbruck, 2001] Uhlenbruck, Stefan. Zur Unterstuẗzung evolutionar̈er Algorithmen bei der
Kostenoptimierung thermodynamischer Prozesse durch exergook̈onomische
Prinzipien., VDI Verlag, 2001.
[Lees, 1995]
Lees, M. The economics of wet versus dry cooling for combined cycle. In: Proceedings of the Institution of Mechanical Engineers, Part A (Journal of Power and
Energy). Volume 209, issue A1, 1995, p. 37-44.
[Maulbetsch, 2002] Maulbetsch, John S. Comparison of Alternate Cooling Technologies for California Power Plants - Economic, Environmental and Other Tradeoffs., Electric Power Research Institute (EPRI) for California Energy Commission; online:
http://www.energy.ca.gov/pier/final˙project˙reports/500-02-079f.html2002.
84
85
A. Appendix - Simulation Characteristics
A. Appendix - Simulation Characteristics
A.1. Control Diagram
86
Figure A.1.: The logical control scheme for the csp plants simulated in this work.
A.2. Power Plant Specifications
A.2. Power Plant Specifications
Common Specifications
Location
Location
Latitude
Longitude
Unit
Value
Comment
[◦ ] N
[◦ ] E
Seville
37.4
5.9
Spain
Table A.1.: Common specifications
Value
Comment
[◦ ] N
[◦ ] E
[kWh/m2 ]
[◦ C]
Seville
37.4
-5.9
2015
25
Spain
For 2005, DLR
From Meteonorm 6.1.0.9
[%]
[mbar]
932
From Meteonorm 6.1.0.9
From Meteonorm 6.1.0.9
[mm:dd - hh]
[W/m2 ]
[◦ C]
[bar]
[%]
06/24 - 14:00
850
25
1.013
0
0-Level for Exergy
Temperature
Enthalpy
Entropy
[◦ C]
[kJ/kg]
[kJ/kgK]
20
293.5
5.678
Input data set
DNI, hourly
Ambient temperature
[W/m2 ]
[◦ C]
file [data˙set.txt]
file [data˙set.txt]
Location
Location
Latitude
Longitude
Annual DNI
Air temperature
(mean/min/max)
Rel. humidity
Ambient pressure (mean)
Design Point
Design point (DP)
DNI
Ambient temperature
Ambient pressure
Rel. humidity
DLR
DLR
87
A. Appendix - Simulation Characteristics
Table A.2.: Solar Parabolic Trough specifications
88
Unit
Value
Solar Field
Field orientation
Number of loops
Number of collectors per loop
Distance between loops
Total area of the power plant
Field availability
HTF temperature at field entrance
HTF temperature at field exit
Design parasitic for pumping
[m]
[m2 ]
[%]
[◦ C]
[◦ C]
[kW]
North-south
144
4
18
1,741,824
99
294
395
2896.2
Collector
Collector type
Length of one collector
Gross aperture width
Net area of one collector
Number of collectors
Total reflective area
Mean reflectivity
Optical peak efficiency
[m]
[m]
[m2 ]
2
[m ]
[%]
[%]
Euro Trough II
150
5.76
817.43
576
470,840
88
75
Heat Transfer Fluid (HTF)
HTF
Density
Freezing point
Max. operation temperature
[kg/m3 ]
[◦ C]
[◦ C]
Therminol VP1
Ca. 1076
12
400
Storage
Type
Storage medium
Density
Operational point
Nominal pressure
Storage capacity
Storage capacity in hours full load
Nominal temp.- hot tank
Nominal temp.- cold tank
Pressure loss oil-sided
Pressure loss salt-sided
3
[kg/m ]
[◦ C]
[bar]
[MWh]
[h]
◦
[ C]
[◦ C]
[bar]
[bar]
2 tanks for molten salt
Salt: 60% NaNO3 + 40% KNO3
Ca. 2090
Max. 621/ min. 260
1
905
7
386
292
5
15
A.2. Power Plant Specifications
Unit
Steam Boiler
Type
[kg/s]
[◦ C]
[◦ C]
[t/h]
[bar]
[bar]
[◦ C]
[bar]
[◦ C]
Benson boiler - single-pressure water
pipe boiler with an upstream superheater and a downstream economizer,
operation with an even-pressure gradient
521
393
295.5
188.46
100 / 16.5
11-Feb
371/ 371
4
239.1
[-]
[MWel ]
[MWel ]
[%]
[%]
Dual pressure- cond.- machine
Siemens
86 / 89 / 83
50
45.9
39.9
36.6
[bar]
[◦ C]
[kg/s]
98
383
52.35
[bar]
[◦ C]
[kg/s]
18.1
382
41.7
Condenser
Type
Nominal power @DP
Steam mass flow @ DP
Steam pressure absolute @ DP
Parasitics @ DP
[MWth ]
[t/h]
[mbar]
[kWel ]
Air condenser
73
123.48
44
1048
Duct Burner
Nominal power
Fuel
Exhaust temperature @DP
Thermal efficiency
Pressure loss oil-sided
[MWth ]
◦
[ C]
[%]
[bar]
295.7
Natural gas
454
43.2
0.003
HTF mass flow @DP
HTF temperature at entrance @DP
HTF temperature at exit @DP
Steam mass flow, main steam (MS) @ DP
Steam pressure absolute (MS, RH) @ DP
Pressure loss (MS, LP) @ DP
Steam temperature (MS, RH)
Pressure loss oil-sided
Feed water temperature
Steam Turbine
Type
Manufacturer
Isentropic efficiency HP/MP/LP
Nominal power @DP
Net power @DP
El. Efficiency, gross @DP
El. Efficiency, net @DP
Main Steam (MS)
Pressure
Temperature
Mass flow
Low Pressure Steam (LP)
Pressure
Temperature
Mass flow
-
Value
89
A. Appendix - Simulation Characteristics
Plant
Number of steam turbines
Nominal power, gross @DP
Nominal power, net @DP
Electrical Efficiency, gross @DP
Electrical Efficiency, net @DP
Spec. Heat consumption @DP
Thermal power of power block @DP
Thermal power fossil @DP
Thermal power solar @DP
Solar share @DP
90
Unit
Value
[MWel ]
[MWel ]
[%]
[%]
[kJ/kWh]
[MWth ]
[MWth ]
[MWth ]
[%]
1
50
45.9
23.3
21.8
2832
12.5
0
251.9
200
A.2. Power Plant Specifications
Table A.3.: OVR Solar Power Tower
Solar Field
Orientation
Number of heliostats
Total area
Optical efficiency of the solar field @DP
Solar Tower
Building type
Height
Solar Receiver
Receiver Type
HTF (heat transfer fluid)
Mass flow @ DP
Receiver aperture
Nominal thermal power @DP
Receiver efficiency @DP
Receiver temperature at entrance @DP
Receiver temperature at exit @DP
Mean radiation density @DP
Pressure in receiver @DP
Share of recycled air
Pressure loss @DP
Compressor
Nominal power receiver comp./HRSG comp. (RC/HC)
Intake mass flow RC/HC @DP
Intake air temperature RC/HC @DP
Intake pressure RC/HC @DP
Compression ratio RC/HC @DP
Isentropic efficiency
Electric efficiency RC/HC @DP
Solid Matter Storage
Storage capacity
Storage capacity in hours full load
Pressure loss @DP
Exit temperature, charging @DP
Exit temperature, discharging @DP
Unit
Value
[m2 ]
[%]
North field
4930
3,055,022
28 - 73
[m]
Ferro-concrete
200
[kg/s]
[m2 ]
[MWth ]
[%]
[◦ C]
[◦ C]
[kW/m2]
[bar]
[%]
[bar]
Air
490.7
820
268.6
66.25
176.8
680
500
0.996
60
0.057
[kW]
[kg/s]
[◦ ]
[bar]
[-]
[-]
[%]
4773.2 / 3286.4
249.3 / 241.4
190.8 / 162.4
0.910 / 0.936
1.124 / 1.093
0,85
93.1 / 95.0
[MWh]
[h]
[bar]
[◦ C]
[◦ C]
900
7
0,056
173.6
650.6
91
A. Appendix - Simulation Characteristics
Heat Recovery Steam Generator (HRSG)
Type
-
HTF mass flow @DP
HTF temperature @DP
HTF exit temperature @DP
Steam mass flow (MS, RH, LP) @ DP
Steam pressure absolute (MS, RH, LP) @ DP
Steam temperature (MS, RH, LP) @ DP
Pressure loss HTF-sided
Pressure loss steam-sided (MS, RH, LP) @DP
Feed water temperature @DP
[kg/s]
[◦ C]
[◦ C]
[kg/s]
[bar]
[◦ C]
[bar]
[bar]
[◦ C]
Steam Turbine
Type
-
Air/water - dual-pressure water pipe
boiler with upstream superheater and
downstream economizer
241.4
680
149.8
35.6 / 35.7 / 4.9
149 / 60 / 10
540 / 540 / 300
0.03
10.1 / 10 / 0.1
45.8
Manufacturer
Isentropic efficiency MS/RH/LP
Nominal power, gross @DP
Nominal power, net @DP
Electric efficiency, gross @DP
Electric efficiency, net @DP
Thermal power, total incl. condenser @DP
Steam fraction at outlet @DP
[MWel ]
[MWel ]
[%]
[%]
[MWth ]
-
Dual pressure- cond.- machine with
low pressure feed-in
MAN Turbo (Hamburg)
87 / 88 / 88-86
50
40.1
36
28.73
239.7
0.9614
Condenser
Type
Nominal power @DP
Steam mass flow @ DP
Steam pressure absolute @ DP
Parasitics @ DP
[MWth ]
[kg/s]
[bar]
[kWel ]
Air condenser
87.4
40.4
0.1
1048.1
Plant
Number steam turbines
Nominal power, gross @DP
Nominal power, net @DP
Electric efficiency, gross @DP
Electric efficiency, net @DP
Heat consumption, net @DP
Thermal power, total @DP
Solar share @DP
[MWel ]
[MWel ]
[%]
[%]
[kW/kWel ]
[MWth ]
[%]
1
50
40.1
27.61
26.04
6.7
268.6
100
92
A.3. Ebsilon Models
A.3. Ebsilon Models
A.3.1. The Parabolic Trough Scheme of the Andasol Power Plant
Figure A.2.: The Ebsilon scheme for the parabolic trough power plant.
93
A. Appendix - Simulation Characteristics
A.3.2. The Open Volumetric Receiver Tower Scheme
Figure A.3.: The Ebsilon scheme for the open volumetric receiver tower.
94
A.4. Development of the Receiver and Solid Bed Storage for Ebsilon
A.4. Development of the Receiver and Solid Bed Storage for Ebsilon
A.4.1. The Receiver
A.4.1.1. The Absorber Programming and Calculation
1
Listing A.1: The Delphi code describes the characteristics of the absorber and is implemented in
Ebsilon.
uses @KernelScripting;//, eta_absorber;
2
3
4
5
6
7
8
9
10
11
12
13
var
eta, eta_abs, T_abs_out, T_abs_in : real;
H_abs_out, H_abs_in, Q_abs, Q_intercept : real;
m_abs, p_in, A_abs : real;
x, y,XX,YY, T: real;
air_substances : array[1..4] of string;
air_fractions : array[1..4] of real;
strEquation : string;
iLZ, iIndex, i,a, itno : integer;
bOk : boolean;
deltaH : real;
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
function AbsorberEfficiencyPolynomial(mode:integer;XX,YY,T:real):real;
//
var
p:array[0..20] of real;
eta:real;
begin
if (mode = 0) then
begin
{
Goodness of fit:
SSE: 0.1088
R-square: 0.9996
Adjusted R-square: 0.9996
RMSE: 0.006762
}
print("\n mode 0 \n");
p[0] :=
0.9606;
p[1] :=
0.03874;
p[2] :=
-0.01721;
p[3] :=
-0.01509;
p[4] :=
0.002681;
p[5] :=
0.002366;
p[6] :=
0.003728;
p[7] :=
-0.003161;
p[8] :=
0.001899;
p[9] := -0.0009159;
p[10] := -0.0004565;
p[11] :=
0.0006098;
95
A. Appendix - Simulation Characteristics
p[12]
p[13]
p[14]
p[15]
p[16]
p[17]
p[18]
p[19]
p[20]
45
46
47
48
49
50
51
52
53
:= -0.0004146;
:=
0.0001202;
:= 1.421e-005;
:=
2.19e-005;
:= -4.124e-005;
:=
3.92e-005;
:= -2.176e-005;
:= 7.873e-006;
:= -2.085e-006;
54
55
56
57
58
59
60
61
62
63
p[0] :=
p[1] :=
p[2] :=
p[3] :=
p[4] :=
p[5] :=
p[6] :=
p[7] :=
p[8] :=
p[9] :=
p[10] :=
p[11] :=
p[12] :=
p[13] :=
p[14] :=
p[15] :=
p[16] :=
p[17] :=
p[18] :=
p[19] :=
p[20] :=
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
end;
IF (mode = 1) THEN
begin
{
Goodness of fit:
SSE: 0.1135
R-square: 0.9996
Adjusted R-square: 0.9996
RMSE: 0.006906
}
print("\n mode 1 \n");
0.9525;
0.05904;
-0.0264;
-0.0205;
0.002066;
0.004156;
0.004557;
-0.003246;
0.002024;
-0.001103;
-0.0005218;
0.0006247;
-0.0004155;
0.0001096;
2.526e-005;
2.435e-005;
-4.349e-005;
4.156e-005;
-2.342e-005;
8.757e-006;
-2.425e-006;
end;
86
87
88
89
90
91
92
93
94
p[0] :=
p[1] :=
p[2] :=
95
96
97
96
IF (mode = 2) THEN
begin
{
Goodness of fit:
SSE: 0.118
R-square: 0.9996
Adjusted R-square: 0.9996
RMSE: 0.007042
}
print("\n mode 2 \n");
0.953;
0.08003;
-0.04011;
A.4. Development of the Receiver and Solid Bed Storage for Ebsilon
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
p[3] :=
-0.02548;
p[4] :=
0.0009903;
p[5] :=
0.006796;
p[6] :=
0.005276;
p[7] :=
-0.003279;
p[8] :=
0.002171;
p[9] :=
-0.001361;
p[10] := -0.0005753;
p[11] :=
0.0006315;
p[12] := -0.0004128;
p[13] := 9.658e-005;
p[14] := 3.938e-005;
p[15] := 2.633e-005;
p[16] := -4.526e-005;
p[17] :=
4.36e-005;
p[18] := -2.496e-005;
p[19] := 9.639e-006;
p[20] := -2.808e-006;
end;
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
p[0] :=
p[1] :=
p[2] :=
p[3] :=
p[4] :=
p[5] :=
p[6] :=
p[7] :=
p[8] :=
p[9] :=
p[10] :=
p[11] :=
p[12] :=
p[13] :=
p[14] :=
p[15] :=
p[16] :=
p[17] :=
p[18] :=
p[19] :=
p[20] :=
IF (mode = 3) THEN
begin
{
Goodness of fit:
SSE: 0.1223
R-square: 0.9996
Adjusted R-square: 0.9996
RMSE: 0.007171
}
print("\n mode 3 \n");
0.9527;
0.1123;
-0.05963;
-0.03239;
-0.001648;
0.01079;
0.00618;
-0.003146;
0.002413;
-0.001745;
-0.0006379;
0.0006277;
-0.0004133;
7.903e-005;
5.931e-005;
2.865e-005;
-4.735e-005;
4.653e-005;
-2.701e-005;
1.079e-005;
-3.32e-006;
end;
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149
150
IF (mode > 3) THEN
begin
97
A. Appendix - Simulation Characteristics
AbsorberEfficiencyPolynomial:=0;
end
else
begin
x := XX/100000;
//Um Surface fitting in Matlab zu
ermöglichen wurden die Werte auf einstellige Einheiten
normalisiert.
y := YY/100;
print ("p[0]", p[0],"\n");
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152
153
154
155
156
157
158
eta := p[0] + p[1]*x + p[2]*y + p[3]*x*x + p[4]*x*y + p
[5]*y*y + p[6]*x*x*x + p[7]*x*x*y + p[8]*x*y*y + p[9]*
y*y*y + p[10]*x*x*x*x + p[11]*x*x*x*y + p[12]*x*x*y*y
+ p[13]*x*y*y*y + p[14]*y*y*y*y + p[15]*x*x*x*x*x + p
[16]*x*x*x*x*y + p[17]*x*x*x*y*y + p[18]*x*x*y*y*y + p
[19]*x*y*y*y*y + p[20]*y*y*y*y*y;
AbsorberEfficiencyPolynomial:= eta;
print ("x: ",x," y: ",y, "\n");
end;
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162
end;
163
164
function AbsorberEfficiency(XX, YY, T:real):real;
var
TB:array[0..4] of real;
i,pol,pol2:integer;
VALUE1,VALUE2,TB_difference:real;
begin
TB[0] := 298;
TB[1] := 356.333;
TB[2] := 414.667;
TB[3] := 473;
TB[3] := 531.333;
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166
167
168
169
170
171
172
173
174
175
176
{Das passende Temperaturintervall bestimmen}
i:=0;
pol:=0;
while (i <= 3) do
begin
if (T >= TB[i])then
begin
pol:= i;
end;
i:=i+1;
end;
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178
179
180
181
182
183
184
185
186
187
188
{Werte aus Polynomen bestimmen}
pol2:= pol +1;
//if pol2 > 3 then begin pol2:=3; end;
VALUE1 :={0.7501;//}AbsorberEfficiencyPolynomial(pol,XX,
YY,T);
VALUE2 :={0.7501;//}AbsorberEfficiencyPolynomial(pol2,XX,
YY,T);
189
190
191
192
193
194
98
A.4. Development of the Receiver and Solid Bed Storage for Ebsilon
print ("Value1: ",Value1," pol: ",pol, "\n");
print ("Value2: ",Value2," pol2: ",pol2, "\n");
195
196
197
{Zwischen Temperaturen interpolieren}
TB_difference:= TB[pol2] - TB[pol];
if TB_difference=0 then begin TB_difference:=1; end;
absorberefficiency := VALUE1 + (VALUE2 - VALUE1) * (T TB[pol]) / (TB_difference);
198
199
200
201
end;
202
203
204
begin
205
206
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208
209
210
211
212
213
214
air_substances[1] := "N2";
air_substances[2] := "O2";
air_substances[3] := "AR";
air_substances[4] := "CO2";
air_fractions[1] := 0.7552000000;
air_fractions[2] := 0.2314000000;
air_fractions[3] := 0.0129000000;
air_fractions[4] := 0.0005000000;
215
216
217
A_abs := ksGetSPEC (1);
//A_abs:=139.17; //[m2] Abändern in nur einen Trichter und der
WVerwendung des Sammlers in Ebsilon!!!
