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Hybrid Poly-generation Energy Systems: Thermal Design and Exergy Analysis
Hybrid Poly-generation Energy Systems: Thermal Design and Exergy Analysis
Hybrid Poly-generation Energy Systems: Thermal Design and Exergy Analysis
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Hybrid Poly-generation Energy Systems: Thermal Design and Exergy Analysis

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Hybrid Poly-generation Energy Systems: Thermal Design and Exergy Analysis provides an analysis of the latest technologies and concepts of hybrid energy systems, focusing on thermal applications. The book guides readers through an introduction to hybrid poly-generation systems and the storage options available before working through the types of hybrid systems, including solar, fuel cells, combustion, and heating and cooling. An analysis of the economic and environmental impact of each system is included, as well as methods and approaches for exergy and energy improvement analysis. This book can be used as a tool for understanding new concepts in this emerging field and as a reference for researchers and professionals working on the integrated cogeneration of power systems.
  • Guides the reader through hybrid processes they can apply to their own system designs
  • Explains operational processes and includes multiple examples of optimization techniques
  • Includes renewable energy sources, CO2 capturing processes in combined systems and advanced exergy analysis methods
LanguageEnglish
Release dateSep 21, 2023
ISBN9780323985741
Hybrid Poly-generation Energy Systems: Thermal Design and Exergy Analysis
Author

Mehdi Mehrpooya

Mehdi Mehrpooya is employed as Full Professor at University of Tehran, Faculty of New Sciences and Technologies. For the past decade as a faculty member, he has participated in teaching and administration duties as well as conducting countless novel research both experimentally and theoretically in several areas. Including process simulation, hydrogen production, storage, and liquefaction, fuel cells and electrochemical systems, energy storage systems and batteries, developing process engineering of several biochemicals production, CO2 separation and reduction, and investigating sustainability though utilization of renewable resources in the process especially by adopting solar energy. As his curriculum vitae illustrates, he has more than 280 papers in the mentioned areas published in reputable peer-reviewed journals

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    Hybrid Poly-generation Energy Systems - Mehdi Mehrpooya

    Front Cover for Hybrid Poly-generation Energy Systems - Thermal Design and Exergy Analysis - 1st edition - by Mehdi Mehrpooya, Majid Asadnia, Amir Hossein Karimi, Ali Allahyarzadeh-Bidgoli

    Hybrid Poly-generation Energy Systems

    Thermal Design and Exergy Analysis

    Mehdi Mehrpooya

    Faculty of New Sciences and Technologies, the University of Tehran, Tehran, Iran

    Majid Asadnia

    Mechanical Engineering Department, Faculty of Engineering at the Kar Higher Education Institute, Tehran, Iran

    Amir Hossein Karimi

    Faculty of New Sciences and Technologies, the University of Tehran, Tehran, Iran

    Ali Allahyarzadeh-Bidgoli

    Department of Mechanical Engineering (PME), Escola Politécnica-University of São Paulo (EP-USP), São Paulo, Brazil

    Table of Contents

    Cover image

    Title page

    Copyright

    1. What does it mean? Hybrid polygeneration systems

    Abstract

    1.1 Background

    1.2 Definition and classification of hybrid polygeneration systems

    1.3 Objectives and necessity of using hybrid polygeneration systems

    References

    2. How to use renewable energy sources in polygeneration systems?

    Abstract

    2.1 Introduction

    2.2 Proposed process frameworks for solar polygeneration systems

    2.3 Solar power plant

    2.4 Solar thermochemical reactors

    2.5 Wind energy-based polygeneration systems

    2.6 Hydrogen production by a multipurpose cycle consisting of wind turbine and heliostats

    2.7 Conceptual configuration of using wind energy and geothermal energy to produce hydrogen chloride

    2.8 Multipurpose combinations of wind and solar energy for power and refrigeration generation, energy storage, water desalination, food drying, and water electrolysis

    2.9 CO2 capturing using wind energy in a multiproduction energy system

    2.10 Geothermal energy and polygeneration systems

    2.11 Biomass energy used in polygeneration systems

    2.12 How to combine hydroenergy systems and polygeneration systems?

    2.13 Hybrid power generation of hydropower

    2.14 Polygeneration systems that use wave energy resources

    References

    3. Energy storage type and size in PGSs

    Abstract

    3.1 Introduction

    3.2 Operational possible ways for thermal energy storage in PGSs

    3.3 Benefits and limitations of mechanical energy storage in PGSs

    3.4 Proposed process configurations for electrochemical energy storage in PGSs

    3.5 How to store electrical energy in PGSs?

    References

    4. Exergy, energy, environmental and economic analysis of hybrid poly-generation systems: methods and approaches

    Abstract

    4.1 Introduction

    4.2 The concept of exergy

    4.3 Preliminary and advanced environmental analysis of PGs

    4.4 Preliminary and advanced economic analysis of PGSs

    References

    5. Solar-based hybrid energy systems

    Abstract

    5.1 Introduction

    5.2 Power production by solar PGSs

    5.3 Heating production by solar PGSs

    5.4 Cooling production by solar PGSs

    5.5 Hydrogen production by solar PGSs

    References

    6. Technical and economic prospects of fuel cells combination with polygeneration systems?

    Abstract

    6.1 Fuel cell

    6.2 Electrolyze

    6.3 SOFCs in polygeneration systems

    References

    7. Biomass-based hybrid energy systems

    Abstract

    7.1 Introduction

    7.2 Thermochemical biomass gasification combined processes

    7.2.3 Hybrid biomass energy systems to produce power

    7.2.4 Tri-generation and integration of cold, heat, and power by biomass-based hybrid systems

    7.2.5 Proposed systems for hybrid solar and biomass power plants

    References

    8. Chemical looping combustion in polygeneration systems

    Abstract

    8.1 Introduction

    8.2 Fuel cell

    8.3 Solid oxide fuel cell

    8.4 Proton exchange membrane fuel cells

    8.5 Expander power process

    8.6 Vapor (or steam) power cycle

    8.7 Gas and combined power cycles

    8.8 Heat recuperation

    8.9 Two reactor conversion process configurations

    References

    9. A framework for sustainable hydrogen production by polygeneration systems

    Abstract

    9.1 Introduction

    9.2 High-temperature hybrid electrolyzers

    9.3 Biomass and photobiological processes to produce hydrogen

    9.4 GS reactor temperature effect on hydrogen production rate

    9.5 Sulfuric acid system

    References

    10. Integration of oxyfuel power plants in polygeneration systems

    Abstract

    10.1 Integration of oxyfuel power plants

    10.2 Energy and exergy analysis of integrated oxyfuel hybrid power plants

    10.3 Environmental and economic analysis of oxyfuel hybrid power plants

    References

    11. Basic power and cooling production systems in combination with polygeneration systems to trigeneration of cold, heat, and power

