DEVELOPING A SOLARBIO HYBRID ENERGY GENERATION SYSTEM FOR SELF-SUSTAINABLE WASTEWATER TREATMENT  By  Mauricio Jose Bustamante                   A DISSERTATION  Submitted to Michigan State University in partial fulfillment of the requirements for the degree of  Biosystems Engineering - Doctor of Philosophy  2016 ABSTRACT  DEVELOPING A SOLARBIO HYBRID ENERGY GENERATION SYSTEM FOR SELF-SUSTAINABLE WASTEWATER TREATMENT  By  Mauricio Jose Bustamante  This study delivers a comprehensive analysis of the integration of renewable energy sources for a self-sustaining organic wastewater treatment operation. The increase in human population and the continuous expansion of residential and industrial activities in the last decades has elevated the generation of wastewater that can irreversibly damage the environment. The current technologies to treat wastewater require significant amounts of energy to operate, and most of them use non-renewable energy sources (fossil-based fuels are the main energy sources), which implies that current treatment technologies are not completely sustainable. The goal of this study is to integrate solar energy into the process of wastewater treatment synergistically.  The first stage of this study evaluates the two options to generate electricity (Rankine and Brayton cycles for steam and gas turbines, respectively) using biogas as a sub-product of anaerobic digestion (the first stage in the proposed wastewater treatment) and incorporating solar energy to balance the thermal energy requirements. The results indicate that a steam turbine is the most convenient technology for the integration into a solarbio concept, although its thermal-to-electrical energy conversion efficiency is lower than that for gas turbines. The second stage studies the steam turbine energy generation system to provide electricity for the wastewater treatment plant (anaerobic and aerobic digestion), considering two options for solarbio hybridization: concentrated solar power (CSP) and photovoltaics (PV).   Results show that PV requires a smaller collection area and biomethane volumetric storage capacity to support the electricity needs. The third stage evaluates the geometrical and operational parameters for a CSP system using refractive Fresnel lenses, as an alternative to parabolic reflectors. The solar concentration ratio and absorber area were the parameters studied to calculate the change in the absorber temperature. The parameters were evaluated using a small bench-scale unit with an accurate solar tracking system using an astronomical algorithm. The results indicate that the absorber area affects the maximum temperature in the solar receiver to a greater degree than the concentration ratio. The last stage involves the design of two solar thermal receivers for a refractive Fresnel lens. The first design is a single path receiver with a conical absorber; the second is a cavity receiver with a spiral groove for multi-path flows. Both receivers were simulated using computational fluid dynamics, obtaining the fluid outlet temperature under different scenarios. The analysis showed that the cavity receiver exhibited higher efficiencies than the conical receiver, but its application is limited to low concentration ratios.  iv             To my father Manuel, my mother Marta, my sister Laura, and my nieces Gloriana and Mariana, for all the encouragement and support that I have received over the years to fulfill my goals. Thanks.  v  ACKNOWLEDGMENTS   I would like to express my gratitude to my advisor, Dr. Wei Liao, for his support and mentorship during my PhD study. I have gained plenty of professional experience thanks to his encouragement, guidance, and generous attitude to help his students pursue quality and excellence in their work; I feel truly privileged to have had the opportunity to work with Dr. Liao. I would also like to give thanks to Dr. Dana Kirk for his support on the elaboration of my research and participation in different projects at the Anaerobic Digestion Research and Educational Center (ADREC).  Thanks to my committee members: Drs. Abraham Engeda, Ilson Lee, and Yan Liu for their comments and advice in the development of this study. My gratitude to the faculty and administrative staff in the Department of Biosystems and Agricultural Engineering at Michigan State University and Universidad de Costa Rica, especially Dr. Ajit Srivastava and Mr. José Aguilar Pereira for their support and advice in pursuing the PhD program. To Eilyn Brenes, thanks for her support and company through this time. To my colleagues in the Bioenergy Research Group and my friends, especially Ronald Aguilar, Jocselyn Chacón,  Cristina Venegas, Beatriz Mazón, Melissa Rojas, Shikha Singh, Mauricio Losilla, Óscar Quesada, José Daniel Bustamante, , Silvia Guillén, Melissa Hernández, Tony Zhong, Ray Chen, and Yuan Zhong. I would also like to thank Universidad de Costa Rica for providing financial support to complete my study program.   vi  TABLE OF CONTENTS  LIST OF TABLES ......................................................................................................................... ix  LIST OF FIGURES ....................................................................................................................... xi  KEY TO ABBREVIATIONS ....................................................................................................... xv  CHAPTER I. INTRODUCTION ................................................................................................. 1 1. Literature review .................................................................................................................. 2 1.1. Wastewater treatment process ...................................................................................... 2 1.1.1. Fundamentals of anaerobic digestion .................................................................... 3 1.1.2. Fundamentals of selected secondary wastewater treatments ................................ 8 1.2. Solar technologies for heat and electricity generation .................................................. 9 1.3. Thermodynamics of heat and energy generation ........................................................ 14 1.3.1. Gas power systems - the air standard Brayton cycle ........................................... 14 1.3.2. Vapor power systems  the Rankine cycle.......................................................... 16 1.4. Solar hybrid power generation system ....................................................................... 17 1.4.1. Biogas utilization for electricity production........................................................ 19 2. Goal, scope, and objectives ................................................................................................ 20  CHAPTER II. SMALL-SCALE SOLARBIO HYBRID POWER GENERATION USING BRAYTON AND RANKINE CYCLES ...................................................................................... 23 Abstract ..................................................................................................................................... 23 1. Introduction ........................................................................................................................ 24 2. The studied small-scale solarbio hybrid power generation system ................................. 26 3. System analysis .................................................................................................................. 34 3.1. Relationship between solar energy, capacity factor, and ratio of solar energy to biomethane energy ................................................................................................................. 34 3.2. Energy requirements for biomethane production ....................................................... 36 3.2.1. Thermal energy requirements for biomethane production .................................. 36 3.2.2. Electricity requirements for biomethane production and upgrading ................... 39 3.3. Selection of solar thermal collectors for the hybrid systems ...................................... 40 4. Discussions ........................................................................................................................ 44 5. Conclusions ........................................................................................................................ 51  CHAPTER III. A SELF-SUSTAINING WASTEWATER TREATMENT PLANT INTEGRATING SOLAR TECHNOLOGIES, ANAEROBIC DIGESTION, AND AEROBIC TREATMENT ........................................................................................................................ 52 Abstract ..................................................................................................................................... 52 1. Introduction ........................................................................................................................ 53 2. The solarbio hybrid wastewater treatment ....................................................................... 55 2.1. Anaerobic digestion (AD) .......................................................................................... 55 2.2. Biogas upgrading ........................................................................................................ 56 2.3. Aerobic treatment (AET) ............................................................................................ 57 vii  2.4. Analytical method for AD and AET ........................................................................... 57 2.5. Solarbio hybridization of power generation ............................................................. 58 2.5.1. Solarthermalbio hybridization power generation ............................................ 58 2.5.2. Solarthermalbio hybridization power generation ............................................ 62 3. System analysis .................................................................................................................. 62 3.1. Mass balance of the wastewater treatment ................................................................. 62 3.2. Energy balance of the solarbio hybridization wastewater treatment ........................ 66 3.2.1. Electricity demands of the wastewater treatment ................................................ 66 3.2.2. Thermal energy requirements of the wastewater treatment ................................ 68 3.2.3. Energy generation ............................................................................................... 69 3.2.3.1. Electricity generation without short-term solar energy storage .................................. 72 3.2.3.2. Electricity generation with short-term solar energy storage ....................................... 77 4. Discussions ........................................................................................................................ 81 5. Conclusions ........................................................................................................................ 83  CHAPTER IV. DESIGN AND EVALUATION OF A TWO-MODULE FRESNEL LENS SOLAR THERMAL COLLECTOR FOR A SCALABLE CONCENTRATED SOLAR POWER GENERATION CONCEPT.......................................................................................................... 84 Abstract ..................................................................................................................................... 84 1. Introduction ........................................................................................................................ 85 2. Design of a bench-scale two-module Fresnel solar thermal collector ............................... 88 2.1. Two-module thermal collector structure .................................................................... 88 2.2. Thermal absorbers for temperature profile at focal area ............................................ 90 2.3. Instruments for solar tracking ..................................................................................... 92 3. Solar tracking model and control mechanism .................................................................... 93 4. FEM simulation of temperature profiles of the receiver .................................................... 95 5. Data Collection .................................................................................................................. 97 6. Statistical analysis .............................................................................................................. 97 7. Experimental results and discussion .................................................................................. 98 7.1. Solar tracking of the two-module collection unit ....................................................... 98 7.2. FEM simulation and verification of temperature profile of thermal absorbers ........ 100 8. Relationship between concentration area and surface temperature ................................. 104 9. Conclusions ...................................................................................................................... 106  CHAPTER V. DESIGN OF NEW SMALL-SCALE SOLAR RECEIVER FOR CONCENTRATED SOLAR THERMAL COLLECTOR ......................................................... 107 Abstract ................................................................................................................................... 107 1. Introduction ...................................................................................................................... 107 2. Design concept ................................................................................................................. 108 3. Modeling solar receivers (computational fluid dynamics) .............................................. 112 4. Results and discussion ..................................................................................................... 116 5. Conclusions ...................................................................................................................... 122  CHAPTER VI. STUDY SUMMARY AND FUTURE WORK ............................................. 123 1. Summary .......................................................................................................................... 123 2. Future work ...................................................................................................................... 124 viii  APPENDICES ............................................................................................................................ 132 Appendix A: Matlab code for system solar bio-hybrid modeling ........................................... 133 Appendix B: Matlab script functions for turbine modeling .................................................... 149 Appendix C: Matlab script function for solar collector modeling .......................................... 155 Appendix D: Matlab code for solarbio hybridization for anaerobic digestion and aerobic treatment .................................................................................................................................. 156 Appendix E: Matlab sub-functions for solarbio hybridization for anaerobic digestion and aerobic treatment ..................................................................................................................... 168 Appendix F: Additional figures for a two-module Fresnel lens solar thermal collector ........ 173 Appendix G: Astronomical algorithm for solar tracking system ............................................ 175 Appendix H: LabVIEW screenshots for control in solar tracking system .............................. 187  REFERENCES ........................................................................................................................... 195    ix  LIST OF TABLES  Table I-1. Types of anaerobic digesters .......................................................................................... 6 Table I-2. Biogas storage options ................................................................................................. 20 Table II-1. Operational parameters of 30 kW steam and gas turbines*........................................ 28 Table II-2. Simulation results of a 30 kW steam turbine .............................................................. 30 Table II-3. Operational parameters of a 30 kW gas turbine ......................................................... 32 Table II-4. Bioreactor volume and daily biomethane production for selected solar utilization* . 39 Table II-5. Energy consumption for biomethane cleaning ........................................................... 40 Table II-6. Required solar collector areas for steam and gas turbines at Lansing and Phoenix on the coldest winter day for a net capacity factor of 0.5 .................................................................. 43 Table III-1. Feedstocks of the anaerobic digester ......................................................................... 56 Table III-2. Operational parameters of 325 kW steam turbine ..................................................... 60 Table III-3. Optical factors for CSP collection ............................................................................. 61 Table III-4. Performance of anaerobic digestion .......................................................................... 63 Table III-5. Characteristics of the AD effluent, AD fiber, and filtrate* ....................................... 63 Table III-6. Characteristics of liquid effluent for secondary wastewater treatment ..................... 65 Table III-7. Electrical energy consumption by the anaerobic digestion system ........................... 66 Table III-8. Biogas balance for the electricity generation (without short-term solar energy storage) .......................................................................................................................................... 75 Table III-9. Biogas balance for the electricity generation (with short-term solar energy storage)79 Table IV-1. Parameters used in FEM simulation*........................................................................ 96 x  Table IV-2. Solar radiation and receiver column temperature for the FEM model .................... 100 Table IV-3. Temperature at the center of the absorbers and statistical comparison ................... 102 Table IV-4. Ac/Aa ratios for different CRs and absorber areas ................................................... 103 Table IV-5. Simulated central temperature of absorbers (°C) .................................................... 104 Table V-1. Design parameters for the absorbers ........................................................................ 111 Table V-2. Convective coefficient for heat loss ......................................................................... 115 Table V-3. Heat transfer efficiency for wind velocity variation ................................................. 117 Table V-4. The effects of DNI on the conical absorber .............................................................. 121 Table V-5. Effects of DNI on the cavity absorber ...................................................................... 122     xi  LIST OF FIGURES  Figure I-1. The key process stages of a solarbio hybrid energy generation system for wastewater treatment ......................................................................................................................................... 2 Figure I-2. Stages in the process of anaerobic digestion ................................................................ 5 Figure I-3. Schematic diagram of solar power generation methods ............................................. 11 Figure I-4. (a) Ordinary and Fresnel lens profile; (b) refractive Fresnel lens ............................... 12 Figure I-5. Schematic of an open- and closed-cycle gas turbine .................................................. 15 Figure I-6. Rankine cycle for a steam turbine............................................................................... 16 Figure I-7. Different scenarios for the solarbio hybrid power system and wastewater treatment plant............................................................................................................................................... 21 Figure II-1. Schematics of the studied solarbio hybrid power generation systems* .................. 27 Figure II-2. Monthly average temperature and DNI for Lansing and Phoenix ............................ 33 Figure II-3. Effects of net capacity factor and solar usage on bioreactor volume and solar energy requirements for different solarbio hybrid systems* .................................................................. 35 Figure II-4. Relationship between the solar utilization and thermal energy requirements of the AD for the solarbio hybridization systems*: a) steam turbine system; (b) gas turbine system. . 38 Figure II-5. Effects of location and month on the net capacity factor of the solarbio hybrid power generation system: (a) Lansing; (b) Phoenix. .................................................................... 44 Figure II-6. Energy balance of small-scale solarbio hybrid power generation systems* ........... 48 Figure III-1. Flow diagram for a conventional anaerobic/aerobic digestion process ................... 57 Figure III-2. Components of energy generation combining biomethane and solar concentrated energy: (a) concentrated solar power, (b) photovoltaic panels ..................................................... 59 Figure III-3. Mass balance of the integrated anaerobic digestion and aerobic treatment ............. 65 xii  Figure III-4. Daily electricity demands of the wastewater treatment ........................................... 66 Figure III-5. Variation of the ambient temperature ), DNI, and GHI for: (a) Lansing; (b) Phoenix ......................................................................................................................................... 70 Figure III-6. Biogas balance without solar energy short-term storage: (a) Phoenix; (b) Lansing*....................................................................................................................................................... 74 Figure III-7. Surplus electricity from solarbio hybridization without short-term energy storage....................................................................................................................................................... 75 Figure III-8. Required and generated thermal energy for the system without short-term solar energy storage: (a) Phoenix, (b) Lansing ...................................................................................... 76 Figure III-9. Biogas balance with solar energy short-term storage: (a) Phoenix, (b) Lansing ..... 79 Figure III-10. Surplus electricity from solarbio hybridization with short-term energy storage . 80 Figure III-11. Required and generated thermal energy for the system with short-term solar energy storage: (a) Phoenix, (b) Lansing .................................................................................................. 80 Figure IV-1. A scalable Fresnel lens solar thermal power generation concept ............................ 87 Figure IV-2. Bench-scale two-module foldable Fresnel solar thermal collector* ........................ 89 Figure IV-3. The receiver and metallic absorbers* ...................................................................... 91 Figure IV-4. The control system of the solar tracking .................................................................. 92 Figure IV-5. The tracking logic diagram of the LabVIEW program ............................................ 95 Figure IV-6. Topocentric azimut and zenith angles of the Fresnel lens position during the solar tracking test on: (a) October 11, 2013; (b) October 13, 2013 ....................................................... 99 Figure IV-7. Temperature profiles obtained using FEM simulation* ........................................ 101 Figure IV-8. Temperature and heat loss of the absorber (Aa)* ................................................... 105 Figure V-1. Solar receivers: (a) with conical absorber; (b) with cavity absorber ....................... 110 Figure V-2. Heat absorbers: (a) conical absorber; (b) cavity absorber ....................................... 110 xiii  Figure V-3. Dimensions of the solar receivers (in mm): (a) with conical absorber; (b) with cavity absorber ....................................................................................................................................... 111 Figure V-4. DNI during a year at Lansing, MI ........................................................................... 113 Figure V-5. Thermal collection efficiency and fluid output temperature of the receivers for two fluid mass flows: (a) cavity absorber; (b) conical absorber ........................................................ 118 Figure V-6. Fluid temperature distribution in the studied receivers for selected scenarios. conical receiver* ...................................................................................................................................... 119 Figure VI-1. Flowchart of the solarbio hybrid energy generation system to treat wastewater . 125 Figure VI-2. (a) CSP using refractive Fresnel lenses and PV collectors for solar thermal energy collection; (b) PV panels in the solarbio hybridization concept ............................................... 127 Figure VI-3. Equipment and reactor distribution of the wastewater treatment plant* ............... 128 Figure VI-4. Fixed-film anaerobic digester ................................................................................ 