218
219
220
221
222
223
224
225
226
227
iLZ:=ksGetItNo;
if ksGetMode = Initializing then
begin
ksRemoveAllEquations;
iIndex:=ksGetMaxEquationIndex;
print("initialisieren \n");
iIndex:=iIndex+1;
strEquation:="M3-M12=0";
bOk:=ksSetEquation (iIndex,strEquation);
228
229
230
231
iIndex:=iIndex+1;
strEquation:="P3-P12=0";
bOk:=ksSetEquation (iIndex,strEquation);
232
233
234
235
236
237
end
else
begin
a:=getcalcProfile;
print ("\n a: ",a,"\n");
238
239
240
241
242
243
244
245
// Einlesen relevanter Leitungswerte
H_abs_in := ksGetPipeValue(3, PhysValueH);
H_abs_out := ksGetPipeValue(12, PhysValueH);
if H_abs_out<500 then begin H_abs_out:=500; end;
Q_intercept:= ksGetSPEC (2);
A_abs:= ksGetSPEC (1);
P_in := ksGetPipeValue(3, PhysValueP);
99
A. Appendix - Simulation Characteristics
T_abs_in := {ksGetPipeValue(3, PhysValueT);//}fluegasTable(1003,
P_in, H_abs_in, air_substances, air_fractions, 4, 1);
T_abs_out:= fluegasTable(1003, P_in, H_abs_out, air_substances,
air_fractions, 4, 1);
// If T_abs_out>920 then T_abs_out:=920;
246
247
248
249
// Berechnung Receiverwirkungsgrades
250
251
print("T_abs_in: ",T_abs_in,"\n","T_abs_out: ",T_abs_out);
//T_abs_out := fluegasTable(1003, P_in, H_abs_out, air_substances
, air_fractions, 4, 1);
252
253
254
///////Absorberberechnung/////////////////////////////////
255
256
XX:= Q_intercept*1000/A_abs;
YY:= T_abs_out +273.15;
T:= T_abs_in +273.15;
eta_abs:=AbsorberEfficiency(XX,YY,T);
257
258
259
260
261
262
263
264
//
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
//
//
280
281
//
282
283
print ("eta_abs vor Dämpfung: ",eta_abs, "\n");
if eta_abs<0.2 then begin eta_abs:=0.2; end;
Dämpfung von eta_abs
if (ksGetItNo() > 10) then
begin
if ((eta_abs - @model.eta_abs_save) > 0.01) then
begin
eta_abs:[email protected]_abs_save + 0.01;
end;
if ((@model.eta_abs_save - eta_abs) > 0.01) then
begin
eta_abs:[email protected]_abs_save - 0.01;
end;
end;
if (ksGetItNo() > 100) then
begin
if (abs(eta_abs - @model.eta_abs_save) > 0.0001) then
begin
eta_abs:=0.5*(@model.eta_abs_save + eta_abs);
end;
end;
@model.eta_abs_save:=eta_abs;
284
285
286
287
288
//
289
290
291
292
293
294
295
100
Q_abs:= Q_intercept*eta_abs;
m_abs:= Q_abs/(H_abs_out-H_abs_in);
m_abs:=ksGetPipeValue(12, physValueM);
if (m_abs > 0.01) then
begin
deltaH:=Q_abs/m_abs;
end
else
begin
A.4. Development of the Receiver and Solid Bed Storage for Ebsilon
deltaH:=0;
296
end;
297
298
print(" m: ",m_abs, "YY: ",YY, " XX: ",XX, " H_abs_in: ",
H_abs_in," H_abs_out: ", H_abs_out," T: ",T,"\n");
print ("eta_abs: ",eta_abs, "\n");
print (" Q_intercept: ",Q_intercept, "\n");
print ("Iterationsnummer: ",ksGetItNo, "\n \n \n");
299
300
301
302
303
304
305
306
//
307
308
309
310
311
//
312
313
314
315
316
317
318
319
320
321
322
323
iIndex:=iIndex+1;
strEquation:=printToString ("M12*H12-M3*H3=",Q_abs);
strEquation:=printToString ("H12-H3=",deltaH);
bOk:=ksSetEquation (iIndex,strEquation);
if (not bOk) then println ("Gleichung 1 konnte nicht
werden.");
iIndex:=iIndex+1;
strEquation:=printToString ("M3=",m_abs);
strEquation:="M3-M12=0";
bOk:=ksSetEquation (iIndex,strEquation);
if (not bOk) then println ("Gleichung 2 konnte nicht
werden.");
iIndex:=iIndex+1;
strEquation:=printToString ("P12=",P_in);
bOk:=ksSetEquation (iIndex,strEquation);
if (not bOk) then println ("Gleichung 3 konnte nicht
werden.");
iIndex:=iIndex+1;
strEquation:=printToString ("H7=",eta_abs);
bOk:=ksSetEquation (iIndex,strEquation);
if (not bOk) then println ("Gleichung 4 konnte nicht
werden.");
end;
gesetzt
gesetzt
gesetzt
gesetzt
324
iIndex:=ksGetMaxEquationIndex;
for i:=1 to iIndex do
begin
strEquation:=ksGetEquation(i);
end;
325
326
327
328
329
330
331
1
2
3
4
end;
Listing A.2: The solid bed storage component is described in this Delphi script. The script also includes the regulation mechanism for the annual simulations.
FUNCTION AbsorberEfficiencyPolynomial(case,X,Y,T)
{Polynom coefficients defined for q_solar= 0...700kW/m2, X
=100...3000}
IF (case = 1) THEN
p_xy[1..36] = [8.269E-01,-7.081E-01,5.035E-01,-2.737E
-01,6.384E-01,-5.373E-01,5.456E-01,-4.963E-01,-1.267E
-01,2.648E-01,-1.701E-01,-9.846E-03,2.063E-01,-1.491E
-02,-7.088E-02,-2.533E-02,9.166E-02,-6.390E-02,-2.240E
101
A. Appendix - Simulation Characteristics
-02,7.259E-03,1.070E-02,1.974E-02,-2.566E-02,5.054E
-03,6.735E-03,6.998E-04,-8.324E-04,-8.580E-04,-2.453E
-03,2.035E-03,3.487E-04,-5.817E-04,-1.586E-04,4.435E
-06,3.303E-05,2.843E-05]
ENDIF
IF (case = 2) THEN
p_xy[1..36] = [6.825E-01,-6.660E-01,7.212E-01,-2.465E
-01,3.997E-01,-6.692E-01,5.942E-01,-4.374E-01,1.675E
-02,3.065E-01,-2.498E-01,1.350E-02,1.504E-01,-5.040E
-02,-7.857E-02,1.288E-02,8.017E-02,-5.799E-02,-1.052E
-02,1.173E-02,1.153E-02,1.204E-02,-2.501E-02,6.231E
-03,5.079E-03,-2.677E-04,-1.123E-03,-9.063E-04,-1.897E
-03,2.192E-03,1.288E-04,-5.195E-04,-8.418E-05,3.298E
-05,4.083E-05,2.959E-05]
ENDIF
IF (case = 3) THEN
p_xy[1..36] = [5.773E-01,-7.940E-01,8.835E-01,6.622E
-02,3.010E-01,-7.791E-01,3.968E-01,-5.221E-01,1.075E
-01,3.475E-01,-2.077E-01,1.154E-01,1.314E-01,-7.640E
-02,-8.775E-02,1.507E-02,4.527E-02,-6.499E-02,-3.529E
-03,1.544E-02,1.276E-02,1.046E-02,-2.086E-02,9.686E
-03,4.447E-03,-9.321E-04,-1.399E-03,-9.972E-04,-1.807E
-03,2.152E-03,-2.531E-04,-5.368E-04,-4.073E-05,5.495E
-05,4.942E-05,3.241E-05]
ENDIF
IF (case = 4) THEN
p_xy[1..36] = [4.139E-01,-7.760E-01,1.099E+00,2.401E
-01,6.364E-02,-9.116E-01,2.676E-01,-4.761E-01,2.452E
-01,3.937E-01,-1.926E-01,1.609E-01,7.718E-02,-1.106E
-01,-9.762E-02,2.911E-02,2.060E-02,-5.895E-02,7.495E
-03,2.001E-02,1.404E-02,5.334E-03,-1.691E-02,1.086E
-02,2.860E-03,-1.816E-03,-1.728E-03,-1.088E-03,-1.302E
-03,2.008E-03,-4.852E-04,-4.707E-04,2.719E-05,8.142E
-05,5.956E-05,3.513E-05]
ENDIF
IF (case = 5) THEN
p_xy[1..36] = [2.392E-01,-7.805E-01,1.305E+00,5.272E
-01,-1.597E-01,-1.029E+00,-1.024E-02,-4.507E-01,3.700E
-01,4.315E-01,-8.184E-02,2.270E-01,2.746E-02,-1.401E
-01,-1.051E-01,9.241E-03,-1.431E-02,-5.399E-02,1.738E
-02,2.375E-02,1.493E-02,6.679E-03,-1.069E-02,1.238E
-02,1.349E-03,-2.572E-03,-1.986E-03,-1.147E-03,-1.321E
-03,1.692E-03,-7.843E-04,-3.925E-04,8.480E-05,1.040E
-04,6.717E-05,3.678E-05]
ENDIF
IF (case = 6) THEN
p_xy[1..36] = [-1.187E-02,-5.279E-01,1.561E+00,4.934E
-01,-5.446E-01,-1.159E+00,-9.073E-02,-2.490E-01,5.348E
-01,4.699E-01,-3.847E-02,2.000E-01,-5.458E-02,-1.750E
-01,-1.121E-01,4.191E-03,-2.459E-02,-3.614E-02,3.008E
-02,2.792E-02,1.570E-02,5.508E-03,-7.194E-03,1.121E
-02,-7.443E-04,-3.474E-03,-2.258E-03,-1.194E-03,-1.087
E-03,1.423E-03,-8.495E-04,-2.664E-04,1.551E-04,1.295E
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
102
A.4. Development of the Receiver and Solid Bed Storage for Ebsilon
-04,7.481E-05,3.798E-05]
ENDIF
20
21
x = X/1000
y = Y/100000
22
23
24
eta = p_xy[1] + p_xy[2]*x + p_xy[3]*y + p_xy[4]*xˆ2 + p_xy[5]*x*y
+ p_xy[6]*yˆ2 + p_xy[7]*xˆ3 + p_xy[8]*xˆ2*y + p_xy[9]*x*yˆ2 +
p_xy[10]*yˆ3 + p_xy[11]*xˆ4 + p_xy[12]*xˆ3*y + p_xy[13]*xˆ2*y
ˆ2 + p_xy[14]*x*yˆ3 + p_xy[15]*yˆ4 + p_xy[16]*xˆ5 + p_xy[17]*x
ˆ4*y + p_xy[18]*xˆ3*yˆ2 + p_xy[19]*xˆ2*yˆ3 + p_xy[20]*x*yˆ4 +
p_xy[21]*yˆ5 + p_xy[22]*xˆ6 + p_xy[23]*xˆ5*y + p_xy[24]*xˆ4*y
ˆ2 + p_xy[25]*xˆ3*yˆ3 + p_xy[26]*xˆ2*yˆ4 + p_xy[27]*x*yˆ5 +
p_xy[28]*yˆ6 + p_xy[29]*xˆ7 + p_xy[30]*xˆ6*y + p_xy[31]*xˆ5*y
ˆ2 + p_xy[32]*xˆ4*yˆ3 + p_xy[33]*xˆ3*yˆ4 + p_xy[34]*xˆ2*yˆ5 +
p_xy[35]*x*yˆ6 + p_xy[36]*yˆ7
25
26
AbsorberEfficiencyPolynomial = eta
27
28
END
29
30
31
32
33
34
35
36
FUNCTION AbsorberEfficiency(X, Y, T)
TB[1] = 298 - 273.15
TB[2] = 373 - 273.15
TB[3] = 448 - 273.15
TB[4] = 523 - 273.15
TB[5] = 598 - 273.15
TB[6] = 673 - 273.15
37
{Determining the right temperature interval}
i:=1
REPEAT
IF (T >= TB[i]) THEN
pol = i
ENDIF
i:=i+1,
UNTIL (i >= 6)
38
39
40
41
42
43
44
45
46
{Determination of of correct variables of polynom}
VALUE1 = AbsorberEfficiencyPolynomial(pol,X,Y,T)
VALUE2 = AbsorberEfficiencyPolynomial(pol+1,X,Y,T)
47
48
49
50
{Interpolate between temperatures}
absorberefficiency = VALUE1 + (VALUE2 - VALUE1) * (T - TB[pol]) /
(TB[pol+1] - TB[pol])
51
52
53
END
54
55
56
57
58
59
60
61
{Nusselt number definition for the ring slit}
FUNCTION nusselt_ringspalt_laminar(mode$, Re, Pr, d_h, d_i, d_a, L)
IF (mode$ = ’i’) THEN
Nu1 = (3.66+1.2*(d_i/d_a)ˆ(-0.8))
f_g = 1.615 * (1+0.14 * (d_i/d_a)ˆ(-0.5))
ELSE
103
A. Appendix - Simulation Characteristics
Nu1 = 3.66 + (4 - 0.102 / ((d_i/d_a) + 0.02)) * (d_i/d_a)
ˆ0.04
f_g = 1.615 * (1 + 0.14 * (d_i/d_a)ˆ0.1)
62
63
ENDIF
Nu2 = f_g * (Re*Pr*d_h/L)ˆ(1/3)
Nu3 = (2/(1+22*Pr))ˆ(1/6) * (Re*Pr*d_h/L)ˆ(1/2)
Nu = (Nu1ˆ3+Nu2ˆ3+Nu3ˆ3)ˆ(1/3) {Konservative Annahme:
Hydrodynamischer Anlauf}
nusselt_ringspalt_laminar = Nu
64
65
66
67
68
69
END
70
71
72
73
74
75
76
77
78
79
80
FUNCTION nusselt_ringspalt_turbulent(mode$, Re, Pr, d_h, d_i, d_a, L)
IF (mode$ = ’i’) THEN
c = 0.86 * (d_i/d_a)ˆ(-0.16)
ELSE
c = (0.86 * (d_i/d_a)ˆ0.84 + (1-0.14*(d_i/d_a)ˆ0.6))/(1+(
d_i/d_a))
ENDIF
Nu_rohr = nusselt_rohr_turbulent(Re, Pr, d_h, L)
Nu = c * Nu_rohr
nusselt_ringspalt_turbulent = Nu
END
81
82
83
84
85
86
87
88
89
{Nusselt number formulations for the pipe}
FUNCTION nusselt_rohr_laminar(Re, Pr, d, L)
Nu_1 = 3.66
Nu_2 = 1.615 * ((Re * Pr* d/L))ˆ(1/3)
Nu_3 = (2/(1+22 * Pr))ˆ(1/6) * (Re*Pr*d/L)ˆ(1/2)
Nu = (Nu_1ˆ3 + 0.7ˆ3 + (Nu_2 - 0.7)ˆ3 + Nu_3)ˆ(1/3)
nusselt_rohr_laminar = Nu
END
90
91
92
93
94
95
FUNCTION nusselt_rohr_turbulent(Re, Pr, d, L)
xi = (1.8 * log10(Re) - 1.5)ˆ(-2)
Nu = (xi/8 * Re * Pr)*(1+(d/L)ˆ(2/3))/(1+12.7*(xi/8)ˆ0.5*(Pr
ˆ(2/3)-1))
nusselt_rohr_turbulent = Nu
END
96
97
98
99
100
101
102
103
104
{Pressure loss formulations}
FUNCTION zeta_laminar(mode$, Re)
IF (mode$ = ’rohr’) THEN
zeta_laminar = 64 / Re
ELSE
zeta_laminar = 1.5 * 64 / Re
ENDIF
END
105
106
107
108
FUNCTION zeta_turbulent(mode$, Re)
zeta_turbulent = 0.3164 / (Reˆ(0.25))
END
109
110
{gives out heat transfer coefficient for ring slit}
104
A.4. Development of the Receiver and Solid Bed Storage for Ebsilon
111
112
113
{streaming of the ring slit related to VDI Wärmeatlas 10th edition}
{mode = ’i’ (Innenrohr beheizt) oder ’b’ (Innen- und Aussenrohr beheizt)}
PROCEDURE ringspalt (Fluid$, mode$, T_m, P_amb, m_dot, d_i, d_a, L, x_H2O
: alpha, Nu, Re, dp)
114
mu = viscosity(Fluid$,T=T_m, P=P_amb, W=x_H2O)
lambda = conductivity(Fluid$,T=T_m, P=P_amb, W=x_H2O)
rho = density(Fluid$,T=T_m, P=P_amb, W=x_H2O)
c_p = cp(Fluid$,T=T_m, P=P_amb, W=x_H2O)
Pr = mu * c_p / lambda
115
116
117
118
119
120
d_h = d_a - d_i
v = m_dot / (rho * pi/4 * (d_aˆ2 - d_iˆ2))
Re = rho * v * d_h / mu
121
122
123
124
IF (Re < 2300) THEN
Nu = nusselt_ringspalt_laminar(mode$, Re, Pr, d_h, d_i,
d_a, L)
zeta = zeta_laminar(’ringspalt’, Re)
ELSE
IF (Re < 10000) THEN
Nu_L = nusselt_ringspalt_laminar(mode$, 2300, Pr,
d_h, d_i, d_a, L)
Nu_T = nusselt_ringspalt_turbulent(mode$, 10000,
Pr, d_h, d_i, d_a, L)
gamma = (Re - 2300) / (10000 - 2300)
Nu = (1 - gamma) * Nu_L + gamma * Nu_T
ELSE
Nu = nusselt_ringspalt_turbulent(mode$, Re, Pr,
d_h, d_i, d_a, L)
ENDIF
zeta = zeta_turbulent(’ringspalt’, Re)
ENDIF
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
alpha = Nu / d_h * lambda
dp = zeta * L / d_i * rho * vˆ2 / 2
140
141
142
END
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144
145
146
147
148
149
150
151
{Gives out heat transfer coefficent for the pipe}
{streaming in the pipe relating VDI Wärmeatlas 10th edition}
PROCEDURE rohrstroemung (Fluid$, T_m, P_amb, m_dot, d, L, x_H2O: alpha,
Nu, Re, dp)
mu = viscosity(Fluid$,T=T_m, P=P_amb, W=x_H2O)
lambda = conductivity(Fluid$,T=T_m, P=P_amb, W=x_H2O)
rho = density(Fluid$,T=T_m, P=P_amb, W=x_H2O)
c_p = cp(Fluid$,T=T_m, P=P_amb, W=x_H2O)
Pr = mu * c_p / lambda
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153
154
v = m_dot / rho / (pi/4*dˆ2)
Re = rho * v * d / mu
155
156
157
IF (Re < 2300) THEN
Nu = nusselt_rohr_laminar(Re, Pr, d, L)
105
A. Appendix - Simulation Characteristics
zeta = zeta_laminar(’rohr’, Re)
158
ELSE
159
IF (Re < 10000) THEN
Nu_L = nusselt_rohr_laminar(2300, Pr, d, L)
Nu_T = nusselt_rohr_turbulent(10000, Pr, d, L)
gamma = (Re - 2300) / (10000 - 2300)
Nu = (1 - gamma) * Nu_L + gamma * Nu_T
ELSE
Nu = nusselt_rohr_turbulent(Re, Pr, d, L)
ENDIF
zeta = zeta_turbulent(’rohr’, Re)
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161
162
163
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167
168
ENDIF
169
170
alpha = Nu / d * lambda
dp = zeta * L / d * rho * vˆ2 / 2
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173
END
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175
{""""""""""""""""""""""""""""""""{Start Main Program}
"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""}
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180
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182