    Abstract

    11.1 Basic power and cooling production systems

    11.2 Thermoelectric/thermionic generators in polygeneration systems

    11.3 Stirling engines and polygeneration systems

    11.4 ORCs in polygeneration systems

    11.5 Joule–Brayton refrigeration processes in combination with polygeneration systems

    11.6 Cryogenic air separation

    11.7 Absorption refrigeration-based polygeneration systems

    References

    12. Integration of carbon dioxide capturing processes in hybrid energy systems

    Abstract

    12.1 Integration of carbon dioxide capturing processes

    12.2 Absorption-based postcombustion capture of carbon systems and polygeneration systems

    12.3 Exergy and energy analysis of hybrid CCSs

    12.4 Environmental and economic analysis of hybrid CCSs

    References

    13. Why advanced analyses?

    Abstract

    13.1 Introduction

    13.2 Advanced economic, environmental, and exergy analyses of polygeneration systems

    13.3 Advanced method procedure

    13.4 Accessible and inaccessible sector variables and assessment

    13.5 Avoidable and unavoidable sector variables and assessment

    13.6 Benefits and disadvantageous of advanced analysis methodology for energy systems

    References

    Index

    Copyright

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    1

    What does it mean? Hybrid polygeneration systems

    Abstract

    In today's world, where the impact of climate change is becoming increasingly evident and the energy demand is on the rise, it is imperative to avoid wasteful energy practices. One approach to achieve this goal is to harness heat at moderate temperatures through optimal heat exchange to generate power. This can be accomplished through a polygeneration system, which not only produces power and meets energy requirements but also optimizes energy efficiency by utilizing waste sources. Additionally, such a system can provide cooling, heating, and even renewable energy sources such as hydrogen, thus rendering it a truly sustainable option. This chapter provides a detailed overview of polygeneration and hybrid polygeneration systems, categorizes and defines these systems, and discusses the equipment prerequisites, energy sources, and objectives of both traditional and innovative hybrid polygeneration systems.

    Keywords

    Climate change; organic Rankine Cycle; polygeneration; hybrid energy systems; renewable energy sources; hydrogen production; energy storage; oxy-fuel power generation; CO2 capture; storage, and liquefaction

    1.1 Background

    The process of producing both electricity and useable heat simultaneously using a thermal turbine or power plant is referred to as combined heat and power or co-generation plant. Co-generation has been in use for quite some time, being the first application of polygeneration system. It originated in Europe during the 19th century and in the United States during the early 1900s, when coal boilers and steam turbine generators were the primary sources of energy for most industries. The steam generated from these facilities was utilized for commercial operations [1,2].

    One or more primary energy sources are combined in a process called polygeneration to produce two or more energy products. Applications for polygeneration systems are numerous in the power plant, energy, industrial, and utility sectors. Using polygeneration systems for concurrent heating, cooling, and power generation is an efficient way to improve energy efficiency. Such systems combined and produces three or more outcomes, including energy outcomes, through one or more natural resources. By doing so, it is possible to improve overall performance significantly and, in turn, reduce pollutants and emitting greenhouse gases. Small-scale polygeneration systems combine old and new technology to produce heating, cooling, power, and additional products such as energy storage, CO2 (in liquid or gas phases), biofuels, and other things. The elements of a polygeneration system can be combined to form its subsystems.

    Hybrid systems can generate electricity by combining two or more technologies. Various configurations can create hybrid systems, such as hydrogen, renewable energy, gas, and steam cycles. Examples of this technology include integrating the fuel cell system with renewable sources such as wind turbines and PVs, co-generation and tri-generation processes integrated with fuel cell technology, etc. Simultaneous electricity and heating, cooling, or both generation is an excellent solution to improve energy efficiency. For co-generation processes, the required fuel to generate power and heating energy is significantly smaller than when power and heat are generated distinctly in conventional systems. Therefore these systems are very suitable in terms of efficiency. Triple-generation systems also include processes that use a single fuel source to generate and consume electricity and heat simultaneously. Simultaneous energy use results in high energy efficiency, fewer emissions, storage safety, less waste, and lower costs.

    1.2 Definition and classification of hybrid polygeneration systems

    Providing a clean, eco-friendly option is increasingly crucial than ever in light of the rise in energy use and the issues of fossil resource shortage. Even though numerous renewable energy sources have already been implemented recently, they have constantly been constrained by problems with the economy, the level of technology, and other factors. As a large portion of fossil fuels are utilized in the current inefficient electricity generation, greenhouse gases (GHG) have been emitted into the environment more frequently in recent years. Co-generation systems that simultaneously produce two different products have been created to increase efficiency, lower costs, and reduce pollutant emissions. By integrating several processes, polygeneration systems enable the production of multiple energy sectors (more than two), such as heat, cold, electricity, and energy carriers like hydrogen [3,4]. High energy efficiency, declining fossil fuel usage, financial impact, combination ability with sustainable power, and minimal pollutant production are only a few benefits of these systems [5,6]. Combining heat and power (CHP), one type of polygeneration technology, is crucial for maximizing energy efficiency and utilizing available energy resources [7]. In order to meet the demand for cooling, integrated cooling, heating, and power (CCHP) processes, which generate heating, refrigerating, and electricity simultaneously, were developed. In this manner, waste heat from conventional systems is utilized to create valuable goods. In essence, it uses the waste heat from primary energy sources, including internal combustion engines, steam turbines, micro gas expanders, Stirling engines, and fuel cells, to create useful products [8]. The polygeneration system’s core components are a prime mover as well as an energy conversion device. The appropriate prime mover and energy conversion device are selected according to the power production, usage, and cost associated. Fig. 1.1 illustrates the potential for manufacturing fuels, energy, and other goods using a polygeneration system. Fig. 1.2 illustrates the various prime movers and energy conversion devices employed.

    Figure 1.1 Polygeneration systems’ potential routes [3].

    Figure 1.2 An illustration of the various prime movers and energy conversion devices [3].