129 Figure VI-5. Electro-coagulation reactor for water clarification ................................................ 130 Figure VI-6. Fresnel lens assembly: (a) collector module; (b) single-collector test unit ........... 131 Figure VII-1. Bipolar parallel connection to connect stepper motor to drive ............................. 173 Figure VII-2. Temperature profiles obtained using FEM simulation* ....................................... 173 Figure VII-3. User interface for the solar tracking system ......................................................... 187 Figure VII-4. Main LabView script. Part 1 (including Sub-VI astronomical algorithm) ........... 188 Figure VII-5. Main LabView script. Part 2 (including Sub-VI Motor steps calculations and Motor sequence).......................................................................................................................... 189 Figure VII-6. Sub-VI astronomical algorithm ............................................................................ 191 Figure VII-7. Sub-VI Motor steps calculations .......................................................................... 192 Figure VII-8. Sub-VI Motor sequence. Part 1 (including Sub-VI VISA device) ....................... 193 xiv  Figure VII-9. Sub-VI VISA device ............................................................................................. 194    xv  KEY TO ABBREVIATIONS  Nomenclature Chapter II   Emittance   Collector area  Absorber area  Net capacity factor  Specific heat  Available solar radiation   Burner efficiency  Regenerator efficiency  Compressor efficiency  Heat exchanger thermal efficiency  Thermal energy requirement of anaerobic digester  Thermal energy generated  Electricity generation in the power generation system ()  Hydraulic retention time  Direct normal irradiance  Enthalpy  xvi   Heat generation in   Convective coefficient  Steam turbine inlet pressure  Steam turbine outlet pressure  Power generation subsystem  Gas turbine pressure ratio   Influent density  Stefan-Boltzmann constant  Heat input gas turbine system  Energy transferred to the working fluid  Heat-extracted steam turbine system  Heat-extracted gas turbine system  Solar heat requirement  Solar thermal energy  Solar collector subsystem  Solar operating factor  Temperature  Anaerobic digestion culture temperature  Influent temperature xvii   Solar energy collection time  Biomethane requirement  Water specific volume  Digester volume  Gross power generated  Pump work  Ratio between air specific heats   Nomenclature Chapter III  Anaerobic digestion  Aerobic digestion  Area of solar collector assembly  Constant  Constants  Chemical oxygen demand  Anaerobic digester (AD) influent specific heat  Constant  Constants  Thermal energy for AD xviii   Heating collecting element  Hydraulic retention time  Air mass flow  Biogas daily balance  Net capacity factor  Turbine thermal-to-electrical efficiency   Fuel-to-steam efficiency  Heat exchanger efficiency  Condenser efficiency   Optical efficiency  Compressor efficiency  Atmospheric pressure  Compressor outlet pressure  Electrical power generated in the turbine  Turbine design power output  Hourly electrical demand after solar utilization  Biogas pressure  Electricity generated by photovoltaics (PV)  Electricity stored in batteries xix   Anaerobic digestion  Compressor power  Biogas standard pressure  AD influent density  Thermal energy extracted in the condenser  Heat requirement of turbine  Turbine design thermal energy input  Thermal energy extracted in the condenser at   Direct normal irradiance  Net thermal energy collected in solar collector assembly (SCA)  Heat loss in the heating collecting element (HCE)  Heat loss in the piping system  Reference heat loss in piping system  Thermal energy from biogas  Solar thermal energy stored  Electrical energy stored  Solar collector assembly  Solar operating factor  AD culture temperature xx   Biogas standard temperature  Average working fluid temperature  AD influent temperature  Average annual ambient temperature  Total solids  Total soluble solids  Total nitrogen  Total phosphate   Anaerobic digester volume  Biogas standard volume  Volatile solids  Compressor power   Nomenclature Chapter IV Aa Absorber area Ac Concentration area Al Lens area CR Solar concentration ratio Lh Horizontal displacement of the lens xxi  Lv Vertical displacement of the lens Lh0 Horizontal distance from the focal point to the rotational point of the lens Lv0 Vertical distance from the focal point to the rotational point of the lens L Distance between the focal point and the rotational point of the lens  Absorbance of the metallic plate  Angle of the location of L at its initial position  Stefan-Boltzmann constant   Emittance of mild steel  Number of steps for motor 1 for horizontal adjustment  Number of steps for motor 2 for vertical adjustment  Number of steps for motor 3 for zenithal adjustment  Number of steps for motor 4 for azimuthal adjustment  Zenith angle  Azimuth angle  Zenith initial angle for lens (90°)  Azimuth initial angle for lens (0°)  Heat inflow at the absorber  Absorber temperature  Simulated temperature from FEM model xxii   Average temperature from data collection   Ambient temperature  Heat flux emitted by the absorber  Heat flux from solar radiation measured by pyranometer  Transmittance of the lens  Transmittance of the thermal glass  Nomenclature Chapter V  Receiver external area  Characteristic length   Thermal conductivity  Convective coefficient  Nusselt number  Prandtl number  Stefan-Boltzmann constant  Reynolds number  Heat loss due to convection  Heat loss due to radiation  Temperature xxiii   Wind velocity  Viscosity    1  CHAPTER I. INTRODUCTION  Water is one of the most important natural resources on Earth. It is the essential compound of plants and animals, which means that no life would exist without water. Rapid growth of the world population, along with rapid industrialization and urbanization, has led to a huge increase in fresh water consumption and wastewater generation. It has been reported that the volume of untreated domestic sewage generated daily per capita is 0.57 m3 in developed countries and 0.19 m3 in developing countries (Chapra, 1997). Although many technologies have been studied and developed for sewage treatment, most of these technologies require a significant amount of energy (both heat and electricity) to reduce the organic matter in the sewage and satisfy the discharge standards. Mizuta et al. (Mizuta & Shimada, 2010) reported that the specific power consumptions per m3 of wastewater ranged from 0.44 to 2.07 kWh for oxidation ditch treatment and from 0.30 to 1.89 kWh for conventional sludge treatment. The high-energy demand and use of non-renewable energy sources (fossil-based fuels are the main energy sources) mean that current wastewater treatment technologies are not completely sustainable and have limited technical and economical flexibility for various scale operations.  In order to replace the fossil energy usage and provide sustainable wastewater treatment (particularly for small- to medium-size operations), renewable energy sources should be synergistically integrated with wastewater treatment. Therefore, the proposed study combines solar and biological technologies to develop a novel self-sustainable solarbio hybrid energy generation system that satisfies the energy needs for small- to medium-scale wastewater treatment. The solarbio hybrid energy generation system includes unit operations consisting of 2  solar thermal collection, anaerobic digestion of wastewater, secondary treatment for anaerobic digestion effluent, and solarbio power generation (Figure I-1).    Figure I-1. The key process stages of a solarbio hybrid energy generation system for wastewater treatment  1. Literature review  1.1. Wastewater treatment process Human activities generate excessive waste with the potential to damage the environment. Wastewater is one of the most harmful byproducts of industrial and residential activities. Untreated wastewater results in ground water and surface water contamination, leading to serious issues, such as a detrimental impact on wildlife, algae bloom, and pathogen proliferation (EPA, 2004). The identification of all pollutants is complicated due to the complexity of the wastewater components. Biological oxygen demand (BOD) is a method to indicate the polluting capacity, 3  where microorganisms decompose the organic matter in the effluent by consuming the dissolved oxygen. BOD is obtained by measuring the oxygen concentration of the sample before and after a 5-day incubation period (BOD5), and the difference in concentration is the amount used in the microbial oxidation of organic matter (Chapra, 1997). The organic content in wastewater can also be obtained using chemical procedures, such as chemical oxygen demand (COD). COD is measured using inorganic chemicals to oxidize organic material. The COD measurement consumes less time, but correlates less well with natural conditions (Wang, Pereira, & Hung, 2009). Biological, physical, and chemical procedures have been studied for wastewater treatment. Among these, biological processes have been widely used and tested to remove organic and inorganic matter, and alleviate the potential environmental issues. Biological wastewater treatment pursues the acceleration of the natural processes to break down the organic compounds, while pollutants such as heavy metals are separated before the discharge of the water into streams. The growth of microbial populations, where the biochemical reactions reduce the organic matter via respiration (oxidative breakdown of organic molecules), is stimulated (Wang et al., 2009).  Anaerobic digestion (AD) and aerobic treatment (AET) are two state-of-art sewage treatment practices. Both technologies possess different target applications, advantages, and disadvantages, depending on the nature of the wastewater.   1.1.1. Fundamentals of anaerobic digestion  AD is an natural and biological conversion process that has been proven effective in converting wet organic wastes into biogas capable of producing clean electricity, while also 4  alleviating many of the environmental concerns associated with the wastes (odor, greenhouse gas emissions, and groundwater contamination) (Caruana & Olsen, 2012). AD is widely used to treat wastewaters of moderatehigh strength (> 50 000 mg/L as COD), and can also be used for dilute wastewater (Grady, Daigger, & Lim, 1999). The overall AD chemical process can be described as        (I.1) where  represents the organic matter in the wastewater, and  (carbon dioxide) and  (methane) are the main products from the AD process. There are four key stages of anaerobic digestion: hydrolysis, fermentation (acidogenesis), acetogenesis, and methanogenesis (Figure I-2, adapted from (R. Chen, 2015)).  Wastewater is usually composed of large organic polymers, such as carbohydrates, fats, and proteins. In order for microbes to carry out the anaerobic digestion and produce biogas, these large polymers must be broken down into smaller constituent monomers. Several of these monomers (i.e. simple sugars, fatty acids, and amino acids) are directly converted into acetate and hydrogen, which are utilized by methanogenic archaea. The remaining monomers need to go through several stages of fermentation to break down the intermediate volatile fatty acids (VFAs) (i.e. propionate, butyrate, succinate, and alcohols) into acetate and hydrogen. Eventually, acetoclastic and hydrogenotrophic methanogenic archaea produce methane, carbon dioxide, and water from the acetate and hydrogen.  5   Figure I-2. Stages in the process of anaerobic digestion  The microbial synthesis of AD does not need oxygen, which significantly reduces the energy demand of the process. Moreover, AD helps to alleviate the energy load in the system. AD generates 1.26 × 104 MJ (stored in CH4) per 100 kg of COD reduced (Speece, 1996). It has been reported that 2,339,339 t of CH4 per year can be generated from wastewater in the United States (NREL, 2013), which can potentially generate 71 × 109 MJ of thermal energy (with a biogas density of 0.75 kg/m3, and a biogas lower heating value of 23 MJ/kg (Colmenar-Santos, Bonilla-Gómez, Borge-Diez, & Castro-Gil, 2015; Sun et al., 2015)). 6  Anaerobic digesters are available in different configurations, and can be classified based on the dry solid content of the feedstock, the number of phases or stages, and the operating temperature (Korres, O'Kiely, & Benzie, 2013). Table I-1 summarizes the general classification of AD systems.  Table I-1. Types of anaerobic digesters Classification basis Digester type Feeding Batch or continuous Culture temperature Mesophilic, thermophilic, psychrophilic Feedstock type High (2040%) and low (< 20%) solid concentration AD Process Single or multi-stage  Moreover, anaerobic digesters include differences in their geometrical design and operational procedure (PennState Extention, 2016). For instance, a covered lagoon is a large digester with a long hydraulic retention time and high dilution. Covered lagoons are usually installed for flush manure management systems (0.52% total solids). Similarly, plug-flow digesters are installed for manure management (without internal agitation) and loaded with thick manure of 1114% total solids. In addition, a continuous stirred tank reactor (CSTR) is a configuration used for AD where the influent is agitated with a motor driver mixer, a liquid recirculation pump, or biogas mixing for an appropriate contact of the microbial community with the degradable organic matter. Similarly, the up-flow anaerobic sludge blanket (UASB) manages a fast-upward wastewater flow passing through the sludge bed on the bottom of the tank, improving the influent-sludge contact and enhancing the separation of inactive particles from the 7  sludge. Another digester type is the anaerobic fixed-film reactor, which is partially filled with an inert medium (such as plastic pall rings) that provides a large surface area for microbial growth without decreasing the volumetric digester capacity. The influent passes through the media and anaerobic microbes attach themselves to it, stimulating an appropriate biomass concentration for organic matter consumption. The energy demand varies based on the AD configuration (the different equipment installed, such as pumps, motors, filters). Moreover, typical AD treatment is operated under reaction temperatures ranging from 3550 °C. Zhong et al. (Zhong et al., 2015) found in their study that for an AD reactor of 10 m3 with R12 insulation, the thermal energy requirements to maintain the reactor temperature ranged between 0.51.1 MJ per m3 of reactor volume, and 25.51 MJ per m3 of reactor volume to heat the incoming waste stream. The thermal energy to maintain the culture temperature and heat the influent can be obtained from the produced biogas, but the biogas consumption for heating decreases its potential use for electricity generation. Studies have reported on the use of solar energy as a thermal source to maintain the culture temperature and heat the influent (El-Mashad, van Loon, & Zeeman, 2003; El-Mashad, van Loon, Zeeman, Bot, & Lettinga, 2004; Yiannopoulos, Manariotis, & Chrysikopoulos, 2008), which is a potential combination to enhance the global biogas utilization efficiency. Although there are several advantages of using AD, the energy requirements (heat and electricity) for the digestion operation and incomplete COD/BOD removal are the main drawbacks that limit its extensive application. Moreover, depending on the final use of the effluent or the discharge standards, additional stages are required to reduce the organic load.  8  1.1.2. Fundamentals of selected secondary wastewater treatments Owing to the incomplete COD/BOD removal in the primary stage of the wastewater treatment, additional stages are needed to satisfy the EPA discharge standards. Technologies such as aerobic treatment (Caruana & Olsen, 2012), electro-coagulation (EC) (Jiang, Graham, André, Kelsall, & Brandon, 2002), electro-deposition, electro-oxidation (G. Chen, 2004), nano-filtration, and reverse osmosis provide solutions to complete the waste treatment.  Aerobic treatment (AET) is a biochemical process that stabilizes the wastewater sludge via oxidation. This method is capable of handling relatively low-strength wastewater (Wang et al., 2009), and has been tested in a sequence operation with anaerobic digesters (Chan, Chong, Law, & Hassell, 2009; Fricke, Santen, & Wallmann, 2005). Influent concentrations in the range of 504,000 mg per liter of COD are effectively treated in the AET processes (Grady et al., 1999). Oxygen or air is supplied by aerators (diffusers) to maintain a dissolved oxygen concentration in the influent in the range of 12 mg/L for microbial growth (EPA, 2000). The overall AET process is described as       (I.2) where  commonly represents the organic matter in the waste stream. AET offers advantages over other treatment processes, such as easy operation (compared with AD), high removal efficiency of volatile solids, odor reduction, production of effluent with low BOD5/COD content, and short hydraulic retention times. However, AET has certain disadvantages, such as producing a digested sludge with poor dewatering characteristics, requiring a high energy consumption for the aeration process, being influenced by ambient temperature, and carrying out a low level of heavy metal removal. 9  The AET procedure is used in batch or in continuous operation. For the batch operation, the influent is pumped after the solid stabilization stage, and during the filling operation, the sludge (influent) is continually aerated at a lower rate initially. When the tank or pond is full, aeration continues at a higher rate for a given period to assure the removal of the organic load. The effluent is clarified by decantation to settle the non-soluble solids. For the continuous operation, the treatment works in a similar way to the batch operation, but the aerator functions at a fixed rate, and the liquid overflows into the solid-liquid separator.  In addition to biological treatments, chemical procedures have been applied to remove impurities in wastewater (used in the petroleum, mining, and chemical industries (Mollah, Schennach, Parga, & Cocke, 2001)). Electro-coagulation (EC) is a technology that involves the generation of coagulants by electrically dissolving (consuming DC electricity) either aluminum or iron ions from aluminum or iron electrodes, respectively (G. Chen, 2004). EC has certain advantages, such as short retention times, the efficient removal of fine particles, no additional coagulation-inducing reagents, and a small footprint, representing a convenient process to polish the AD effluent. However, due to the high-energy demand of EC technology, it has not been widely used for wastewater treatment. On the other hand, Liu et al. (Z. G. Liu & Liu, 2016) has studied a case that treats high-strength wastewater from anaerobic digestion for reclaimed water, concluding that the EC process simultaneously coagulates and floats solid particles in the solution, achieving a good removal performance for the wastewater with high organic loading.  1.2. Solar technologies for heat and electricity generation Solar radiation is the most abundant energy source on the planet. The greatest advantage of solar energy as compared with other forms of energy is that it is clean and can be supplied 10  without negative environmental consequences (Kalogirou, 2009). Solar radiation can be categorized in three forms. First, direct normal irradiance (DNI) is the amount of solar radiation received by a surface held perpendicular to the rays that arrive in a straight line from the direction of the sun (this quantity is of particular interest to concentrating solar thermal installations and installations that track the position of the sun). Second, diffuse horizontal irradiance (DHI) is the amount of radiation received by a surface that does not arrive in a direct path from the sun, but has been dispersed by particles in the atmosphere and comes equally distributed from all directions. Third, global horizontal irradiance (GHI) is the total amount of radiation received from above by a surface horizontal to the ground (GHI is of particular consideration for photovoltaic uses and includes both DNI and DHI).  Depending on the types of energy generation (combined heat and power generation (CHP) or electricity generation only), solar technologies are available as depicted in Figure I-3 (modified from Siva Reddy et al. (Siva Reddy, Kaushik, Ranjan, & Tyagi, 2013)). Moreover, solar thermal technologies for CHP can be classified according to the working fluid temperature (Siva Reddy et al., 2013). Low- and medium-temperature technologies, such as parabolic solar concentrators, collect energy of up to 50 kW (with a fluid temperature of 400 °C and collecting 6070% of incident solar radiation). High-temperature solar technologies, such as the parabolic dish Stirling engine and central tower receiver, are operated at temperatures higher than 600 °C, and are used in large solar power plants (megawatt or above) to generate electricity and heat.  For low-temperature solar technologies (less than 50 kW), the Fresnel lens (FL) and parabolic trough (PT) are the common configurations (Giostri, Binotti, Silva, Macchi, & Manzolini, 2013). The PT has been widely used in the past decades, presenting an optical efficiency of 75%, higher than the FL (67%). Although the FL has a lower optical efficiency, it 11  still has certain advantages compared to the PT, such as having inexpensive, thin, and lightweight elements. With a lightweight supportive structure, the energy consumption required for the tracking system is lower than that required for systems with massive metallic reflectors.   Figure I-3. Schematic diagram of solar power generation methods  The FL applies the same principles as an ordinary lens, but it has a different geometric configuration. The ordinary lens has a thick lens to achieve the focus, which is impractical for lens collector installations. In principle, it is segmented to create several refractive/reflective surfaces, replacing the curved surface of the convectional lens with a series of concentric grooves. These contours perform as individual refracting/reflecting surfaces, bending parallel light rays to a common focal length (Figure I-4 (EdmundOptics, 2016)). Solar power generation Solar photovoltaic Solar thermal Solar aided Coal fired thermal plant Gas fired combined cycle power plant Solar alone Fresnel reflector/refractor Rankine Cycle Parabolic trough Rankine Cycle Parabolic dish Stirling /Rankine Cycle Central tower receiver Rankine/Brayton Cycle 12   Figure I-4. (a) Ordinary and Fresnel lens profile; (b) refractive Fresnel lens  Fresnel lenses are very useful for solar energy collection (imaging or non-imaging systems) (Xie, Dai, Wang, & Sumathy, 2011), especially in large installations (concentrating light onto a photovoltaic cell or to heat a surface). Linear Fresnel lenses can be used instead of parabolic trough reflectors, as presented by Zhu et al. (G. D. Zhu, Wendelin, Wagner, & Kutscher, 2014) and Zhai et al. (Zhai, Dai, Wu, Wang, & Zhang, 2010). In addition, spherical Fresnel lenses can be used instead of parabolic dish reflectors (Xie, Dai, & Wang, 2013). As the solar collection area increases, the size of the parabolic collectors causes mechanical problems resulting from the increase in weight, such as requiring heavy structures to hold the elements, as well as the high energy consumption of the solar tracking system. In practice, it appears to be uneconomical to build parabolic collectors with aperture areas much larger than 100 m2 SpringerLink, 1986). These problems can be solved by Fresnel lenses.  In the CSP systems, concentrating receivers form an important subsystem that must be analyzed based on the nature of the solar collection (reflected, refracted), and geometry 13  configuration (convex, concave, flat, covered, uncovered) (Duffie & Beckman, 2006). A ratio that is commonly used for the solar receiver design is the concentration ratio ():           (I-3) where  is the collection area of the reflective or refractive element; and  is the absorber area of the solar receiver. In the concentration ratio, the acceptance angle defines the limits of the solar concentration and tracking requirements, and is defined as the angular range over which all or almost all of the incident rays are accepted without moving all or part of the collector . The maximum concentration ratio () for a given acceptance half-angle () and for a two-dimensional (2D) (linear) concentrator is given by         (I-4) For three-dimensional (3D) collectors, the maximum concentration ratio is calculated as         (I-5) The angular radius of the sun () is approximately 5 mrad (0.25°), and the maximum values of concentration for 2D and 3D concentrators are 200 and 40,000, respectively.  In addition to combined heat and power generation, photovoltaic panels are an option to generate energy by directly converting the sunlight into electricity (the operational process of converting light to electricity is called the PV effect). Traditional solar cells are made from silicon. Second-generation solar cells are called thin-film solar cells (consisting of layers of semiconductor that are a few micrometers thick), and are made from amorphous silicon or non-silicon materials, such as cadmium telluride. Third-generation solar cells are made from a variety of materials besides silicon, including solar inks, solar dyes, and conductive plastics (NREL, 14  2016a). Furthermore, new solar cells use plastic lenses or mirrors to concentrate solar radiation onto a small area of high efficiency PV material (called concentrated photovoltaics (CPV)).  