{General}
x_H2O = humrat(Fluid$, T=T_amb, P=P, R=humidity)
h_rec_in = enthalpy(Fluid$, T=T_rec_in, P=P, W=x_H2O)
{h_rec_out = enthalpy(Fluid$, T=T_rec_out, P=P, W=x_H2O)
}
h_abs_cub_out = enthalpy(Fluid$, T=T_abs_cub_out, P=P, W=x_H2O)
h_amb = enthalpy(Fluid$, T=T_amb, P=P, W=x_H2O)
183
184
185
186
{Result evaluation}
dp_tot = SUM(dp[1][j], j=3,6) + SUM(dp[2][j], j=3,6)
{dT_rec = T[1][6] - T[1][1]
}
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195
196
197
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199
200
201
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203
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{Geometry}
A_abs = 5.67 [mˆ2] / n_abs
A_trichter = 6.5
n_abs = 270
B_abs = 140 / 1000
d_i = 83.5 / 1000
d_a = 90.5 / 1000
d_trichter = 1.8
d_sammelrohr = 0.7
s_iso = 9.5 / 1000
s_iso_trichter = 30 / 1000
s_iso_sammelrohr = 100 / 1000
s_wand = 1.5 / 1000
s_abs = 4.5 / 1000
s_spalt = 5 / 1000
B_kanal = 0.0019 [m]
n_kanal = 2500
205
206
207
lambda_stahl = 40
lambda_sisic = 35
106
A.4. Development of the Receiver and Solid Bed Storage for Ebsilon
208
lambda_iso = 0.25
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210
211
212
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214
215
L[1]
L[2]
L[3]
L[4]
L[5]
L[6]
=
=
=
=
=
=
1700 / 1000
A_trichter / (pi * d_trichter)
150 / 1000
50 / 1000
100 / 1000
43 / 1000
216
217
218
219
{Absorber}
h_abs_in = h[1][7]
h_return_out = h[2][7]
220
221
222
223
224
X = (Q_intercept / m_dot) / 1000
Y = q_solar
eta_abs = AbsorberEfficiency(X, Y, T_abs_in)
225
226
227
228
229
Q_intercept = A_abs * q_solar
Q_abs = eta_abs * A_abs * q_solar
T_abs_in = T[1][7]
T_abs_out = T[1][6]
230
231
232
{Receiver} {/Absorber Cub}
{h_rec_out = h[1][1]
}
233
234
235
236
237
238
h_rec_in = h[2][3]
h_abs_cub_out = h[1][3]
Q_abs_cub= m_dot * (h_abs_cub_out - h_rec_in)
{Q_rec = m_dot * (h_rec_out - h_rec_in)
}
eta_cub = Q_abs_cub/ Q_intercept
{ef = eta_rec / eta_abs "Relative Bewertungsgröße für internen
Wärmeaustausch"
}
239
240
241
242
243
244
245
246
{Heat transfer/ input over/in wall (e.g. through conduction or radiation)
}
Q_w[3] = 0
Q_w[4] = 0
Q_w[5] = 0
Q_w[6] = pi * ((d_bez[5] + d_bez[6]))/2 * lambda_sisic * (Tw[6] - Tw[5])
{Q_w[6] = 0}
Q_w[7] = Q_abs
247
248
249
250
251
252
253
{General Formulations or balances}
DUPLICATE j=3,6
k[1][j] = alpha[1][j]
"Wärmeübergang Hauptströmung"
k[2][j] = 1/(1/k_wand[j] + 1/alpha[2][j])
"Wärmeüber- und Durchgang bei Rückführluft"
Q[1][j] = A[1][j] * k[1][j] * (Tm[1][j] - Tw[j])
"Wärmeaufnahme vom Fluid der Hauptströmung"
Q[2][j] = A[2][j] * k[2][j] * (Tw[j] - Tm[2][j])
107
A. Appendix - Simulation Characteristics
"Wärmeaufnahme vom Fluid auf Rückführseite"
254
Q[1][j] = m_dot * (h[1][j+1] - h[1][j])
"Energiebilanz Hauptströmung"
Q[2][j] = m_dot * (h[2][j+1] - h[2][j])
"Energiebilanz Rückführluft"
Q_w[j+1] + Q[1][j] = Q_w[j] + Q[2][j]
"Energiebilanz Wandelement"
255
256
257
258
END
259
260
261
262
263
{Exergetic Efficiency}
eta_ex_abs = (e_ph[1][3]*m_dot -e_ph[2][3]*m_dot)/ ( Q_intercept)
{eta_ex_rec = (e_ph[1][1]*m_dot - e_ph[2][3]*m_dot + (1-arr)*E[2][7]) / (
Q_intercept+e_amb* (1-arr) *m_dot)
}
{e_ph[2][3] = Eingang
der Luft in den Reciever!}
eta_ex_abs_structure=(e_ph[1][6]*m_dot-e_ph[2][6]*m_dot) / ( Q_intercept)
264
265
266
267
268
269
270
271
272
273
274
{Exergetic losses or destructions}
{0=Sum(Eq)-Wcv+Sum(Ein)-Sum(Eout)-E_D}
{DUPLICATE j=1,2
E_D[j] = E[1][j+1]-E[1][j]
END
}
E_D[3] = E[1][4]-E[1][3]+ E[2][3]-E[2][4]
E_D[4] = E[1][5]-E[1][4]+ E[2][4]-E[2][5]
E_D[5] = E[1][6]-E[1][5]+ E[2][5]-E[2][6] + (1-(T_rel+273.15)/(273.15+T
[1][6])) * Q_w[6]
E_D[6] = E[1][7]-E[1][6]+ E[2][6]-E[2][7] + Q_w[7] - (1-(T_rel+273.15)/(T
[1][6]+273.15)) * Q_w[6]
E_D[7] = e_amb*m_dot*0.4-E[1][7]+ E[2][7]-0.4*E[2][7]
275
276
277
278
279
280
281
282
283
284
285
DUPLICATE j=3,7
DUPLICATE i=1,2
h[i][j] = enthalpy(Fluid$, T=T[i][j], P=P, W=x_H2O)
"Enthalpieberechnung"
H_th[i][j] = h[i][j] * m_dot
s[i][j] = Entropy(Fluid$,T=T[i][j],P=P, W=x_H2O)
e_ph[i][j] = h[i][j]-h_rel-( T_rel + 273.15 ) * (s[i][j]s_rel)
E[i][j] = e_ph[i][j] * m_dot
END
END
286
287
288
289
DUPLICATE j=3,6
DUPLICATE i=1,2
Tm[i][j] = (T[i][j] + T[i][j+1])/2
"Mitteltemperaturen"
END
290
291
END
292
293
108
A.4. Development of the Receiver and Solid Bed Storage for Ebsilon
294
{Formulation of the local heat transfer coefficients}
295
296
297
298
{Section 1 - Collection Pipe}
{
Tm[1][1] = (T[1][1] + T[1][2])/2
Tm[2][1] = T_amb + 10 [C]
299
300
301
302
303
304
d_bez[1] = d_sammelrohr
CALL rohrstroemung
(Fluid$, Tm[1][1], P, (n_abs *
m_dot), d_bez[1], L[1], x_H2O: alpha[1][1], Nusselt[1][1], Re
[1][1], dp[1][1])
alpha[2][1] = 10ˆ10
1 / k_wand[1] = d_bez[1] / 2 * 1 / lambda_iso * ln ((d_bez[1] + 2
* s_iso_sammelrohr)/d_bez[1])
dp[2][1] = 0
305
306
307
A[1][1] = pi * d_bez[1] * L[1] / n_abs {1/n_abs um übertragene
Wärmemenge auf einen Absorber runterzurechnen}
A[2][1] = A[1][1]
}
308
309
310
311
{Section 2 - Hopper}
{
Tm[1][2] = (T[1][2] + T[1][3])/2
Tm[2][2] = T_amb + 10 [C]
312
313
314
315
316
317
d_bez[2] = d_trichter
CALL rohrstroemung
(Fluid$, Tm[1][2], P, (n_abs *
m_dot), d_bez[2], L[2], x_H2O: alpha[1][2], Nusselt[1][2], Re
[1][2], dp[1][2])
alpha[2][2] = 10ˆ10
1 / k_wand[2] = d_bez[2] / 2 * 1 / lambda_iso * ln ((d_bez[2] + 2
* s_iso_trichter)/d_bez[2])
dp[2][2] = 0
318
319
320
A[1][2] = pi * d_bez[2] * L[2] / n_abs {1/n_abs um übertragene
Wärmemenge auf einen Absorber runterzurechnen}
A[2][2] = A[1][2]
}
321
322
323
324
325
326
{Section 3 - Pipe with insulations}
d_bez[3] = d_i
CALL rohrstroemung
(Fluid$, Tm[1][3], P, m_dot, (
d_bez[3] - 2 * (s_wand+s_iso)), L[3], x_H2O: alpha[1][3],
Nusselt[1][3], Re[1][3], dp[1][3])
CALL ringspalt
(Fluid$, ’i’, Tm[2][3], P, m_dot,
d_i, d_a, L[3], x_H2O: alpha[2][3], Nusselt[2][3], Re[2][3],
dp[2][3])
1 / k_wand[3] = d_bez[3] / 2 * (1 / lambda_stahl * ln(d_i/(d_i-2*
s_wand)) + 1 / lambda_iso *ln(((d_i-2*s_wand))/((d_i-2*(s_wand
+ s_iso)))))
109
A. Appendix - Simulation Characteristics
327
A[1][3] = pi * d_bez[3] * L[3]
A[2][3] = A[1][3]
328
329
330
331
332
333
334
335
{Section 4 - Pipe with absorber neck}
d_bez[4] = d_i
CALL rohrstroemung
(Fluid$, Tm[1][4], P, m_dot, (
d_bez[4] - 2 * (s_wand + s_abs + s_iso)), L[4], x_H2O: alpha
[1][4], Nusselt[1][4], Re[1][4], dp[1][4])
CALL ringspalt
(Fluid$, ’i’, Tm[2][4], P, m_dot,
d_bez[4], d_a, L[4], x_H2O: alpha[2][4], Nusselt[2][4], Re
[2][4], dp[2][4])
k_wand[4] = 1/ (d_i / 2 * (1 / lambda_stahl * ln(d_i/(d_i-2*
s_wand)) + 1 / lambda_sisic * ln(((d_i-2*s_wand))/((d_i-2*(
s_wand + s_abs)))) + 1 / lambda_iso * ln(((d_i-2*(s_wand+s_abs
)))/((d_i-2*(s_wand + s_abs + s_iso))))))
336
A[1][4] = pi * d_bez[4] * L[4]
A[2][4] = A[1][4]
337
338
339
340
341
{Section 5 - Absorber Funnel}
d_bez[5] = (d_i + B_abs)/2 {Mittlerer Aussendurchmesser des
Absorberkelches}
342
CALL rohrstroemung
(Fluid$, Tm[1][5], P, m_dot, (
d_bez[5] - 2 * s_abs), L[5], x_H2O: alpha[1][5], Nusselt
[1][5], Re[1][5], dp[1][5])
CALL ringspalt
(Fluid$, ’i’, Tm[2][5], P, m_dot,
d_bez[5], (d_bez[5] + 2 * s_spalt), L[5], x_H2O: alpha[2][5],
Nusselt[2][5], Re[2][5], dp[2][5])
k_wand[5] = 1 / (d_bez[5] / 2 * (1 / lambda_sisic * ln(d_bez[5]/(
d_bez[5] - 2*s_abs))))
343
344
345
346
A[1][5] = pi * d_bez[5] * L[5]
A[2][5] = A[1][5]
347
348
349
350
351
{Section 6 - Absorber Structure}
d_bez[6] = 4 * B_abs / pi {Umfangsäquivalenter Durchmesser des
Absorbers}
352
CALL ringspalt
(Fluid$, ’b’, Tm[2][6], P, 2 *
m_dot, d_bez[6], (d_bez[6] + 2 * s_spalt), L[6], x_H2O: alpha
[2][6], Nusselt[2][6], Re[2][6], dp[2][6]) {Massenstrom
verdoppelt wg. benachbartem Absorber}
CALL rohrstroemung
(Fluid$, Tm[1][6] , P, (m_dot/
n_kanal), B_kanal, L[6], x_H2O: alpha[1][6], Nusselt[1][6], Re
[1][6], dp[1][6]) {Nur zur Druckverlustrechnung}
353
354
355
k_wand[6] = lambda_sisic / (0.005 [m])
356
357
A[1][6] = n_kanal * 4 * B_kanal * L[6]
A[2][6] = 4 * B_abs * L[6]
358
359
360
110
A.4. Development of the Receiver and Solid Bed Storage for Ebsilon
361
{Section 7 - Mixing in front of the receiver}
362
363
364
365
{Verification equation for entire energy balance (Q_pruef must be 0)}
dT_abs = T_abs_out - T_abs_in
366
367
{ERR_T_rec = 100 * (T_rec_out / T_rec_out_mess - 1)
368
ERR_m_dot = 100 * (m_dot / m_dot_mess - 1)
}
369
370
371
372
373
374
375
376
377
{Ambient}
Fluid$ = ’AirH2O’
"Determination of Fluid$"
test$ = Name$
P = 101325
h_rel =Enthalpy(Fluid$, T=T_rel, P=P, W=x_H2O)
s_rel =Entropy(Fluid$, T=T_rel, P=P, W=x_H2O)
s_amb =Entropy(Fluid$, T=T_amb, P=P, W=x_H2O)
e_amb = h_amb -h_rel - (T_rel+273.15)*(s_amb - s_rel)
378
379
380
381
382
383
{Validation}
q_solar = P_solar / (A_abs * n_abs) * 1000 [W/kW]
cp[1]=Cp(Air,T=T[1][7])
cp[2]=Cp(Air,T=T[1][3])
kA=(Q[1][3]+Q[1][4]+Q[1][5])*(ln(T[1][5]-T[2][5])-ln(T[1][3]-T[2][3]))/(T
[1][5]-T[2][5]-T[1][3]+T[2][3])
384
385
386
387
388
389
"Space holder: For normal calculations defined, commended out for
validation"
m_dot_mess = 2
T_abs_out_mess = 2
T_rec_out_mess = 2
Name$ = ’gnaa’
390
391
392
393
394
395
396
397
398
399
"Design Point: For normal calculations defined, commended out for
parameter studies"
{q_solar = 500000
}
T_abs_in=155
T_abs_cub_out=689.28
T_rec_in = 120
arr = 0.6
T_rel = 0
humidity = 0.6
T_amb = 20
111
A. Appendix - Simulation Characteristics
A.4.1.2. Polynomial Equations for the Receiver Components in Ebsilon
Figure A.4.: The diagram contains values for the K-value and the upper temperature difference that
have been calculated with the EES receiver model for various mass flows. The polynomial
equation calculated with Excel allows to adjust partial characteristics of the parts in the
Ebsilon model.
Figure A.5.: The component representing the collecting hopper in the Ebsilon model is considering
the heat losses that occur in the component. The condition under partial load is shown in
the diagram. The polynomial equation is used in the Ebsilon model.
112
A.4. Development of the Receiver and Solid Bed Storage for Ebsilon
Figure A.6.: The black curve represents the polynomial equation derived from the EES values. Additionally, this diagram includes a comparison with the polynom of adjustment suggested by
Ebsilon.
A.4.2. The Solid Bed Storage
1
2
3
4
5
6
Listing A.3: The solid bed storage component is described in this Delphi script. The script also includes the regulation mechanism for the annual simulations.
{-------------------------------------------Einleitung:
1) Maximale Speicherkapazität in "@model.SM" sezten
2) Austrittstemperaturen beim Be-/Entladen des Speichers (@model.T_low,
@model.T_high) setzen
3) Abfragen je nachdem Ein- oder Ausschalten:
Für Excel-Makro muss nur
"Auslesen der Receiverleistung" aktiv sein!!! Für die interaktive
Eingabe in Ebsilon (Messagebox) kann die jeweilige Imputbox
auskomentieren und "Auslesen der Receiverleistung" komentieren werden
4) Speicherwirkungsgrad "eta_speicher" setzen
7
8
9
10
11
12
13
14
15
16
17
18
Bedeutung von FLAG:
1: Berechnung beendet mit Kommentaren
2: Berechnung beendet mit Warnungen
3: Berechnung beendet mit Fehlern
4: Berechnung nicht möglich
5: Fatales Problem
6: Genauigkeit nach maximaler Anzahl der Iterationen nicht erreicht,
sonst erfolgreich
7: Genauigkeit nach maximaler Anzahl der Iterationen nicht erreicht,
sonst lediglich Warnungen
-----------------------------------------------}
PROCEDURE SetEingabeWerte (VAR Wert : real);
BEGIN
113
A. Appendix - Simulation Characteristics
::Receivermodell.SPEC2:=Wert;
19
20
END;
21
22
23
24
25
26
FUNCTION T_LADEN(Qsp, deltaTn :real):real;
BEGIN
T_Laden:[email protected]_low+0.1*deltaTn*(Qsp/@model.SM);
END;
27
28
29
30
31
32
FUNCTION T_ENTLADEN(Qsp, deltaTn :real):real;
BEGIN
T_Entladen:[email protected]_high-0.1*deltaTn*(1-Qsp/@model.SM);
END;
33
34
35
36
37
38
39
40
VAR i, id, AUX : integer;
VAR QC, QC1, QL_ist, QL, QD, QD_HTF, QS, QA, QL_PB : real;
VAR Q_Intercept_grenze, Q_rec_grenze, Q_PB_referenz, QN_rec, Q_dumping :
real;
VAR Q_referenz, flag, deltaTn_Speicher : real;
VAR a : integer;
VAR Qdefokusieren, QN_Feld, eta_speicher : real;
41
42
BEGIN
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
QL_PB:=0;
{Lastwärmestrom
im Powerblock}
QL_ist:=0;
{Lastwärmestrom
im Receiver}
QD:=0;
{
Dumpingwärmestrom}
QA:=0;
{Auxilary Power}
QS:=0;
{Wärmestrom zum/
vom Speicher}
QL := 0;
{in kW:
minimale Receiverleistung für Subprofile LADEN, wird in der
Initialisierungs-Simulation ermittelt}
@model.SM:=::Speicherkapazität.Q; {in kWh:
max. Speicherkapazität}
@model.T_low:=150;
//Nomimale
Austrittstemperatur im Speicher beim Laden
@model.T_high:=680;
//Nomimale
Austrittstemperatur im Speicher beim Entladen
//@model.ES:=::Speicherstand.Q; //Aktivieren, wenn Speicherstand
vorgegeben werden soll.