    Renewable energy sources, as sustainable, easily accessible, and reproducible, are the best choice among other energy sources for a polygeneration system. These energy sources can be converted to other forms of energy conventionally, resulting in heat, cooling, power, and other energy source generations. Wind, solar, biomass, and geothermal are the primary and most used renewable energy sources, including for hybrid polygeneration systems. Wind energy is applicable in wind turbines for power production. As shown in Fig. 1.3, solar energy can be used by thermal applications such as solar collectors, photovoltaics, and thermoelectrics—for instance, the solar organic Rankine cycle. Biomass is used by two utilization: thermochemical and biochemical. Gasification and pyrolysis are the solutions for using biomass’s thermochemical cycle in polygeneration systems. Biodiesel and biogases are the products of the biochemical process as the energy sources of energy generation systems. Geothermal renewable energy sources can be implemented by geothermal wells and boreholes (heat exchangers) in a hybrid polygeneration system. However, each energy source can be integrated with another to complete a production process or generate a second production, such as heating, cooling, and power in a hybrid polygeneration system presented in this book’s following chapters.

    Figure 1.3 Most used renewable energy sources for polygeneration energy systems.

    The utilization of renewable resources presents a significant challenge due to their intermittent nature, particularly in power delivery systems such as the electrical grid. This issue is especially evident in solar energy, which is not accessible during nighttime hours. Consequently, implementing an energy storage system is imperative for preserving surplus energy and utilizing it during periods of unavailability. Energy storage is a highly viable solution, as it enables energy production units to store their excess output and retrieve it when necessary, thereby ensuring a consistent and stable energy supply [9].

    Fig. 1.4 shows the critical energy storage used in hybrid polygeneration energy systems. Energy storage can be categorized into various types such as biological, thermal, chemical, mechanical, electrochemical, and electrical. Among these categories, some of the most well-known energy storage methods include phase change materials of thermal and methanol dimethyl ether ammonia from the chemical category. However, there are also more conventional energy storage methods such as flywheel, hydraulic accumulator, compressed air, solid mass gravitational, and pumped hydro from mechanical and supercapacitors from electrical. These energy storage methods play a critical role in ensuring that energy is efficiently stored and utilized in hybrid polygeneration energy systems.

    Figure 1.4 Most used energy storage used for polygeneration energy systems.

    The system depicted in Fig. 1.5 is designed to incorporate the sweet process of flue gases, utilizing two distinct mechanical energy storage mechanisms, namely turbines and compressors, in conjunction with amine. The heating generated by the system is harnessed to prepare the amine for its removal duties. Chapter 3 of this book delves into the subject of energy storage methods and offers an in-depth explanation of their applications in hybrid polygeneration energy systems.

    Figure 1.5 Application of mechanical energy storage methods for preparing amine for the separation process [10].

    1.3 Objectives and necessity of using hybrid polygeneration systems

    The hybrid polygeneration objectives can be categorized into the following item: (1) maximizing the application of sustainable energy systems; (2) utilizing a variety of energy inputs to operate fuel cells applications; (3) optimizing the polygeneration system; and (4) utilizing various polygeneration system applications in residences, business, and industrial usages [11].

    To achieve the primarily mentioned objectives, the following criteria are typically used to decentralize the hybrid polygeneration systems: (1) heat engines (rotary internal combustion, micro gas expanders, fuel cells); (2) low-turn equipment (absorption or electric chillers); (3) supplementary equipment (heating systems, fuel burner absorption cooling systems or heat pumps, engine-based chiller); (4) potential source of renewable energy (solar, organic matter, wind, hydroelectric); and (5) ethanol, hydrogen, etc. As a result, numerous possible designs for polygeneration systems can be found. Given the wide range of hybrid topologies that can be used, such as hydrogen, renewable energy, gas cycles, etc., the designs, including fuel cells, are especially interesting among these options [3,12].

    Therefore the main objectives of hybrid polygeneration systems are power production, providing heating or auxiliary heating demands, cooling and refrigeration systems, preparing energy storage devices, and generating energy resources. Moreover, natural or wasting energy resources, heat exchangers, separators, boilers, burners, compressors, expanders, and pressure valves are the most common and necessary equipment for conventional hybrid polygeneration systems.

    Fig. 1.6 shows the diagram of a polygeneration process. The combustible, air, and GT parameters of this system’s Brayton power-generating cycle are in a power plant. This hybrid polygeneration system provides a solvent process for carbon dioxide sequestration from exhaust gases, a natural gas-based generating process, a SECLR for hydrogen production, an high-pressure steam generator, and an absorption cooler for temperature reduction of requirement. Concurrent hydrogen liquefaction and carbon dioxide capture are advantages of using SECLR rather than traditional SMR. Furthermore, this unit’s CLC eliminates the need for an outside heat source during the hydrogen production process. The system is sustainable and dramatically reduces CO2 emissions thanks to MEA-based CO2 sequestration for the combustion gases.

    Figure 1.6 Conceptual diagram of a hybrid polygeneration system [12].

    One of the most used energy carriers and the fuel of the future is hydrogen. Hydrogen production was considered the objective of several systems such as energy, cryogenic, chemical, poly, and hybrid polygeneration systems [13–25]. Instead of being an energy source, hydrogen is an energy carrier. By combining different technologies, including electrolysis, steam methane reformation, or gasification in combination with either direct combustion of fossil fuels or power produced from renewable, fossil, or nuclear energy sources, hydrogen may be created from an energy source. Climate effects from different hydrogen-generating processes vary. There are several classification schemes to identify hydrogens produced from various fuels and electric suppliers. The color categorization of hydrogen is based on the original energy source and manufacturing method, as shown in Fig. 1.7 [26].

    Figure 1.7 Hydrogen production categorization by color classification [26].

    Fig. 1.8 presents the hydrogen production methods that are categorized into biomass, water splitting, reforming, and chemical looping methods. This book discusses various methods for producing hydrogen, including biomass, water splitting, reforming, and chemical looping. To achieve a diverse range of options for hydrogen production, it is crucial to integrate these methods into a hybrid-polygeneration cycle. Throughout the book, the production of hydrogen as a key objective is thoroughly explored in several chapters.

    Figure 1.8 Hydrogen production methods applicable in hybrid polygeneration systems.