Mathematical models predict the behavior of PV configurations under different ambient conditions (Bellia, Youcef, & Fatima, 2014). Although a high value of GHI increases the solar energy availability to generate electricity, the increment in the cell temperature decreases the electricity generation (Skoplaki & Palyvos, 2009). The nominal operating cell temperature (NOCT) is one of the methods used to quantify the energy generation under different solar radiation values. Low cell temperature and high GHI value are the optimal parameters to enhance the conversion efficiency, but these factors are not obtained simultaneously without a cooling system.  1.3. Thermodynamics of heat and energy generation  1.3.1. Gas power systems - the air standard Brayton cycle Gas power systems utilize gas as a heat transfer fluid (HTF) to complete power generation. The energy remains in the gas-phase during the thermodynamic cycle. In the turbine, shaft-work is produced by a rotor while the HTF expands in a controlled volume (Figure I-5 adapted from (Massoud, 2005)). Air is compressed and forced into a combustion chamber for heat addition. Inside the turbine, the air flows through the static blades and rotates the dynamic blades connected to the rotor. A percentage of this work is transferred to the compressor. When the air leaves the turbine, it also carries a portion of its energy to the heat sink (heat exchanger).   15   Figure I-5. Schematic of an open- and closed-cycle gas turbine  The following assumptions are often used to simplify the analysis of the air standard cycle: (1) the HTF acts as an ideal gas (this allows the internal energy to be described in terms of temperature and specific heat); (2) the mass flow is fixed for the cycle; and (3) all processes are reversible and the effects of kinetic and potential energies are negligible. The compression and expansion occurs in isentropic processes, and heat addition and rejection in isobaric processes. Three ratios are associated with the energy generation consumption in the cycle: (1) the compression ratio () is defined as the ratio of the gas volume before compression to the gas volume after compression, ; (2) the pressure ratio or compressor pressure ratio () is defined as the ratio of gas pressure after compression to gas pressure before compression,  (for an isentropic compression, ,  is the ratio between the specific heat at constant pressure and the specific heat at constant volume); and (3) the temperature ratio () is defined as 16  the ratio of the maximum to the minimum temperature in a cycle, . The thermal efficiency can be derived from the temperatures in the cycle:         (I.6)  1.3.2. Vapor power systems  the Rankine cycle The vapor power system is based on the Rankine cycle (Figure I-6, adapted from (Massoud, 2005)). The power is generated based on the phase change of the HTF.    Figure I-6. Rankine cycle for a steam turbine  For steam utilization in the turbine, water is pumped isentropically into the boiler (heat source) that is maintained at constant pressure. Saturated or superheated steam is generated from the boiler, and enters the turbine. The stationary blades direct the flow through the rotary blades fixed on the work shaft. In the Rankine cycle, the expansion occurs isentropically. The steam leaves the turbine and a condenser extracts heat at constant pressure, and then the water is 17  pumped to the heat source for the next cycle. The thermal efficiency of the Rankine cycle is given by the following equation:      (I.7) where  is the net work of the system;  is the heat added;  is the mass flow; and is the enthalpy.  1.4. Solar hybrid power generation system For electricity generation, hybridization has become a strategy incorporating several different energy sources that are collectively used to achieve the benefits of energy stability, electricity flexibility, and efficiency improvement. Several solar-hybrid power generation systems have been studied and implemented (Jamel, Abd Rahman, & Shamsuddin, 2013) (Olivenza-Leon, Medina, & Hernandez, 2015). Popov (Popov, 2014) presents a concept combining gas turbines with solar energy, in which the system uses the solar energy in a chiller to cool down the inlet air in the compressor (point 1 in Figure I-5) (a lower temperature entails a higher mass flow). In addition, Schwarzbozl (Schwarzbözl et al., 2006) uses solar energy to increase the temperature of the compressed air (point 2 in Figure I-5), and consequently reduce the heat demand of the gas burner for the gas turbine system. Casati et al. (Casati, Galli, & Colonna, 2013) conducted a study of a 100 kW power generation plant using a solar-facilitated Rankine cycle. Solar energy was used to generate the steam (approximately 300 °C) for the thermodynamic cycle (line 2 in Figure I-5). Bao et al. (Bao, Zhao, & Zhang, 2011) studied a concept similar to the solar-facilitated Rankine cycle for power generation except that isopentane/R245fa was used as the HTF. 18  However, most of these studies focused on large-scale solar-hybrid power generation systems, and only a few were for small-scale micro-power generation. Koai et al. (Koai, Lior, & Yeh, 1984) presented in their study a steam turbine for 22 kW (30 hp) of electrical power. In addition, The Office of Energy Efficiency and Renewable Energy (Energy, 2007) analyzed the case of heat and power gas turbines for 30 kW electricity production. From the results of these studies, it was concluded that the key limitation for small-medium solar-hybrid power plants is low system efficiency.  Additionally, solar hybridization can be implemented by installing photovoltaic panels (Deshmukh & Deshmukh, 2008), which can directly supply the electrical energy generated to cover the power load required. The system can be connected to the national or local electrical grid to supply energy when the PV generation is greater than the demand, and obtain electricity from the grid when the solar radiation is insufficient to cover the power load. For self-sustaining systems, a battery bank can store the excess electrical generation and supply energy during deficit production. Lead acid and lithium ion batteries are used, both differing in their capacity storage, minimum discharge capacity, lifetime, and cost. PV solarbio hybridization has been integrated with anaerobic digestion treatments (Bhatti, Joshi, Tiwari, & Al-Helal, 2015), which utilizes heat recovered from the PV cell cooling device to maintain the AD culture temperature at 35 °C. Further, Borges et al. (Borges Neto, Carvalho, Carioca, & Canafístula, 2010) present a system that combines biogas from goat manure and PV panels for a small-scale rural community in Brazil. Moreover, for high electricity demand, studies have shown the feasibility of PV hybridization, such as Gazda et al. (Gazda & Stanek, 2016), who presented a bio-hybrid system that provides heat, cooling, and electricity. Gonzáles et al. (González-González, Collares-Pereira, Cuadros, & Fartaria, 2014) studied a feasible bio-PV hybridization for a pig slaughterhouse in 19  Spain (79 kWe from biogas and 225 kWe from PV installation). Indeed, PV hybridization is an option to cover the energy demand of the wastewater treatment plant.   1.4.1. Biogas utilization for electricity production Solarbio hybridization requires biogas to be utilized when solar energy is not available to generate electricity. Biological treatments such as anaerobic and aerobic digestion have a continuous electricity demand for the biological reactions to occur. Solar energy, unless it has massive thermal energy storage, can supply energy for electricity generation for a few hours. At night or during prolonged cloudy days, the reserve in solar energy storage may become unavailable. Long-term biogas storage is an option to continue producing electricity continuously, balancing the thermal energy sources from the hybridization. Biogas from wastewater treatment plants is capable of being stored and upgraded for electrical power generation (Osorio & Torres, 2009). Before storage, it is upgraded into biomethane by removing most of its components, while the heating value is increased, corrosion in the storage tanks is avoided, and undesired components are removed for the biomethane combustion.  Water, hydrogen sulfide (removed during or after digestion), organic silicon, and carbon dioxide are the typical components to remove in the biogas upgrading (Basu, Khan, Cano-Odena, Liu, & Vankelecom, 2010; Ryckebosch, Drouillon, & Vervaeren, 2011). Different processes are available to remove one or more components simultaneously, such as water scrubbing, cryogenic separation, physical or chemical absorption, pressure swing absorption, and membrane separation technology. Whatever the process or processes selected, electricity is required to performed the cleaning and upgrading process (Sun et al., 2015). 20  Biomethane is not stored easily, as the liquefaction does not occur under ambient pressure and temperature (the critical temperature and pressure required are -82.5 °C and 47.5 bar, respectively) (Kapdi, Vijay, Rajesh, & Prasad, 2005). Most of the processes for biogas upgrading are conducted under high pressure, and the biogas can be stored long-term in commercial gas cylinders. Typical pressures and materials for biogas/biomethane storage are presented in Table I-2 (Kapdi et al., 2005)  Table I-2. Biogas storage options Pressure Storage device Material Low (0.1380.414 bar) Water sealed gas holder Steel Low (0.1380.414 bar) Gas bag Rubber, plastic Medium (1.051.97 bar) Propane or butane tanks Steel High (200 bar) Commercial gas cylinders Alloy   2. Goal, scope, and objectives The goal of the proposed research is to develop a solarbio hybrid concept for electricity and heat generation that enables the establishment of a self-sustaining small-scale wastewater treatment system. The hypothesis is that a combination of solar energy and biological methane generation could provide stable and sufficient energy to satisfy the requirements of the unit operations of the small-scale treatment system (thermophilic anaerobic digestion, secondary wastewater treatment, water purification, and solar energy collection). Further, this concept could overcome the disadvantages of individual technologies, such as the unsteady energy flow 21  from solar power generation, low conversion efficiency of mesophilic anaerobic digestion, and excessive thermal and electrical energy requirements of the wastewater treatment operations. The study considers different options to complete the key processes of wastewater treatment (Figure I-7). Solar collection technologies, the characteristics of influent treatment, power generation technologies, and secondary treatments were systematically studied to balance the overall efficiency and overcome potential disadvantages of individual processes.    Figure I-7. Different scenarios for the solarbio hybrid power system and wastewater treatment plant  Four solar collection technologies: Fresnel lenses, parabolic dishes, parabolic troughs, and photovoltaic panels were selected for solar energy collection. Feedstock consisting of food waste, cow manure, and combined food-waste and municipal wastewater were studied for the AD treatment to generate the biomethane. Energy is generated by the combined heat and power (CHP) technologies. Three configurations consisting of CHP with gas turbine, CHP with steam turbine, and CHP with PV electricity and thermal heat were investigated.  22  The specific objectives of the proposed study were:  (1) To perform a technical analysis of small-scale solarbio hybrid power generation systems using the Rankine and Brayton cycles to supply the balance in the thermal energy requirements by the anaerobic digestion process (presented in Chapter 2).  (2) To establish an energy and mass balance for the wastewater treatment by a self-sustaining bio-hybrid operation using solar energy (presented in Chapter 3).  (3) To obtain the geometrical and thermal parameters for the design of a solar thermal collector for electricity generation using small refractive Fresnel lenses (presented in Chapter 4). (4) To design a novel receiver for concentrated solar energy from refractive Fresnel lenses (presented in Chapter 5).  23  CHAPTER II. SMALL-SCALE SOLARBIO HYBRID POWER GENERATION USING BRAYTON AND RANKINE CYCLES  Abstract This study conducted a detailed technical analysis of small-scale solarbio hybrid power generation systems using the Rankine (steam turbine) and Brayton (gas turbine) cycles. Thermodynamic models have been developed to characterize the state of the working fluid and select the most suitable solar collection technology for individual power generation systems. The net capacity factor of power generation and utilization efficiencies of solar and biomethane energy were used as parameters to evaluate the energy generation and optimize the system configuration. The analysis elucidated that the global thermal efficiency of the steam turbine system (54.87%) was higher than that of the gas turbine system (41.43%), although the electricity generation efficiency of the steam turbine system (14.69%) was lower than that of the gas turbine system (27.32%). The study also analyzed the effects of different climates on the selection of suitable hybrid systems. Considering global thermal efficiency and system footprint, the steam turbine system was found to be more suitable for both cold and warm climate locations. Appendices for this chapter: i. Appendix A: Matlab code for system solar bio-hybrid modeling ii. Appendix B: Matlab script functions for turbine modeling iii. Appendix C: Matlab script functions for solar collector modeling   24  1. Introduction Hybridization of power generation is a strategy that several different energy sources are collectively used to achieve benefits of energy stability, electricity flexibility, and energy efficiency improvement. Many hybridization studies have focused on combining solar energy with fossil fuels (Pihl, Spelling, & Johnsson, 2014; Zhao, Hong, & Jin, 2014), in which the concentrated solar energy is used as the heat source to raise the temperature of the working fluid prior to the fuel combustion and improve energy generation efficiency (Jamel et al., 2013; Popov, 2014). With increasing attention on utilization of more renewable resources for power generation, combining concentrated solar energy with biomethane becomes a potential alternative to solar-fossil-fuel hybrid power generation (Colmenar-Santos et al., 2015; San Miguel, Miguel, & Corona, 2014). However, current research and development on solarbio hybridization has focused on large-scale power generation ranging from a few hundred kW to several MW (Immanuel Selwynraj, Iniyan, Polonsky, Suganthi, & Kribus, 2015; Livshits & Kribus, 2012; San Miguel et al., 2014; Schwarzbözl et al., 2006). Only a few studies have been reported on solarbio hybrid micro-power (less than 100 kW) generation (Buck & Friedmann, 2007; Koai et al., 1984). Considering the end-users of such hybridization power generation technologies, there is a high demand for small-scale distributed renewable systems for farm/food operations and remote villages/towns. Therefore, in-depth studies on small-scale solarbio hybrid power generation are very much needed to extend the hybridization concept to a wider range of applications.  Anaerobic digestion (AD) is an existing natural and biological conversion process that has been proven effective in converting wet organic wastes into biomethane. It is capable of producing clean electricity, while also alleviating many of the environmental concerns associated 25  with the wastes (odor, greenhouse gas emissions, and groundwater contamination) (Caruana & Olsen, 2012). In addition, contrasting to large-scale power plant operations, AD can be set up in small- or medium-scale biomethane generation plants, such as wastewater treatment plants, food processing plants, and animal farms (e.g., more than 80% of U.S. animal farms have less than 500 heads of animals) (USDA National Agricultural Statistics Service, 2009). Combining the AD operation and solar thermal collection to develop small-scale solarbiomethane hybrid power generation could provide a win-win solution to treat organic wastes and satisfy the energy demands of farm or residential operations.  Solar thermal technologies are classified as low-, medium-, and high-temperature solar thermal collection (Siva Reddy et al., 2013). Due to the temperature requirements of the turbines for power generation, medium- and high-temperature solar thermal collection are the solar thermal technologies that can be used for the hybridization system. Medium-temperature (approximately 400 °C) solar thermal technologies often use parabolic troughs to collect solar energy. Central tower receivers and parabolic dishes are high-temperature (more than 500 °C) solar thermal technologies. Considering the scale of power plants, central tower receivers are mainly used by solar thermal power plants to generate electricity in the magnitude of 100 MW or above. It requires large solar fields, and the operating temperature typically ranges from 600 °C to 1,400 °C (Siva Reddy et al., 2013). However, parabolic dishes and parabolic troughs are solar thermal technologies that could be used for small- and medium-scale power operations and generate electricity in the magnitude of kW.  In order to develop small-scale solarbio hybrid power generation, 30 kW power generation systems, including three unit operations consisting of AD, solar thermal collector, and engines were comprehensively analyzed in this paper. Biomethane from anaerobic digestion and 26  thermal energy from solar collection were used as the energy sources to power engines to generate electricity and heat. Gas and steam turbines as engine units were compared to determine the most suitable for the studied solarbio hybrid system. The net capacity factor (the ratio of the energy output to the total energy generation of the system in a given time duration) and solar and biogas utilization factors (the percentage of each energy source used to generate the electrical energy) were used as parameters to evaluate the energy generation and optimize the system configuration.  2. The studied small-scale solarbio hybrid power generation system Thermodynamic models were established to analyze the solarbio hybrid systems consisting of gas and steam turbines (Figure II-1). The biomethane production for the studied systems was based on a biomethane plant using thermophilic anaerobic digestion on a mixture feed of dairy manure and food wastes (90:10 ratio, 5% total solids) (R. Chen et al., 2016). The anaerobic digestion with a culture temperature of 50 °C and a hydraulic retention time (HRT) of 20 days produced 0.38 m3 methane per m3 digestion solution per day (the low heating value of methane is 34 MJ/m3 (Sun et al., 2015)). The steam turbine includes a condenser to recycle the water in a closed-loop circuit (Figure II-1a). The gas turbine uses a regenerator to transfer energy from the exhaust gases into the compressed air in an open-loop air circuit (Figure II-1c). Both systems contain water heat storage to collect energy from the thermodynamic cycle for the heat demand of the anaerobic digester (to maintain the digestion temperature and heat the influent). The solarbio hybrid power generation systems (which include a secondary heat source of solar energy) have slightly more complicated configurations than the turbine power generation systems. Molten salt is used as the solar thermal storage (Halotechnics, 2013).  27   (a)                                                                                 (b)  (c)                                                                                 (d) Figure II-1. Schematics of the studied solarbio hybrid power generation systems* *: (a) the biomethane steam turbine; (b) the solarbio hybrid power system with steam turbine; (c) the biomethane gas turbine; (d) the solarbio hybrid power system with gas turbine.  In the solarbio hybrid system with steam turbine, a heat exchanger was implemented to use the heat from the solar thermal storage to heat the working fluid prior to entering the biomethane boiler. The boiler further heats the working fluid to generate superheated steam to power the steam turbine (Figure II-1b). The solarbio hybrid system with gas turbine uses the heat from the solar thermal storage to raise the temperature of the hot air from the regenerator in 28  the heat exchanger. This is done before the air is mixed with biomethane fuel in the burner to generate heat for the gas turbine (Figure II-1d). The analyses were based on a constant electricity generation of 30 kW for all studied systems. The operational parameters of the thermodynamic models are listed in Table II-1.   Table II-1. Operational parameters of 30 kW steam and gas turbines* System Parameter Unit Value Steam turbine (30 kW) Water mass flow kg/s 0.0807 Steam inlet pressure (turbine) bar 10 Condenser pressure bar 0.2 Steam inlet temperature (turbine) °C 200 Gas turbine (30 kW) Air mass flow kg/s 0.31 Air inlet temperature (turbine)  K 1,113 Compression ratio - 3.2 Air inlet temperature (compressor)  K 300 Air temperature after expansion  K 912 *: The parameters are from commercial steam and gas engines (A. Liu & Weng, 2009; NextGrid, 2014).  The Rankine cycle was used to simulate the performance of the biomethane steam turbine. The working fluid consisting of water is pumped into the boiler that is maintained at constant pressure (Figure II-1a and b). The power consumption of the pump and the enthalpies at points 2 and 4 in Figure II-1a and b are calculated by        (II-1) 29            (II-2)         (II-3) where  is the pump work (kJ/kgwater);  is the pump efficiency (set at 0.65);  is the specific volume (m3/kg);  and  are the inlet and outlet pressures in the turbine;  is the enthalpy at given temperature and pressure conditions (kJ/kgwater);  is the gross power generated (shaft work (30 kW), pump power (), and vacuum pump (0.5 kW)); and  is the steam requirement (0.0807 kg/s). The fuel efficiency of the system is calculated based on the fluid properties at the inlets and outlets of the turbine and pump:          (II-4) where  is the work performed in the turbine (kJ/kgwater). The enthalpy at condenser conditions () is calculated considering an isentropic turbine efficiency. To satisfy the required temperature and pressure of the feedwater for the selected 30 kW steam engine, the heat input  and the heat extracted  of the system are calculated as follows:         (II-5)        (II-6) where  is boiler efficiency (set at 0.85); and  is the condenser efficiency (heat sink) (set at 0.85). The simulation results for the steam turbine are presented in Table II-2. The enthalpies at points 1, 2, and 3 (Figure II-1) were 243.03 kJ/kgwater, 244.57 kJ/kgwater, and 2828.3 kJ/kgwater, respectively (Table II-1). The temperatures at points 2 and 4a were 58.23 °C and 103.54 °C, respectively. The corresponding heat input and heat extraction were 245.33 kW and 134.61 kW, respectively. The thermal efficiency calculated for this particular equipment under 30  the working parameters showed that 14.69% of the biomethane fuel was transformed into shaft work for electricity generation, and 54.87% of the biomethane fuel was turned into heat.  Table II-2. Simulation results of a 30 kW steam turbine Parameter Unit Simulation results  bar abs 0.2  kJ/kgwater 1.53  kJ/kgwater 243.03  kJ/kgwater 244.57  °C 58.06  °C 58.23  kJ/kgwater 2,828.30  kJ/kgwater 2,205.2  °C 60.06  - 0.1469  kW 245.33  kW 134.61  In the solarbio hybrid steam power system (Figure II-1b), the solar thermal energy reduces the amount of heat required by the boiler, and consequently decreases the biomethane consumption. The solar thermal energy () heats the water and generates a mixture of saturated steam and liquid at 99.60 °C. The boiler then converts the rest of the liquid into 31  saturated steam and superheats the steam to satisfy the required temperature and pressure by the turbine (200 °C at 10 bar abs). The enthalpy of the mixture after the solar heating is:         (II-7) The heat added in the boiler (only required if  is lower than ) is calculated by                   (II-8) where  is the boiler efficiency. As for the gas turbine, the Brayton cycle was used to simulate the turbine performance. The temperature () after the compressor (point 2 in Figure II-1c and d) was calculated by        (II-9)          (II-10) where  is the pressure ratio between the inlet and outlet in the compressor;  is a constant;  is the ratio between the specific heat at constant pressure and the specific heat at constant volume; and  is the compressor efficiency (. The temperature after the regenerator (Point X in Figure II-1c and d) is given by       (II-11) where  is the regenerator efficiency (). The heat input to the burner () is calculated by        (II-12) where  is the specific heat at  [kJ/kg·K]; and  is the burner efficiency (). The temperature of the exhaust gases after the regenerator (Point Y in Figure II-1c and d) is given by  32        (II-13) The fuel efficiency for the gas turbine is:          (II-14) The heat extracted from the exhaust gases () is calculated by       (II-15) where  is the specific heat at  [kJ/kg·K];  is the temperature of the exhaust gases (assumed as 85 °C); and  is the efficiency of the heat exchanger and set at 0.75. The simulation results for the gas turbine analysis are listed in Table II-3. For a constant air inlet temperature, the heat input and heat extracted was 109.83 kW and 45.50 kW, respectively. The compression increased the air temperature from 300 K at point 1 to 444.58 K at point 2. The regenerator further increased the air temperature to 806.83 K at point X before the air was mixed with biomethane in the burner. The gas turbine unit uses 27.32% of the biomethane for the shaft work of electricity generation, and 41.43% of the biomethane to generate heat.   