Qdefokusieren:=0;
//gedumpte Wärmestrom
durch defokusieren
QN_Feld:=0;
//
Receiverleistung @DP
eta_speicher:=0.8;
//Speicherwirkungsgrad
AUX:= 1;
//Mit auxiliary
burner setze AUX:=1, für Solar Only setze AUX:=0
58
114
A.4. Development of the Receiver and Solid Bed Storage for Ebsilon
59
60
61
62
63
64
//<<<<<<<<<<<<<Abfrage für die Eingabe der Receiverleistung
{inputBox ("Bitte geben Sie die gewünschte Receiverleistung ein in [MW]",
QC);
QC:=QC*1000;
}
//>>>>>>>>>>>>>>>>>>>>>>>>>>>>
65
66
67
68
69
//<<<<<<<<<<<<<Auslesen der Interceptleistung
QC:=::SQC.Q;
//QC in kW
//>>>>>>>>>>>>>>>>>>>>>>>>>>>>
print("QC= ", QC, "\n");
70
71
72
73
74
75
76
77
78
79
80
81
82
83
//<<<<<<<<<<<<<<<<<<<<<<INITIALISIEREN
@model.ES_alt:[email protected];
deltaTn_Speicher:[email protected][email protected]_low;
id:=getCalcProfile;
setcalcprofile(0);
QN_Feld:=::SQC.Q;
QN_rec:=::L_Receiverleistung.H;
::Regler_Generator.L2MAX:=::DP_Dummy.M1N;
setCalcProfile(3);
Q_referenz:=::SQC.Q;
//Scheitelpunkt zwischen Speichern und Laden
Q_PB_referenz:=::DP_Dummy.M1N*(::DP_Dummy.H1N-::DP_PB.H1N);
//Benötigte Powerblockleitung
setCalcProfile(id);
84
85
86
87
88
89
90
91
92
93
{if (([email protected])>Q_referenz*0.94 AND ([email protected])<Q_referenz*1.02)
then
BEGIN
{Berechnung von minimaler
notwendiger Wärmeeinkopplung im Profil: LADEN}
{setCalcProfile(3);
//flag:=simulate;
QL:=::L_Receiverleistung.Q;
if (QC<floor(QL)+100) AND (QC>floor(QL)-100) then QC:=floor(QL)
-100;
{umgehung der nummerischen unstabilen Bereich zwischen
Laden und Entladen}
{
END
else }
94
95
if (QC<(floor(Q_referenz)+100)) AND (QC>(floor(Q_referenz)-5700)) then QC
:=floor(Q_referenz)-5700;
{umgehung der nummerischen unstabilen
Bereich zwischen Laden und Entladen}
96
97
98
Q_Intercept_grenze:=0.995*Q_referenz;
Q_rec_grenze:=0.995*Q_PB_referenz;
99
100
101
if QC>=1.1*QN_Feld then
Defokusieren wenn QC >= 1,1 Qnenn_feld
//
115
A. Appendix - Simulation Characteristics
BEGIN
Qdefokusieren:=QC-1.1*QN_Feld;
QD:=Qdefokusieren;
QC:=1.1*QN_Feld;
END;
102
103
104
105
106
107
108
109
//>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
print("QC= ", QC, "\n", "Q_Intercept_grenze= ", Q_Intercept_grenze, "\n
","QC_neu= ", QC, "\n");
110
111
112
113
114
115
116
117
118
119
120
121
122
if QC>0 then
BEGIN
if QC>Q_Intercept_grenze then
BEGIN
if @model.ES > @model.SM then
BEGIN
a:=1; print("a=", a, "\n");
{a ist ein Dummy und dient nur zu
Lokalisierung}
setCalcProfile(1);
{dumping}
clear (::Regler.FACT);
clear (::Receiversperre.FFU);
SetEingabeWerte(QC);
flag:=simulate;
123
QD:=Qdefokusieren+QC;
@model.ES := @model.SM;
END
124
125
126
else
127
BEGIN
a:=2; print("a= ", a, "\n");
setCalcProfile(1);
{laden}
SetEingabeWerte(QC);
clear (::Regler.FACT);
clear (::Receiversperre.FFU);
::T_austritt_Laden.MEASM:=T_laden(@model.ES,
deltaTn_Speicher);
flag:=simulate;
128
129
130
131
132
133
134
135
136
QL_ist:=::L_Receiverleistung.Q;
QS:=::L_SpeicherLaden.Q;
if (@model.ES + QS) < @model.SM then
BEGIN
a:=3; print("a= ", a, "\n");
@model.ES:[email protected] + QS*
eta_speicher;
QS:=QS*eta_speicher;
END
else
BEGIN
a:=4; print("a= ", a, "\n");
137
138
139
140
141
142
143
144
145
146
147
116
A.4. Development of the Receiver and Solid Bed Storage for Ebsilon
QD_HTF:= @model.ES + QS - @model.
SM; {dumping}
QS:=QS - QD_HTF;
@model.ES:= @model.ES + QS*
eta_speicher;
QS:=QS*eta_speicher;
END;
148
149
150
151
152
END;
153
END
154
155
156
157
158
159
160
161
162
163
164
else
BEGIN
if (@model.ES>0) then
BEGIN
setCalcProfile(2);
//Entladen
a:=5; print("a= ", a, "\n");
SetEingabeWerte(QC);
::T_austritt_Entladen.MEASM:=T_entladen(@model.ES
,deltaTn_Speicher);
clear (::Regler.FACT);
clear (::Receiversperre.FFU);
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
flag:=simulate;
QL_ist:=::L_Receiverleistung.Q;
QS:=::L_SpeicherEntladen.Q;
if (@model.ES+QS)>0 then
BEGIN
//Speicherkapazität ist
ausreichend
a:=6; print("a= ", a, "\n");
@model.ES:= @model.ES + QS;
END
else
BEGIN
if AUX=0 then
begin
a:=70; print("a= ", a, "\n");
if QC<159000 then QC:=0;
setCalcProfile(6);
//Receiver ohne
Speicher und ohne Brenner
SetEingabeWerte(QC);
clear (::Regler.FACT);
clear (::Receiversperre.FFU);
184
flag:=simulate;
QL_ist:=::L_Receiverleistung.Q;
QS:=0;
@model.ES := @model.ES + QS;
185
186
187
188
189
190
191
end
else
begin
117
A. Appendix - Simulation Characteristics
//Speicherkapazität ist NICHT
ausreichend -> nur Receiver und
Brennkammer
a:=71; print("a= ", a, "\n");
if QC>(Q_referenz-24000)
then
//
Dieser Bereich bringt
Probleme für Brenner,
da der Massenstrom vom
Receiver noch zu groß
ist. -->Muss umgangen
werden.
begin
setCalcProfile(6)
;
SetEingabeWerte(
QC);
a:=716; print("a=
", a, "\n");
end
else
begin
setCalcProfile(4)
;
192
193
194
195
196
197
198
199
200
201
//
Receiver ohne
Speicher + aux
. Brenner
SetEingabeWerte(
QC);
202
end;
clear (::Regler.FACT);
clear (::Receiversperre.FFU);
203
204
205
206
flag:=simulate;
QL_ist:=::L_Receiverleistung.Q;
QS:=0;
@model.ES := @model.ES + QS;
207
208
209
210
end;
END;
211
212
END
213
else
214
BEGIN
if AUX=1 then
begin
a:=81; print("a= ", a, "\n");
//
Receiver ohne Speicher + aux. Brenner
setCalcProfile(4);
SetEingabeWerte(QC);
clear (::Regler.FACT);
clear (::Receiversperre.FFU);
215
216
217
218
219
220
221
222
223
118
A.4. Development of the Receiver and Solid Bed Storage for Ebsilon
flag:=simulate;
QL_ist:=::L_Receiverleistung.Q;
QS:=0;
@model.ES := @model.ES + QS;
224
225
226
227
end
else
begin
228
229
230
a:=80; print("a= ", a, "\n");
Receiver ohne Speicher
if QC<159000 then QC:=0;
setCalcProfile(6);
SetEingabeWerte(QC);
clear (::Regler.FACT);
clear (::Receiversperre.FFU);
231
232
233
234
235
236
//
237
flag:=simulate;
QL_ist:=::L_Receiverleistung.Q;
QS:=0;
@model.ES := @model.ES + QS;
238
239
240
241
end;
END;
242
243
END;
244
END
245
246
247
248
249
250
251
252
253
254
255
256
else
BEGIN
QL_ist:=0;
if @model.ES>0 then
BEGIN
//QC=0 und Speicherkapazität ist nicht Null
a:=9; print("a= ", a, "\n");
setCalcProfile(2);
Entladen}
SetEingabeWerte(QC);
::regler.fact:=-2;
::Receiversperre.FFU:=1;
::T_austritt_Entladen.MEASM:=T_entladen(@model.ES,
deltaTn_Speicher);
{
257
258
259
260
261
262
263
264
265
266
267
268
269
flag:=simulate;
QS:=::L_SpeicherEntladen.Q;
if (@model.ES+QS)>0 then
BEGIN
//Speicherkapazität ist ausreichend
a:=10; print("a= ", a, "\n");
@model.ES:= @model.ES + QS;
END
else
BEGIN
if AUX=1 then
begin
//Speicherkapazität ist
NICHT ausreichend
a:=111; print("a= ", a, "\n");
119
A. Appendix - Simulation Characteristics
setCalcProfile(4);
//ohne Receiver ohne Speicher
+ aux. Brenner
SetEingabeWerte(QC);
::Regler.fact:=-2;
::Receiversperre.FFU:=1;
270
271
272
273
274
flag:=simulate;
QS:=0;
@model.ES := @model.ES + QS;
275
276
277
end
else
begin
278
279
280
a:=110; print("a= ", a, "\n");
if QC<159000 then begin QC:=0; end;
setCalcProfile(6);
//ohne Receiver ohne Speicher
ohne Brenner
SetEingabeWerte(QC);
::Regler.fact:=-2;
::Receiversperre.FFU:=1;
281
282
283
284
285
286
287
flag:=simulate;
QS:=0;
@model.ES := @model.ES + QS;
288
289
290
end;
END;
291
292
END
293
else
294
BEGIN
if AUX=1 then
begin
a:=121; print("a= ", a, "\n");
setCalcProfile(4);
//Nur aux. Brenner
SetEingabeWerte(QC);
::Regler.fact:=-2;
::Receiversperre.FFU:=1;
295
296
297
298
299
300
301
302
303
flag:=simulate;
QS:=0;
@model.ES := @model.ES + QS;
304
305
306
end
else
begin
307
308
309
a:=120; print("a= ", a, "\n");
if QC<159000 then QC:=0;
setCalcProfile(6);
//Abgestellt
SetEingabeWerte(QC);
::Regler.fact:=-2;
::Receiversperre.FFU:=1;
310
311
312
313
314
315
316
120
A.4. Development of the Receiver and Solid Bed Storage for Ebsilon
flag:=simulate;
QS:=0;
@model.ES := @model.ES + QS;
317
318
319
end;
END;
320
321
322
END;
323
324
325
326
327
QA:=::L_Brenner.Q;
//aux. Brenner im Powerblock
if QA < 1 then QA:=0;
QL_PB:=::L_PB_in.M*(::L_PB_in.H-::L_PB_out.H);
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
if QC<0 OR (flag>=3 AND flag<=6) then
BEGIN
setCalcProfile(3);
flag:=flag+a/10;
//dient zur Lokalisierung des Fehlers
a:=13; print("a= ", a, "\n");
QL_PB:=0;
@model.ES:[email protected]_alt+QC;
::SQC.Q:=0;
::SQL_ist.Q:=0;
::SQS.Q:=0;
::SQD.Q:=0;
::SQA.Q:=0;
::Generator_DT.QREAL:=0;
::P_ges_netto.Q:=0;
::P_Parasitics.Q:=0;
::L_Parasitics_Receiver.Q:=0;
::L_Parasitics_PB.Q:=0;
::L_Brenner.Q:=0;
::L_Qges_Sol_u_AUX.Q:=0;
::L_PB_in.P:=0;
::L_PB_in.T:=0;
::L_PB_in.M:=0;
::L_PB_out.P:=0;
::L_PB_out.T:=0;
::L_PB_out.M:=0;
::Rauchgas_nach_Receiver.P:=0;
::Rauchgas_nach_Receiver.T:=0;
::Rauchgas_nach_Receiver.M:=0;
358
359
END;
360
361
if (@model.ES > -1) AND (@model.ES < 1) then @model.ES:=0;
362
363
364
365
366
id:=getcalcprofile;
setCalcProfile(0);
gelöscht, wird normal nicht gebraucht!
//Habe ::SQC.Q:=QC
121
A. Appendix - Simulation Characteristics
367
368
369
370
371
372
373
374
375
376
377
378
//Dummys für die Ausgabe in Excel
::SQL_ist.Q:=QL_ist;
::SQS.Q:=QS;
::SQD.Q:=QD;
::SQD_HTF.Q:=QD_HTF;
::SQA.Q:=QA;
::SSpeicher_alt.Q:[email protected]_alt;
::SSpeicher_ist.Q:[email protected];
::SSpeicherMax.Q:[email protected];
::SFlag.H:=flag;
setCalcProfile(id);
::SQC.Q:=QC;
379
380
381
382
383
384
385
386
387
388
389
390
//if flag=4 then saveModel;
print("QS= ", QS, "\n");
print("QL= ", QL, "\n");
print("QL_ist= ", QL_ist, "\n");
print("QL_PB= ", QL_PB, "\n");
print("QD= ", QD, "\n");
print("QA= ", QA, "\n");
print("QA+QC= ", QA+QC, "\n");
print("Speicher alt= ", @model.ES_alt, "\n");
print("Speicher ist= ", @model.ES, "\n");
391
392
393
end.
122
B. Appendix - Results
B.1. Steady State Simulation
The simulations are conducted under all characteristic operation modes of the power plant under reference configuration. Steady state simulation means a discrete simulation under a specific condition.
The abbreviations are determined as the following:
Table B.1.: Table of abbreviations for the simulations of all characteristic operations of the solar power
tower.
Abbreviation
Initialize
SE1
SE2
SNE2
SNE3
100%DNI
80%DNI
60%DNI
40%DNI
20%DNI
Explanation
The solar irradiation is set to operate the power plant exactly under full load without any excess thermal energy to
charge the storage
=Storage Empty 1: The storage of the plant is empty. It
can be charged but not discharged
=Storage Empty 2: The storage of the plant is empty. It
can be charged but not discharged
=Storage Not Empty 2: The storage of the plant is NOT
empty or full, respectively. It cannot be charged but discharged
=Storage Not Empty 3: The storage of the plant is NOT
empty or full, respectively. It cannot be charged but discharged
100% of the solar irradiation at the design point
(=850W/m2 )
80% of the solar irradiation at the design point
(=850W/m2 )
60% of the solar irradiation at the design point
(=850W/m2 )
40% of the solar irradiation at the design point
(=850W/m2 )
20% of the solar irradiation at the design point
(=850W/m2 )
Input
DNI=500W/m2
DNI=850W/m2 , storage
level = 0kW
DNI=300W/m2 , storage
level = 0MW
DNI=300W/m2 , storage
level = 900MW
DNI=0W/m2 ,
level = 900MW
storage
DNI=850W/m2 ,
level = 0MW
DNI=680W/m2 ,
level = 0MW
DNI=510W/m2 ,
level = 0MW
DNI=340W/m2 ,
level = 0MW
DNI=170W/m2 ,
level = 0MW
storage
storage
storage
storage
storage
123
B. Appendix - Results
Figure B.1.: A Sankey diagram of the exergy flow in the heat transfer unit of the solar power tower in
operation mode SE1.
Figure B.2.: A Sankey diagram of the exergy flow in the heat transfer unit of the solar power tower in
operation mode SNE3.
124
B.1. Steady State Simulation
Figure B.3.: A Sankey diagram of the exergy flow in the power block of the solar power tower in operation mode SE1 under full load.
125
B. Appendix - Results
Figure B.4.: Solar Only - Energy and exergy efficiencies of the solar power tower in comparison.
Figure B.5.: With Auxiliary Burner - Energy and exergy efficiencies of the solar power tower in
comparison.
126
B.1. Steady State Simulation
Figure B.6.: Solar Only - Energy losses in comparison on a logarithmic scale.
Figure B.7.: With Auxiliary Burner - Energy losses in comparison on a logarithmic scale.
127
B. Appendix - Results
Figure B.8.: Solar Only - Exergy destruction in comparison on a logarithmic scale.
Figure B.9.: With Auxiliary Burner - Exergy destruction in comparison on a logarithmic scale.
128
B.2. Annual Performance Simulation
B.2. Annual Performance Simulation
Table B.2.: Table of abbreviations for the annual performance simulations of the solar power tower.
Abbreviation
Solar Only Basis
Explanation
The solar power tower plant under reference configurations without an auxiliary burner
Solar Only 80%
Recovery
Solar
Only
100% Recovery
With
Burner
Basis
Modified air stream recovery at the receiver with 80%; No auxiliary burner
Modified air stream recovery at the receiver with 100%; No auxiliary burner
The solar power tower plant under reference configurations with an auxiliary
burner
With
Burner
80% Recovery
With
Burner
100% Recovery
Solar Only 550
Modified air stream recovery at the receiver with 80%; Auxiliary burner
Modified air stream recovery at the receiver with 100%; Auxiliary burner
Concentrated solar irradiation on the
receiver is increased to 550kW/m2 under design conditions; No auxiliary
burner
Concentrated solar irradiation on the
receiver is increased to 600kW/m2 under design conditions; No auxiliary
burner
Increase of the pressure in the feed water pipe after the first economizer; No
auxiliary burner
Due to the higher pressure the temperature can be higher in the feed water
pipe. No auxiliary burner
Due to the higher pressure the temperature can be higher in the feed water
pipe. No auxiliary burner
Solar Only 600
Solar Only 3bar
135◦ C
Solar Only 3bar
145◦ C
Solar Only 3bar
155◦ C
Input
Concentrated solar irradiation on
the receiver = 550kW/m2 , recovery
of the air stream = 60%, pressure
of the feed water pipe after the first
economizer = 1.5bar and its temperature = 135◦ C
Recovery of air stream 80%
Recovery of air stream 100%
Concentrated solar irradiation on
the receiver = 550kW/m2 , recovery
of the air stream = 60%, pressure
of the feed water pipe after the first
economizer = 1.5bar and its temperature = 135◦ C
Recovery of air stream 80%
Recovery of air stream 100%
Energy density
q=550kW/m2
on
receiver
Energy density
q=600kW/m2
on
receiver
In feed water pipe p=3bar, T=135◦ C
In feed water pipe p=3bar, T=145◦ C
In feed water pipe p=3bar, T=155◦ C
129
B. Appendix - Results
Figure B.10.: Overall exergy efficiencies of an annual performance simulation for the different configurations of the solar power tower in comparison.