    It is crucial to utilize renewable energy sources to establish a sustainable energy system. However, reducing carbon emissions is still necessary to address environmental and climate change concerns. Carbon capture and storage remain practical approaches to sequester carbon, but they require significant energy consumption for heating and power. To enhance this system's energy efficiency, it can be integrated into a hybrid-polygeneration energy system. Fig. 1.9 showcases CO2 capture, separation, and liquefaction techniques, including postcombustion, oxy-fuel combustion, electroreduction, and reverse water gas shift reaction. Meanwhile, in Fig. 1.9, the CO2 sequestration and liquefaction methods are discussed in this book's chapters.

    Figure 1.9 CO2 capturing, separation, and liquefaction methods.

    In Fig. 1.10, a hybrid polygeneration energy system is presented to use a part of a natural gas flow for power generation by an oxy-fuel power plant. The produced power and flue gases are forwarded to the refrigeration system (mixed and propane refrigeration). LNG production and CO2 capturing and liquefaction as subsystem is integrated into an oxyfuel power plant. In other words, this hybrid polygeneration system receives natural gas at 35°C and 40 bar, oxygen and delivers LNG at -164°C and 1 bar, liquid CO2 at -1°C and 35 bar, and water. The required power of this liquefaction system is more than 122 MW, which is supplied through a mass flow of the receiving gas.

    Figure 1.10 Oxyfuel power plant integrated with LNG liquefaction, CO2 capture, and liquefaction [27].

    The main subject of this publication is the study of Hybrid Polygeneration Energy Systems: Thermal Design and Exergy Analysis. This book delves into the latest developments and concepts in hybrid energy systems, with a specific emphasis on thermal applications. The authors begin by offering an overview of hybrid polygeneration and storage possibilities before exploring six distinct types of hybrid systems: solar, fuel cells, combustion, heating, and cooling. Furthermore, the publication examines the economic and environmental impacts of each system and provides techniques and approaches for analyzing energy and efficiency.

    References

    1. W.D. Sawyer, A History of Industrial Power in the United States, 1780–1930. Vol. 2: Steam Power. 1988, JSTOR.

    2. Babcock and W. Company. Steam: Its Generation and Use with Catalogue of the Manufactures of the Babcock and Wilcox Company. Vol. 36 The Company 1923;.

    3. Murugan S, Horák B. Tri and polygeneration systems-a review. Renewable and Sustainable Energy Reviews. 2016;60:1032–1051.

    4. Sheykhi M, et al. Investigation of the effects of operating parameters of an internal combustion engine on the performance and fuel consumption of a CCHP system. Energy. 2020;211:119041.

    5. Yan J. Handbook of Clean Energy Systems, 6 Volume Set. Vol. 5 John Wiley & Sons 2015;.

    6. I. Dincer, Y. Bicer, Integration of renewable energy systems for multigeneration. Integrated Energy Systems for Multigeneration, 2020: pp. 287–402.

    7. Roman KK, Hasan M, Azam H. CCHP System Performance Based on Economic Analysis, Energy Conservation, and Emission Analysis. Energy Systems and Environment London, UK: IntechOpen; 2018;.

    8. Segurado R, et al. Techno-economic analysis of a trigeneration system based on biomass gasification. Renewable and Sustainable Energy Reviews. 2019;103:501–514.

    9. Alsagri AS, Chiasson A, Gadalla M. Viability assessment of a concentrated solar power tower with a supercritical CO2 Brayton cycle power plant. Journal of Solar Energy Engineering. 2019;141.

    10. Mehrpooya M, Pakzad P. Introducing a hybrid mechanical – Chemical energy storage system: Process development and energy/exergy analysis. Energy Conversion and Management. 2022;211:112784 https://doi.org/10.1016/j.enconman.2020.112784.

    11. Calise F. Design of a hybrid polygeneration system with solar collectors and a solid oxide fuel cell: dynamic simulation and economic assessment. International Journal of Hydrogen Energy. 2011;36(10):6128–6150.

    12. Habibi R, et al. A natural gas-based eco-friendly polygeneration system including gas turbine, sorption-enhanced steam methane reforming, absorption chiller and flue gas CO2 capture unit. Sustainable Energy Technologies and Assessments. 2022;52:101984.

    13. H. Quack, The key role of the cryotechnology in the hydrogen energy industry. Die Schluesselrolle der Kryotechnik in der Wasserstoff-Energiewirtschaft. Wissenschaftliche Zeitschrift der Technischen Universität Dresden, 2001. 50.

    14. Quack H. Conceptual design of a high efficiency large capacity hydrogen liquefier. AIP Conference Proceedings American Institute of Physics 2002;.

    15. Steinfeld A. Solar thermochemical production of hydrogen—a review. Solar energy. 2005;78(5):603–615.

    16. J. Stang, P. Neksa, E. Brendeng, On the Design of an Efficient Hydrogen Liquefaction Process. 2006.

    17. Z’Graggen A, et al. Hydrogen production by steam-gasification of petroleum coke using concentrated solar power—II Reactor design, testing, and modeling. International Journal of Hydrogen Energy. 2006;31(6):797–811.

    18. Z’Graggen A, Steinfeld A. Hydrogen production by steam-gasification of carbonaceous materials using concentrated solar energy–V Reactor modeling, optimization, and scale-up. International Journal of Hydrogen Energy. 2008;33(20):5484–5492.

    19. Walnum, H.T., et al., Principles for the liquefaction of hydrogen with emphasis on precooling processes, in: 12th Cryogenics, 2012: pp. 8.

    20. Khalid F, Dincer I, Rosen MA. Analysis and assessment of an integrated hydrogen energy system. International Journal of Hydrogen Energy. 2016;41(19):7960–7967.

    21. Cai D, et al. Integration of wind turbine with heliostat based CSP/CPVT system for hydrogen production and polygeneration: a thermodynamic comparison. International Journal of Hydrogen Energy. 2020;47.

    22. Luqman M, Bicer Y, Al-Ansari T. Thermodynamic analysis of an oxy-hydrogen combustor supported solar and wind energy-based sustainable polygeneration system for remote locations. International Journal of Hydrogen Energy. 2020;45(5):3470–3483.

    23. Zhuang R, et al. Waste-to-hydrogen: Recycling HCl to produce H2 and Cl2. Applied Energy. 2020;259:114184.

    24. Mehrpooya M, Ghorbani B, Khalili M. A new developed integrated process configuration for production of hydrogen chloride using geothermal and wind energy resources. Sustainable Energy Technologies and Assessments. 2021;45:101173.