Table II-3. Operational parameters of a 30 kW gas turbine Parameter Unit Simulation results  - 0.273  K 444.5  K 806.83  K 549.75  kW 109.83 33  Table II-3.   kW 45.50  With the addition of solar thermal energy (Figure II-1d), the heat demand of the biomethane burner is also reduced. The temperature after the solar collector is calculated as follows:         (II-16) where  is the specific heat at  [kJ/kg·K]. In addition, due to seasonal and geographical variation of solar radiation, the location of the studied systems has a great impact on their performance. The direct normal irradiance (DNI) and ambient temperature decrease with an increase in latitude. Therefore, the two locations of Lansing (MI) and Phoenix (AZ) in the United States, which have significant temperature differences and solar radiation, were selected for this study. Figure II-2 represents solar radiation and ambient temperature during a year for both locations (NREL, 2015; U.S.ClimateData, 2015).    Figure II-2. Monthly average temperature and DNI for Lansing and Phoenix -10-50510152025303540123456789101112Average Ambient Temperature (C) Month LansingPhoenix05101520253035123456789101112Direct Normal Irradiance (MJ/m2·day) Month LansingPhoenix34  3. System analysis  3.1. Relationship between solar energy, capacity factor, and ratio of solar energy to biomethane energy The biomethane consumption of solarbio hybrid power systems (steam and gas turbines) depends on the usage of solar energy (the heat input from solar energy) and the net capacity factor of the power generation. The effects of capacity factor and solar usage on bioreactor volume and solar energy requirements for solarbio hybrid steam and gas turbine systems are presented in Figure II-3. With an increase in net capacity factor and solar usage, the solar energy demands of both systems linearly increase. At the same time, the hybrid steam engine system demands more solar energy than the hybrid gas turbine system (Figure II-3a and b). During full utilization of solar energy (100% solar usage and 1 net capacity factor) to power the hybrid systems, the hybrid steam turbine system requires 18,017 MJ/day of solar energy, which is approximately double the demand of the hybrid gas turbine system (9299.4 MJ/day). Meanwhile, the required bioreactor volume to generate biomethane for 30 kW electricity generation increases with an increase in net capacity factor and decrease in solar usage for both systems, and the hybrid steam engine system requires a larger bioreactor volume than the hybrid gas engine system (Figure II-3c and d). At the point of 0% solar usage and a net capacity factor of 1, the hybrid steam engine system requires a bioreactor volume of 1,435.3 m3, while the hybrid gas turbine only requires a bioreactor volume of 642.53 m3.   35   (a)                                                                         (b)    (c)                                                                         (d) Figure II-3. Effects of net capacity factor and solar usage on bioreactor volume and solar energy requirements for different solarbio hybrid systems* *: (a) Solar energy requirements for the solarbio hybrid steam turbine system; (b) solar energy requirements for the solarbio hybrid gas turbine system; (c) bioreactor volume for the solarbio hybrid steam turbine system; (d) bioreactor volume for the solarbio hybrid gas turbine system.  36  3.2. Energy requirements for biomethane production  3.2.1. Thermal energy requirements for biomethane production  Thermal energy is needed by the anaerobic digestion of biomethane production to heat the feed and maintain the culture temperature at 50 °C. The energy requirement per day ( (MJ/day)) is calculated as follows (Yue, MacLellan, Liu, & Liao, 2013):            (II-17) where  is the digester volume (m3);  is the hydraulic retention time (days);  is the feed density (1220 kg/m3);  is the feed specific heat (3606 J/kg·°C);  is the culture temperature (50 °C);  is the feed temperature and assumed to be the same as that for ambient temperature when the ambient temperature is above 4 °C (the feed temperature is set at 4 °C when the ambient temperature is below 4 °C); and 30% is the additional heat that is needed to maintain the thermophilic culture condition of the digester.  The maximum thermal energy demands at Lansing on the coldest winter day under the conditions of a net capacity factor of 1 without solar utilization for steam and gas turbines are 18,880 MJ/day and 8451.9 MJ/day, respectively. The corresponding thermal energy demands at Phoenix for steam and gas turbines are 15,186 MJ/day and 6,798.2 MJ/day, respectively. To satisfy the requirements of year-round power generation, the solarbio hybrid system should have a positive energy balance on the coldest winter days. Thus, the maximum thermal energy demands at the two locations were used to determine the size of the solar unit and anaerobic bioreactor for 30 kW electricity output.  The solar utilization value was selected based on the balance between thermal energy required by the anaerobic digester and thermal energy generated in the power generation system 37  at a given net capacity factor. The thermal energy generated in the power system (MJ/day) is calculated as follows:                                                   (II-18) where  is the heat generated ( or ) (kW) and  is the net capacity factor. The energy requirements per day ( (MJ/day)) given by Equation II-17 can also be expressed as   (II-19.a)            (II-19.b)        (II-19.c) where  is the biomethane requirement (m3);  is the biomethane productivity (m3CH4/m3digester);  is the energy provided by the biomethane (MJ/day);  is the heat of combustion of methane ( MJ/m3);  is the heat input ( or ) (for the turbine) (kW); and  is the solar utilization factor. Substituting Eq. II-19.b and Eq. II-19.c into Eq. II-19.a, and combining with Eq. II-18, the solar utilization factor can be calculated. For instances of a given net capacity factor of 0.5, the relationship between solar utilization and the required thermal energy by the AD is shown in Figure II-4. To satisfy the energy demands of heating the influent and maintaining the digestion temperature, the solar utilization required at Lansing for steam and gas turbines is 0.3840 and 0.5349, respectively; and the corresponding values at Phoenix for steam and gas turbines are 0.2341 and 0.4217, respectively. These values at the capacity factor of 0.5 are used as the base numbers to select the anaerobic digester volume and solar collector for each location and power system (Table II-4). 38  (a) (b) Figure II-4. Relationship between the solar utilization and thermal energy requirements of the AD for the solarbio hybridization systems*: a) steam turbine system; (b) gas turbine system. *: A net capacity factor of 0.5 was used to calculate these numbers.    39  Table II-4. Bioreactor volume and daily biomethane production for selected solar utilization* Location Reactor volume (m3) Biomethane production (m3/day) Steam Gas Steam Gas Lansing 442.08 149.43 166.34 56.23 Phoenix 549.62 185.78 206.81 69.90 *: The net capacity factor of 0.5 was used to calculate these numbers.  3.2.2. Electricity requirements for biomethane production and upgrading Besides the thermal energy demand, biomethane production and upgrading also require electricity to power the liquid handling equipment and biomethane upgrading process. It has been reported that the electricity consumption by the liquid handling equipment (pumps, agitators, and screw compressor) is 0.0509 MJ per m3 digester per hour (Lijó et al., 2014). Biomethane also has many other compounds, such as carbon dioxide, moisture, hydrogen sulfide (H2S), siloxanes, hydrocarbons, ammonia, and carbon monoxide. Among these compounds, H2S and water vapor are the most corrosive compounds. The H2S can be converted into SO2 and SO3 during the biomethane combustion, and consequently damage turbines and other necessary equipment. The water vapor in biomethane reacts with H2S, NH3, and CO2 to form corrosive acids (Ryckebosch et al., 2011). Thus, they must be removed before the biomethane is sent to the boiler or combustion chamber for heat and electricity generation. The typical biomethane upgrading process includes three steps consisting of water scrubbing and regeneration, cryogenic separation, and physical absorption. The electricity demands for the individual cleaning steps are listed in Table II-5 (Sun et al., 2015). Depending on the engine units, they can be configured differently. The Brayton cycle (gas turbine) requires fuel gas and 40  air to be mixed in the burner and directly expanded in the turbine, so that it requires all three steps to clean up the biomethane and protect the turbine. The Rankine cycle (steam turbine) does not require direct contact between the biomethane and turbine, so a single step treatment of water scrubbing and regeneration is a suitable clean-up method for steam turbine application.   Table II-5. Energy consumption for biomethane cleaning Cleaning technology Electricity consumption (kWh/normalized m3 biomethane) Water scrubbing and regeneration 0.275 Cryogenic separation 0.24 Physical absorption 0.25  To calculate the electricity consumption required to treat the amount of biomethane from the studied thermophilic digester (Table II-4), the following conversion equation was used to determine the effect of temperature on normalized biomethane volume from Table II-5.         (II-20) where ; ; ; and . The calculation data show that the electricity demands for biomethane cleaning for the solarbio hybrid gas and steam turbine systems were 2.517 MJ/m3 and 0.9048 MJ/m3 biogas (containing 58.6% biomethane), respectively.    3.3. Selection of solar thermal collectors for the hybrid systems The selection of solar thermal collectors for the solarbio hybrid systems was based on the desired temperature of the heating fluid for the steam and gas turbines. The central tower, 41  parabolic dish, and parabolic trough are the three most popular solar thermal collection technologies (Jamel et al., 2013; Popov, 2014; Siva Reddy et al., 2013). Central tower solar collection can generate extremely high temperatures (above 1,000 °C), but requires a large footprint to accommodate the solar reflectors, which is not suitable for small-scale solar power generation. Parabolic dish solar thermal collection also generates high temperatures (500900 °C). However, parabolic troughs generate medium temperatures (200400 °C), so are more suitable for small-scale solar power generation (Siva Reddy et al., 2013). For the small-scale solarbio hybrid power generation systems, considering the required temperature of the heating fluid for steam (200 °C) and gas turbines (840 °C), parabolic trough collectors were selected to be integrated with the steam turbines and parabolic dish collectors with the gas turbines.  It has been reported that the optical efficiencies for parabolic trough and parabolic dish are approximately 0.76 and 0.93, respectively (Giostri et al., 2013; Siva Reddy et al., 2013). The solar concentration ratio () is another important parameter for solar thermal collectors, and is expressed as the absorber area () vs. the collector area (). The numbers of 70 and 750 are used as the concentration ratios for parabolic trough and parabolic dish collectors (Siva Reddy et al., 2013; Skouri, Bouadila, Ben Salah, & Ben Nasrallah, 2013).  Based on the collector type, working fluid temperature, and solar concentration ratio, the solar energy can be calculated by the following equation:    (II-21) where  is the solar heat required (MJ/day);  is the optical efficiency;  is the collector area (m2);  is the direct normal irradiance (MJ/m2·day);  is the solar operating factor (which, for parabolic trough and parabolic dish collectors, is 0.878 and 0.429, respectively, at Lansing and 0.934 and 0.4752, respectively, at Phoenix);  is the absorber emittance (0.27, 42  stainless steel Type 312 (M. F. Modest, 2013));  is the Stefan-Boltzmann constant (5.67 × 10-8 W/m2·K4);  is the absorber area (m2);  is the ambient temperature (K);  is the convective coefficient (8 W/m2·K);  is the solar energy collection time (which, for the parabolic dish and parabolic trough collectors is 5.65 and 5.88 h per day, respectively, at Lansing; and 9.66 and 9.69 h per day, respectively, at Phoenix); and assumed to be 25% higher than the maximum temperature of the working fluid (water or air) in the system. The solar operating factor () is defined as the ratio of direct normal irradiance that can be used by the solar collection technology for electricity generation, and is calculated as the ratio of the total thermal power produced and the absorbed thermal energy. The  values were obtained using the software System Advisor Model (NREL, 2016b).  In addition, the working fluids (water and air) have a large impact on the thermal efficiency of the heat exchanger (). The overall heat transfer coefficient (the capability of the heat exchanger to transfer thermal energy) is several orders of magnitude higher for water than for air , and the thermal efficiency of air is correspondingly lower than that of water. The  values for air and water were selected as 0.70 and 0.85, respectively, in this study. Therefore, the heat that the working fluid transfers from the absorber to the boiler and burner can be calculated as                  (II-22) where  is the energy transferred (MJ/day) from the absorber to the working fluid; and  is the thermal efficiency of the heat exchanger.  Under the conditions of the coldest winter day and a net capacity factor of 0.5, the solar collector area required by the solarbio hybrid systems to generate 30 kW electricity can be calculated using Equations 24 and 25 (Table II-6). Because Phoenix has a much higher ambient 43  temperature and DNI than Lansing year-round, the required solar collector areas at Phoenix for steam and gas turbines were 180.4 m2 and 330.1 m2, respectively, much smaller than those in Lansing, which for steam and gas turbines were 1,034.8 m2 and 1,502.1 m2, respectively.   Table II-6. Required solar collector areas for steam and gas turbines at Lansing and Phoenix on the coldest winter day for a net capacity factor of 0.5 Location Solar collector area (m2) Steam Gas Lansing 1,034.8 1,502.1 Phoenix 180.4 330.1  Based on the selected solar collector area at the coldest time, the monthly net capacity factors were simulated for both systems at Phoenix and Lansing (Figure II-5). Since the coldest time of the year is used as a reference state to select the solar collector area, the solar thermal energy generated during most of the year exceeds the value for the minimum heat requirements. The biomethane is therefore used to extend the operating hours of the power generation system, and the net capacity factor is correspondingly increased. In the warm climate location (Phoenix), during the month of July, which has the highest ambient temperature, the net capacity factors for the steam and gas turbine systems were increased by 13.82% and 24.50%, respectively (Figure II-5b). In the cold climate location (Lansing), the net capacity factors changed more dramatically. During July, the net capacity factors for the steam and gas turbine systems were increased by 70.88% and 95.82%, respectively (Figure II-5a).  44   (a)  (b) Figure II-5. Effects of location and month on the net capacity factor of the solarbio hybrid power generation system: (a) Lansing; (b) Phoenix.  4. Discussions The system analysis shows the relationship between the net capacity factor, bioreactor volume, solar thermal utilization, and geographic location for both the Brayton and Rankine cycles. According to the system configurations (Figure II-1), the highest temperatures required for individual thermal cycles determine the solar collector technologies that can be integrated  0,40 0,50 0,60 0,70 0,80 0,90 1,00JanFebMarAprMayJunJulAugSepOctNovDecNET CAPACITY FACTOR MONTH Steam turbineGas turbine 0,40 0,45 0,50 0,55 0,60 0,65 0,70JanFebMarAprMayJunJulAugSepOctNovDecNET CAPACITY FACTOR MONTH Steam turbineGas turbine45  into the solarbio hybrid power generation systems. In the case of the steam turbine (Rankine cycle), the maximum temperature (turbine inlet) is 200 °C (Figure II-1b), which can be achieved by medium-temperature solar thermal technologies, such as the parabolic trough proposed by this study. However, the working fluid in the gas turbine (Brayton cycle) needs to be heated by solar thermal energy from 533 °C at the outlet of the regenerator to 840 °C before entering the burner (Figure II-1d). High-temperature solar thermal technologies, such as the parabolic dish selected by this study, are required to satisfy the need of such a high temperature increase. However, 840 °C is at the higher end of the temperature range that conventional parabolic dishes (with a reflector area ranging from 43 m2 to 117 m2) can achieve (Baharoon, Rahman, Omar, & Fadhl, 2015; Mancini et al., 2003). This is a limiting factor for the further increase of solar thermal energy utilization in the gas turbine hybrid system. Although it is theoretically possible to raise the temperature at the absorber of a parabolic dish to above 1,000 °C by extending the reflection area, fabricating such large parabolic dishes may pose certain manufacturing and installation difficulties, as well as economic barriers for small-scale applications. Since the solar radiation and ambient temperature vary significantly between seasons and locations (Figure II-2), the bioreactor volume must be large enough to produce sufficient methane to satisfy the system energy demands when the solar thermal energy is not able to fulfill the heating requirements (i.e., in the winter months at Lansing). This is the reason that the minimum solar utilization values for the system design were selected by this study based on maintaining the capacity factor of 0.5 on the coldest day of a year. Moreover, due to the thermodynamic difference in fuel efficiency between the gas and steam turbines, the required bioreactor volumes are different for the hybrid systems. The fuel efficiency for the gas turbine (27.32%) is much higher than that for the steam turbine (14.69%). The corresponding bioreactor 46  of the steam turbine hybrid system is approximately 2.95 times larger than that of the gas turbine hybrid system (Table II-4). In addition, as mentioned previously, the ambient temperature and solar radiation have a strong influence on the configuration of hybrid systems. The simulation results demonstrated that the solarbio hybrid steam turbine system required a smaller solar collector area (1,034.8 m2 and 180.4 m2 for Lansing and Phoenix, respectively) than the gas turbine system (1,502.1 m2 and 330.1 m2 for Lansing and Phoenix, respectively) (Table II-6). This is mainly caused by the low value of the solar operating factor for the gas turbine systems. The solar collector area must be over-sized to satisfy the energy demand of the working fluid when the direct normal irradiance is weak during the winter months. Considering the fact that a smaller footprint is desirable for small-scale systems, the solarbio hybrid steam turbine power generation with a smaller solar collector area is thus preferred The overall energy balance for the coldest and hottest months at the two locations elucidates the comprehensive energy distribution profiles for both systems (Figure II-6). Because of the low thermal efficiency of the steam turbine, the solarbio hybrid steam turbine system (245.33 kW) demanded 2.23 times more heat than the hybrid gas turbine system (109.83 kW) to generate 30 kW electricity (Tables II-2 and II-3). The steam turbine hybrid system had a higher ratio of heat generation to total energy input (0.5487) than the gas turbine hybrid system (0.4143); and the corresponding heat generated for the steam and gas turbine hybrid systems was 134.61 kW and 45.50 kW, respectively. During the coldest winter month, the heat was completely used to maintain the culture temperature of the anaerobic digestion for biomethane production and ensure the generation of the target electricity amount.  47  During the hottest summer month, extra heat was generated from both systems in both locations (Figure II-6a, c, e, and f). In addition, although the fuel efficiency of the gas turbine is higher than that of the steam turbine, the global efficiencies (electricity and heat outputs vs. biomethane and solar energy inputs) of the solarbio hybrid steam turbine system (47.75% in July and 49.00% in December at Lansing, 58.13% in July and 58.92% in December at Phoenix) were significantly higher than those of the solarbio hybrid gas turbine system (21.52% in July and 23.64% in December at Lansing, 30.84% in July and 32.69% in December at Phoenix). Moreover, due to the temperature differences between winter and summer for both locations, the larger temperature difference requires larger solar collectors and correspondingly more heat. The hybrid steam and gas turbine systems located at Lansing generate 38.9% and 45.9% more heat, respectively, than those located at Phoenix. As for electricity generation, the solarbio hybrid steam turbine system requires more biomethane to maintain the net electricity output of 30 kW. The parasitic electricity energy required by the hybrid steam turbine system (279 MJ/day and 347 MJ/day for Lansing and Phoenix, respectively) was higher than that required by the hybrid gas turbine systems (249 MJ/day and 310 MJ/day for Lansing and Phoenix, respectively), although the gas turbine requires more electricity to clean up the biomethane for power generation. In addition, the systems at the location with lower solar thermal utilization (i.e., Phoenix) require more biomethane energy, and correspondingly increase the consumption of parasitic electricity, which leads to a lower net electricity output (Figure II-6). The analysis in this study is based upon the use of solar thermal energy as a supplemental energy source to facilitate the utilization of the biofuelbiomethane, and indirectly improve the power generation performance of the system. As a matter of the fact, the net capacity factor can be significantly increased if the solar thermal energy can be utilized directly as a single energy 48  source in the thermodynamic cycle for several hours per day (once solar radiation is able to bring the working fluid to the desired temperatures for the gas and steam turbines). Further studies are needed to explore such scenarios.   Figure II-6. Energy balance of small-scale solarbio hybrid power generation systems*          (a) (b) 49  Figure II-6.      (c) (d) (e) (f) 50  Figure II-6.   *: (a) Steam power generation system in Lansing in July; (b) steam power generation system in Lansing in December; (c) gas power generation system in Lansing in July; (d) gas power generation system in Lansing in December; (e) steam power generation system in Phoenix in July; (f) steam power generation system in Phoenix in December; (g) gas power generation system in Phoenix in July; (h) gas power generation system in Phoenix in December. DSR: available direct solar radiation; Biomethane: energy obtained from biomethane combustion; SC: solar collector subsystem; PGS: power generation subsystem; Thermal losses: losses in the solar collector due to radiation, convection, and solar operating factor influence; Optical losses: losses in the solar collector due to absorptivity of the reflector and reflectivity of the absorber; Irreversible losses: energy losses in the heat transfer equipment; EG: electricity generation in the PGS; NEG: net electricity generation; HG: heat generation in the PGS; AD: (g) (h) 51  electricity required in the anaerobic digestion subsystem; and Extra heat: heat generated in the power generation system not used by the anaerobic digestion process.  5. Conclusions This study carried out a comprehensive analysis on small-scale solarbio hybrid power generation (30 kW). The relationship between net capacity factor, solar utilization efficiency, and biomethane utilization efficiency has been determined. The analysis demonstrated that the hybrid steam turbine system had better global thermal efficiency (54.87%) than the hybrid gas turbine system (41.43%), although the electricity generation efficiency of the hybrid steam turbine system (14.69%) was lower than that of the hybrid gas turbine system (27.32%). Moreover, the global efficiencies of the solarbio hybrid steam turbine system were significantly higher than those of the solarbio hybrid gas turbine system, regardless of location. It was found from the analysis that, in order to reduce the system footprint, the hybrid steam turbine is preferable to the hybrid gas turbine system.    