Figure B.11.: Exergy destruction including exergy losses in the main parts of the solar power tower for
the different configurations.
130
B.3. Exergoeconomic Results Ordered by Importance
Figure B.12.: The cost rate of exergy destruction C of the different configurations and main parts in
comparison.
Figure B.13.: The cost importance C+Z (cost rate + cost of components) of the different configurations
and main parts in comparison.
B.3. Exergoeconomic Results Ordered by Importance
131
B. Appendix - Results
Table B.3.: Solar Only Basis, recycling of the air stream: 60%, concentrated solar irradiation on the
receiver: 500kW/m2 , pressure of the water pipe after first economizer: 1.5bar.
Solar field
Absorber
Condenser+Dry Cooler
Air mixing unit in absorber
Storage discharging
Storage charging
Turbine 6-8
Steam generator HP
HTX in absorber
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
Pipes and hoppers
HTX superheater HP 2 (HTX 34)
HTX reheater 2 (HTX12)
HTX reheater 1 (HTX23)
Compressor storage
Pump HP
Dearator
HTX superheater LP
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
132
epsilon
[%]
56.55%
41.09%
0.00%
47.12%
98.90%
98.95%
88.63%
89.71%
58.98%
82.47%
93.29%
86.94%
95.11%
57.36%
94.02%
82.51%
88.93%
98.23%
90.64%
83.10%
80.51%
79.68%
78.02%
96.85%
81.12%
99.89%
99.91%
73.96%
99.81%
99.99%
78.04%
79.57%
100.00%
0.00%
0.00%
0.00%
0.00%
E˙D
[MWh/a]
0
496625
3594
9008
0
0
11779
9357
23205
8915
3914
6724
8313
5929
1521
1508
1791
5695
1370
2150
2369
974.2
538.2
328
475.3
192.3
158.1
137.1
64.25
28.2
5.658
3.948
0.06256
0
0
0
0
E˙L
[MWh/a]
647711
0
25369
26688
821.2
1043
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
E˙D+E˙L
[MWh/a]
647711
496625
28963
35696
821.2
1043
11779
9357
23205
8915
3914
6724
8313
5929
1521
1508
1791
5695
1370
2150
2369
974.2
538.2
328
475.3
192.3
158.1
137.1
64.25
28.2
5.658
3.948
0.06256
0
0
0
0
B.3. Exergoeconomic Results Ordered by Importance
Solar field
Absorber
Condenser+Dry Cooler
Air mixing unit in absorber
Storage discharging
Storage charging
Turbine 6-8
Steam generator HP
HTX in absorber
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
Pipes and hoppers
HTX superheater HP 2 (HTX 34)
HTX reheater 2 (HTX12)
HTX reheater 1 (HTX23)
Compressor storage
Pump HP
Dearator
HTX superheater LP
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
gamma˙D
[%]
0.00%
31.73%
0.23%
0.58%
0.00%
0.00%
0.75%
0.60%
1.48%
0.57%
0.25%
0.43%
0.53%
0.38%
0.10%
0.10%
0.11%
0.36%
0.09%
0.14%
0.15%
0.06%
0.03%
0.02%
0.03%
0.01%
0.01%
0.01%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
gamma˙L
[%]
41.39%
0.00%
1.62%
1.71%
0.05%
0.07%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
c˙F
[e/MWh]
0
18.08
155
111
89.75
61.95
108.2
80.24
61.95
80.24
107.6
80.24
132.2
80.24
107.2
155
80.24
61.95
80.24
80.24
80.24
155
155
148.1
80.24
107.1
107.4
80.24
116.8
80.23
155
155
108.2
0
0
0
0
c˙P
[e/MWh]
18.08
61.95
108.2
139.8
126.3
89.75
132.2
108.6
61.95
123.2
130.2
107.1
155
150.2
131.9
121.1
111.6
61.95
107.2
107.6
107.4
110.5
166.2
153
112.1
107.3
107.5
152.4
117.1
80.24
110.2
154.8
108.2
80.24
0
0
0
133
B. Appendix - Results
Solar field
Absorber
Condenser+Dry Cooler
Air mixing unit in absorber
Storage discharging
Storage charging
Turbine 6-8
Steam generator HP
HTX in absorber
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
Pipes and hoppers
HTX superheater HP 2 (HTX 34)
HTX reheater 2 (HTX12)
HTX reheater 1 (HTX23)
Compressor storage
Pump HP
Dearator
HTX superheater LP
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
134
C˙D+C˙L
[e/a]
0
8981000
4488000
3964000
73700
64634
1274000
750862
1438000
715343
421216
539536
899273
475793
163059
233680
143697
352785
109924
172492
190111
150978
83403
84734
38142
50023
41154
10997
14879
5309
876.8
611.8
13.74
0
0
0
0
Z
[e/a]
15240000
3736000
2581000
0
2661500
2661500
1096000
797822
0
626361
764361
460299
0
158858
426680
254086
241081
0
237644
139861
107578
145048
54746
0
33682
0
0
13994
0
0
2088
1690
0
0
0
9883
0
(C˙D+C˙L)+Z
[e/a]
15240000
12717000
7069000
3964000
2735200
2726134
2370000
1548684
1438000
1341704
1185577
999835
899273
634651
589739
487766
384778
352785
347568
312353
297689
296026
138149
84734
71824
50023
41154
24991
14879
5309
2964.8
2301.8
13.74
0
0
0
0
r
[-]
0
1.98
0
2.122
0.4144
0.4488
0.2387
0.2365
1.696
0.3986
0.2024
0.2784
1.051
0.9917
0.2301
0.4424
0.3333
1.018
0.3266
0.3682
0.3792
0.5001
0.4666
1.033
0.4382
1.001
1.001
0.8
1.002
1
0.9518
0.9657
1
0
0
0
0
f
[-]
1
0.2938
0.3651
1
0.9731
0.9763
0.4625
0.5152
1
0.4668
0.6447
0.4604
1
0.2503
0.7235
0.5209
0.6265
1
0.6837
0.4478
0.3614
0.49
0.3963
1
0.469
1
1
0.56
1
1
0.7043
0.7342
1
0
0
0
0
B.3. Exergoeconomic Results Ordered by Importance
Table B.4.: Solar only, recycling of the air stream: 80%, concentrated solar irradiation on the receiver:
500kW/m2 , pressure of the water pipe after first economizer: 1.5bar.
Solar field
Absorber
Condenser+Dry Cooler
Storage charging
Storage discharging
Turbine 6-8
Air mixing unit in absorber
HTX in absorber
Steam generator HP
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Pipes and hoppers
Steam generator LP
HTX superheater HP 2 (HTX 34)
Compressor storage
HTX reheater 2 (HTX12)
HTX reheater 1 (HTX23)
Pump HP
HTX superheater LP
Dearator
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
epsilon
[%]
56.52%
42.07%
0.00%
98.93%
99.14%
88.65%
71.56%
59.40%
89.75%
82.48%
93.31%
86.94%
95.15%
57.10%
94.05%
81.82%
98.19%
89.20%
90.60%
79.98%
83.06%
80.46%
78.46%
81.12%
97.40%
99.91%
99.92%
76.06%
99.74%
99.97%
78.22%
80.21%
100.00%
0.00%
0.00%
0.00%
0.00%
E˙D
[MWh/a]
0
488118
3729
0
0
12279
6329
25522
9700
9291
4062
7000
8601
6215
1575
1568
6231
1818
1427
1146
2236
2469
550.1
504.3
280.5
177.2
146.6
206.1
94.5
85.97
5.839
4.036
0.1084
0
0
0
0
E˙L
[MWh/a]
648128
0
27080
1253
714.7
0
14715
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
E˙D+E˙L
[MWh/a]
648128
488118
30809
1253
714.7
12279
21044
25522
9700
9291
4062
7000
8601
6215
1575
1568
6231
1818
1427
1146
2236
2469
550.1
504.3
280.5
177.2
146.6
206.1
94.5
85.97
5.839
4.036
0.1084
0
0
0
0
135
B. Appendix - Results
Solar field
Absorber
Condenser+Dry Cooler
Storage charging
Storage discharging
Turbine 6-8
Air mixing unit in absorber
HTX in absorber
Steam generator HP
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Pipes and hoppers
Steam generator LP
HTX superheater HP 2 (HTX 34)
Compressor storage
HTX reheater 2 (HTX12)
HTX reheater 1 (HTX23)
Pump HP
HTX superheater LP
Dearator
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
136
gamma˙D
[%]
0.00%
31.01%
0.24%
0.00%
0.00%
0.78%
0.40%
1.62%
0.62%
0.59%
0.26%
0.44%
0.55%
0.39%
0.10%
0.10%
0.40%
0.12%
0.09%
0.07%
0.14%
0.16%
0.03%
0.03%
0.02%
0.01%
0.01%
0.01%
0.01%
0.01%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
gamma˙L
[%]
41.17%
0.00%
1.72%
0.08%
0.05%
0.00%
0.93%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
c˙F
[e/MWh]
0
18.09
152.2
62.42
86.06
106.9
109.6
62.42
79.72
79.72
106.5
79.72
130.3
79.72
106
152.2
62.42
79.72
79.72
152.2
79.72
79.72
152.2
79.72
147.1
106
106.2
79.72
113.9
79.69
152.2
152.2
106.9
0
0
0
0
c˙P
[e/MWh]
18.09
62.42
106.9
86.06
119
130.3
121.8
62.42
107.4
121.7
128.3
106
152.2
149.1
129.9
119.2
62.42
109.9
106
107.3
106.5
106.2
163.6
110.4
151
106.1
106.3
144
114.2
79.72
108.9
152.7
106.9
79.72
0
0
0
B.3. Exergoeconomic Results Ordered by Importance
Solar field
Absorber
Condenser+Dry Cooler
Storage charging
Storage discharging
Turbine 6-8
Air mixing unit in absorber
HTX in absorber
Steam generator HP
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Pipes and hoppers
Steam generator LP
HTX superheater HP 2 (HTX 34)
Compressor storage
HTX reheater 2 (HTX12)
HTX reheater 1 (HTX23)
Pump HP
HTX superheater LP
Dearator
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
C˙D+C˙L
[e/a]
0
8832000
4690000
78194
61507
1313000
2305000
1593000
773223
740689
432461
558009
919875
495403
166992
238764
388957
144951
113791
174503
178271
196802
83749
40205
71837
45531
37704
16429
21403
15597
888.9
614.5
23.5
0
0
0
0
Z
[e/a]
1.52E+07
3.74E+06
2.58E+06
2.66E+06
2.66E+06
1.10E+06
0.00E+00
0.00E+00
7.98E+05
6.26E+05
7.64E+05
4.60E+05
0.00E+00
1.59E+05
4.27E+05
2.54E+05
0.00E+00
2.41E+05
2.38E+05
1.45E+05
1.40E+05
1.08E+05
5.47E+04
3.37E+04
0.00E+00
0.00E+00
0.00E+00
1.40E+04
0.00E+00
0.00E+00
2.09E+03
1.69E+03
0.00E+00
0.00E+00
0.00E+00
9.88E+03
0.00E+00
(C˙D+C˙L)+Z
[e/a]
1.52E+07
1.26E+07
7.27E+06
2.74E+06
2.72E+06
2.41E+06
2.31E+06
1.59E+06
1.57E+06
1.37E+06
1.20E+06
1.02E+06
9.20E+05
6.54E+05
5.94E+05
4.93E+05
3.89E+05
3.86E+05
3.51E+05
3.20E+05
3.18E+05
3.04E+05
1.38E+05
7.39E+04
7.18E+04
4.55E+04
3.77E+04
3.04E+04
2.14E+04
1.56E+04
2.98E+03
2.30E+03
2.35E+01
0.00E+00
0.00E+00
0.00E+00
0.00E+00
r
[-]
0.00
1.88
0.00
0.38
0.38
0.23
1.40
1.68
0.23
0.39
0.20
0.27
1.05
0.99
0.22
0.46
1.02
0.32
0.32
0.46
0.36
0.38
0.45
0.43
1.03
1.00
1.00
0.58
1.00
1.00
0.93
0.93
1.00
0.00
0.00
0.00
0.00
f
[-]
1.00
0.30
0.36
0.97
0.98
0.46
1.00
1.00
0.51
0.46
0.64
0.45
1.00
0.24
0.72
0.52
1.00
0.62
0.68
0.45
0.44
0.35
0.40
0.46
1.00
1.00
1.00
0.46
1.00
1.00
0.70
0.73
1.00
0.00
0.00
0.00
0.00
137
B. Appendix - Results
Table B.5.: Solar only, recycling of the air stream: 100%, concentrated solar irradiation on the receiver:
500kW/m2 , pressure of the water pipe after first economizer: 1.5bar.
Solar field
Absorber
Condenser+Dry Cooler
Storage charging
Storage discharging
Turbine 6-8
HTX in absorber
Steam generator HP
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Pipes and hoppers
Steam generator LP
HTX superheater HP 2 (HTX 34)
Compressor storage
HTX reheater 2 (HTX12)
HTX reheater 1 (HTX23)
Pump HP
HTX superheater LP
Dearator
Mixing unit discharging
Air mixing unit in absorber
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Mixing unit charging
Eco LP
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
138
epsilon
[%]
56.56%
43.43%
0.00%
98.83%
99.36%
88.67%
59.50%
89.78%
82.44%
93.31%
86.96%
95.23%
56.79%
93.99%
81.38%
98.03%
88.90%
90.58%
81.25%
82.96%
80.37%
79.08%
81.09%
97.42%
99.88%
99.45%
99.92%
99.93%
99.68%
73.84%
78.39%
79.55%
100.00%
0.00%
0.00%
0.00%
0.00%
E˙D
[MWh/a]
0
477016
3885
0
0
12882
25963
10144
9811
4267
7339
8897
6600
1670
1641
7528
1973
1500
1404
2352
2602
564.3
522.7
292
388.2
436.1
150.7
126
133.7
151.4
6.077
4.375
1.949
0
0
0
0
E˙L
[MWh/a]
647505
0
28515
1699
596.9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.00007
0
0
0
0
0
0
0
0
0
0
0
E˙D+E˙L
[MWh/a]
647505
477016
32400
1699
596.9
12882
25963
10144
9811
4267
7339
8897
6600
1670
1641
7528
1973
1500
1404
2352
2602
564.3
522.7
292
388.2
436.10007
150.7
126
133.7
151.4
6.077
4.375
1.949
0
0
0
0
B.3. Exergoeconomic Results Ordered by Importance
Solar field
Absorber
Condenser+Dry Cooler
Storage charging
Storage discharging
Turbine 6-8
HTX in absorber
Steam generator HP
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Pipes and hoppers
Steam generator LP
HTX superheater HP 2 (HTX 34)
Compressor storage
HTX reheater 2 (HTX12)
HTX reheater 1 (HTX23)
Pump HP
HTX superheater LP
Dearator
Mixing unit discharging
Air mixing unit in absorber
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Mixing unit charging
Eco LP
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
gamma˙D
[%]
0.00%
30.12%
0.25%
0.00%
0.00%
0.81%
1.64%
0.64%
0.62%
0.27%
0.46%
0.56%
0.42%
0.11%
0.10%
0.48%
0.12%
0.09%
0.09%
0.15%
0.16%
0.04%
0.03%
0.02%
0.02%
0.03%
0.01%
0.01%
0.01%
0.01%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
gamma˙L
[%]
40.88%
0.00%
1.80%
0.11%
0.04%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
c˙F
[e/MWh]
0
18.08
147.4
61.71
81.01
104
61.71
77.71
77.71
103.5
77.71
126.5
77.71
103.1
147.4
61.71
77.71
77.71
147.4
77.71
77.71
147.4
77.71
143.6
77.62
106.6
103.1
103.3
108.9
77.71
147.4
147.4
104
0
0
0
0
c˙P
[e/MWh]
18.08
61.71
104
81.01
110.7
126.5
61.71
104.5
118.3
124.5
103.1
147.4
145.6
126
114.8
61.71
107.2
103.1
103.1
103.5
103.3
159.1
107.6
147.4
77.71
107.2
103.1
103.4
109.3
146.4
105.9
149.1
104
77.71
0
0
0
139
B. Appendix - Results
Solar field
Absorber
Condenser+Dry Cooler
Storage charging
Storage discharging
Turbine 6-8
HTX in absorber
Steam generator HP
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Pipes and hoppers
Steam generator LP
HTX superheater HP 2 (HTX 34)
Compressor storage
HTX reheater 2 (HTX12)
HTX reheater 1 (HTX23)
Pump HP
HTX superheater LP
Dearator
Mixing unit discharging
Air mixing unit in absorber
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Mixing unit charging
Eco LP
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
140
C˙D+C˙L
[e/a]
0
8624000
4774000
104835
48353
1340000
1602000
788347
762426
441681
570356
925348
512872
172151
241799
464559
153309
116571
206909
182804
202204
83156
40623
72892
66936
46489
37753
31581
29139
11765
895.4
644.6
411.3
0
0
0
0
Z
[e/a]
1.52E+07
3.74E+06
2.58E+06
2.66E+06
2.66E+06
1.10E+06
0.00E+00
7.98E+05
6.26E+05
7.64E+05
4.60E+05
0.00E+00
1.59E+05
4.27E+05
2.54E+05
0.00E+00
2.41E+05
2.38E+05
1.45E+05
1.40E+05
1.08E+05
5.47E+04
3.37E+04
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
0.00E+00
1.40E+04
2.09E+03
1.69E+03
0.00E+00
0.00E+00
0.00E+00
9.88E+03
0.00E+00
(C˙D+C˙L)+Z
[e/a]
1.52E+07
1.24E+07
7.36E+06
2.77E+06
2.71E+06
2.44E+06
1.60E+06
1.59E+06
1.39E+06
1.21E+06
1.03E+06
9.25E+05
6.72E+05
5.99E+05
4.96E+05
4.65E+05
3.94E+05
3.54E+05
3.52E+05
3.23E+05
3.10E+05
1.38E+05
7.43E+04
7.29E+04
6.69E+04
4.65E+04
3.78E+04
3.16E+04
2.91E+04
2.58E+04
2.98E+03
2.33E+03
4.11E+02
0.00E+00
0.00E+00
0.00E+00
0.00E+00
r
[-]
0.00
1.77
0.00
0.31
0.36
0.23
1.68
0.23
0.39
0.20
0.27
1.05
1.00
0.22
0.47
1.02
0.32
0.32
0.39
0.36
0.37
0.44
0.43
1.03
1.00
1.01
1.00
1.00
1.00
0.78
0.92
0.93
1.00
0.00
0.00
0.00
0.00
f
[-]
1.00
0.30
0.35
0.96
0.98
0.45
1.00
0.50
0.45
0.63
0.45
1.00
0.24
0.71
0.51
1.00
0.61
0.67
0.41
0.43
0.35
0.40
0.45
1.00
1.00
1.00
1.00
1.00
1.00
0.54
0.70
0.72
1.00
0.00
0.00
0.00
0.00
B.3. Exergoeconomic Results Ordered by Importance
Table B.6.: With auxiliary burner, recycling of the air stream: 60%, concentrated solar irradiation on
the receiver: 500kW/m2 , pressure of the water pipe after first economizer: 1.5bar.