    25. Mehrpooya M, et al. Conceptual design and performance evaluation of a novel cryogenic integrated process for extraction of neon and production of liquid hydrogen. Process Safety and Environmental Protection. 2022;164:228–246.

    26. Tanya Stasio, J.C. The Colors of Hydrogen. 2021; Available from: https://aeclinic.org/aec-blog/2021/6/24/the-colors-of-hydrogen.

    27. Mehrpooya TM, Ghorbani B. Introducing a hybrid oxy-fuel power generation and natural gas/carbon dioxide liquefaction process with thermodynamic and economic analysis. Journal of Cleaner Production. 2018;204:1016–1033 https://www.sciencedirect.com/science/article/pii/S0959652618327197#fig1.

    2

    How to use renewable energy sources in polygeneration systems?

    Abstract

    Research on renewable energy has recently focused on identifying practical solutions to reduce global warming, greenhouse gases, carbon emissions, climate change, fossil fuel usage, environmental pollution, and ozone depletion. Renewable energy is widely recognized as the optimal alternative for addressing these issues and creating a more sustainable environment. Solar, wind, geothermal, hydro, and wave energy are unlimited sources that can meet the energy demands of polygeneration systems. However, hybrid polygeneration systems require equipment preparation for renewable energy usage or the generation of alternative sources such as blue or green hydrogen production. This chapter presents the theories behind renewable resources and their energy transformation, followed by their application in polygeneration and hybrid polygeneration systems.

    Keywords

    Renewable energy sources; polygeneration systems; solar energy; solar collector; photovoltaic; thermophotovoltaic; biomass; wave energy; hydro; wind energy; geothermal

    2.1 Introduction

    Renewable energy sources lead to clean, green energy generation and possibly sustainable and polygeneration systems (PGSs). These sources can be divided into renewable fuels such as biomass and hydrogen, solar power and heating, and wind and wave energy. These energy sources are usually available at a low cost. The cost is only for exploiting these resources. Therefore using these resources in the context of energy crises and environmental problems related to fossil fuels is precious. These energy sources are used in different ways discussed in the following section.

    As we observed in the previous chapter, renewable energy sources play as both prime mover and conversion energy devices in a typical polygeneration system. A renewable energy source can be converted to electrical power or mechanical output. Heating directly by a solar collector and cooling indirectly, for instance, in an absorption refrigeration system, are achievable in PGSs. In the following section, these applications are theoretically introduced for each renewable energy source.

    2.2 Proposed process frameworks for solar polygeneration systems

    Today, using solar energy as a primary source of power generation is unavoidable. The use of solar energy technology has many positive effects on the environment, such as reducing greenhouse gases and toxic emissions, reducing the requirements for transmission lines in the electricity network, rehabilitating barren lands, and improving the quality of water resources. Socio-economic benefits of solar technologies include increased national and regional energy independence, increased job opportunities, increased acceleration of rural electricity supply in remote areas, diversity, and security of energy supply. In general, since solar energy is an inexhaustible, safe, and clean energy source, it has attracted much attention as an alternative to conventional energy sources.

    Solar energy is used in two ways: photovoltaic and solar thermal technology. In the first method, sunlight is converted directly into electricity, which is done by photovoltaics. In the second method, first, the heat of the sun is absorbed by the fluid inside the collector, then this heat is converted to power or its heat is used to provide the heat load of another system. This type of solar application is called a solar power plant.

    2.2.1 Photovoltaic

    In photovoltaic cells, there is an electric field with the positive side behind the cell and the negative side with the cell facing the radiation. As a result of the collision of photons scattered on the cell surface, electrons are separated from atoms in semiconductor materials, creating an electron-cavity pair. An electrical circuit is formed if the electrical conductors are connected positively and negatively. The electric current from electrons is called photocurrent (Iph). As can be seen from this description, a photovoltaic cell cannot function in the dark; thus it acts as a diode. In other words, the p-n bond in the dark produces no current or voltage. If the connector is connected to a large external voltage source, it passes through what is called a diode current or dark current (ID). As such, a photovoltaic cell is typically electrically modeled with a diode. Fig. 2.1 shows the equivalent electrical circuit of a photovoltaic cell.

    Figure 2.1 Equivalent electrical circuit of a cell.

    The circuit in Fig. 2.1 is used for a single cell, a module consisting of several cells, and an array consisting of several modules. Fig. 2.1 shows that the equivalent electrical circuit consists of a current source (Iph), a diode, and a series resistor (Rs), indicating intracellular resistance. The diode also has an internal resistor indicated by the circuit’s parallel resistance (RSH). The net current equals the difference between the photocurrent and diode current. So in Eq. (2.1), we have [1,2]:

    Equation

    (2.1)

    2.2.1.1 Γ: diode ideal factor

    It should be noted that the parallel resistor is usually much larger than the load resistor, while the series resistor is much smaller than the load resistor, thus wasting a tiny amount of power generated inside the cell. Given these two resistances, the net current is equal to the difference between the photocurrent and the cell current obtained from Eq. (2.2) [1,2].

    Equation (2.2)

    where k is the Boltzmann constant (1.381×10−23j/k), TC is the Cell temperature (k), q0 is the electron charge (1.602×10−19j/v), V is the voltage applied to the two ends of the cell (v), I0 is the Dark saturation current, which strongly depends on temperature (A)

    If the two ends of the junction cell are shortened, the current [short circuit current (Isc)] is maximized, and the voltage is zero. If the two ends of the photovoltaic cell circuit are open, the voltage of the two circuits [open-circuit voltage (Voc)] is maximized, and the current is zero. In both cases (open circuit and short circuit), the power is zero but between these two states has a nonzero value. As a result, the maximum power density (Pel) can be obtained from the Eq. (2.3) [3]:

    Equation (2.3)

    where Voc is the ppen circuit voltage, FF is the density coefficient, jsc is the short circuit current density.

    2.2.1.2 Thermophotovoltaic

    The thermophotovoltaic system increases combustion chamber heat recovery, power generation, and overall efficiency in the following process. It is worth noting that power generation in a thermovoltage system requires emitting radiation. For this purpose, we assume the combustion chamber’s temperature and the emitter surface’s temperature [4], assuming that the heat transfer between the combustion chamber and the emitter surface is 100% efficient. The assumption is valid and reasonable. As mentioned earlier, a thermophotovoltaic system for heat recovery consists of four main parts:

    1. Emitter

    2. Optical filter

    3. Cells

    4. Cooling system

    In the meantime, another essential component is not part of the system but affects the system’s performance. The conceptual model structure of a thermophotovoltaic system is shown in Fig. 2.2.