52  CHAPTER III. A SELF-SUSTAINING WASTEWATER TREATMENT PLANT INTEGRATING SOLAR TECHNOLOGIES, ANAEROBIC DIGESTION, AND AEROBIC TREATMENT  Abstract This chapter focuses on system analysis of the self-sustaining wastewater treatment concept combining solar technologies, anaerobic digestion, and aerobic treatment to reclaim clean water. A solar bio-hybrid power generation unit was adopted to power the wastewater treatment (with a volume of 76 m3 influent per day for the studied case). The results showed that the synergistic integration of biogas and solar energy generation could satisfy the power demands of the wastewater treatment. Concentrated solar power (CSP) and photovoltaics (PV) were compared for the solarbio hybrid power generation at two locations (Lansing and Phoenix). With short-term solar energy storage (a battery for PV and molten salt for CSP), the PV-bio hybrid power unit requires a smaller solar collection area and biogas storage than the CSP-bio hybrid power unit regardless of location. In addition, using biogas to store the extra energy generated by the solarbio hybrid unit during the warm months enables the year-round wastewater treatment operation to be completely self-sustainable. It was determined from the energy balance analysis that the PV-bio hybrid power unit is the preferred energy unit to realize the self-sustaining wastewater treatment. Appendices for this chapter: i. Appendix D: Matlab code for solarbio hybridization for anaerobic digestion and aerobic treatment ii. Appendix E: Matlab sub-functions for solarbio hybridization for anaerobic digestion and aerobic treatment  53  1. Introduction It has been reported by the United Nations Environment Programme (UNEP) that two billion tons of sewage as well as industrial and agricultural wastewater is discharged into the % of all wastewater in developing countries is directly discharged untreated into rivers, lakes, and the ocean. The wastewater has affected approximately 245,000 km2 of marine ecosystems (Corcoran, UNEP, & Arendal, 2010). In addition, methane and nitrous oxide from the degradation of organic matter in the wastewater greatly contribute to global greenhouse gas emissions. On the other hand, the wastewater is rich in organic matter, which represents a good carbon and nutrient (P and N) source for microbes to synthesize energy and chemical products. However, fecal matters and low nutrient concentrates in the wastewater present certain technical challenges to recover the nutrients and utilize them for energy and chemical production. New scientific and engineering solutions seek to address the challenge of transforming the wastewater from a major environmental and health hazard into a clean and environmentally attractive resource through technical and economical means. Current wastewater treatment technologies mainly rely on aerobic treatment (AET) in which aerobic microbes metabolize the soluble and colloidal organics, which flocculate and settle out so that reclaimed water is achieved (Wang et al., 2009; Water Environment & ebrary, 2008). However, the energy-intensive aeration operations of current aerobic treatment practices (the carbon is not balanced, and additional carbon from the energy sources is consumed to clean up the water) still lead to a relatively large carbon footprint. Therefore, next-generation wastewater treatment technologies must be carbon neutral, robust, and self-sustainable. Compared to conventional aerobic treatment, anaerobic digestion (AD) is another biological means that is able to simultaneously treat wastewater and generate bioenergy, and has the 54  potential to be further developed into a carbon neutral process (Sun et al., 2015). However, due to the microbial community structure and their metabolic pathways, the growth of anaerobic microbes is much slower than aerobic microbes, so that the nutrient removal of AD is not very efficient, and the wastewater cannot be reclaimed completely. It has been demonstrated that integrating anaerobic and aerobic treatments to treat wastewater is an effective approach to take advantage of both systems (i.e., capability of handling high-strength wastewater and its high energy production, and efficient nutrient removal). It can thus be used to completely reclaim water from a wide range of organic wastewater streams (Deshpande, Satyanarayan, & Ramakant, 2012; Martin, Pidou, Soares, Judd, & Jefferson, 2011; Novak, Banjade, & Murthy, 2011; Zhou et al., 2015). Although the AD in the integrated system can provide a certain amount of energy to support the operations, the integrated system, including biogas cleaning and upgrading, maintaining the temperature of AD, and aeration of AET demands more energy than can be provided by the biogas energy of the AD. Therefore, in order to develop a self-sustaining wastewater, additional energy sources are required.  In response to this need for a hybridization treatment system, a second renewable energy source is needed to satisfy the energy demand. A power generation concept using biogas and solar energy is investigated in this study. In the past decades, many solar energy conversion technologies, such as evacuated-tube solar thermal collectors, parabolic trough systems, central tower systems, dish solar systems, Fresnel reflectors, and photovoltaic cells have been developed (Mills, 2004). They are mainly classified into two categories: solar thermal and electrical (PV) conversion. In this study, both types were studied. The parabolic trough collector was selected as the solar thermal conversion technology, due to the fact that its temperature is compatible with the steam generation system (< 400 °C (Siva Reddy et al., 2013)). In addition, PV cells were 55  investigated as the solar electric conversion technology, considering their simplicity for direct electricity generation. One of the key criteria for the hybridization power system is that the energy sources of solar and biogas energy must be balanced for a continuous power supply to satisfy the wastewater operation need. Therefore, the solar collection area (for CSP and PV) must be determined to match the storage needs of biogas for year-round operation. The objectives of this study were to model a solarbio hybrid wastewater treatment that could self-sustainably reclaim agricultural wastewater, and to understand the effects of the seasonal and temporal variation (direct normal irradiance and global horizontal irradiance) on the energy uses of the solarbio hybrid wastewater treatment system.  2. The solarbio hybrid wastewater treatment  2.1. Anaerobic digestion (AD) The simulation of the AD of animal manure and food waste was based on the data obtained from a commercial anaerobic digester located at Michigan State University (MSU) south campus (42.6988, -84.4880). The animal feed of the dairy farm consisted of alfalfa and corn silage blended according to the Natural Research Council Rations (TMRs) for dairy cattle. The food waste came from dining halls at MSU campus. The digester is a completely stirred tank reactor (CSTR), operated at a temperature of 40 °C and with a retention time of 25 days. The characteristics of the feedstock are listed in Table III-1. The animal manure and food waste were collected in two pits with volumes of 7 m3 and 12 m3. The waste in the pits was ground and diluted with the filtrate to reach an average of 8% total solids, and pumped into a mixing tank (with a volume of 27 m3). The mixed AD influent was then pumped into the digester (with a volume of 1,570 m3). In order to maintain the culture 56  temperature, a heating loop was installed to circulate the hot water continuously (heated by the power generation system) to the digester. A double high-density polyethylene (HDPE) membrane covers the top of the digester. The AD effluent was separated by a liquid/solid separator to obtain AD fiber and liquid filtrate. A conveyor moved the wet AD fiber to a storage barn, and the liquid filtrate was transferred to a tank for the secondary treatment (Figure III-1).   Table III-1. Feedstocks of the anaerobic digester Description Total solids (%) Volatile solids (%) pH Animal manure A 9.9 ± 1.3 8.3 ± 1.2 7.13 ± 0.98 Food waste B 8.5 ± 2.8 7.7 ± 2.4 4.60 ± 0.82 Mixed AD influent C 8.5 ± 2.2 7.2 ± 1.9 6.21 ± 0.93 A: Data are the average of 25 samples with standard deviation. B: Data are the average of 24 samples with standard deviation.  C: Data are the average of 45 samples with standard deviation.  2.2. Biogas upgrading The mass balance and energy consumption of the biogas upgrading was based on the literature (Ryckebosch et al., 2011; Sun et al., 2015). The raw biogas was cleaned and upgraded using a two-stage process of water scrubbing and cryogenic separation to remove humidity, CO2, and other chemical compounds. The upgraded biogas was stored in a metallic heavy-duty tank to be used as the fuel for the power generation.   57  2.3. Aerobic treatment (AET) After the solid/liquid separation, the AD effluent (filtrate) was further treated by a conventional AET operation (Figure III-1). The simulation of the AET was based on the laboratory and literature data. The filtrate entered into the aeration chamber, where the dissolved oxygen concentration was maintained between 12 mg/L (EPA, 2000; Wang et al., 2009). The daily operation consisted of two batches (12 hours operation time). The AET effluent was pumped into a clarifier tank where solids were settled out and recycled back to the AD. The reclaimed water after the clarification, which satisfied the EPA discharging standard, was then used for other non-potable agricultural applications.    Figure III-1. Flow diagram for a conventional anaerobic/aerobic digestion process  2.4. Analytical method for AD and AET The methane and carbon dioxide content were quantified using a SRI 8610c gas chromatograph (Torrance, CA). The system was equipped with a thermal conductivity detector. The detector was maintained at 150 °C during the analysis. Hydrogen and helium were carrier 58  gases, and maintained at 21 psi. The biogas sample volume was 100 µL, and the syringe was purged three times before sample injection. The chemical oxygen demand (COD), total phosphate (TP) and total nitrogen (TN) of the animal manure and food waste, AD effluent, and liquid filtrate were measured using Hach methods. The total solids (TS) and volatile solids (VS) were analyzed using the methods developed by the National Renewable Energy Laboratory (NREL).  2.5. Solarbio hybridization of power generation  2.5.1. Solarthermalbio hybridization power generation The solarbio hybridization is shown in Figure III-2a. The energy requirements (thermal and electrical) of the wastewater treatment were set to be provided by steam power generation. A concentrated solar collector (CSP) was installed to collect and transfer solar energy into a working fluid to preheat the feedwater. The preheated water was then sent into the boiler to produce superheated steam using the upgraded biogas as the fuel. The steam was then expanded in the turbine, generating shaft work that was used as an electric generator. The expanded steam was cooled and condensed, in order to be returned to the feedwater tank to continue with the cycle. The extracted thermal energy was used to maintain the AD temperature.   59  (a)                                                                                (b) Figure III-2. Components of energy generation combining biomethane and solar concentrated energy: (a) concentrated solar power, (b) photovoltaic panels  The power generator consisted of a 325 kWe steam turbine that was designed to accommodate the use of both biogas and solar energy. The heat input () required to satisfy the temperature and pressure of the superheated steam, is calculated as                                                                            (III-1) where  is the turbine efficiency (thermal to electrical energy); and  is the heat exchanger () efficiency (set at 0.85), or the fuel-to-steam efficiency (). The thermal energy extracted in the condenser () is defined as follows:                                                          (III-2) where  is the condenser efficiency. The parasitic energy required by the power generation system was set at 5% of the designed electricity power output (16.25 kWe), which considers the energy consumed by pumps, gas fans, and miscellaneous equipment for the operation. The parameters for the steam turbine are summarized in Table III-2. 60  Table III-2. Operational parameters of 325 kW steam turbine Parameter Value Unit Maximum electricity output 390 kWe Minimum electricity output 81.25 kWe Turbine efficiency 0.35 - Design heat input  928.57 kWt Maximum heat input 1,111.2 kWt Minimum heat input 275.62 kWt Thermal energy extracted 464.2 kWt  The steam was generated by a commercial boiler, model CBEX Elite 125 BHP (Cleaver-Brooks, 2011). For load capacities of 25%, 50%, 75%, and 100%, the fuel-to-steam efficiencies were 84.2%, 84.7%, 84.6%, and 84.4%, respectively. An average fuel-to-steam efficiency of  = 84.48% was considered for the thermal energy input calculation ( includes convection and radiation losses, combustion efficiency, heat exchanger efficiency, and 15% excess air in the exhaust flue gas for the selected model).  In addition, the relationship between electricity generation and thermal energy input can be expressed by a polynomial equation (NREL, 2016b) as follows:        (III-3) where  is the electrical power generated (kWe);  is the input thermal energy (kWt);  are coefficients for turbine modeling (-0.0572; 1.0041; 0.1255; -0.0724, respectively). The extracted thermal energy in the condenser can also be defined by the polynomial equation: 61          (III-4) Siemens SunField solar collector assembly (SCA) parabolic reflectors (aperture reflecting area 6 m2, average focal length 1.5 m) were selected as the solar collectors. The heating collection elements (HCE) consisted of model 2008 Schott PTR70 vacuum tubes. The optical factors for the SCA and HCE are listed in Table III-3.   Table III-3. Optical factors for CSP collection Parameter Value Tracking error 0.99 Geometric accuracy 0.968 Surface reflectance 0.925 Concentration factor 0.97 Cleanliness factor 0.98 Shadow factor 0.95 Transmissivity 0.96 Absorptivity 0.96  A single-axis tracing system (the trough is placed from east to west) was used to concentrate solar radiation into vacuum tubes, where synthetic oil (working fluid) absorbed and transferred the thermal energy. The heated synthetic oil was then used to preheat the feedwater before the boiler. Two buffer tanks (hot and cold storage) were used to store the thermal energy and heat the feedwater.   62  2.5.2. Solarthermalbio hybridization power generation The PV-electricity-bio hybridization power unit was also studied to supply extra electricity energy instead of thermal energy to the wastewater treatment system (Figure III-2b). The analysis was performed by modeling the installation of panels, model SolarWorld SW235 mono, 60 cells per module, 30° tilted, degradation of 0.5% per year, and maximum power of 235 W under reference conditions (cell temperature at 25 °C and 1000 W/m2 of solar radiation). The nominal operating cell temperature (NOCT) was used to quantify the energy generation under different solar radiation values. System losses include losses in the DC and AC energy conversion, such as in the diodes and connections (0.5%), DC wiring (2%), soiling (5%), AC wiring (1%), and transformer (1%).   3. System analysis  3.1. Mass balance of the wastewater treatment A mass balance was conducted to evaluate the system performance. The operational parameters for the anaerobic digester used for the mass balance analysis are listed in Table III-4. The AD system generated 2,919.9 m3/day of biogas, 11.41 m3/day of solid digestate (AD fiber), and 64.66 m3/day of liquid filtrate under the conditions of 25 days hydraulic retention time (HRT) and a digestion temperature of 40 °C (Figure III-3). The corresponding TS and COD removal were 41% and 62%, respectively. However, there was still a significant quantity of nutrients remaining in the filtrate, particularly TN (4,290 mg/L) and total soluble solids (23,734 mg/L) (Table III-5). Further treatment was needed to reclaim the water for other uses.   63  Table III-4. Performance of anaerobic digestion Description Unit Value Operating temperature °C 40 Hydraulic retention time day 25 Feed pH A - 6.22 ± 0.93  Feed COD B mg/L 133,250 ± 21,173  Biogas production m3/day 2,919.9 Methane composition - 0.60 Daily waste feeding  m3/day 76.07 Liquid filtrate  m3/day 64.66 Solid digestate (AD fiber) m3/day 11.41 Average energy demand for the AD operation kWh/day 1,276 A: Data is the average of 45 samples with standard deviation. B: Data is the average of 8 samples with standard deviation.  Table III-5. Characteristics of the AD effluent, AD fiber, and filtrate* Sample Parameter Value Number of samples AD effluent Total solids (%) 5.04 ± 1.51 125 Total soluble solids (mg/L) 28,553.30 ± 8,896.92 37 Volatile solids (%) 3.85 ± 1.30 125 COD (mg/L) 51,183.3 ± 1,874 6 TP (mg/L) 538 ± 22 2 TN (mg/L) 3,909 ± 832 16  64  Table III-5.  AD effluent pH 7.82 ± 0.22 135 AD fiber Total solids (%) 25.41 ± 3.60 57 Volatile solids (%) 22.42 ± 3.24 57 Filtrate Total solids (%) 3.68 ± 0.75 58 Total soluble solids (mg/L) 23,734 ± 3,227 7 COD (mg/L) 47,250 ± 3,106 8 TP (mg/L) 427 ± 5 2 TN (mg/L) 4290 ± 788 9 pH 7.86 ± 0.16 56 *: Data are the average with standard deviation.   The AD filtrate was then treated by the AET process, including an aeration chamber and clarifier tank (Figure III-1). The minimum nutrient removal requirement for secondary treatments is shown in Table III-6 (Federation, 2009), as well as the water quality standard for agricultural use (Lazarova & Bahri, 2005). According to these parameters, the total soluble solids (TSS), COD, TP, and TN in the influent of the AET process must be less than 250 mg/L, 400 mg/L, 15 mg/L, and 20 mg/L, respectively. Because the AD filtrate had much higher concentrations than these values (Table III-5), the AD filtrate needed to be diluted. The COD was used as the critical parameter to perform the dilution. The volume of the aeration chamber needed to treat the diluted AD filtrate (AET influent) was 5,080.98 m3 (Figure III-3).     65  Table III-6. Characteristics of liquid effluent for secondary wastewater treatment Parameter Minimum removal requirement (%) Water for agricultural uses (mg/L) TSS  90 550 COD  75 50100 TP  75 130 TN 80 1030     Figure III-3. Mass balance of the integrated anaerobic digestion and aerobic treatment  The AD treatment produced 38.37 m3 of biogas per m3 of influent wastewater per day, generating 1,751 m3 of biomethane and 11.41 m3 (wet basis) of fiber. After the AET, the system generated 32.33 m3 of reclaimed water every 12 hours of the quality applicable to agronomic uses.  66  3.2. Energy balance of the solarbio hybridization wastewater treatment  3.2.1. Electricity demands of the wastewater treatment Table III-7 shows the electricity demand by the AD operation. The electricity usage of the different equipment during the AD operation has been arranged to enable a relatively even distribution of the electricity loading throughout a day, which avoids the uncertainty of engine operation and improves the engine efficiency. The average electricity demand for the AD operation was 293 kW (Figure III-4).   Figure III-4. Daily electricity demands of the wastewater treatment  Table III-7. Electrical energy consumption by the anaerobic digestion system Location Equipment Power (kW) Operating time (hours/day) Food waste pit Pump 13.35 1 Mixer 22.38 1 Animal manure pit Pump 29.84 1 Mixer 11.19 24 050100150200250300350400123456789101112131415161718192021222324ELECTRICITY REQUIREMENT (KW) TIME (HOUR) AD influent/effluent handlingBiogas water scrubbingAerationBiogas cryogenic separationTotal67  Table III-7.  Mixing tank Grinder 5.60 5 Pump 11.19 5 Mixer 2.98 24 Digester Mixer 22.38 17 Mixer 22.38 18 Fan 0.18 24 Heating unit Pump 7.46 24 Solid/liquid separator Pump solid separator 14.92 3 Pump filtrate 7.46 1 Scrub Motor 7.46 3 Solids conveyor 0.75 3   The biogas cleaning and upgrading had the highest electricity requirements. It has been reported that the electricity demands of water scrubbing and methane cryogenic separation are 0.275 kWh/Nm3biogas and 0.35 kWh/Nm3biogas, respectively (Sun et al., 2015). The effect of temperature on normalized biogas volume is expressed as follows:                                                                (III-5) where ; ; ; and . Equation (III-5) was then used to calculate the conversion factor between real biogas and normalized biogas. The electricity demands for water scrubbing and cryogenic separation were 1.068 MJ/m3biogas and 1.359 MJ/m3biogas.  68  As for the AET operation, it has been reported that the aeration ranges from 3.75 to 15 m3air/m3influent in order to maintain the dissolved oxygen concentration between 12 mg/L (Wang et al., 2009). An intermediate value of 9.375 m3air/m3influent was selected by this study to carry out the energy analysis. Since the volume of each AET operation was 5,080 m3 influent each 12 hours, the aeration rate needed to be 1.103 m3 air/s (0.013 m3 air/ m3 influent per min) to satisfy the required dissolved oxygen concentration. The power for the air compressor can be correspondingly calculated as                                                            (III-6)                                                    (III-7) where  is the air flow requirement (m3air/s);  is the compressor efficiency (0.90);  is the ratio between the specific heat at constant pressure and the specific heat at constant volume (= 1.4); is the atmospheric pressure (101,000 Pa); and  is the outlet air pressure (303,000 Pa). The compressor requires 159.70 kW to provide the air needed for the process. Figure III-4 indicates that aeration is the largest energy consumer among the unit operations of the wastewater treatment.  3.2.2. Thermal energy requirements of the wastewater treatment Thermal energy is needed by the anaerobic digestion to heat the feed and maintain the culture temperature at 40 °C. The energy requirement per day ( (MJ/day)) is calculated as follows (Yue et al., 2013):      (III-8) 69  where  is the digester volume (m3);  is the hydraulic retention time (days);  is the feed density (1220 kg/m3);  is the feed specific heat (4,120 J/kg·°C);  is the culture temperature (40 °C);  is the feed temperature and assumed to be the same as the ambient temperature when the ambient temperature is above 4 °C (the feed temperature is set at 4 °C when the ambient temperature is below 4 °C); and 0.3 is the additional heat that is needed to maintain the mesophilic culture condition of the digester. Due to the lower atmospheric temperature year-round in Lansing, the thermal energy needed to maintain the AD culture was an average of 323,099 MJ for the operation, which was almost double that in Phoenix (153,182 MJ) (Figure III-8).   3.2.3.  Energy generation In the studied systems, the AD, as the first stage of the wastewater treatment, generates energy that is used for the treatment system. However, the generated electricity (5,548.14 kWh/day with the AD on 76 m3influent per day) is still insufficient to cover the energy demand (7,032 kWhe/day) of the wastewater treatment system, owing to the high electricity demand of the AET operation. Solar energy was then added into the system as the secondary energy source.  Since solar energy collection is largely influenced by the geographical location and season, a year-round and hourly-based analysis was carried out at the two locations (Lansing, MI and Phoenix, AZ) to compare the energy generation of the solarbio hybrid unit at different seasonal and geographical conditions. Figure III-5 shows the variation of solar radiation (Direct Normal Irradiance (DNI) and Global Horizontal Irradiance (GHI)) and ambient temperature during a year for both locations (NREL, 2015). The DNI is the amount of solar radiation received by a surface held perpendicular to the rays that arrive in a straight line from the 70  direction of the sun; DNI is of particular interest to concentrating solar thermal installations, such as parabolic troughs. GHI is the amount of solar radiation received by a surface horizontal to the ground, and consists of a combination of direct and diffuse solar radiation. GHI is used for static collection systems, such as photovoltaic panels. Phoenix has much higher DNI, GHI, and atmospheric temperature than Lansing. However, the ratios between DNI and GHI are different for the two locations. Lansing has a higher GHI than DNI, while Phoenix has a higher DNI (Figure III-5).     (a)                                                                                     (b) Figure III-5. Variation of the ambient temperature ), DNI, and GHI for: (a) Lansing; (b) Phoenix  The parabolic trough collectors use SCA and HCE to collect and transfer solar heat via the HTF to support electricity production. The optical efficiency was calculated ( from Table III-3), and the energy loss of HTF can be obtained as     (III-9) -10-50510152025303540050100150200250300123456789101112Temperature (°C) Energy (kWh/m2) Month DNIGHIT amb0510152025303540050100150200250300123456789101112Temperature (°C) Energy (kWh/m2) Month DNIGHIT amb71  where  is the heat loss in the piping system (kW);  are coefficients (0.001693, -1.68 × 10-5, 6.78 × 10-8);  is the average temperature of the working fluid for this study (325 °C);  is the ambient temperature (°C);  is the reference heat loss in the piping system when  (10 W/m2SCA); and is the area of the SCA (m2). Furthermore, heat loss in the HCE has been documented as  for the selected vacuum tube model (NREL, 2016b). The net thermal energy collected from the SCA () is then calculated as                 (III-10) where  is the direct normal irradiance (kW/m2). The net heat used for steam generation is obtained as . Equation (III-3) is used to calculate the electricity generation.  