Solar field
Absorber
Condenser+Dry Cooler
Mixing unit/ burner (Mixer2)
Turbine 6-8
Air mixing unit in absorber
Storage charging
Storage discharging
Steam generator HP
Generator
Eco HP
HTX superheater HP 1 (HTX 45)
Turbine 3-4
HTX in absorber
HTX preheater
Compressor HRSG
Turbine 1-2
Steam generator LP
HTX reheater 1 (HTX23)
HTX reheater 2 (HTX12)
HTX superheater HP 2 (HTX 34)
Pipes and hoppers
Mixing unit/ bypass of receiver (Mixer1)
Compressor storage
Pump HP
Air preheater for burner (HTX)
Water injection superheater (Mixer25)
Dearator
Water injection reheater (Mixer22)
HTX superheater LP
Eco LP
Duct burner
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
epsilon
[%]
56.43%
43.03%
0.00%
96.09%
88.49%
47.09%
93.95%
104.70%
89.69%
95.74%
82.59%
86.90%
93.35%
58.75%
54.71%
75.21%
94.06%
89.17%
80.60%
83.19%
90.55%
98.30%
99.51%
79.34%
76.56%
100.00%
99.83%
97.53%
99.88%
81.32%
74.40%
99.89%
99.83%
99.99%
77.31%
76.37%
100.00%
E˙D
[MWh/a]
0
479234
9178
30398
32043
9066
0
0
24091
19138
22734
17618
10090
22363
16516
3970
3901
4344
6203
5686
3710
5777
1562
993.4
1489
2103
776.3
655.4
562
1183
338.3
484.6
60.87
26.37
15.29
11.94
12.77
E˙L
[MWh/a]
649433
0
70313
0
0
14461
6074
-3353
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
E˙D+E˙L
[MWh/a]
649433
479234
79491
30398
32043
23527
6074
-3353
24091
19138
22734
17618
10090
22363
16516
3970
3901
4344
6203
5686
3710
5777
1562
993.4
1489
2103
776.3
655.4
562
1183
338.3
484.6
60.87
26.37
15.29
11.94
12.77
141
B. Appendix - Results
Solar field
Absorber
Condenser+Dry Cooler
Mixing unit/ burner (Mixer2)
Turbine 6-8
Air mixing unit in absorber
Storage charging
Storage discharging
Steam generator HP
Generator
Eco HP
HTX superheater HP 1 (HTX 45)
Turbine 3-4
HTX in absorber
HTX preheater
Compressor HRSG
Turbine 1-2
Steam generator LP
HTX reheater 1 (HTX23)
HTX reheater 2 (HTX12)
HTX superheater HP 2 (HTX 34)
Pipes and hoppers
Mixing unit/ bypass of receiver (Mixer1)
Compressor storage
Pump HP
Air preheater for burner (HTX)
Water injection superheater (Mixer25)
Dearator
Water injection reheater (Mixer22)
HTX superheater LP
Eco LP
Duct burner
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
142
gamma˙D
[%]
0.00%
24.00%
0.46%
1.52%
1.61%
0.45%
0.00%
0.00%
1.21%
0.96%
1.14%
0.88%
0.51%
1.12%
0.83%
0.20%
0.20%
0.22%
0.31%
0.28%
0.19%
0.29%
0.08%
0.05%
0.07%
0.11%
0.04%
0.03%
0.03%
0.06%
0.02%
0.02%
0.00%
0.00%
0.00%
0.00%
0.00%
gamma˙L
[%]
32.52%
0.00%
3.52%
0.00%
0.00%
0.72%
0.30%
-0.17%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
c˙F
[e/MWh]
0
18.12
103.4
61.2
80.61
92.06
57.57
89.49
63.69
92.8
63.69
63.69
80.4
57.57
63.69
103.4
80.05
63.69
63.69
63.69
63.69
57.57
74.18
103.4
103.4
84.99
80.15
113.7
80.24
63.69
63.69
50.14
86.52
73.79
103.4
103.4
80.61
c˙P
[e/MWh]
18.12
57.57
80.61
63.69
92.8
115.9
89.49
117.4
81.12
103.4
90.86
80.13
90.53
57.57
117.4
84.99
90.67
81.77
80.23
80.4
80.05
57.57
74.55
88.98
121.8
81.47
80.28
116.6
80.34
82.12
113.1
52.05
86.67
73.8
81.85
117.3
80.61
B.3. Exergoeconomic Results Ordered by Importance
Solar field
Absorber
Condenser+Dry Cooler
Mixing unit/ burner (Mixer2)
Turbine 6-8
Air mixing unit in absorber
Storage charging
Storage discharging
Steam generator HP
Generator
Eco HP
HTX superheater HP 1 (HTX 45)
Turbine 3-4
HTX in absorber
HTX preheater
Compressor HRSG
Turbine 1-2
Steam generator LP
HTX reheater 1 (HTX23)
HTX reheater 2 (HTX12)
HTX superheater HP 2 (HTX 34)
Pipes and hoppers
Mixing unit/ bypass of receiver (Mixer1)
Compressor storage
Pump HP
Air preheater for burner (HTX)
Water injection superheater (Mixer25)
Dearator
Water injection reheater (Mixer22)
HTX superheater LP
Eco LP
Duct burner
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
C˙D+C˙L
[e/a]
0
8684000
8217000
3848000
2583000
3300000
349710
-300034
1534000
1543000
1448000
1122000
811257
1287000
1052000
410369
312267
276670
395030
362150
236251
332608
247978
102690
153954
178713
152694
129778
110603
75346
21546
24295
10590
4614
1581
1234
2075
Z
[e/a]
1.52E+07
3.74E+06
2.08E+06
0.00E+00
8.82E+05
0.00E+00
2.66E+06
2.66E+06
7.98E+05
6.98E+05
6.26E+05
4.60E+05
6.15E+05
0.00E+00
1.59E+05
2.54E+05
3.43E+05
2.41E+05
1.08E+05
1.40E+05
2.38E+05
0.00E+00
0.00E+00
1.45E+05
5.47E+04
9.88E+03
0.00E+00
0.00E+00
0.00E+00
3.37E+04
1.40E+04
0.00E+00
0.00E+00
0.00E+00
2.09E+03
1.69E+03
0.00E+00
(C˙D+C˙L)+Z
[e/a]
1.52E+07
1.24E+07
1.03E+07
3.85E+06
3.46E+06
3.30E+06
3.01E+06
2.36E+06
2.33E+06
2.24E+06
2.07E+06
1.58E+06
1.43E+06
1.29E+06
1.21E+06
6.64E+05
6.55E+05
5.18E+05
5.03E+05
5.02E+05
4.74E+05
3.33E+05
2.48E+05
2.48E+05
2.09E+05
1.89E+05
1.53E+05
1.30E+05
1.11E+05
1.09E+05
3.55E+04
2.43E+04
1.06E+04
4.61E+03
3.67E+03
2.92E+03
2.08E+03
r
[-]
0.00
1.85
0.00
1.04
0.17
2.12
0.55
0.35
0.17
1.04
0.30
0.21
0.13
1.70
0.95
0.53
0.13
0.23
0.31
0.28
0.21
1.02
1.01
0.63
0.42
0.00
1.00
1.03
1.00
0.33
0.57
0.00
1.00
1.00
0.68
0.73
1.00
f
[-]
1.00
0.30
0.20
1.00
0.25
1.00
0.88
1.13
0.34
1.00
0.30
0.29
0.43
1.00
0.13
0.38
0.52
0.47
0.21
0.28
0.50
1.00
1.00
0.59
0.26
0.05
1.00
1.00
1.00
0.31
0.39
1.00
1.00
1.00
0.57
0.58
1.00
143
B. Appendix - Results
Table B.7.: With auxiliary burner, recycling of the air stream: 80%, concentrated solar irradiation on
the receiver: 500kW/m2 , pressure of the water pipe after first economizer: 1.5bar.
Solar field
Absorber
Condenser+Dry Cooler
Turbine 6-8
Mixing unit/ burner (Mixer2)
Storage charging
Storage discharging
Steam generator HP
Eco HP
Air mixing unit in absorber
Turbine 3-4
HTX superheater HP 1 (HTX 45)
HTX in absorber
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
HTX reheater 2 (HTX12)
HTX superheater HP 2 (HTX 34)
HTX reheater 1 (HTX23)
Pipes and hoppers
Compressor storage
Mixing unit/ bypass of receiver (Mixer1)
Pump HP
Air preheater for burner (HTX)
Water injection superheater (Mixer25)
HTX superheater LP
Dearator
Water injection reheater (Mixer22)
Eco LP
Duct burner
Mixing unit discharging
Mixing unit charging
Pump feed water
Pump LP
Mixing unit turbine
144
epsilon
[%]
56.44%
44.10%
0.00%
88.51%
96.26%
98.95%
99.34%
89.69%
82.49%
71.50%
93.38%
86.87%
58.95%
95.75%
54.60%
94.08%
74.96%
89.16%
83.14%
90.53%
80.54%
98.26%
79.68%
99.55%
76.52%
100.00%
99.84%
81.25%
97.84%
99.88%
74.15%
99.89%
99.97%
99.77%
77.07%
80.38%
100.00%
E˙D
[MWh/a]
0
470125
9168
31956
29008
0
0
24084
22853
6264
10046
17656
23520
19088
16557
3882
3966
4347
5701
3715
6220
6367
1183
1487
1490
2048
761.5
1188
571.3
556.4
341.7
439.1
83.35
88.22
15.45
9.373
2.641
E˙L
[MWh/a]
649077
0
70485
0
0
1265
570.1
0
0
14461
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
E˙D+E˙L
[MWh/a]
649077
470125
79653
31956
29008
1265
570.1
24084
22853
20725
10046
17656
23520
19088
16557
3882
3966
4347
5701
3715
6220
6367
1183
1487
1490
2048
761.5
1188
571.3
556.4
341.7
439.1
83.35
88.22
15.45
9.373
2.641
B.3. Exergoeconomic Results Ordered by Importance
Solar field
Absorber
Condenser+Dry Cooler
Turbine 6-8
Mixing unit/ burner (Mixer2)
Storage charging
Storage discharging
Steam generator HP
Eco HP
Air mixing unit in absorber
Turbine 3-4
HTX superheater HP 1 (HTX 45)
HTX in absorber
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
HTX reheater 2 (HTX12)
HTX superheater HP 2 (HTX 34)
HTX reheater 1 (HTX23)
Pipes and hoppers
Compressor storage
Mixing unit/ bypass of receiver (Mixer1)
Pump HP
Air preheater for burner (HTX)
Water injection superheater (Mixer25)
HTX superheater LP
Dearator
Water injection reheater (Mixer22)
Eco LP
Duct burner
Mixing unit discharging
Mixing unit charging
Pump feed water
Pump LP
Mixing unit turbine
gamma˙D
[%]
0.00%
23.56%
0.46%
1.60%
1.45%
0.00%
0.00%
1.21%
1.15%
0.31%
0.50%
0.88%
1.18%
0.96%
0.83%
0.19%
0.20%
0.22%
0.29%
0.19%
0.31%
0.32%
0.06%
0.07%
0.07%
0.10%
0.04%
0.06%
0.03%
0.03%
0.02%
0.02%
0.00%
0.00%
0.00%
0.00%
0.00%
gamma˙L
[%]
32.52%
0.00%
3.53%
0.00%
0.00%
0.06%
0.03%
0.00%
0.00%
0.72%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
c˙F
[e/MWh]
0
18.13
87.68
66.48
49.81
56.45
79.4
51.74
51.74
84.63
66.27
51.74
56.45
78.22
51.74
65.99
87.68
51.74
51.74
51.74
51.74
56.45
87.68
71.35
87.68
70.57
66.05
51.74
93.96
66.13
51.74
31.43
71.36
74.69
87.68
87.68
66.48
c˙P
[e/MWh]
18.13
56.45
66.48
78.22
51.74
79.4
107.2
66.89
75.23
94.12
76.58
66.03
56.45
87.68
96.98
77.05
70.57
67.75
66.27
65.99
66.13
56.45
80.17
71.67
101.3
67.75
66.16
68.03
96.03
66.22
93.7
33.61
71.38
74.86
67.64
96.73
66.48
145
B. Appendix - Results
Solar field
Absorber
Condenser+Dry Cooler
Turbine 6-8
Mixing unit/ burner (Mixer2)
Storage charging
Storage discharging
Steam generator HP
Eco HP
Air mixing unit in absorber
Turbine 3-4
HTX superheater HP 1 (HTX 45)
HTX in absorber
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
HTX reheater 2 (HTX12)
HTX superheater HP 2 (HTX 34)
HTX reheater 1 (HTX23)
Pipes and hoppers
Compressor storage
Mixing unit/ bypass of receiver (Mixer1)
Pump HP
Air preheater for burner (HTX)
Water injection superheater (Mixer25)
HTX superheater LP
Dearator
Water injection reheater (Mixer22)
Eco LP
Duct burner
Mixing unit discharging
Mixing unit charging
Pump feed water
Pump LP
Mixing unit turbine
146
C˙D+C˙L
[e/a]
0
8521000
6984000
2125000
3054000
71408
45270
1246000
1182000
1754000
665776
913556
1328000
1269000
856693
256166
347741
224921
294960
192211
321829
359437
103696
211067
130693
144488
123416
61466
93391
90232
17680
13801
13639
13298
1355
821.9
354.7
Z
[e/a]
1.52E+07
3.74E+06
2.58E+06
1.10E+06
0.00E+00
2.66E+06
2.66E+06
7.98E+05
6.26E+05
0.00E+00
7.64E+05
4.60E+05
0.00E+00
0.00E+00
1.59E+05
4.27E+05
2.54E+05
2.41E+05
1.40E+05
2.38E+05
1.08E+05
0.00E+00
1.45E+05
0.00E+00
5.47E+04
9.88E+03
0.00E+00
3.37E+04
0.00E+00
0.00E+00
1.40E+04
0.00E+00
0.00E+00
0.00E+00
2.09E+03
1.69E+03
0.00E+00
(C˙D+C˙L)+Z
[e/a]
1.52E+07
1.23E+07
9.57E+06
3.22E+06
3.05E+06
2.73E+06
2.71E+06
2.04E+06
1.81E+06
1.75E+06
1.43E+06
1.37E+06
1.33E+06
1.27E+06
1.02E+06
6.83E+05
6.02E+05
4.66E+05
4.35E+05
4.30E+05
4.29E+05
3.59E+05
2.49E+05
2.11E+05
1.85E+05
1.54E+05
1.23E+05
9.51E+04
9.34E+04
9.02E+04
3.17E+04
1.38E+04
1.36E+04
1.33E+04
3.44E+03
2.51E+03
3.55E+02
r
[-]
0.00
1.76
0.00
0.20
1.04
0.41
0.40
0.19
0.32
1.40
0.15
0.23
1.70
1.04
0.99
0.17
0.58
0.25
0.30
0.23
0.32
1.02
0.61
1.01
0.44
0.01
1.00
0.36
1.02
1.00
0.62
0.00
1.00
1.00
0.76
0.75
1.00
f
[-]
1.00
0.30
0.27
0.34
1.00
0.97
0.98
0.39
0.35
1.00
0.53
0.34
1.00
1.00
0.16
0.62
0.42
0.52
0.32
0.55
0.25
1.00
0.58
1.00
0.30
0.06
1.00
0.35
1.00
1.00
0.44
1.00
1.00
1.00
0.61
0.67
1.00
B.3. Exergoeconomic Results Ordered by Importance
Table B.8.: With auxiliary burner, recycling of the air stream: 100%, concentrated solar irradiation on
the receiver: 500kW/m2 , pressure of the water pipe after first economizer: 1.5bar.