    Figure 2.2 Conceptual model of the thermophotovoltaic system [5].

    Fig. 2.2 shows that current (1) represents the radiation power emitted from the transmitter to the optical filter system. The current (2) reflects the reflected radiation from the filter to the transmitter because, in the general case, the collision of electromagnetic waves with any surface may occur in three states: pass, reflection, and absorption. Each of these three situations is likely to depend on the type of filter. Therefore current (2) represents the general relationship between the emitter and the optical filter. Also, in general, the viewing angle should be taken into account. The current (3) represents the radiation power that passes through the filter; since it contains two convertible and nonconvertible parts by the cells, part of it is converted into electrical current, and the remainder is divided into two parts: reflection and absorption. The reflection part is determined by the current (4), and the absorbed and nonconvertible part causes the cells to warm. If the optical filter performs poorly due to limitations in fabrication or cost, the cell temperature rises in such a way as to affect the overall performance of the system, forcing the use of cooling. The cooling system may consist of a combination of blades and fans for proper operation. Flow (7) reflects the effect of the cooling system on cell function. The current (6) reflects the power required to operate the cooling system. The task of the cooling system is to transfer heat from the cells to the environment, the power generated by the system is transferred to the load, but the type and amount of consumption in this part, depending on the current required, partially affects the cell’s performance. Therefore the current shows a dominant relationship between this part and the cells (5). Since both the coolant and the filter are responsible for preventing the cell temperature from rising, their performance is affected by the relationship reflected by the current (8).

    Given the flow and relationships governing the entire system, two essential factors determine the system’s overall performance. These two factors are:

    1. Emitter temperature

    2. Cell temperature

    Other factors affect system performance, such as cell type (by energy bandwidth), filter type (by irreversible radiation reflectance), and emitter type, including wavelength selector and constant wavelength selector. They are important and somehow subject to temperature (especially emitter temperature), so the influence of temperature will be of greater importance, which is considered in the computational model.

    The short-circuit current density is obtained from Eq. (2.4) [4]:

    Equation (2.4)

    where Equation denotes the wavelength emission factor λ, Equation denotes the Planck spectral relation emission power distribution, Equation denotes the spectral response proportional to the type of thermophotovoltaic cell, Equation denotes the coefficient of the passage of the optical filter at wavelengths λ, λ denotes the wavelength, Equation denotes the low wavelength limit, Equation denoted the cell cutoff wavelength, and Equation denotes the visibility coefficient between cell and emitter.

    For the emitters used in thermophotovoltaic systems, silicon carbide emitters with a Gaussian coefficient of about 0.9 is typically considered. This emitter type is most commonly used in thermophotovoltaic systems that use the combustion chamber as a heating source.

    The German physicist Max Planck proposed the spectral dependence of the power emitted by the unit of surface emission at different temperatures for a black body in the form of Eq. (2.5) [2].

    Equation (2.5)

    Using Eq. (2.6), one can obtain the wavelength intensity for the black object. The temperature dependence of the wavelength distribution of radiation intensity is shown in Fig. 2.2 [2].

    As shown in Fig. 2.3, as the emitter temperature increases, the wavelength with the highest radiation reaches the smallest wavelength. It should be noted that only a few objects behave like the ideal black body. Many objects at the same temperature as the black body have less radiation. The emission rate (ε) is the amount that determines the relationship between actual radiation and black body radiation.

    Figure 2.3 Distribution of radiation intensity in terms of wavelength at different temperatures [6].

    The spectral response determines the amount of radiation that the cell converts to electric current and is obtained from Eq. (2.6) [3].

    Equation (2.6)

    Equation is the external quantum efficiency, q0 is the charge of an electron [q0=1.602×10−19 (C)], h is the Planck’s constant [h=6.626×10−34 (j.s)], c is the speed of light Equation .

    The spectral response depends on the cell type. The quantity that reflects cell-type dependence in Fig. 2.4 is the external quantum efficiency ( Equation ).

    Figure 2.4 External quantum efficiency of thermophotovoltaic cells [3].

    To estimate the conversion efficiency of a cell, one of the basic parameters is the external quantum efficiency, which is the probability that a photon with λ wavelength is absorbed by the cell and produces an electron that is absorbed by the output port (positive terminal). This quantum efficiency considers the probability of reflection and absorption of the incoming photons and the probability of producing and collecting minority carriers. Thus the external quantum efficiency describes the behavior of the p-n bond very precisely. External quantum yields for different semiconductors selected as thermophotovoltaic have been calculated and their behavior is shown in Fig. 2.4 [7].

    Fig. 2.5 shows that most materials used to make thermophotovoltaic cells have high external quantum efficiency over a wide range of wavelengths near their energy band to smaller wavelengths. The amount of external quantum efficiency for photons with wavelengths drops sharply to about 1000 (nm), but it should be noted that this region has wavelengths in standard thermophotovoltaic systems, and the system also has an optical filter with negligible emission. For this reason, thermophotovoltaic cells can convert a considerable portion of the radiation of a black body to electricity [7]. In all the papers reviewed, the external quantum efficiency for all the transverse wavelengths to a fixed cell and an average value assumed to correspond to the cell’s energy bandgap is presented in Table 2.1 [3].

    Figure 2.5 External quantum efficiency of GaSb cells [3].

    Table 2.1

    Since external quantum efficiency has a direct impact on the cell’s electrical output density, it has a significant influence on the cell’s output power density. As shown in Fig. 2.5, as the wavelength of the input spectrum to the cell increases, its external quantum efficiency decreases rapidly. Therefore it is suggested that the external quantum efficiency be entered into the model as a function of the wavelength of the input spectrum. The quantum efficiency for thermophotovoltaic cells has been measured experimentally, so the relation obtained is also experimental. According to Fig. 2.5, one can fit a function to any of the curves in Fig. 2.4 to obtain the quantum efficiency relation in terms of the wavelength of the input-cell spectrum. In this study, two GaSb and InGaAsSb cells were examined. Because these cells have the highest output and utilization, GaSb’s external quantum efficiency graph, Fig. 2.5, and InGaAsSb cell, Fig. 2.6 have been used to fit the quantum efficiency function in terms of wavelength [8].

    Figure 2.6 InGaAsSb external quantum efficiency [8].