The electricity load of the wastewater treatment (Figure III-4) is compared hourly with the electricity generation from the solarbio hybrid unit. In the hybrid configuration, if the energy amount collected from the DNI is insufficient to satisfy the superheated steam demand of the turbine for electricity generation, biogas is burned to compensate the energy deficiency and generate extra superheated steam (Colmenar-Santos et al., 2015; Sun et al., 2015). If the energy quality (temperature) collected from the DNI is lower than the requirement for superheated steam generation, the energy collected in the SCA is then used to preheat the feedwater for the boiler and reduce the biogas demand during the superheated steam generation. It is apparent that combining biogas and solar energy can synergistically mitigate the issues of unstable solar energy flow and limited biogas production.  The PV-bio hybrid power unit functions differently from the CSP-bio hybrid unit to provide electricity to the wastewater treatment system (Figure III-2b). Biogas is the thermal 72  energy source of the power unit and is only utilized when the electricity from the PV (after DC to AC conversion, parasitic, and system losses) is insufficient to cover the electricity demands of the system (Figure III-4).  In order to understand the performance of the solarbio hybrid power unit to satisfy the energy demands of the wastewater treatment, two scenarios of electricity generation with and without short-term solar energy storage were analyzed.  3.2.3.1. Electricity generation without short-term solar energy storage A solar collection system without solar energy storage means that both thermal heat from CSP and electricity from PV are directly used by the solarbio hybrid unit for energy generation when DNI and GHI are available.  For the CSP-bio hybrid power unit, the hourly energy required from biogas () is calculated as the difference between the hourly thermal energy required to generate the needed electricity (), and the hourly thermal heat collected from solar radiation () (Equation III-11.a). However, the biogas energy needed for the PV-bio hybrid unit is the thermal energy required by the turbine to generate the electricity that compensates the insufficient electricity from the PV () (Equation III-11.b).                                                            (III-11.a)                                                                (III-11.b) The solar operation factor (SOF) is a critical parameter to determine whether the solarbio hybrid unit is a feasible solution to power the integrated AD and AET process. The SOF is defined as the time when CSP or PV units can collect net useful energy (the energy from biogas 73  and solar energy collected after thermal and electricity losses to fulfill the minimum requirements of the solarbio hybrid unit).  Since the solarbio hybrid units need to provide a minimum energy input of 324.3 kWt (including , Table III-2) to power the combined AD and AET processes, was used to calculate the biogas daily balance of the solarbio hybrid units. A positive biogas daily balance (, m3biogas/day, the biogas amount required to generate ) means that extra biogas is produced and can be stored for use at night or on cloudy days. A negative balance indicates that the daily biogas production is insufficient to cover the electricity demands of the wastewater treatment. An iterative approach was then applied to calculate the annual biogas balance. The annual biogas balance was used to evaluate the performance of the solarbio hybrid power units. The CSP-bio hybrid unit at Phoenix and the PV-bio hybrid units at Lansing and Phoenix all have positive net annual biogas balances, while the CSP-bio hybrid unit at Lansing has a negative net annual biogas balance (Figure III-6). These results indicate that PV-bio hybrid power generation works for both Phoenix and Lansing, while CSP-bio hybrid power generation only works for Phoenix. The low DNI and short daylight time during winter in Lansing are the main reasons that the CSP-bio hybrid unit cannot accumulate sufficient solar radiation to generate the required amount of the energy. It was also determined from the simulation results that in Phoenix, the  of the CSP-bio hybrid and PV-electricity-bio hybrid power units were 21,498 m2 and 6,128 m2, respectively, and in Lansing the  of the PV-electricity-bio hybrid unit was 12,030 m2 (Table III-8). These  values enable the solarbio hybrid units to store 87,304 m3biogas for the CSP-bio-hybrid unit in Phoenix, 36,175 m3biogas for the PV-bio-hybrid unit in Phoenix, and 68,507 m3biogas for the PV-bio-hybrid unit in Lansing (Table III-8). These are all larger than the corresponding biogas demands, so that self-sustaining wastewater treatment can be realized by 74  PV-bio hybrid and CSP-bio hybrid power generation in Phoenix, and PV-bio hybrid power generation in Lansing. However, since there is no short-term solar storage for the solarbio hybrid power units, a very large area of solar collection is needed to generate energy during the daylight time to save the biogas energy for use at night or when cloudy. The large collection area leads to the generation of excess electricity and thermal energy from solar collection when DNI and GHI are at their maximum values (Figure III-7).  In addition, the thermal energy generated from solarbio hybrid units is sufficient to support the heat needed by the wastewater treatment for all solarbio hybrid operations (Figure III-8). In Phoenix, the thermal energy extracted from both CSP-bio hybrid and PV-bio hybrid units is much greater that the wastewater treatment requirements. However, the thermal energy extracted from the PV-bio hybrid unit in Lansing has an improved thermal energy balance compared to that in Phoenix (Figure III-8).    (a)                                                                        (b) Figure III-6. Biogas balance without solar energy short-term storage: (a) Phoenix; (b) Lansing* *: Biogas balance at Lansing using an area of 500,000 m2 (CSP). -40000-30000-20000-100000100002000030000400001 32 60 91 121 152 182 213 244 274 305 335 Biogas volume (m3) Day CSPPV-300000-250000-200000-150000-100000-500000500001000001 32 60 91 121 152 182 213 244 274 305 335 Biogas volume (m3) Day CSPPV75  Table III-8. Biogas balance for the electricity generation (without short-term solar energy storage) Location Solar collection system Solar collection Area (m2) Biogas deficit (m3/yr) A Biogas stored (m3/yr) B Biogas stored initial volume (m3) Biogas reserved (m3) Biogas tank capacity (m3) C Phoenix CSP 21,498  84,647 87,304 31,905 2,656 76.75  PV  6,128.6 35,175 36,275 14,454 1,100  34.61 Lansing  PV  12,030.5 67,098 68,507 20,073 1,408 68.88 A: Biogas deficit is the total biogas daily requirement that exceeds the daily generation of the AD. B: Biogas stored is the non-used biogas from the daily generation in the AD. C: Tank capacity considering a biomethane compression factor of 500.   Figure III-7. Surplus electricity from solarbio hybridization without short-term energy storage  020000400006000080000100000120000140000123456789101112ELECTRICAL ENERGY (KWH) MONTH PV LANSINGCSP PHOENIXPV PHOENIX76    (a)   (b)        Figure III-8. Required and generated thermal energy for the system without short-term solar energy storage: (a) Phoenix, (b) Lansing                                                                      -2000200400600800100012001400123456789101112THERMAL ENERGY (1000 MJ) MONTH Energy to heat (PHO)PV: Energy extracted (PHO)CSP: Energy extracted (PHO)0200400600800100012001400123456789101112THERMAL ENERGY (1000 MJ) MONTH Energy to heat (LAN)PV: Energy extracted (LAN)77  3.2.3.2. Electricity generation with short-term solar energy storage Considering the large energy surplus from the solarbio hybrid units without short-term solar energy storage, it is not a technically feasible solution to use the solarbio hybrid units without short-term solar energy storage to power the wastewater treatment. Short-term solar energy storage needs to be investigated to determine the optimal conditions of solarbio hybrid power generation, so that  and the solar collection footprint can both be significantly reduced. A thermal reservoir for the CSP-bio hybrid unit and a battery bank for the PV-bio hybrid unit were used to store the extra solar energy when the DNI and GHI were higher than the requirements to fulfill the electricity demands of the wastewater treatment. The stored energy in the short-term storage was then used during the times when the DNI and GHI were not available to power the system and save on biogas usage. Thermal collection for CSP uses a massive storage tank and saves the extra energy for electricity generation in the form of sensible heat, and the thermal storage selected was one-day sensible heat storage. Electricity storage for the PV consisted of battery storage that was selected as half of the maximum daily electricity production in a year. Equation (III-11) can be modified to include the energy from thermal or electrical storage for the biogas balance.                                                            (III-12.a)                                                                (III-12.b) where  is the thermal energy stored; and  is the electrical energy stored. The size for the energy storage was based on the thermal and electrical energy over-generated in the CSP and PV installation. Thermal storage for CSP for Phoenix and Lansing was 8,851 kWht (thermal) and 26,722 kWht, and the battery bank size was 425 kWhe (electrical) and 1,236 kWhe, respectively. 78  The iteration process calculated the based on zero biogas balance in a year. It was determined from the calculations with short-term storage that in Phoenix, the required for CSP- and PV-collection was 3,054 m2 and 4,032 m2, respectively; and in Lansing, the required for CSP- and PV-collection was 6,756 m2 and 5,821 m2, respectively. Figure III-9 shows the biogas accumulation for the selected solar collection area in a year. It was found from the annual biogas balance that, in order to maintain a net positive energy balance, in Phoenix the additional biogas amounts for the CSP-bio hybrid and PV-bio hybrid power units were 135,217 m3 and 45,054 m3, respectively; and in Lansing, for the CSP-bio hybrid and PV-bio solar units, they were 292,486 m3 and 113,386 m3, respectively. In Phoenix, the calculated  allows the CSP-bio hybrid and PV bio-hybrid units to store 137,684 m3 and 46,002 m3 biogas, respectively; and in Lansing 298,098 m3 and 117,301 m3 biogas, respectively. Since the solarbio hybrid power units with short-term storage generate slightly more biogas than the requirements of the wastewater treatment, both the CSP-bio hybrid and PV-bio hybrid units are capable of handling the weather variation and support the wastewater treatment in both Phoenix and Lansing (Table III-9). In addition, the monthly surplus electricity of the solarbio hybrid units with short-term solar storage is much lower than for units without short-term solar storage (Figures III-7 and III-10). The corresponding values were much smaller than for units without short-term solar storage, which makes the solarbio hybrid units more feasible (Table III-8 and III-9).  As for the thermal energy balance, the solarbio hybrid units with short-term storage have a similar trend to the solarbio hybrid units without the storage (Figures III-8 and III-11).   79   (c)                                                                        (d) Figure III-9. Biogas balance with solar energy short-term storage: (a) Phoenix, (b) Lansing  Table III-9. Biogas balance for the electricity generation (with short-term solar energy storage) Location Solar collection system Solar collection Area (m2) Biogas deficit (m3/yr) A Biogas stored (m3/yr) B Biogas stored initial volume (m3) Biogas reserved (m3) Biogas tank capacity (m3) C Phoenix CSP 3,054 135,217 137,684 42,380 2,466 93.05 PV 4,032 45,054 46,002 15,848 475 35.43 Lansing CSP 6,756 292,486 298,098 74,920 5,612 218.13 PV 5,821.2 113,386 117,301 28,864 3,916 105.33 A: Biogas deficit is the total biogas daily requirement that exceeds the daily productivity in the AD. B: Biogas stored is the biogas non-used from the daily generation in the AD. C: Tank capacity considering a biomethane compression factor of 500.  -100000-80000-60000-40000-200000200004000060000800001000001200001 32 60 91 121 152 182 213 244 274 305 335 Biogas volume (m3) Day CSPPV-50000-40000-30000-20000-100000100002000030000400001 32 60 91 121 152 182 213 244 274 305 335 Biogas volume (m3) Day CSPPV80   Figure III-10. Surplus electricity from solarbio hybridization with short-term energy storage   (a) Figure III-11. Required and generated thermal energy for the system with short-term solar energy storage: (a) Phoenix, (b) Lansing   0300006000090000120000150000123456789101112ELECTRICAL ENERGY (KWH) MONTH CSP LANSINGPV LANSINGCSP PHOENIXPV PHOENIX-2000200400600800100012001400123456789101112THERMAL ENERGY (1000 MJ) MONTH Energy to heat (PHO)PV: Energy extracted (PHO)CSP: Energy extracted (PHO)81  Figure III-11.     (b)  4. Discussions This study presents a self-sustaining wastewater treatment concept for agricultural applications. Solar and biogas energy were used to support the treatment process completely, including AD and AET. Based on the geographic location of the treatment system, the effects of ambient temperature, DNI, and GHI on the system configuration and performance has been comprehensively investigated. The AD unit in the self-sustaining system plays a dual role of reducing the organic matter (mainly carbon) and producing the biogas for electricity generation. The total solids in the AD influent (8.5%) were reduced by 41%, producing an average of 2,919 m3biogas/day (0.48 m3biogas/kg volatile solids ·day). The biogas from the AD is the major energy component to enable the realization of the self-sustaining nature of the system (of the 7,043.5 kWhe required for the wastewater treatment, biogas can supply 5,548.13 kWhe).  0200400600800100012001400123456789101112THERMAL ENERGY (1000 MJ) MONTH Energy to heat (LAN)PV: Energy extracted (LAN)CSP: Energy extracted (LAN)82   Since AD has limited capability to remove other nutrients, such as P and N, and reclaim the water, AET is needed to post-treat the AD effluent and complete the wastewater treatment. AET requires a considerable amount of electricity (3,832.8 kWhe per day, which is 54.4% of the total electrical consumption) to support the growth of aerobic microbes, leading to a negative energy balance for the wastewater treatment if the biogas is the only energy source for the combined AD and AET processes. Thus, a second energy source, solar energy, needs to be integrated into the system to satisfy the energy demands of the AD and AET. CSP and PV were the two selected solar energy collection methods for the solarbio hybrid power units. The CSP-bio hybrid unit has the advantages of collecting energy at medium temperatures (< 350 °C) and increasing the solar energy utilization efficiency (). The PV-bio hybrid unit has the advantages of generating electricity from diffuse solar radiation and having a higher SOF.  Energy balance analysis indicates that there is a significant difference in the solar collection area between solarbio hybrid systems with and without short-term solar energy storage. Without the storage, the SOF must be maximized by increasing  to collect solar energy to obtain sufficient thermal energy for the CSP-bio hybrid unit, or sufficient DC current for the PV-bio hybrid unit to satisfy the energy demands of the wastewater treatment. With the storage, the SOF is significantly reduced for both CSP-bio hybrid and PV-bio hybrid units. Correspondingly, the values of  were also greatly decreased (Tables 8 and 9). In addition, the PV-bio hybrid unit had a lower  and smaller biogas storage tank than the CSP-bio hybrid unit at both locations of Phoenix and Lansing. It is apparent that the PV-bio hybrid unit is the preferred power solution for the studied self-sustaining wastewater treatment. 83  5. Conclusions A self-sustaining wastewater treatment concept using solar- and bio-energy to power AD and AET was studied. The results indicate that the combination of AD and AET can effectively reclaim the water from the agricultural wastewater. The solarbio hybrid power generation addresses the challenge of the high energy demand of the AET. The energy balance analysis demonstrates that biogas storage to store the extra energy generated by the solarbio hybrid unit during the warm months enables the wastewater treatment operation to be completely self-sustainable year-round. The PV-bio hybrid unit with short-term energy storage requires a smaller solar collection area and smaller biogas storage tank than the CSP-bio hybrid unit at both studied locations. Therefore, synergistically integrating PV-bio hybrid power generation, biogas storage, AD, and AET provides a technically feasible solution of a self-sustaining wastewater treatment.   84  CHAPTER IV. DESIGN AND EVALUATION OF A TWO-MODULE FRESNEL LENS SOLAR THERMAL COLLECTOR FOR A SCALABLE CONCENTRATED SOLAR POWER GENERATION CONCEPT  Abstract This study analyzed a two-module Fresnel lens solar thermal collector to facilitate the development of a scalable solar power generation concept. The two-module structure enables the connection of multiple Fresnel lenses, with a view to enhancing the collection of solar thermal energy, and correspondingly addressing the scaling issue facing Fresnel lens solar thermal collectors. A bench-scale two-module collector was developed in this study to evaluate the performance of solar thermal collection. The experimental results indicated that a two-module structure with a high-resolution control system enables accurate solar tracking. Finite element method (FEM) simulated the temperature profile of the absorber under different concentration ratios and demonstrated that the absorber area has a greater impact on the surface temperature of the absorber than the concentration ratio. The relationship between absorber area, surface temperature, and heat loss was determined by combining the incident heat radiation model and FEM simulation. It was found that heat loss reduction could be achieved by increasing the absorber area with a relatively small temperature drop. The two-module Fresnel lens thermal collection unit decouples the thermal collector and receiver, so that a scalable concentrated solar power generation concept can be achieved.  Appendices added for this chapter: i. Appendix F: Additional figures for a two-module Fresnel lens solar thermal collector ii. Appendix G: Astronomical algorithm for solar tracking system iii. Appendix H: Labview screenshots for control in solar tracking system 85  1. Introduction Solar energy, the most abundant source of energy on the planet, represents a renewable alternative to fossil fuels. Many solar thermal technologies have been developed in the past decades, such as parabolic reflector concentrators, flat-panel collectors, evacuated tube collectors, central tower systems, and Fresnel lens refractive collectors (Franchini, Perdichizzi, Ravelli, & Barigozzi, 2013; Mills, 2004; Ávila-Marín, 2011). Among these, Fresnel lenses have recently attracted increasing attention as one of the concentrated solar energy technologies because of its advantages of light weight, relatively low cost, and high efficiency in increasing solar energy density (Lv et al., 2015; Xie et al., 2011). However, current research and development of Fresnel lens thermal collectors mainly focuses on the use of single module structures (the lens and thermal receiver are on a fixed structure) to concentrate solar energy (Wu, Eames, Mallick, & Sabry, 2012; Xie et al., 2013; Zhai et al., 2010). The single module design encounters several key technical issues as follows.  1) Due to the fact that Fresnel lenses use multiple refracting surfaces to densify the solar radiation, it is inevitable that using large lenses to obtain a high concentration of solar radiation leads to a significant reflection loss. This is caused by the increasing angles of incidence and emergence as the margin of the large lens is approached, so that the solar thermal efficiency may be greatly reduced.  2) Besides the reflection loss, large single-module collectors also require rigid and heavy structures to withstand high wind velocities and other severe weather conditions, which need large motors and gearboxes to move the units. Therefore, the low-weight advantage of Fresnel lenses is neutralized by the heavy supportive structure and thermal receiving units (Lovegrove & Stein, 2012; G. D. Zhu et al., 2014).  86  These issues significantly limit the use of Fresnel lens thermal collectors. A two-module Fresnel lens collector could be an effective approach to address the issues and establish a scalable concentrated solar power generation (Figure IV-1). The two-module structure splits the solar collection system into two separate unit operations of moving the Fresnel lens solar collector and the light reflector or static thermal receiver. The two-module solar collection system only moves the Fresnel lenses, which significantly reduces the energy demand related with rotating and braking the Fresnel lens module. Fresnel lens modules with small- or medium-sized lenses track the sun and concentrate the solar radiation. The light reflector and thermal receiver modules at the focal point are fixed on the ground to transfer and collect the solar radiation (a similar concept to heliostat array concentrated solar power generation). Since the reflector and receiver modules are static (instead of hanging up and moving in the air), it is feasible to use the reflectors to transfer the concentrated solar radiation to a centrally located thermal receiver to generate a relatively large amount of heat. This could provide flexibility to accommodate a variety of thermal applications, such as heat exchangers, engines, and boilers. Correspondingly, a scalable concentrated solar power generation concept based on a two-module Fresnel lens solar energy collector can be realized (Figure IV-1).   87   Figure IV-1. A scalable Fresnel lens solar thermal power generation concept  This study focused on developing a two-module Fresnel lens thermal collector (the Fresnel lens and fixed thermal receiver) to elucidate the feasibility of the scalable concentrated solar power generation concept. Since the two-module Fresnel lens collector requires different control mechanisms to track and concentrate the solar radiation on the receiver, a high-resolution tracking system has to be developed to realize the solar tracking. In addition, the receiver temperature and heat absorber area are critical to maximize the efficiency of solar energy collection. The relationship between absorber surface temperature, absorber area, and heat loss needs to be determined for the two-module solar collector. Therefore, the specific objectives of this study were to: 1) design a bench-scale Fresnel solar thermal collector unit; 2) evaluate the solar tracking for the two-module Fresnel lens thermal collector; and 3) investigate the relationship between heat loss, absorber temperature, and absorber area.  88  2. Design of a bench-scale two-module Fresnel solar thermal collector  2.1. Two-module thermal collector structure A bench-scale two-module Fresnel solar thermal collector was designed and fabricated to carry out the study (Figure IV-2). A supportive platform was fixed on the bench ( in Figure IV-2a) to support the Fresnel lens, which was slowly moved according to the topocentric azimuth angle (measured from the north vector, clockwise). Two mechanical actuators (model TB055 PBC Linear Co. Roscoe, IL) were used to move the lens, which were horizontally and vertically positioned on the platform ( and  in Figure IV-2a). During the operation of the solar thermal collection (Figure IV-2a and b), a Fresnel lens (50 grooves per in, diameter of 18.25 in, focal length of 24 in, index of refraction of 1.49, transmittance of 0.92) was placed in the carriage of the vertical actuator ( in Figure IV-2a). The lens rotated according to the zenith angle (measured from the vertical direction opposite to the apparent gravitational force). The receiver was fixed on the supportive platform.  In order to align the lens toward the sun and maintain a fixed focal distance between the Fresnel lens and fixed receiver, two automatic movements were required: 1) the lens rotated according to the zenith angle; and 2) the platform rotated according to the azimuth angle. These movements were achieved by actuators and gearboxes. The actuators used for the solar collector unit had a position accuracy of lower than 0.05 mm between repeated movements. The gearboxes with a 15:1 ratio (23VL015 NEMA 23 Planetary Gearhead) were used to adjust the horizontal and vertical displacement movements. The gearboxes with a 70:1 ratio (23VL070 NEMA 23 Planetary Gearhead) were used for the lens rotation and platform rotation. The resolutions were 0.00885 mm/step and 0.025°/step for linear displacement and rotation, respectively. In this particular study, steel plates were used as the thermal absorbers. The parts 89  for the bench-scale unit presented in Figure IV-2 are:  stepper motor for vertical adjustment of the lens (gearbox 15:1);  stepper motor for horizontal adjustment of the lens (gearbox 15:1);  stepper motor for zenith angle adjustment (gearbox 70:1);  stepper motor for azimuth angle adjustment (gearbox 70:1);  horizontal linear actuator (700 mm stroke);  foldable vertical linear actuator (1,280 mm stroke);  Fresnel lens (24 in focal length);  receiver for solar radiation; and  supportive platform.    (a)                                                               (b) Figure IV-2. Bench-scale two-module foldable Fresnel solar thermal collector*       90  Figure IV-2.   (c)                                                               (d)  (e) *(a) CAD drawing of the solar thermal collector in working mode; (b) the bench-scale solar thermal collector; (c) initial position of the solar thermal collector; (d) zenith angle and lens adjustment at mid-position; (e) concentration ratio for temperature measurement.  