Solar field
Absorber
Condenser+Dry Cooler
Turbine 6-8
Storage charging
Mixing unit/ burner (Mixer2)
Storage discharging
Steam generator HP
Eco HP
Turbine 3-4
HTX in absorber
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
HTX reheater 2 (HTX12)
HTX superheater HP 2 (HTX 34)
HTX reheater 1 (HTX23)
Pipes and hoppers
Compressor storage
Mixing unit/ bypass of receiver (Mixer1)
Pump HP
Air preheater for burner (HTX)
Water injection superheater (Mixer25)
Dearator
HTX superheater LP
Water injection reheater (Mixer22)
Mixing unit discharging
Air mixing unit in absorber
Eco LP
Mixing unit charging
Duct burner
Mixing unit turbine
Pump feed water
Pump LP
epsilon
[%]
56.44%
45.37%
0.00%
88.50%
93.89%
96.42%
105.10%
89.66%
82.49%
93.32%
59.24%
86.85%
95.76%
54.67%
94.05%
74.67%
89.14%
83.07%
90.49%
80.49%
98.11%
80.95%
99.59%
77.40%
100.00%
99.84%
97.80%
81.64%
99.88%
99.90%
99.44%
81.22%
99.70%
99.89%
99.99%
77.09%
85.14%
E˙D
[MWh/a]
0
459319
7788
32026
0
27794
0
24175
22890
10139
24904
17700
19065
16541
3905
4002
4362
5729
3736
6245
7544
1426
1422
1423
1981
742.2
583.6
1164
542.2
344.1
447.8
248.6
130.5
425.4
52.81
15.48
6.978
E˙L
[MWh/a]
648849
0
70654
0
8957
0
4549
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.00125
0
0
0
0
0
0
E˙D+E˙L
[MWh/a]
648849
459319
78442
32026
8957
27794
4549
24175
22890
10139
24904
17700
19065
16541
3905
4002
4362
5729
3736
6245
7544
1426
1422
1423
1981
742.2
583.6
1164
542.2
344.1
447.80125
248.6
130.5
425.4
52.81
15.48
6.978
147
B. Appendix - Results
Solar field
Absorber
Condenser+Dry Cooler
Turbine 6-8
Storage charging
Mixing unit/ burner (Mixer2)
Storage discharging
Steam generator HP
Eco HP
Turbine 3-4
HTX in absorber
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
HTX reheater 2 (HTX12)
HTX superheater HP 2 (HTX 34)
HTX reheater 1 (HTX23)
Pipes and hoppers
Compressor storage
Mixing unit/ bypass of receiver (Mixer1)
Pump HP
Air preheater for burner (HTX)
Water injection superheater (Mixer25)
Dearator
HTX superheater LP
Water injection reheater (Mixer22)
Mixing unit discharging
Air mixing unit in absorber
Eco LP
Mixing unit charging
Duct burner
Mixing unit turbine
Pump feed water
Pump LP
148
gamma˙D
[%]
0.00%
23.12%
0.39%
1.61%
0.00%
1.40%
0.00%
1.22%
1.15%
0.51%
1.25%
0.89%
0.96%
0.83%
0.20%
0.20%
0.22%
0.29%
0.19%
0.31%
0.38%
0.07%
0.07%
0.07%
0.10%
0.04%
0.03%
0.06%
0.03%
0.02%
0.02%
0.01%
0.01%
0.02%
0.00%
0.00%
0.00%
gamma˙L
[%]
32.66%
0.00%
3.56%
0.00%
0.45%
0.00%
0.23%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
c˙F
[e/MWh]
0
18.13
87.23
66.07
55.53
49.57
78.49
51.41
51.41
65.88
55.53
51.41
77.79
51.41
65.59
87.23
51.41
51.41
51.41
51.41
55.53
87.23
69.4
87.23
70.16
65.65
93.3
51.41
65.74
69.31
82.92
51.41
73.67
31.43
66.07
87.23
87.23
c˙P
[e/MWh]
18.13
55.53
66.07
77.79
78.49
51.41
99.73
66.48
74.72
76.19
55.53
65.63
87.23
96.28
76.65
70.16
67.21
65.88
65.59
65.73
55.53
77.39
69.69
100.4
67.39
65.75
95.4
67.47
65.81
69.38
83.38
90.99
73.89
33.59
66.07
67.23
96.03
B.3. Exergoeconomic Results Ordered by Importance
Solar field
Absorber
Condenser+Dry Cooler
Turbine 6-8
Storage charging
Mixing unit/ burner (Mixer2)
Storage discharging
Steam generator HP
Eco HP
Turbine 3-4
HTX in absorber
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
HTX reheater 2 (HTX12)
HTX superheater HP 2 (HTX 34)
HTX reheater 1 (HTX23)
Pipes and hoppers
Compressor storage
Mixing unit/ bypass of receiver (Mixer1)
Pump HP
Air preheater for burner (HTX)
Water injection superheater (Mixer25)
Dearator
HTX superheater LP
Water injection reheater (Mixer22)
Mixing unit discharging
Air mixing unit in absorber
Eco LP
Mixing unit charging
Duct burner
Mixing unit turbine
Pump feed water
Pump LP
C˙D+C˙L
[e/a]
0
8328000
6842000
2116000
497390
2871000
357037
1243000
1177000
667915
1383000
909965
1260000
850388
256142
349062
224232
294536
192085
321046
418906
124407
198416
124153
138952
119518
94748
59852
87363
53434
37127
12781
19261
13368
7042
1350
608.7
Z
[e/a]
1.52E+07
3.74E+06
2.58E+06
1.10E+06
2.66E+06
0.00E+00
2.66E+06
7.98E+05
6.26E+05
7.64E+05
0.00E+00
4.60E+05
0.00E+00
1.59E+05
4.27E+05
2.54E+05
2.41E+05
1.40E+05
2.38E+05
1.08E+05
0.00E+00
1.45E+05
0.00E+00
5.47E+04
9.88E+03
0.00E+00
0.00E+00
3.37E+04
0.00E+00
0.00E+00
0.00E+00
1.40E+04
0.00E+00
0.00E+00
0.00E+00
2.09E+03
1.69E+03
(C˙D+C˙L)+Z
[e/a]
1.52E+07
1.21E+07
9.42E+06
3.21E+06
3.16E+06
2.87E+06
3.02E+06
2.04E+06
1.80E+06
1.43E+06
1.38E+06
1.37E+06
1.26E+06
1.01E+06
6.83E+05
6.03E+05
4.65E+05
4.34E+05
4.30E+05
4.29E+05
4.19E+05
2.69E+05
1.98E+05
1.79E+05
1.49E+05
1.20E+05
9.47E+04
9.35E+04
8.74E+04
5.34E+04
3.71E+04
2.68E+04
1.93E+04
1.34E+04
7.04E+03
3.44E+03
2.30E+03
r
[-]
0.00
1.65
0.00
0.20
0.41
1.04
0.31
0.19
0.33
0.15
1.69
0.23
1.04
0.98
0.17
0.59
0.25
0.30
0.24
0.32
1.02
0.51
1.00
0.42
0.01
1.00
1.02
0.35
1.00
1.00
1.01
0.48
1.00
0.00
1.00
0.76
0.66
f
[-]
1.00
0.31
0.27
0.34
0.84
1.00
1.16
0.39
0.35
0.53
1.00
0.34
1.00
0.16
0.62
0.42
0.52
0.32
0.55
0.25
1.00
0.54
1.00
0.31
0.07
1.00
1.00
0.36
1.00
1.00
1.00
0.52
1.00
1.00
1.00
0.61
0.74
149
B. Appendix - Results
Table B.9.: Solar only, recycling of the air stream: 60%, concentrated solar irradiation on the receiver:
550kW/m2 , pressure of the water pipe after first economizer: 1.5bar.
Solar field
Absorber
Condenser+Dry Cooler
Air mixing unit in absorber
Storage discharging
Storage charging
Turbine 6-8
Steam generator HP
HTX in absorber
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
Pipes and hoppers
HTX superheater HP 2 (HTX 34)
HTX reheater 2 (HTX12)
Compressor storage
HTX reheater 1 (HTX23)
Pump HP
Dearator
HTX superheater LP
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
150
epsilon
[%]
56.56%
42.16%
0.00%
47.11%
98.95%
98.96%
88.64%
89.73%
59.06%
82.46%
93.30%
86.93%
95.15%
57.48%
94.03%
82.44%
88.89%
98.22%
90.60%
83.05%
79.63%
80.46%
78.35%
96.59%
81.11%
99.90%
99.92%
74.02%
99.79%
99.98%
78.01%
79.64%
100.00%
0.00%
0.00%
0.00%
0.00%
E˙D
[MWh/a]
0
487709
3661
9277
0
0
12008
9528
23704
9118
3986
6864
8423
6037
1548
1537
1837
5894
1400
2195
1026
2421
542
362.3
485.6
179.3
146.6
139.7
71.67
48.71
5.785
4.023
0.6079
0
0
0
0
E˙L
[MWh/a]
647505
0
25971
27473
815.6
1090
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
E˙D+E˙L
[MWh/a]
647505
487709
29632
36750
815.6
1090
12008
9528
23704
9118
3986
6864
8423
6037
1548
1537
1837
5894
1400
2195
1026
2421
542
362.3
485.6
179.3
146.6
139.7
71.67
48.71
5.785
4.023
0.6079
0
0
0
0
B.3. Exergoeconomic Results Ordered by Importance
Solar field
Absorber
Condenser+Dry Cooler
Air mixing unit in absorber
Storage discharging
Storage charging
Turbine 6-8
Steam generator HP
HTX in absorber
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
Pipes and hoppers
HTX superheater HP 2 (HTX 34)
HTX reheater 2 (HTX12)
Compressor storage
HTX reheater 1 (HTX23)
Pump HP
Dearator
HTX superheater LP
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
gamma˙D
[%]
0.00%
31.10%
0.23%
0.59%
0.00%
0.00%
0.77%
0.61%
1.51%
0.58%
0.25%
0.44%
0.54%
0.39%
0.10%
0.10%
0.12%
0.38%
0.09%
0.14%
0.07%
0.15%
0.03%
0.02%
0.03%
0.01%
0.01%
0.01%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
gamma˙L
[%]
41.29%
0.00%
1.66%
1.75%
0.05%
0.07%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
c˙F
[e/MWh]
0
18.08
151.2
108
86.75
60.35
105.5
78.21
60.35
78.21
105
78.21
129
78.21
104.6
151.2
78.21
60.35
78.21
78.21
151.2
78.21
151.2
144.3
78.21
104.5
104.8
78.21
113.4
78.2
151.2
151.2
105.5
0
0
0
0
c˙P
[e/MWh]
18.08
60.35
105.5
135.9
121.9
86.75
129
106
60.35
120.2
127
104.5
151.2
146.3
128.7
118
109
60.35
104.6
105
107
104.7
162.1
149.3
109.4
104.6
104.8
148.7
113.7
78.21
107.5
151.2
105.5
78.21
0
0
0
151
B. Appendix - Results
Solar field
Absorber
Condenser+Dry Cooler
Air mixing unit in absorber
Storage discharging
Storage charging
Turbine 6-8
Steam generator HP
HTX in absorber
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
Pipes and hoppers
HTX superheater HP 2 (HTX 34)
HTX reheater 2 (HTX12)
Compressor storage
HTX reheater 1 (HTX23)
Pump HP
Dearator
HTX superheater LP
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
152
C˙D+C˙L
[e/a]
0
8818000
4481000
3968000
70753
65789
1267000
745266
1431000
713166
418424
536870
888682
472221
161824
232385
143703
355758
109523
171672
155152
189370
81957
91211
37985
45500
37243
10930
16123
8880
874.8
608.3
130.3
0
0
0
0
Z
[e/a]
1.52E+07
3.74E+06
2.58E+06
0.00E+00
2.66E+06
2.66E+06
1.10E+06
7.98E+05
0.00E+00
6.26E+05
7.64E+05
4.60E+05
0.00E+00
1.59E+05
4.27E+05
2.54E+05
2.41E+05
0.00E+00
2.38E+05
1.40E+05
1.45E+05
1.08E+05
5.47E+04
0.00E+00
3.37E+04
0.00E+00
0.00E+00
1.40E+04
0.00E+00
0.00E+00
2.09E+03
1.69E+03
0.00E+00
0.00E+00
0.00E+00
9.88E+03
0.00E+00
(C˙D+C˙L)+Z
[e/a]
1.52E+07
1.26E+07
7.06E+06
3.97E+06
2.73E+06
2.73E+06
2.36E+06
1.54E+06
1.43E+06
1.34E+06
1.18E+06
9.97E+05
8.89E+05
6.31E+05
5.89E+05
4.86E+05
3.85E+05
3.56E+05
3.47E+05
3.12E+05
3.00E+05
2.97E+05
1.37E+05
9.12E+04
7.17E+04
4.55E+04
3.72E+04
2.49E+04
1.61E+04
8.88E+03
2.96E+03
2.30E+03
1.30E+02
0.00E+00
0.00E+00
0.00E+00
0.00E+00
r
[-]
0.00
1.90
0.00
2.12
0.41
0.44
0.24
0.24
1.69
0.40
0.20
0.28
1.05
0.99
0.23
0.45
0.33
1.02
0.33
0.37
0.50
0.38
0.46
1.04
0.44
1.00
1.00
0.80
1.00
1.00
0.95
0.97
1.00
0.00
0.00
0.00
0.00
f
[-]
1.00
0.30
0.37
1.00
0.97
0.98
0.46
0.52
1.00
0.47
0.65
0.46
1.00
0.25
0.73
0.52
0.63
1.00
0.68
0.45
0.48
0.36
0.40
1.00
0.47
1.00
1.00
0.56
1.00
1.00
0.70
0.74
1.00
0.00
0.00
0.00
0.00
B.3. Exergoeconomic Results Ordered by Importance
Table B.10.: Solar only, recycling of the air stream: 60%, concentrated solar irradiation on the receiver:
600kW/m2 , pressure of the water pipe after first economizer: 1.5bar.
Solar field
Absorber
Condenser+Dry Cooler
Air mixing unit in absorber
Storage discharging
Storage charging
Turbine 6-8
Steam generator HP
HTX in absorber
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
Pipes and hoppers
HTX superheater HP 2 (HTX 34)
HTX reheater 2 (HTX12)
Compressor storage
HTX reheater 1 (HTX23)
Pump HP
Dearator
HTX superheater LP
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit discharging
Mixing unit charging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
epsilon
[%]
56.56%
43.01%
0.00%
47.09%
98.99%
98.96%
88.66%
89.72%
59.12%
82.44%
93.30%
86.89%
95.18%
56.88%
94.09%
82.40%
88.89%
98.19%
90.57%
82.98%
79.61%
80.39%
78.59%
97.29%
81.10%
99.91%
99.93%
73.91%
99.96%
99.78%
78.08%
79.64%
100.00%
0.00%
0.00%
0.00%
0.00%
E˙D
[MWh/a]
0
480429
3706
9487
0
0
12175
9674
24089
9277
4045
6992
8504
6221
1555
1558
1865
6095
1425
2233
1065
2466
545.1
291
493.8
168.1
137
142.6
124.1
77.64
5.846
4.095
0.1721
0
0
0
0
E˙L
[MWh/a]
647284
0
26424
28081
809.3
1125
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
E˙D+E˙L
[MWh/a]
647284
480429
30130
37568
809.3
1125
12175
9674
24089
9277
4045
6992
8504
6221
1555
1558
1865
6095
1425
2233
1065
2466
545.1
291
493.8
168.1
137
142.6
124.1
77.64
5.846
4.095
0.1721
0
0
0
0
153
B. Appendix - Results
Solar field
Absorber
Condenser+Dry Cooler
Air mixing unit in absorber
Storage discharging
Storage charging
Turbine 6-8
Steam generator HP
HTX in absorber
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
Pipes and hoppers
HTX superheater HP 2 (HTX 34)
HTX reheater 2 (HTX12)
Compressor storage
HTX reheater 1 (HTX23)
Pump HP
Dearator
HTX superheater LP
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit discharging
Mixing unit charging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
154
gamma˙D
[%]
0.00%
30.60%
0.24%
0.60%
0.00%
0.00%
0.78%
0.62%
1.53%
0.59%
0.26%
0.45%
0.54%
0.40%
0.10%
0.10%
0.12%
0.39%
0.09%
0.14%
0.07%
0.16%
0.03%
0.02%
0.03%
0.01%
0.01%
0.01%
0.01%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
gamma˙L
[%]
41.23%
0.00%
1.68%
1.79%
0.05%
0.07%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
c˙F
[e/MWh]
0
18.08
148.5
105.7
84.59
59.18
103.6
76.74
59.18
76.74
103.1
76.74
126.7
76.74
102.6
148.5
76.74
59.18
76.74
76.74
148.5
76.74
148.5
142.7
76.74
102.6
102.8
76.74
76.7
111
148.5
148.5
103.6
0
0
0
0
c˙P
[e/MWh]
18.08
59.18
103.6
133.1
118.8
84.59
126.7
104
59.18
118
124.7
102.6
148.5
144.8
126.3
115.7
107
59.18
102.6
103.1
104.4
102.8
159.2
146.7
107.4
102.7
102.9
146.1
76.74
111.2
105.5
148.5
103.6
76.74
0
0
0
B.3. Exergoeconomic Results Ordered by Importance
Solar field
Absorber
Condenser+Dry Cooler
Air mixing unit in absorber
Storage discharging
Storage charging
Turbine 6-8
Steam generator HP
HTX in absorber
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
Pipes and hoppers
HTX superheater HP 2 (HTX 34)
HTX reheater 2 (HTX12)
Compressor storage
HTX reheater 1 (HTX23)
Pump HP
Dearator
HTX superheater LP
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit discharging
Mixing unit charging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
C˙D+C˙L
[e/a]
0
8689000
4473000
3971000
68456
66549
1261000
742312
1426000
711878
416814
536534
880850
477349
159584
231329
143147
360682
109381
171378
158152
189219
80932
72277
37891
41912
34200
10946
22085
17096
867.9
608
36.21
0
0
0
0
Z
[e/a]
1.52E+07
3.74E+06
2.58E+06
0.00E+00
2.66E+06
2.66E+06
1.10E+06
7.98E+05
0.00E+00
6.26E+05
7.64E+05
4.60E+05
0.00E+00
1.59E+05
4.27E+05
2.54E+05
2.41E+05
0.00E+00
2.38E+05
1.40E+05
1.45E+05
1.08E+05
5.47E+04
0.00E+00
3.37E+04
0.00E+00
0.00E+00
1.40E+04
0.00E+00
0.00E+00
2.09E+03
1.69E+03
0.00E+00
0.00E+00
0.00E+00
9.88E+03
0.00E+00
(C˙D+C˙L)+Z
[e/a]
1.52E+07
1.24E+07
7.05E+06
3.97E+06
2.73E+06
2.73E+06
2.36E+06
1.54E+06
1.43E+06
1.34E+06
1.18E+06
9.97E+05
8.81E+05
6.36E+05
5.86E+05
4.85E+05
3.84E+05
3.61E+05
3.47E+05
3.11E+05
3.03E+05
2.97E+05
1.36E+05
7.23E+04
7.16E+04
4.19E+04
3.42E+04
2.49E+04
2.21E+04
1.71E+04
2.96E+03
2.30E+03
3.62E+01
0.00E+00
0.00E+00
0.00E+00
0.00E+00
r
[-]
0.00
1.85
0.00
2.12
0.41
0.43
0.24
0.24
1.69
0.40
0.20
0.28
1.05
1.01
0.23
0.45
0.34
1.02
0.33
0.37
0.49
0.38
0.46
1.03
0.44
1.00
1.00
0.80
1.00
1.00
0.96
0.97
1.00
0.00
0.00
0.00
0.00
f
[-]
1.00
0.30
0.37
1.00
0.97
0.98
0.47
0.52
1.00
0.47
0.65
0.46
1.00
0.25
0.73
0.52
0.63
1.00
0.68
0.45
0.48
0.36
0.40
1.00
0.47
1.00
1.00
0.56
1.00
1.00
0.71
0.74
1.00
0.00
0.00
0.00
0.00
155
B. Appendix - Results
Table B.11.: Solar only, recycling of the air stream: 60%, concentrated solar irradiation on the receiver:
500kW/m2 , pressure of the water pipe after first economizer: 3bar and 135◦ C.