    As shown in Fig. 2.5, the GaSb quantum efficiency diagram has two local maximums relative to the wavelength of the input spectrum. The first peak in this graph corresponds to a wavelength of 0.5μm, which is the threshold of the visible blue spectrum, and the second peak is to the wavelength of 1.5μm, that is, the beginning of the infrared region (near the visible spectrum). Therefore if the wavelength of the emitted spectrum decreases either too much (below the blue spectrum) or too much (beyond the infrared spectrum), the quantum efficiency rapidly tends to zero, in other words, disrupting the system’s performance. The reason for the decrease in quantum efficiency at shorter wavelengths than the blue spectrum is that they are likely to pass through the semiconductor potential barrier.

    So the best way to solve this problem is to convert Fig. 2.5 into two curves so that each local maximum is in one curve. So we have two curves, each with an absolute maximum, and as a result, the external quantum efficiency function becomes a binomial function. The sum of the least squares is given in Table 2.2.

    Table 2.2

    Thus the quantum yield relationship of the GaSb cell is given by Eq. (2.7).

    Equation

    (2.7)

    Since λmax is the wavelength with the highest radiation at the corresponding temperature and λ0 is the smallest wavelength at which the temperature exists Equation , it is recommended to put the mean value in the EQE(λ) relation. In other words in Eq. (2.8):

    Equation (2.8)

    According to the Vienna Displacement Law [9]:

    Equation (2.9)

    The model’s operating temperature range is based on quantum yields in the range of 852°C–4727°C:

    EquationEquation

    Thermophotovoltaic systems use optical filters to reflect part of the radiation into the emitter with wavelengths larger than the cell’s energy bandgap. Therefore the filter results in two effects:

    1. Prevent excessive warming of the cell

    2. Reduce emitter cooling rate

    The filter operation mechanism is schematically illustrated in Fig. 2.7 [10].

    Figure 2.7 Concept of optical filter [10,11].

    Fig. 2.7 shows that the optical filter reflects the irreversible part of the radiation (less energy than the cell’s energy band gap). This specificity is not possible for normal solar cells, which causes thermophotovoltaic cells to reach potential. They achieve a high conversion rate of the incoming photon to the electric current because the incoming radiation corresponds to the area where the external quantum efficiency is maximal; how the spectrum of radiation corresponds to the external quantum efficiency for GaSb and InGaAsSb cells is shown in Fig. 2.8 [11].

    Figure 2.8 How the radiation spectrum of the emitter is distributed at different temperatures [11].

    As shown in Fig. 2.8, the maximum external quantum efficiency for the GaSb cell occurs at 1500K for the emitter and decreases with the emitter temperature decreasing very rapidly and tilting to zero. By lowering the energy band gap of a thermophotovoltaic cell, such as InGaAsSb, at lower temperatures, the emitter can be expected to have higher external quantum efficiency [11]. The optical filter system is not limited to one object or one type, but there are several mechanisms for filtering the spectrum inappropriately:

    1. Interference filters

    2. Plasma filters

    3. Combination of interference and plasma filters

    4. Resonant array filters

    5. Spectral control using the back surface reflector (BSR)

    In an isotropic, homogeneous, linear, and stable environment, without an electric charge, the electric field follows the wave Eq. (2.10).

    Equation (2.10)

    The results of the solution of Eq. (3.32) are flat wave harmonics, which are shown in Eq. (2.11).

    Equation (2.11)

    where Equation is the wave vector that specifies the direction of wave propagation.

    One feature of the flat wave is that interacting can increase or decrease the electromagnetic fields. This process is called interference. An optical filter can produce interference with high throughput for a particular spectral region and high reflectivity outside the region. Interference can be achieved by controlling the path of the flat waves, the wave vector ( Equation ) or the ambient refractive index Equation . An interference filter consists of several thin layers with different refractive indexes. The thickness of the layers is an adjustable parameter for reaching the desired path length. Interfering filters are generally composed of dielectric materials whose refractive indexes are true and constant, so their absorption rate can be neglected [2].

    2.3 Solar power plant

    The technologies for converting solar energy to thermal energy are thought to have great potential and the majority of the applications refer to medium to high temperatures. In other words, solar collectors are a particular type of heat exchanger that converts solar radiant energy into thermal energy. By absorbing the incoming solar radiation and converting it to heat, this device transfers heat to the operating fluid through the collectors. Solar collectors are classified into two types depending on whether they are stationary or mobile.

    2.3.1 Stationary collectors

    The primary differences among solar energy collectors are their motion—stationary, single-axis tracking, and two-axis tracking—as well as their working temperature. These types of collectors do not follow the sun since they are set in place all the time. This category includes three different kinds of collectors [12]:

    1. Flat-plate collector (FPC).

    2. Stationary compound parabolic collector (CPC).

    3. Evacuated tube collector (ETC).

    2.3.2 Concentrating collectors

    Concentrating collectors are typically known as parabolic trough solar collectors (PTC) concentrating solar power plants. This is primarily because PTC is a proven technology with a competitive price (about US$ 200 per square meter) and a respectable thermal performance [13].

    In a typical PTC, the mirrors focus the inbound solar radiation onto the collector, which typically has a tiny contact area. The receiver comprises an absorber tube that distributes the absorbed heat to the working fluid and a concentric transparent cover, which is often made of glass. Stainless steel is commonly used for the absorber tube that is covered with a coating to improve thermal and optical efficiency (higher absorptivity and lower emissivity). The concentric translucent cover reduces heat leaks to the surrounding air, guards against absorber deterioration, and preserves the pressure differential between the cover and absorber tube. The vacuum cage is primarily utilized to reduce the losses in heat transfer by convection and to protect the selected surface from oxidation brought on by the absorber’s high-temperature operation. In order to maintain the vacuum pressure at the specified design ranges and prevent heat transfer between the tube and cover, sealing and metal bellows are placed at either end of the receiver. To increase the thermal efficiency of the PTC module and provide the necessary safety standards, chemical getters are applied in the vacuum zone to absorb the hydrogen that is produced by the heat transfer fluid (HTF). Fig. 2.9 shows the most common collector that is used for solar PGSs.

    Figure 2.9 Types of solar collectors (A) flat plate collector, (A-a) illustration of a flat plate collector, (A-b) photo of cutting the upper part and riser of flat plate collector; (B) vacuum tube collector; (C) Linear parabolic collector; (D) Fresnel collector, (D-a) Fresnel lens collector, (D-b) Fresnel type linear parabolic collector; (E) parabolic dish collector; (F) Heliostat collector [12, 14].