Solar field
Absorber
Condenser+Dry Cooler
Storage charging
Storage discharging
Turbine 6-8
Air mixing unit in absorber
HTX in absorber
Steam generator HP
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Pipes and hoppers
Steam generator LP
HTX superheater HP 2 (HTX 34)
Compressor storage
HTX reheater 2 (HTX12)
HTX reheater 1 (HTX23)
Pump HP
HTX superheater LP
Dearator
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
156
epsilon
[%]
56.59%
40.52%
0.00%
93.91%
104.30%
88.54%
47.12%
60.15%
89.70%
84.73%
93.23%
87.09%
95.06%
59.69%
93.90%
82.71%
98.29%
87.91%
90.68%
79.78%
83.11%
80.52%
77.22%
81.76%
98.82%
99.90%
99.91%
87.68%
99.76%
99.99%
78.76%
82.91%
99.96%
0.00%
0.00%
0.00%
0.00%
E˙D
[MWh/a]
0
497607
3449
0
0
11482
9730
27914
8929
6603
3760
6328
8068
5921
1481
1431
5190
2377
1298
883.1
2049
2256
538.1
560.9
164.9
176.3
150
27.3
72.36
30.44
10.66
3.341
55.14
0
0
0
0
E˙L
[MWh/a]
641593
0
29520
5462
2798
0
28949
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
E˙D+E˙L
[MWh/a]
641593
497607
32969
5462
2798
11482
38679
27914
8929
6603
3760
6328
8068
5921
1481
1431
5190
2377
1298
883.1
2049
2256
538.1
560.9
164.9
176.3
150
27.3
72.36
30.44
10.66
3.341
55.14
0
0
0
0
B.3. Exergoeconomic Results Ordered by Importance
Solar field
Absorber
Condenser+Dry Cooler
Storage charging
Storage discharging
Turbine 6-8
Air mixing unit in absorber
HTX in absorber
Steam generator HP
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Pipes and hoppers
Steam generator LP
HTX superheater HP 2 (HTX 34)
Compressor storage
HTX reheater 2 (HTX12)
HTX reheater 1 (HTX23)
Pump HP
HTX superheater LP
Dearator
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
gamma˙D
[%]
0.00%
32.25%
0.22%
0.00%
0.00%
0.74%
0.63%
1.81%
0.58%
0.43%
0.24%
0.41%
0.52%
0.38%
0.10%
0.09%
0.34%
0.15%
0.08%
0.06%
0.13%
0.15%
0.03%
0.04%
0.01%
0.01%
0.01%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
gamma˙L
[%]
41.58%
0.00%
1.91%
0.35%
0.18%
0.00%
1.88%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
c˙F
[e/MWh]
0
18.22
160.6
64.06
99.78
111.7
113.6
64.06
83.27
83.27
111.3
83.27
136.9
83.27
110.8
160.6
64.06
83.27
83.27
160.6
83.27
83.27
160.6
83.27
140.9
110.7
111.1
83.27
123.3
83.26
160.6
160.6
111.6
0
0
0
0
c˙P
[e/MWh]
18.22
64.06
111.7
99.78
134.3
136.9
143.3
64.06
112.2
126.2
134.9
110.7
160.6
150
136.7
128
64.06
113
110.8
116.1
111.3
111.1
155.5
113.3
142.6
110.8
111.2
145.8
123.6
83.27
114.7
143.8
111.7
83.27
0
0
0
157
B. Appendix - Results
Solar field
Absorber
Condenser+Dry Cooler
Storage charging
Storage discharging
Turbine 6-8
Air mixing unit in absorber
HTX in absorber
Steam generator HP
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Pipes and hoppers
Steam generator LP
HTX superheater HP 2 (HTX 34)
Compressor storage
HTX reheater 2 (HTX12)
HTX reheater 1 (HTX23)
Pump HP
HTX superheater LP
Dearator
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
158
C˙D+C˙L
[e/a]
0
9068000
5296000
349861
279195
1282000
4396000
1788000
743522
549826
418602
526959
900987
493038
164130
229820
332429
197964
108092
141852
170636
187859
86433
46711
43166
44663
38059
2273
17664
6039
1712
536.6
12385
0
0
0
0
Z
[e/a]
1.52E+07
3.74E+06
2.58E+06
2.66E+06
2.66E+06
1.10E+06
0.00E+00
0.00E+00
7.98E+05
6.26E+05
7.64E+05
4.60E+05
0.00E+00
1.59E+05
4.27E+05
2.54E+05
0.00E+00
2.41E+05
2.38E+05
1.45E+05
1.40E+05
1.08E+05
5.47E+04
3.37E+04
0.00E+00
0.00E+00
0.00E+00
1.40E+04
0.00E+00
0.00E+00
2.09E+03
1.69E+03
0.00E+00
0.00E+00
0.00E+00
9.88E+03
0.00E+00
(C˙D+C˙L)+Z
[e/a]
1.52E+07
1.28E+07
7.88E+06
3.01E+06
2.94E+06
2.38E+06
4.40E+06
1.79E+06
1.54E+06
1.18E+06
1.18E+06
9.87E+05
9.01E+05
6.52E+05
5.91E+05
4.84E+05
3.32E+05
4.39E+05
3.46E+05
2.87E+05
3.10E+05
2.95E+05
1.41E+05
8.04E+04
4.32E+04
4.47E+04
3.81E+04
1.63E+04
1.77E+04
6.04E+03
3.80E+03
2.23E+03
1.24E+04
0.00E+00
0.00E+00
0.00E+00
0.00E+00
r
[-]
0.00
2.02
0.00
0.56
0.35
0.24
2.12
1.66
0.24
0.39
0.21
0.28
1.05
0.89
0.23
0.44
1.02
0.30
0.33
0.51
0.37
0.38
0.48
0.38
1.01
1.00
1.00
1.01
1.00
1.00
0.60
0.86
1.00
0.00
0.00
0.00
0.00
f
[-]
1.00
0.29
0.33
0.88
1.12
0.46
1.00
1.00
0.52
0.53
0.65
0.47
1.00
0.24
0.72
0.53
1.00
0.55
0.69
0.51
0.45
0.36
0.39
0.42
1.00
1.00
1.00
0.86
1.00
1.00
0.55
0.76
1.00
0.00
0.00
0.00
0.00
B.3. Exergoeconomic Results Ordered by Importance
Table B.12.: Solar only, recycling of the air stream: 60%, concentrated solar irradiation on the receiver:
500kW/m2 , pressure of the water pipe after first economizer: 3bar and 145◦ C.
Solar field
Absorber
Condenser+Dry Cooler
Storage charging
Storage discharging
Turbine 6-8
Air mixing unit in absorber
HTX in absorber
Steam generator HP
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Pipes and hoppers
Steam generator LP
HTX superheater HP 2 (HTX 34)
Compressor storage
HTX reheater 2 (HTX12)
HTX reheater 1 (HTX23)
Pump HP
HTX superheater LP
Dearator
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
epsilon
[%]
56.59%
40.53%
0.00%
93.91%
104.30%
88.53%
47.12%
60.15%
89.70%
84.73%
93.23%
87.09%
95.05%
59.70%
93.90%
82.71%
98.29%
87.91%
90.69%
79.78%
83.11%
80.53%
77.17%
81.76%
98.82%
99.90%
99.91%
87.69%
99.76%
99.99%
78.76%
82.91%
99.96%
0.00%
0.00%
0.00%
0.00%
E˙D
[MWh/a]
0
497407
3449
0
0
11480
9730
27912
8927
6599
3760
6326
8072
5918
1481
1430
5189
2376
1298
883.3
2049
2255
539.1
560.6
164.7
178
151.3
27.27
72.81
30.47
10.66
3.339
55.13
0
0
0
0
E˙L
[MWh/a]
641447
0
29506
5462
2795
0
28950
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
E˙D+E˙L
[MWh/a]
641447
497407
32955
5462
2795
11480
38680
27912
8927
6599
3760
6326
8072
5918
1481
1430
5189
2376
1298
883.3
2049
2255
539.1
560.6
164.7
178
151.3
27.27
72.81
30.47
10.66
3.339
55.13
0
0
0
0
159
B. Appendix - Results
Solar field
Absorber
Condenser+Dry Cooler
Storage charging
Storage discharging
Turbine 6-8
Air mixing unit in absorber
HTX in absorber
Steam generator HP
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Pipes and hoppers
Steam generator LP
HTX superheater HP 2 (HTX 34)
Compressor storage
HTX reheater 2 (HTX12)
HTX reheater 1 (HTX23)
Pump HP
HTX superheater LP
Dearator
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
160
gamma˙D
[%]
0.00%
32.25%
0.22%
0.00%
0.00%
0.74%
0.63%
1.81%
0.58%
0.43%
0.24%
0.41%
0.52%
0.38%
0.10%
0.09%
0.34%
0.15%
0.08%
0.06%
0.13%
0.15%
0.03%
0.04%
0.01%
0.01%
0.01%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
gamma˙L
[%]
41.58%
0.00%
1.91%
0.35%
0.18%
0.00%
1.88%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
c˙F
[e/MWh]
0
18.23
160.6
64.06
99.79
111.7
113.7
64.06
83.27
83.27
111.3
83.27
136.9
83.27
110.8
160.6
64.06
83.27
83.27
160.6
83.27
83.27
160.6
83.27
140.9
110.7
111.1
83.27
123.3
83.26
160.6
160.6
111.6
0
0
0
0
c˙P
[e/MWh]
18.23
64.06
111.7
99.79
134.3
136.9
143.3
64.06
112.2
126.2
135
110.7
160.6
150
136.7
128
64.06
113.1
110.8
116.1
111.3
111.1
155.5
113.3
142.6
110.8
111.2
145.8
123.6
83.27
114.7
143.8
111.7
83.27
0
0
0
B.3. Exergoeconomic Results Ordered by Importance
Solar field
Absorber
Condenser+Dry Cooler
Storage charging
Storage discharging
Turbine 6-8
Air mixing unit in absorber
HTX in absorber
Steam generator HP
Eco HP
Turbine 3-4
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Pipes and hoppers
Steam generator LP
HTX superheater HP 2 (HTX 34)
Compressor storage
HTX reheater 2 (HTX12)
HTX reheater 1 (HTX23)
Pump HP
HTX superheater LP
Dearator
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit charging
Mixing unit discharging
Pump feed water
Pump LP
Mixing unit turbine
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
C˙D+C˙L
[e/a]
0
9067000
5294000
349918
278889
1282000
4396000
1788000
743375
549504
418582
526766
901432
492761
164122
229788
332401
197855
108078
141895
170604
187786
86603
46685
43112
45096
38394
2271
17772
6045
1713
536.4
12384
0
0
0
0
Z
[e/a]
1.52E+07
3.74E+06
2.58E+06
2.66E+06
2.66E+06
1.10E+06
0.00E+00
0.00E+00
7.98E+05
6.26E+05
7.64E+05
4.60E+05
0.00E+00
1.59E+05
4.27E+05
2.54E+05
0.00E+00
2.41E+05
2.38E+05
1.45E+05
1.40E+05
1.08E+05
5.47E+04
3.37E+04
0.00E+00
0.00E+00
0.00E+00
1.40E+04
0.00E+00
0.00E+00
2.09E+03
1.69E+03
0.00E+00
0.00E+00
0.00E+00
9.88E+03
0.00E+00
(C˙D+C˙L)+Z
[e/a]
1.52E+07
1.28E+07
7.88E+06
3.01E+06
2.94E+06
2.38E+06
4.40E+06
1.79E+06
1.54E+06
1.18E+06
1.18E+06
9.87E+05
9.01E+05
6.52E+05
5.91E+05
4.84E+05
3.32E+05
4.39E+05
3.46E+05
2.87E+05
3.10E+05
2.95E+05
1.41E+05
8.04E+04
4.31E+04
4.51E+04
3.84E+04
1.63E+04
1.78E+04
6.05E+03
3.80E+03
2.23E+03
1.24E+04
0.00E+00
0.00E+00
0.00E+00
0.00E+00
r
[-]
0.00
2.02
0.00
0.56
0.35
0.24
2.12
1.66
0.24
0.39
0.21
0.28
1.05
0.89
0.23
0.44
1.02
0.31
0.33
0.51
0.37
0.38
0.48
0.38
1.01
1.00
1.00
1.01
1.00
1.00
0.60
0.86
1.00
0.00
0.00
0.00
0.00
f
[-]
1.00
0.29
0.33
0.88
1.12
0.46
1.00
1.00
0.52
0.53
0.65
0.47
1.00
0.24
0.72
0.53
1.00
0.55
0.69
0.51
0.45
0.36
0.39
0.42
1.00
1.00
1.00
0.86
1.00
1.00
0.55
0.76
1.00
0.00
0.00
0.00
0.00
161
B. Appendix - Results
Table B.13.: Solar only, recycling of the air stream: 60%, concentrated solar irradiation on the receiver:
500kW/m2 , pressure of the water pipe after first economizer: 3bar and 155◦ C.
Solar field
Absorber
Condenser+Dry Cooler
Air mixing unit in absorber
Storage charging
Turbine 6-8
Storage discharging
Steam generator HP
Eco HP
Turbine 3-4
HTX in absorber
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
Pipes and hoppers
HTX superheater HP 2 (HTX 34)
HTX reheater 2 (HTX12)
Compressor storage
HTX reheater 1 (HTX23)
Pump HP
Dearator
HTX superheater LP
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit discharging
Mixing unit charging
Pump feed water
Mixing unit turbine
Pump LP
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
162
epsilon
[%]
56.56%
41.56%
0.00%
47.21%
93.97%
88.69%
104.50%
89.73%
84.50%
93.34%
57.74%
86.96%
95.18%
54.74%
94.10%
82.37%
87.79%
98.19%
90.63%
83.00%
79.64%
80.41%
78.45%
96.84%
81.19%
99.92%
99.93%
80.36%
99.97%
99.85%
79.90%
99.99%
82.14%
0.00%
0.00%
0.00%
0.00%
E˙D
[MWh/a]
0
489530
3620
8115
0
12125
0
9638
7309
4006
17226
6928
8478
5905
1548
1563
2626
6069
1408
2218
1080
2453
552.4
488.1
632.3
148.2
125.6
47.65
89.35
53.34
10.51
11.82
3.775
0
0
0
0
E˙L
[MWh/a]
643411
0
29437
24046
6653
0
3450
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
E˙D+E˙L
[MWh/a]
643411
489530
33057
32161
6653
12125
3450
9638
7309
4006
17226
6928
8478
5905
1548
1563
2626
6069
1408
2218
1080
2453
552.4
488.1
632.3
148.2
125.6
47.65
89.35
53.34
10.51
11.82
3.775
0
0
0
0
B.3. Exergoeconomic Results Ordered by Importance
Solar field
Absorber
Condenser+Dry Cooler
Air mixing unit in absorber
Storage charging
Turbine 6-8
Storage discharging
Steam generator HP
Eco HP
Turbine 3-4
HTX in absorber
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
Pipes and hoppers
HTX superheater HP 2 (HTX 34)
HTX reheater 2 (HTX12)
Compressor storage
HTX reheater 1 (HTX23)
Pump HP
Dearator
HTX superheater LP
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit discharging
Mixing unit charging
Pump feed water
Mixing unit turbine
Pump LP
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
gamma˙D
[%]
0.00%
31.42%
0.23%
0.52%
0.00%
0.78%
0.00%
0.62%
0.47%
0.26%
1.11%
0.44%
0.54%
0.38%
0.10%
0.10%
0.17%
0.39%
0.09%
0.14%
0.07%
0.16%
0.04%
0.03%
0.04%
0.01%
0.01%
0.00%
0.01%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
gamma˙L
[%]
41.30%
0.00%
1.89%
1.54%
0.43%
0.00%
0.22%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
c˙F
[e/MWh]
0
18.2
150.4
109.3
60.81
105.2
90.39
78.43
78.43
104.8
60.81
78.43
128.5
78.43
104.4
150.4
78.43
60.81
78.43
78.43
150.4
78.43
150.4
133.4
78.43
104.4
104.6
78.43
78.41
111.7
150.4
105.2
150.4
0
0
0
0
c˙P
[e/MWh]
18.2
60.81
105.2
137.1
90.39
128.5
119.3
105.7
119.4
126.6
60.81
104.3
150.4
153
128.2
115.7
106.7
60.81
104.4
104.8
106.1
104.6
148.9
137.8
107
104.4
104.7
141.2
78.43
111.9
108
105.2
138.9
78.43
0
0
0
163
B. Appendix - Results
Solar field
Absorber
Condenser+Dry Cooler
Air mixing unit in absorber
Storage charging
Turbine 6-8
Storage discharging
Steam generator HP
Eco HP
Turbine 3-4
HTX in absorber
HTX superheater HP 1 (HTX 45)
Generator
HTX preheater
Turbine 1-2
Compressor HRSG
Steam generator LP
Pipes and hoppers
HTX superheater HP 2 (HTX 34)
HTX reheater 2 (HTX12)
Compressor storage
HTX reheater 1 (HTX23)
Pump HP
Dearator
HTX superheater LP
Water injection superheater (Mixer25)
Water injection reheater (Mixer22)
Eco LP
Mixing unit discharging
Mixing unit charging
Pump feed water
Mixing unit turbine
Pump LP
Mixing unit/ burner (Mixer2)
Mixing unit/ bypass of receiver (Mixer1)
Air preheater for burner (HTX)
Duct burner
164
C˙D+C˙L
[e/a]
0
8908000
4973000
3516000
404572
1275000
311853
755944
573207
420007
1047000
543361
891748
463094
161612
235069
205967
369081
110410
173974
162480
192356
83104
126047
49591
35884
30457
3737
16092
11831
1581
2503
567.9
0
0
0
0
Z
[e/a]
1.52E+07
3.74E+06
2.58E+06
0.00E+00
2.66E+06
1.10E+06
2.66E+06
7.98E+05
6.26E+05
7.64E+05
0.00E+00
4.60E+05
0.00E+00
1.59E+05
4.27E+05
2.54E+05
2.41E+05
0.00E+00
2.38E+05
1.40E+05
1.45E+05
1.08E+05
5.47E+04
0.00E+00
3.37E+04
0.00E+00
0.00E+00
1.40E+04
0.00E+00
0.00E+00
2.09E+03
0.00E+00
1.69E+03
0.00E+00
0.00E+00
9.88E+03
0.00E+00
(C˙D+C˙L)+Z
[e/a]
1.52E+07
1.26E+07
7.55E+06
3.52E+06
3.07E+06
2.37E+06
2.97E+06
1.55E+06
1.20E+06
1.18E+06
1.05E+06
1.00E+06
8.92E+05
6.22E+05
5.88E+05
4.89E+05
4.47E+05
3.69E+05
3.48E+05
3.14E+05
3.08E+05
3.00E+05
1.38E+05
1.26E+05
8.33E+04
3.59E+04
3.05E+04
1.77E+04
1.61E+04
1.18E+04
3.67E+03
2.50E+03
2.26E+03
0.00E+00
0.00E+00
0.00E+00
0.00E+00
r
[-]
0.00
1.95
0.00
2.12
0.49
0.24
0.32
0.24
0.38
0.20
1.73
0.28
1.05
1.11
0.23
0.45
0.30
1.02
0.33
0.37
0.48
0.38
0.46
1.03
0.39
1.00
1.00
1.16
1.00
1.00
0.58
1.00
0.86
0.00
0.00
0.00
0.00
f
[-]
1.00
0.30
0.34
1.00
0.87
0.46
1.13
0.51
0.52
0.65
1.00
0.46
1.00
0.26
0.73
0.52
0.54
1.00
0.68
0.45
0.47
0.36
0.40
1.00
0.40
1.00
1.00
0.79
1.00
1.00
0.57
1.00
0.75
0.00
0.00
0.00
0.00
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