    In collectors with a concentration ratio greater than one, reflective surfaces are used to increase radiation over a small area. Concentrating the sun’s rays on a small surface is done in order to achieve high temperatures. Use flat concentrators to increase the number of direct beams emitted to the collector surface. Table 2.3 shows the characteristics of each collector, and Fig. 2.9 shows the types of static and concentrating collectors [12].

    Table 2.3

    2.3.2.1 Governing equations of geometry

    It is considering that the concentration coefficient of the flat mirror is one and is obtained to calculate the concentration coefficient composed of the multiplication of this variable, and considering the assumption that the flat mirror is larger than the parabolic dish collector. The pattern of solar radiation affects how much energy from the sun is absorbed in the reception cavity in parabolic solar collectors. It is difficult to quickly acquire the radiation pattern on the inside surface of the receiving using the empirical system for a cavity with inversion symmetry and a parabolic collector. A mechanism like this ensures that the dish’s surface is perfectly parabolic (with no contour defects) and that the sun’s core beam strikes it parallel to the concentration axis. The realistic parabolic system is referred to as a real system even though it only approximates a genuine system since these two requirements cannot be satisfied in practice.

    A half-length cross-section of an ideal parabolic collector (Fig. 2.10A) and its actual counterpart (Fig. 2.10B), as well as its design, are shown in Fig. 2.10. D and f, respectively, are the collector diameter and focal lengths. The collector is described by an x, y, and z Cartesian coordinate system. The reference is at the top of the container, and the optical axis’ z-axis is also positioned there. On the surface of the real collector, at point P, with radius R, are the coordinates x, y, and z given in Eq. (2.12). These coordinates follow the equation of conic cut, which is:

    Equation (2.12)

    Figure 2.10 Half-length collector: (A) Ideal parabolic collector. (B) Real collector [15].

    The following analysis assumes relatively modest deviations from the ideal x and y coordinates of the locations on the collector surface in front of the z component. Furthermore, it is presumable that the divergence from the z component is more considerable the further they are from the focal axis. As a result, the true collector’s surface point P’ has the coordinates x, y, and z. The circumference of two circles with the same radius passes through these two places (Fig. 2.10). The ideal collector is represented by the first, and the level of the real collector by the second. If the maximum deviation on the component z is denoted by Δzmax then Δz for the point P’ is obtained as follows:

    Equation (2.13)

    Given that in Eq. (2.13), R is obtained as follows:

    Equation (2.14)

    From Eq. (2.3), it follows that for the component z the point P’ is calculated as follows:

    Equation (2.15)

    Substituting the equation z from Eq. (2.1) into Eq. (2.3), the real collector equation is obtained as follows:

    Equation (2.16)

    It should be noted that Eq. (2.17) is used to calculate the collector diameter as follows:

    Equation (2.17)

    To investigate the radiation distribution within the receiving walls, we first examine Fig. 2.11, which shows the design of a real parabolic dish collector with diameter D and focal length f. The collector’s head is the source of the Cartesian coordinates system x, y, z where the z-axis is the same as the optical axis, b. A plate ξ is in a random position in the space above the collector; it can be, for example, in the line of one of the internal surfaces of the receiver. The typical unit vector nξ specifies its orientation relative to the Cartesian coordinate system. Point C is located on plane ξ. Its coordinates, which are removed from the figure for clarity, are xc, yc, and zc. When viewed from the ground to a parabolic dish, the solar disk is inside a radiant cone with an angle of 32 degrees. A radiant cone of this type has its central beam at an angle of 8 degrees (solar tracking error) to the optical axis of the collector, as shown in Fig. 2.11. The solar radiation is also reflected at point P on the collector, whose coordinates are xp, yp, and zp (again removed from the figure), and produces an elliptical image of the solar reflection on the ξ plane.

    Figure 2.11 Parabolic dish collector [16].

    A section perpendicular to the central beam through point C of the reflected beam cone has a circular cross-section with center M, radius Rc, and surface Ac. To continue the solution, it is appropriate to define the orientation of this cross-section by a unit vector nPM that goes from point P to point M and is perpendicular to the plane Ac. The line Equation is between the points P and M shown in Fig. 2.11. Moreover, it is obtained as follows:

    Equation (2.18)

    where ζ is the angle between the center beam and the line Equation . Since the C points are considered to be within the elliptical region, the following criterion for the angle ζ is considered:

    Equation

    The radius Rc of this circular section is obtained as follows:

    Equation (2.19)

    According to Eqs. (2.18) and (2.19), it results that for the area Ac, this part is calculated as follows:

    Equation (2.20)

    A small differential area of the dACol collector is assumed to exist on the xy surface and receives radiant energy as intense as s:

    Equation (2.21)

    where s only involves direct contact of sunlight reaching the earth’s surface. That part of the energy that is emitted by the suspended particles as they pass through the atmosphere cannot be used and reduces the total radiation [17]. If the collector reflection coefficient for short-wavelength solar radiation is indicated by ρCol, Eq. (2.22) shows the amount of radiant energy considering the reflection coefficient:

    Equation (2.22)

    while we know that the sun is slightly brighter in its center than its surroundings [17], this effect is small and is not considered here. Therefore the intensity of distribution in the solar plane is homogeneous. The surface Ac, which is oriented perpendicular to the central ray of the reflected cone, is irradiated evenly by the point P of the collector with the following energy flux:

    Equation (2.23)

    The plane ξ and the area Ac are generally not parallel to each other. For example, their normal unit vectors nPM and nξ collide with an angle γ (Fig. 2.11). The intensity of radiation reflected at point P on the collector and radiation at point C perpendicular to the plate ξ is obtained from the following equation:

    Equation (2.24)

    According to Eqs. (2.20) and (2.23), it follows that:

    Equation (2.25)

    From the size Equation we get from Fig. 2.11 according to Eq. (2.26):

    Equation (2.26)

    where (xC, yC, zC) and (xP, yP, zP) are the coordinates of points P and C.

    To determine the angles γ and ζ in Eq. (2.24), the normal vectors nPM and nPC must first be obtained. The normal vector nPC in the direction of the line Equation in the form of Eq. (2.26):

    Equation (2.27)

    To obtain the normal vector nPM, following the radiation cones and the

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