2.2. Thermal absorbers for temperature profile at focal area In order to determine the temperature profile at the focal area of the collector unit, a thermal receiver was specially designed to collect solar radiation for this study (Figure IV- 3). 91  The receiver includes a metallic cylindrical column (with a height of 65 mm and a diameter of 92 mm), a square thermal glass (with a size of 158 ×158 mm, a thickness of 6.35 mm, and a transmittance of 0.9) covering the top of the column (Figure IV-3a). Three layers (10 mm each) of Pyrogel XT (an insulation material with the thermal conductivity of 90 mW·m-1·K-1 at 650 °C) were placed at the bottom of the column. The absorbers were fixed on the top of the Pyrogel XT layers. The absorbers consisted of mild steel plates of different sizes (4,032 mm2; 2,580 mm2; and 1,451 mm2) (Figure IV-3c). In addition, two layers of Pyrogel XT were used to cover the sides of the metallic column to prevent excess heat loss.    (a)        (b)  (c) Figure IV-3. The receiver and metallic absorbers* 92  Figure IV-3. ( *: (a) Dimensions of the receiver (one-quarter size); (b) geometric model of the receiver (one-quarter size); (c) metallic absorbers of three different sizes (4,032 mm2; 2,580 mm2; and 1,451 mm2).  2.3. Instruments for solar tracking Four stepper motors (NEMA 23, 20,000 steps per revolution in increments of 100 steps, 24 V DC) were used to control the linear displacement and rotation of the Fresnel lens collector. The stepper motors were powered by four power supplies (model PS150A24, input 120 V AC, output 24 V DC, 150 W) via the drives (model ST5-Si-NN) that were programmed using the -4). The stepper motors were connected to the drives using bipolar parallel connection (Appendix F). A hub (model SiNet-Hub 444) transmitted the control signals to the drives via a RJ 11 connection. A RJ11-RS232 connector was used to connect the control hub to a computer.   Figure IV-4. The control system of the solar tracking 93  3. Solar tracking model and control mechanism An astronomical algorithm (Reda & Andreas, 2008) was programmed in Matlab 2011a (MathWorks, Natick, MA) (Appendix G) to calculate the position of the sun. The software program LabVIEW 2011 (National Instruments Co, Austin, TX) was used to run the Matlab function to track the position of the sun, and control the stepper motors to move the Fresnel lens solar thermal collector (Figure IV-5) (Appendix H). A virtual clock provided time parameters to the algorithm (processes 1 and 2 in Figure IV-5).  The displacement of the linear actuators was calculated based on the following equations in the Matlab® function.         (IV-1)        (IV-2) where  and are the horizontal and vertical displacements of the lens (mm), respectively;  and  are the horizontal and vertical distances from the focal point to the rotational point of the lens in the initial position (mm), respectively;  is the distance between the focal point and the rotational point of the lens;  is the angle of the position of L at its initial position (rad); and  is the topocentric zenith angle of the ures IV-2c and IV-2d).  The displacement and rotation of the lens were then converted to steps by LabVIEW using the following equations to control the movement of the stepper motors 12 and 34 (the corresponding gearboxes had ratios of 1:15 and 1:70, respectively) (Figure IV-5).                                             (IV-3a)       (IV-3b) 94         (IV-4a)        (IV-4b) where  and  are the number of steps for the motors 1 and 2 (for the horizontal and vertical adjustments, respectively);  is the linear displacement per actuator-shaft revolution (0.04 rev/mm);  and  are the number of steps for motors 3 and 4 (for the zenith and azimuth adjustments, respectively);  and  are topocentric angles for the initial position (, );  and  are the zenith and azimuth angles for the position of the sun. The speed of the stepper motors was set at 5 rev/s. According to the sun position in East Lansing, MI, a filter code was included to limit the range of movement of the step motors 3 and 4, so that the movements of the azimuth and zenith angles were 90270° and 090°, respectively (process 4 in Figure IV-5).  During the operation, the sequence of actions was set up as azimuth angle rotation, horizontal displacement, vertical displacement, zenith angle rotation, and receiver inclination adjustment. Structured Control Language (SCL) was used to send commands to the motors. The acceleration and deceleration of the movements were set at 25 rev·s-2. A delay of 1.5 s between the motor movement commands was included to avoid data saturation in the control hub. The continuous loop (Figure IV-5) was repeated every 30 s.    95   Figure IV-5. The tracking logic diagram of the LabVIEW program  4. FEM simulation of temperature profiles of the receiver The temperature profiles of the absorbers under different concentration ratios (CR) and absorber areas were simulated using finite element methods (FEM). ANSYS 14.5 (ANSYS, Inc. Canonsburg, PA) was used to perform the analysis. The energy input for the FEM model was the solar radiation values collected at East Lansing, MI. The geometric model of the receiver and absorbers for the FEM model is presented in Figures IV-3b and c. The temperature inside the 96  receiver was measured and used for the simulation. The heat inflow received by the absorber is described as                                                   (IV-5) where is the heat flux from the solar radiation measured by the pyranometer;  and  are the transmittance of the lens and the thermal glass, respectively;  is the absorbance of the metallic plate; and  is the area of the lens. The transmittances were obtained from the technical specifications of the metallic absorber manufacturer (and). The absorbance was assumed to be equal to the emittance () of mild steel. It has been reported that  ranges from 0.3 for clean and polished surfaces to 0.8 for oxidized surfaces (M. F. Modest, 2013). For this study, since the absorber surface was neither polished nor totally oxidized (Figure IV-3c),  was set at 0.5. Other parameters for the FEM simulation are listed in Table IV-1. For the model,  was assumed to be completely absorbed by the metallic plate. Additionally, it was assumed that the absorber total emissive power was constantly emitted in all directions, and calculated as , where Ta is the absorber temperature, and T is the ambient temperature.   Table IV-1. Parameters used in FEM simulation* Concentration ratio (CR) 256 576 1,000 Absorber area (mm2) 1,451 2,580 4,032 1,451 2,580 4,032 1,451 2,580 4,032 Heat flow (W) 11.06 11.78 11.87 10.87 11.63 11.36 10.77 11.65 11.71 *: Ambient temperature: 20 °C; external convection: 8 W/m2·°C; and internal convection: 10 W/m2·°C.  97  5. Data Collection The distance  between the lens and the absorber was adjusted () to achieve different concentration ratios () (Figure IV-2e). The temperature at the center of the absorber was measured by a type K thermocouple that was connected to a CR800 Data Acquisition System (DAQ) (Campbell Scientific, Inc. Logan, UT). The solar radiation was measured using a LI 200 pyranometer (LI-COR, Lincoln, NE) that was also connected to the DAQ. The absorber temperature and solar radiation were recorded every 30 s. The temperature inside the receiver (Figure IV-3) was measured using a type K thermocouple connected to a multimeter MN35 (Extech Instruments), which was read manually every 10 min. The LabVIEW recorded the movement of the collector every 60 s.   6. Statistical analysis The one-sample t-test was used to compare the measured temperature and simulated temperature from the FEM model. The confidence interval of the mean was set at 90%, and the corresponding p-value was 0.1. The t-value was determined by the following equation.                                                                           (IV-6) where t is the t-value; T0 is the simulated temperature;  is the average temperature from multiple measurements; s is the sample standard deviation of the temperature measurements; and n is the number of measurements.    98  7. Experimental results and discussion  7.1. Solar tracking of the two-module collection unit   The Fresnel lens solar thermal collector was operated and tested in East Lansing, Michigan (elevation 262 m, latitude 42°43'27.8" N, longitude 84°28'38.6" W) from July 2013 to October 2013. As demonstrated in Figure IV-2, the accuracy of the solar tracking was mainly dependent on the movement of Fresnel lens (stepper motors and linear actuators). The calculated decimal position data from the astronomical algorithm were converted into integer numbers (step numbers of the stepper motors) before being transferred to the step motors. Large step numbers should be used to achieve a high position resolution, which is the reason that the stepper motors with 20,000 steps per revolution were selected to move the Fresnel lens collector. In addition, high and low integer step numbers generated by the round function in LabVIEW were able to compensate each other during the operation, which also facilitated reducing the position errors. The comparison between the theoretical position (astronomical algorithm) and the position obtained from the solar tracker verified that the control system enabled the two-module unit to realize the solar tracking accurately (Figure IV-6). During the tracking test, differences in azimuth and zenith angles between the lens and actual sun positions were 0.221° ± 0.238° and 0.025° ± 0.019°, respectively, which were very small and had no significant influence on solar thermal collection.  99   (a)  (b) Figure IV-6. Topocentric azimut and zenith angles of the Fresnel lens position during the solar tracking test on: (a) October 11, 2013; (b) October 13, 2013  020406080100120140160180200220240020406080100120140160180Angle (°) Time (min) Azimut (algorithm)Zenith (algorithm)020406080100120140160180200220020406080100120140160180Angle (°) Time (min) Azimut (algorithm)Zenith (algorithm)100  7.2. FEM simulation and verification of temperature profile of thermal absorbers The solar radiation and receiver column temperature (inside the receiver) were measured and used for the FEM simulation (Table IV-2). The FEM simulation results are presented in Table IV-3 and Figure IV-7 (see Figure VII-2 Appendix F for all results). The data demonstrate that, under the same operational conditions (ambient temperature and solar radiation), the larger the CR, the higher the temperatures at the center of the absorber. However, the increase of temperature was not proportional to the increase of CR or decrease of absorber area. For instance, when the CR was increased from 256 to 1,000, the temperatures were only increased by 3.49%, 4.85%, and 6.28% for absorber areas of 1,451 mm2, 2,580 mm2, and 4,032 mm2, respectively. However, compared to the temperature response to the CR changes, the absorber temperatures changed more dramatically according to the change in size of the absorbers. When the absorber area was decreased from 4,032 mm2 to 1,451 mm2, the temperatures at the center of absorber increased by 36.75%, 37.00%, and 33.16% for concentration ratios of 256, 576, and 1000, respectively.  Table IV-2. Solar radiation and receiver column temperature for the FEM model  CR Area Aa (mm2) Solar radiation (W/m2) Number of measurements*A Inside receiver temperature (°C) Number of measurements*B 256 1,451 633.17 ± 18.66 163 204.36 ± 36.35 11 2,580 674.16 ± 5.19 106 217.00 ± 21.33 9 4,032 679.54 ± 5.22 107 181.67 ± 31.40 9 576 1,451 622.48 ± 15.13 85 256.80 ± 9.20 5  101  Table IV-2.  576 2,580 665.78 ± 7.11 69 274.20 ± 15.80 5 4,032 650.63 ± 14.32 94 209.40 ± 14.72 5 1,000 1,451 616.72 ± 23.53 86 301.80 ± 7.98 5 2,580 666.82 ± 4.49 81 278.60 ± 15.97 5 4,032 670.64 ± 4.37 73 241.75 ± 24.51 4 *A: Data were collected every 1 min; *B: Data were collected every 10 min.                        (a)                                                                      (b)                      (c)                                                                      (d) Figure IV-7. Temperature profiles obtained using FEM simulation*   102  Figure IV- *(a) 1,451 mm2 absorber area and 256 CR; (b) 1,451 mm2 absorber area and 1,000 CR; (c) 4,032 mm2 absorber area and 256 CR; (d) 4,032 mm2 absorber area and 1000 CR.  The simulation results were verified by measuring the temperatures of the absorbers for the two concentration ratios of 256 and 576 (Table IV-3). A one-sample t-test found that all measurements were in the 90% confidence interval of the model results (Table IV-3).    Table IV-3. Temperature at the center of the absorbers and statistical comparison  CR Area Aa (mm2) Temperature from the FEM model (°C) Measured temperature (°C) Number of measurements *1 One-sample t-test t- value p- value 256 1,451 592.94 564.49 ± 38.75 163 4.643 > 0.1 2,580 508.76 531.79 ± 51.67 106 2.819 > 0.1 4,032 433.58 410.79 ± 31.36 107 4.596 > 0.1 576 1,451 603.83 633.28 ± 13.17 85 14.143 > 0.1 2,580 525.70 533.94 ± 24.17 69 1.983 > 0.1 4,032 440.74 418.66 ± 24.20 125 5.771 > 0.1 1000 1,451 613.65 - - - - 2,580 533.44 - - - - 4,032 460.83 - - - - *1: Data were collected every 1 min.  103  As for the temperature distribution of the absorber, a homogenous temperature profile requires that the ratio of concentration area (Ac) to absorber area (Aa) should be close to 1. However, high Ac/Aa ratios require extreme accuracy of movement, which is difficult to achieve for most reflective and refractive solar thermal collectors. Therefore, the Ac/Aa ratios of the studied two-module collector were varied between 0.042 and 0.454 (Table IV-4). The simulation results indicate that a temperature gradient occurred for all combinations of CR and absorber area (Figure IV-7). The temperature difference between the center and corners of the absorbers increased with an increase in Ac/Aa ratio (Tables IV-3 and IV-5). For a CR of 256, for the three absorbers with sizes of 1,451 mm2, 2,580 mm2, and 4,032 mm2, the percentage temperature differences were 3.19%, 4.63%, and 5.54%, respectively. For a CR of 576, the corresponding percentage temperature differences for the absorbers were 5.16%, 6.87%, and 8.07 %, respectively; and for a CR of 1,000, they were 7.27%, 9.13%, 10.48%, respectively. The smallest difference of 3.19% was obtained for the 1,451 mm2 absorber with a CR of 256 and an Ac/Aa ratio of 0.454; and the largest difference of 10.48% was obtained for the 4,032 mm2 absorber and the CR of 1,000 with an Ac/Aa ratio of 0.042.  Table IV-4. Ac/Aa ratios for different CRs and absorber areas  CR Area Aa (mm2) 1,451 2,580 4,032 256 0.454 0.255 0.163 576 0.202 0.114 0.073 1,000 0.116 0.065 0.042  104  Table IV-5. Simulated central temperature of absorbers (°C) Absorber (mm2) Concentration ratio (CR) 256 576 1,000 1,451 574.00 575.90 579.68 2,580 482.51 489.56 490.39 4,032 402.06 400.50 412.54  8. Relationship between concentration area and surface temperature  Solar thermal collectors are intended to transfer as much solar energy as possible via a receiver to various heat applications. It is apparent that the surface temperature and absorber area are two key factors that determine the quality and quantity of the heat transfer of solar radiation. However, these two factors are oppositely related for a given lens area (fixed solar radiation). According to the discussion in the previous sections, the increase of the surface temperature can only be achieved by reducing the absorber area. In addition, heat losses (i.e., radiation and convection heat losses) of the absorber are associated with the absorber area and surface temperature, which further influences the net heat flux of the absorber. Therefore, the relationship between surface temperature, absorber area, and heat loss should be evaluated to facilitate the selection and design of the receiver to transfer solar thermal energy efficiently.  Integrating the results from both the incident heat radiation model and FEM analysis shows the relationship between heat loss, surface temperature, and absorber area (Figure IV-8). The heat loss and absorber temperature both decreased with an increase in absorber area, although the decrease in the heat loss was much greater than the decrease in absorber temperature. This means that the heat loss is more sensitive to the change of absorber area than 105  the absorber temperature. When the absorber area (Aa) was increased from 1,451 mm2 to 4,032 mm2 under the fixed lens area (0.17 m2), the heat loss decreased by 60% from 30 kW/m2 absorber to 12 kW/m2 absorber, although the corresponding decrease in the absorber temperature was only 26%, dropping from 603 °C to 445 °C (Figure IV-8). Therefore, within the targeted temperature range of the absorber, sacrificing the temperature to achieve low heat loss could be an effective approach to enhance the thermal efficiency of the Fresnel solar thermal collector. Considering the configuration of a scalable concentrated solar power generation system (Figure IV-1), the heat loss during solar radiation transfer needs to be reduced by as much as possible. Increasing the absorber (or reflector in Figure IV-1) area could be an effective way to enhance the thermal performance of the solar power generation.   Figure IV-8. Temperature and heat loss of the absorber (Aa)* *: The lens area was fixed at 0.17 m2.   0100200300400500600700051015202530350,0010,0020,0030,0040,005Temperature (°C) Heat loss (kW/m2 absorber) Absorber area (m2) Observed heat lossSimulated temperature106  9. Conclusions The study demonstrates that the two-module structure can be used to develop Fresnel lens thermal collectors for a scalable concentrated solar power generation system. With high-resolution stepper motors, the bench-scale solar collector can accurately realize the solar tracking. The FEM simulation of the thermal absorber indicates that the absorber area has a greater impact on the surface temperature of the absorber than the concentration ratio. The relationship between absorber area, absorber heat loss, and absorber temperature was determined from the combination of incident heat radiation model and FEM simulation. Heat loss reduction can be achieved by increasing the absorber area with a relatively small temperature drop. Due to the decoupling of the solar thermal collector and receiver, a scalable Fresnel-lens-based concentrated solar power generation concept can be achieved by combining multiple two-module Fresnel lens collectors with a centralized thermal receiver.  107  CHAPTER V. DESIGN OF NEW SMALL-SCALE SOLAR RECEIVER FOR CONCENTRATED SOLAR THERMAL COLLECTOR  Abstract Two solarthermal receiver designs for concentrated solar thermal collection are presented in this study. The first design applies a cavity absorber with multiple flow paths for the working fluid. The second design uses a conical absorber with single flow path to heat the working fluid. Computational fluid dynamics (CFD) was used to determine the heating fluid temperature profiles of both receivers under different oil mass flows, direct normal irradiance (DNI), and wind velocities. The results elucidate that the cavity receiver has an uneven surface temperature distribution although it has a good overall thermal transfer efficiency. However, the conical receiver with single flow path overcomes the issue of surface temperature distribution, and can be used for applications with high solar concentration ratios (CR).  1. Introduction Solar thermal power generation technologies have been intensively studied over the past several decades (Michael F. Modest, 2013; Siva Reddy et al., 2013). According to the temperature of the working fluid, solar thermal power generation technologies can be classified into three categories of low-, medium-, and high-temperature technologies. For low- and medium-temperature technologies, such as parabolic trough and Fresnel lens thermal collection, the working fluid temperature is often less than 400 °C and the efficiency of incident solar radiation collection is approximately 6070% (Siva Reddy et al., 2013). High-temperature 108  technologies, such as the parabolic dish and central tower receiver, operate at temperatures higher than 600 °C.  In spite of the differences in solar thermal power generation technologies, all require a thermal receiver to transfer solar radiation to the working fluid (heat transfer fluid) efficiently for power generation. Water, air, molten salt, mineral and synthetic oil are the typical working fluids (Behar, Khellaf, & Mohammedi, 2013) (Ávila-Marín, 2011). Different types of solar receivers have been designed and used with parabolic trough, parabolic dish, and heliocentric solar thermal collection systems. For instance, Zhu et al. (J. Zhu et al., 2015) designed a coiled tube for a parabolic dish receiver (with an aperture area of 56.8 m2). A small-particle heat exchanger has also been modified as the receiver to enhance the thermal absorption using air as the working fluid (Fernández & Miller, 2015). However, the majority of these receivers are designed for large collection areas and high power generation. Solar receivers for small-scale solar thermal power generation technologies have not been widely reported. Therefore, the objective of this study was to design a receiver for a small-scale generation system (in kW), and overcome the issue of small heat transfer area (high heat loss during solar thermal collection) that small- and medium-size solar collection units encounter.  2. Design concept Two new receiver designs consisting of cavity and conical solar thermal absorbers were designed for small-scale solar thermal collection (Figure V-1). Transferring thermal energy in small-scale systems is always accompanied by the issue of how to use a small heat transfer area to heat a relatively large amount of working fluid to the targeted temperature. In addition, energy 109  loss to the ambient environment is another problem that significantly reduces the thermal efficiency of such receiver units. In order to address these issues, the objective is to increase the contact time of the working fluid with the heat source to overcome the disadvantage of the small heat transfer area, and to apply a vacuum to reduce heat losses significantly, so that the thermal efficiency of small solar receivers can be significantly improved. Based on this idea, the new receivers were housed in a vacuum chamber with a quartz thermal-glass (Novatec 825F, with a thickness of 9.525 mm (0.375 in)) at the top, a heat exchanger sitting in the vacuum chamber, and thermal insulation (Pyrogel XT) to cover the entire chamber. The vacuum chamber was sealed with O-rings (Parker S455-70) to maintain the inner pressure at -0.84 bar abs (25 inHg). In order to address the issue of a small transfer area, the contact time of the working fluid with the absorber of the receiver needs to be extended. The conical absorber has a single fluid path so that the working fluid enters the absorber from its bottom and leaves from its top (Figure V-2a). Since the conical shape of the absorber provides an effective heat transfer area, the heat transfer area is significantly increased. The cavity absorber has a spiral cave in the receiver. The working fluid pumping through the cavity absorber has multiple flow paths. The residence time of the working fluid is also increased. In the spiral cavity, the working fluid enters the absorber from the bottom of the chamber, reaches the center of the heating area, rotates in the spiral shape, and exits at one side of the receiver. During the process, the working fluid needs to travel along several parallel paths to extend the residence time and improve the efficiency.   110   (a)                                                                         (b) Figure V-1. Solar receivers: (a) with conical absorber; (b) with cavity absorber   (a)                                                                  (b) Figure V-2. Heat absorbers: (a) conical absorber; (b) cavity absorber  The geometric characteristics of both absorbers are listed in Table V-1. The inner volumes of the conical and cavity absorbers (single flow path and multiple flow paths) were 16,527 mm3 and 229,645 mm3, respectively. For volumetric flows of 11,507 mm3/s and 5,753 mm3/s, the residence times for the conical absorber were 1.44 s and 2.88 s, respectively; while 111  those for the cavity absorber were 19.96 s and 39.92 s, respectively. The dimensions of the two receivers are shown in Figure V-3. The receiver size was selected based on a solar collection area of 1 m2. A refractive Fresnel lens was used as the solar thermal concentrator for this study.   Table V-1. Design parameters for the absorbers Receiver type Fluid contact area (mm2) Volume (mm3) Fluid volumetric flow (mm3/s) Residence time (s) Conical absorber 11,426 16,527 11,507 1.44 5,753 2.88 Cavity absorber 59,001 229,645 11,507 19.96 5,753 39.92  (a) Figure V-3. Dimensions of the solar receivers (in mm): (a) with conical absorber; (b) with cavity absorber 112  Figure V-3.   (b)  3. Modeling solar receivers (computational fluid dynamics) Synthetic oil (Dowtherm A) was selected as the working fluid. Energy from solar radiation was transferred to the oil used for steam generation. A micro-turbine of 1.4 kW (NextGrid, 2014) was selected as the power generation unit. The operational parameters of the micro-turbine were used to carry out the calculation and receiver modeling. This particular turbine needs superheated steam at 180220 °C and 810 bar. The temperature of the feeding water was 45 °C. In the model, the temperature change of the synthetic oil due to the solar radiation was set in the range of 220250 °C. The ambient conditions (average direct normal irradiance (DNI) (Figure V-4)) in Lansing were used as the environmental parameters to run the simulation, and average wind velocities were used to calculate the convection heat loss. 113   Figure V-4. DNI during a year at Lansing, MI  Simulation CFD software (Autodesk, 2015) was used to carry out the analysis. Both receivers were discretized, and the mesh size was tested using a heat input value (with no heat losses). The heat input must be completely transferred to the fluid, and the corresponding fluid outlet temperature can be calculated. Using the correlation , where mass flow, heat capacity, and temperature difference are known, the absorbed heat was calculated and compared with the heat input. The difference between the heat input and the absorbed heat was set at less than 1%. The analysis used the K-epsilon to model turbulent flow. The outlet working fluid temperature and heat transfer efficiency under steady-state receiver operation for two oil mass flows (5 g/s and 10 g/s) and three DNI values (750 W/m2, 940 W/m2, and 1125 W/m2) were then determined.  Since Fresnel lenses were the targeted solar thermal collection technology, optical efficiencies for the lens and the thermal glass were considered for the total heat flux receiver in the absorber area. The transmittances for the Fresnel lens and thermal glass reported by the 02004006008001000120002000400060008000Direct Normal Irradiance (W/m2) Time (hour) 114  manufacturers were 0.92 and 0.90, respectively. The DNI was then adjusted to the losses in the transmittance for the glass and the lens. Moreover, heat losses due to convection and radiation were taken into account for the external receiver surfaces. The calculation of the heat loss due to forced convection included the wind velocity (4.69 m/s (annual average at Lansing) and 2 m/s (the wind velocity reduced by a screen installation to cover the refractive collector sides)). The heat loss due to convection was         (V-1) where  is the heat loss due to convection (W);  is the convective coefficient (W/m2·°C);  is the surface in contact with the external air (m2);  is the surface temperature (°C); and  is the ambient temperature (20 °C). Furthermore, the convective coefficient was calculated as            (V-2) where  is the Nusselt number;  is the ambient air thermal conductivity (W/m·°C); and  is the characteristic length for the receiver geometry (m) (outside diameter). The dimensionless Nusselt number was calculated using the empirical correction for cylinders :        (V-3)          (V-4) where  is the Reynolds number;  is the Prandtl number;  is the wind velocity (m/s); and  is the ambient air viscosity (m2/s). Table V-2 summarizes the calculation of the convective heat transfer coefficient.   115  Table V-2. Convective coefficient for heat loss Parameter Cavity absorber Conical absorber Diameter (mm) 409.58 361.95 Height (mm) 122.56 206.38 Wind speed (m/s) 2 4.69 2 4.69  (°C) 20 20  assumed (°C) 45 45  (m2/s) @  1.75 × 10-5 1.75 × 10-5 Re 4.68 × 104 1.10 × 105 4.14 × 104 9.70 × 104 Pr @  0.7323 0.7323 Nu 227.0 468.4 204.4 421.8 k (W/m·°C) @  0.02476 0.02476 h (W/m2·°C) 13.723 28.319 13.98 28.856  In addition to the convective heat loss, the energy losses of solar receivers due to radiation can be calculated as         (V-5) where  is the material emmisivity;  is the Stefan-Boltzmann constant (W/m2·K4);  is the surface area (m2); and  and  are the surface and ambient temperature, respectively. The conical receiver material consisted of aluminum, with an emissivity of 0.18, and the cavity receiver had a emissivity of 0.27 (that of stainless steel) (M. F. Modest, 2013) 116  Both receiver designs allowed the refractive Fresnel lens to concentrate 750 times solar radiation into the absorber area (1,333.33 mm2). A homogenous distribution of input heat in the absorber area is assumed as the boundary condition in the CFD analysis.   4. Results and discussion The fluid temperature at the outlet of the receivers was significantly influenced by different values of DNI, working fluid mass flows, and wind velocities. When the wind velocity changed from 2 m/s to 4.69 m/s, the convective factor increased from 13 W/m2·°C to 28 W/m2·°C (Table V-2). In addition, the CFD results show that, for a mass flow of 5 g/s, when the wind velocity changed from 2 m/s to 4.69 m/s, the heat transfer efficiencies for cavity absorbers decreased from 57.92% to 48.11%, respectively; while that for conical absorbers decreased from 61.09% to 51.92%, respectively (Table V-3). For a high mass flow of 10 g/s, when the wind velocity changed from 2 m/s to 4.69 m/s, the heat transfer efficiencies for cavity absorbers decreased from 51.91% to 45.37%, respectively, and for conical absorbers from 53.74% to 46.88%, respectively (Table V-3). Although the heat transfer efficiencies for a high mass flow were significantly lower than those for a low mass flow, the changes in the heat transfer efficiencies corresponding to the increase in convective factor were smaller than those for the low mass flow. For the high mass flow, the changes in the heat transfer efficiencies for the cavity and conical absorbers were 6.54% and 6.86%, respectively, while the corresponding changes for the low mass flow were 9.81% and 9.17%, respectively. In addition, there were no significant differences in the final working fluid temperature between the two absorbers for the same wind velocity and mass flow (Table V-3).  117  Table V-3. Heat transfer efficiency for wind velocity variation Receiver Cavity absorber Conical absorber Wind velocity (m/s) 4.69 2 4.69 2 4.69 2 4.69 2 Mass flow (g/s) 5 5 10 10 5 5 10 10 T initial (°C) 220 220 220 220 220 220 220 220 T final (°C) 248 253.71 235.11 237.78 246.41 250.21 233.64 235.64 Q absorbed (W) 298.76 359.65 322.4 379.36 281.76 322.38 291.12 333.74 Transfer efficiency 48.1% 57.9% 51.9% 61.0% 45.4% 51.9% 46.9% 53.7%  The DNI is the most critical parameter that has an effect on the thermal transfer efficiency and working fluid temperature. An increase in the net DNI can significantly improve the solar thermal collection for both receivers. When the net DNI increased from 621 W to 931 W, the thermal transfer efficiency of the cavity receiver increased from 58% to 68% for a mass flow of 5 g/s, and from 61% to 72% for a mass flow of 10 g/s. The corresponding increase for the conical absorber was from 52% to 66% for a mass flow of 5 g/s, and from 54% to 68% for a mass flow of 10 g/s (Figure V-5). Comparing the impact of change of net DNI on heat collection efficiencies, those of the conical receiver (single path) were affected more than those of the cavity receiver (multiple paths).    118   (a)  (b) Figure V-5. Thermal collection efficiency and fluid output temperature of the receivers for two fluid mass flows: (a) cavity absorber; (b) conical absorber  Tables V-4 and V-5 summarize the results from the CFD analysis for both cavity and conical receivers, and Figure V-6 shows the fluid temperature profile for selected scenarios. For the conditions of a net DNI of 931 W and the lower mass flow of 5 g/s, the maximum temperatures of the working fluid were 582.31 °C and 399.19 °C for the cavity and conical receivers, respectively.    50%55%60%65%70%621778931THERMAL COLLECTION EFFICIENCY NET DIRECT NORMAL IRRADIANCE (W) 5 g/s10 g/s200210220230240250260270280290621778931OUTLET FLUID TEMPERATURE (°C) NET DIRECT NORMAL IRRADIANCE (W) 5 g/s10 g/s50%55%60%65%70%621778931THERMAL COLLECTION EFFICIENCY NET DIRECT NORMAL IRRADIANCE (W) 5 g/s10 g/s200210220230240250260270280290621778931OUTLET FLUID TEMPERATURE (°C) NET DIRECT NORMAL IRRADIANCE (W) 5 g/s10 g/s119   (a)  (b) Figure V-6. Fluid temperature distribution in the studied receivers for selected scenarios. conical receiver* *(a) 621 W at 10 g/s, (b) 931 W at 5 g/s; cavity receiver: (c) 621 W at 10 g/s, (d) 931 W at 5 g/s    120  Figure V-6.   (c)  (d)   Since the synthetic oil (Dowtherm A) used by this paper has a maximum operating temperature of 400 °C, the maximum temperature for the cavity receiver exceeds the limit of the synthetic oil. Due to the multiple paths in the spiral hole, the fluid molecules around the heating surface have a longer residence time, increasing their temperature much higher than the average, hich could cause a dangerous degradation of the synthetic oil. Reduction of the concentration 121  ratio (CR) and increase of the mass flow of the working fluid can be used to limit the maximum temperature that the fluid reaches. By reducing the CR by half (to CR = 375), the surface absorber temperature decreases from 772.72 °C to 516.70 °C, which limits the maximum working fluid temperature to 474.70 °C, still exceeding the recommendation for the synthetic oil. However, since the cavity absorber has multiple paths for the working fluid, the temperature profile is not evenly distributed on the surface. The cavity absorber has zones with low velocities near the heating surfaces (hot spots), which lead to an uneven heating and a high working fluid temperature at these spots (exceeding the temperature limit of the synthetic oil) even at the low CR. As mentioned previously, a low CR and high fluid mass can reduce the thermal transfer efficiency. Therefore, the conical (single path) absorber, which has a relatively homogenous temperature distribution in the working fluid, represents a preferable design for the solar thermal receiver.   Table V-4. The effects of DNI on the conical absorber Parameter Value Direct normal Irradiance (W) 621 621 778.3 778.3 931 931 Wind velocity (m/s) 2 2 2 2 2 2 Mass flow (g/s) 5 10 5 10 5 10 T initial (°C) 220 220 220 220 220 220 T final (°C) 250.2 235.6 260.0 240.8 277.4 249.9 Cp (J/kg·°C) 2,134 2,134 2,134 2,134 2,134 2,134 Q absorbed (W) 322.4 333.7 427.1 444.1 612.0 637.3 Transfer efficiency 51.9% 53.7% 54.9% 57.1% 65.7% 68.5% 122  Table V-5. Effects of DNI on the cavity absorber Parameter Value Direct normal Irradiance (W) 621 621 778.3 778.3 931 931 Wind velocity (m/s) 2 2 2 2 2 2 Mass flow (g/s) 5 10 5 10 5 10 T initial (°C) 220 220 220 220 220 220 T final (°C) 253.7 237.8 266.7 244.6 279.2 251.2 Cp (J/kg·°C) 2,134 2,134 2,134 2,134 2,134 2,134 Q absorbed (W) 359.7 379.4 498.1 525.2 631.8 666.5 Transfer efficiency 57.9% 61.1% 64.0% 67.5% 67.9% 71.6%   5. Conclusions Two solar thermal receiver designs have been presented. The receiver with the cavity absorber, which has multiple paths and provides a longer residence time of the working fluid, presents a higher thermal transfer efficiency than the receiver with conical absorber, which has a single path and provides a short residence time of the working fluid. However, the cavity absorber has hot spots, where the high working fluid temperature at the spots exceeds the temperature limit of the synthetic oil. Reducing the concentration ratio and increasing the mass flow can solve the issue, although the fluid outlet temperature is reduced correspondingly. The receiver with the conical absorber demonstrates similar thermal efficiencies to the cavity receiver and avoids the adverse effects of low local velocities that the cavity receiver encounters. Therefore, the conical absorber represents a preferable design to collect solar thermal energy considering the currently available synthetic oil. 123  CHAPTER VI. STUDY SUMMARY AND FUTURE WORK  1. Summary  Solarbio hybridization for power generation offers an alternative to provide electricity for a self-sustaining wastewater treatment plant using anaerobic digestion as the main process for organic load reduction. Chapter II of this dissertation presented a comprehensive analysis of two turbo-machines (steam and gas turbines), which are both feasible systems combining biogas and solar energy. The analysis demonstrated that the steam turbine has a higher global efficiency (heat and electricity) than the gas turbine, although the electrical generation efficiency of the gas turbine is higher than that of the steam turbine. In addition, due to the complexity of collecting solar energy at elevated temperatures and high concentration ratios for the gas turbine system, the steam turbine presents favorable conditions for its use in the solar hybridization, both in medium-temperature solar collection systems and in its global efficiency.  Thus, it is necessary to determine proper mechanisms combining biogas and solar energy to enable the self-sustainable operation of the power plant. Chapter III of this dissertation presented a model to set up a self-sustaining wastewater treatment plant by balancing the biogas produced and the solar energy collected for their incorporation in the hybrid power generation. The storage capacity for upgraded biogas and the solar collection area were the parameters that could be balanced to provide stable and continuous electrical energy. In addition, a comparison between photovoltaic panels (PV) and a parabolic trough collector (PT) was conducted, showing that PV collectors require a smaller collection area and biogas storage capacity than a PT, but implying a complex operating and control mechanism in the PV-bio hybrid power generation. Moreover, in Chapter IV, solar collection using a refractive Fresnel lens was presented. The bench-scale unit constructed showed that a two-module system, with high-resolution stepper 124  motors, can achieve an accurate movement for the dual-solar tracking. This enables the possibility to expand the use of small Fresnel lenses for medium-scale solar field collectors by decoupling the refractor and the solar receiver. Additionally, the analysis of the solar energy absorber using finite element methods showed that the absorber area has a greater impact on the average surface temperature of the receiver than the solar concentration ratio, which is an important parameter in the solar receiver design to avoid local hot points. In Chapter V, two solar receiver designs for refractive Fresnel lens collectors were presented. The receiver with a longer working fluid residence time (cavity receiver) exhibited higher thermal transfer efficiency than the receiver with a lower residence time (conical receiver). The computational fluid dynamics model showed that the cavity receiver presented a zone with low velocities near the heating surface, creating local hot points. A low concentration ratio and higher mass flow can solve the issue of local hot points without modifying the receiver geometry.  2. Future work The analysis performed in the previous chapters has provided the design parameters to establish a self-sustaining small-scale pilot plant for wastewater treatment, where the energy required by the processes is generated from biogas and solar radiation.  The studied technologies to treat wastewater can provide water that satisfies the EPA discharge standards. However, the secondary treatment of AET requires a large area for the aeration, which is not feasible for small-scale systems. In order to overcome this disadvantage, it is necessary to research and develop alternatives for water clarification.  125  As presented in Section 1.1.2, electro-chemical reactions can be used as a secondary treatment for water reclamation. The processes of electro-coagulation (EC), centrifuge, and filtration (reverse osmosis and carbon filters) can complete the secondary treatment for a high-strength organic wastewater, such as the AD effluent. Moreover, a pilot-scale solarbio hybrid power generation system for the wastewater treatment plant has been implemented and will be tested (Figure VI-1). Anaerobic digesters will produce biogas for the solarbio hybridization and stabilize solid residues, while an EC unit, centrifuge, and filter unit will carry out the water reclamation process. Photovoltaic panels and CSP collectors (refractive Fresnel lenses) will provide energy to complement the biogas energy for electricity and heat generation.   Figure VI-1. Flowchart of the solarbio hybrid energy generation system to treat wastewater 126  A biogas storage bag serves as the fuel storage for engine use to compensate unsteady solar radiation. The boiler uses both solar and biogas energy to produce steam. The steam is then used by the turbine to generate power. During the daytime, when solar radiation is available, the concentrated solar power (CSP) unit collects heat via the heat-transfer fluid (synthetic oil) and stores it the buffer tank. The heat from solar radiation is used to generate steam, and the steam is superheated in the biogas boiler. The superheated steam then drives the turbine for power generation. The electricity generated from the solarbio hybrid unit is used in the self-sustaining system to power the pumps, centrifuge, DC power supply, and control panel to satisfy operational requirements. The residual heat from the turbine is used to maintain the anaerobic digester at thermophilic conditions (50 °C) to enhance solid reduction, eliminate pathogens, and improve biogas production. The extra electricity and heat from the combined treatment system is used for other on-site applications. The wastewater treatment plant and solar collection system will be installed in a shipping container, and tested at the MSU Anaerobic Digestion Research and Educational Center (ADREC). Figures VI-2 and VI-3 show the configuration of the treatment processes and the equipment distribution in the container.  127   (a)  (b) Figure VI-2. (a) CSP using refractive Fresnel lenses and PV collectors for solar thermal energy collection; (b) PV panels in the solarbio hybridization concept    128    Figure VI-3. Equipment and reactor distribution of the wastewater treatment plant* *: a) fixed-film AD digesters; b) water heater; c) AD effluent tank; d) AD influent tank; e) long-term storage AD effluent; f) electro-coagulation reactor; g) centrifuge; h) clarified water tank before filtration (not shown); i) air compressor for automatic valves.  a a b c d e f g h i 129  A high-efficiency thermophilic fixed-film anaerobic digester (0.4 m3) has been designed for the small-scale wastewater treatment (Figure VI-4). This configuration significantly enhances the accumulation of microbial biomass (using Pall rings between Screens #1 and #2 to retain the biomass), and consequently improves the performance of the digestion. A copper coil is installed inside the reactor to transfer heat from the hot water in order to maintain the thermophilic culture temperature.   Figure VI-4. Fixed-film anaerobic digester  Electro-coagulation is the secondary treatment to further reclaim the water from the AD effluent (Figure VI-5) The equipment consists of six metallic pipes (mild steel anodes) to provide 130  the ions, and a cylindrical metallic sheet (with a thickness of 3 mm) completes the DC circuit for the electrochemical reaction. On the lid, a port is installed for further biogas cleaning.    Figure VI-5. Electro-coagulation reactor for water clarification  In addition, the solarbio hybrid power generation includes both solar technologies of photovoltaics and concentrated solar power. The photovoltaic unit has been designed to generate 4 kW under reference conditions (a cell temperature of 25 °C and a power of 1000 W/m2); to achieve this, 14 SolarWorld SW235 mono PV panels have been installed (Figure IV-2). In addition, a battery bank is used to store the electricity, consisting of 16 batteries (170 Ah) to 131  store the energy from the PV and supply power to the inverter (Radian 4048 4kW) for AC conversion. The concentrated solar power consists of two modules of four refractive Fresnel lenses (with an area of 1 m2 each) to collect energy and transfer it to a solar receiver (Figures VI-2 and VI-6) using synthetic oil (Dowtherm A) as the transfer media. The solar receiver is installed on the aluminum frame, moved by a gearbox connected to brushless motors. The tracking system consists of a control module, with the NREL solar position algorithm, a power supply, two drivers, and magnetic limit switches to control the positions of the lenses.  (a)  (b) Figure VI-6. Fresnel lens assembly: (a) collector module; (b) single-collector test unit  The integration of the processes for the self-sustaining small-scale wastewater treatment plant will be tested in the near future to treat a mixture of black water and food waste.     132           VII. APPENDICES         133  Appendix A: Matlab code for system solar bio-hybrid modeling  clear close all clc %Directories to read libraries addpath('C:\Users\Mauricio\Desktop\Projects MSU\PUBLICATIONS\SOLAR HYBRID POWER SYSTEM\EVERYTHING NEW VACUUM PUMP\Gas an steam turbine analysis\MATLAB water properties') addpath('C:\Users\Mauricio\Desktop\Projects MSU\PUBLICATIONS\SOLAR HYBRID POWER SYSTEM\EVERYTHING NEW VACUUM PUMP\Gas an steam turbine analysis\MATLAB air properties') addpath('E:\WORKING PROJECTS\Gas an steam turbine analysis\MATLAB water properties') addpath('E:\WORKING PROJECTS\Gas an steam turbine analysis\MATLAB air properties') GLOBAL VARIABLES global Percent_solar Biogas_p HC_biogas T_AD HRT rho_inf n_b e_HC CpInfluent Perc_methane Elec_AD Percent_solar=0:0.05:1;                                         %[]                         Solar utilization Biogas_p=0.6421;                                                %[m3biogas/m3reactor·day]   Daily biogas production HC_biogas=23;                                                   %[MJ/m3]                    Biogas heat of combustion T_AD=50;                                                        %[°C]                       Culture temperature AD HRT=20;                                                         %[days]                     Hydraulic retention time rho_inf=1220;                                                   %[kg/m3]                    Density influent n_b=0.85;                                                       %[]                         Efficiency boiler e_HC=0.98;                                                      %[]                         Combustion chamber efficiency CpInfluent=3606;                                                %[J/kg·°C]                  Specific heat influent Perc_methane=0.586;                                             %[]                         Percentage methane in biogas  global e_o_parabolic e_o_dish ems c_SB Cr_Parabolic Cr_Dish UL E_r1 E_r2 THS_1 THS_2 T_Fin Biogas_CU_steam_N Biogas_CU_gas_N Biogas_CU_steam Biogas_CU_gas global t_collection_Steam_LAN t_collection_Gas_LAN t_collection_Steam_PHO t_collection_Gas_PHO global percent_Solar_useful_steam_LAN percent_Solar_useful_gas_LAN percent_Solar_useful_steam_PHO percent_Solar_useful_gas_PHO e_o_parabolic=0.775;                                            %[]             Optical efficiency e_o_dish=0.933;                                                 %[]             Optical efficiency ems=0.27;                                                       %[]             Emisivity steel c_SB=5.670373*10^-8;                                            %[W/m^2·K^4]    Stefan-Boltzman constant Cr_Parabolic=70;                                                %[]             Concentration ratio Cr_Dish=750;                                                    %[]             Concentration 134  ratio UL=8;                                                           %[W/m^2·K]      Convection coeficient E_r1=0.85;                                                      %[]             Efficiency heat exchanger Steam-Molten Salt E_r2=0.70;                                                      %[]             Efficiency heat exchanger Gas-Molten Salt THS_1=(200+273)*1.25;                                           %[K]            Temperature absorber for steam system THS_2=800+273.15;                                               %[K]            Temperature absorber for gas system T_Fin=700+273.15;                                               %[K]            Temperature after solar energy addition in the gas cycle %COLLECTION TIMES AND SOLAR UTILIZATION FACTORS (obtanined from a simulation using SAM) t_collection_Steam_LAN=5.88*3600;                               %[s]             time for solar energy collection Parabolic trough t_collection_Gas_LAN=5.65*3600;                                 %[s]             time for solar energy collection Parabolic dish t_collection_Steam_PHO=9.69*3600;                               %[s]             time for solar energy collection Parabolic trough t_collection_Gas_PHO=9.66*3600;                                 %[s]             time for solar energy collection Parabolic dish percent_Solar_useful_steam_LAN=0.8778; percent_Solar_useful_gas_LAN=0.429; percent_Solar_useful_steam_PHO=0.9337; percent_Solar_useful_gas_PHO=0.4752;  % Electricity for biogas cleaning and upgrading Biogas_CU_steam_N=0.275;                                                            %[kWh/Nm3biogas] From reference Biogas_CU_gas_N=0.765;                                                              %[kWh/Nm3biogas] From reference Biogas_CU_steam=(Biogas_CU_steam_N/(((T_AD+273.15)/288.15)*(1/1.025)))*(3.6/1);     %[MJ/m3biogas] corrected Biogas_CU_gas=(Biogas_CU_gas_N/(((T_AD+273.15)/288.15)*(1/1.025)))*(3.6/1);         %[MJ/m3biogas] corrected t_biogas_cleaning=1*3600;                                                           %[s] Operating time for biogas cleaning and upgrading  % Electricity for influent handling Elec_AD=0.0509;                                                         %[MJ/h·m3digester] From reference. Electricity for influent handling (digester), except for biogas improvement stages POWER SYSTEMS %STEAM  SYSTEMS************************************************************ %WITHOUT SOLAR [Qboiler_n,Qsink,n_turb_steam] = Steam_30kW( ); %SOLAR HYBRID [DATA_table_STEAM] = Steam_30kW_solar(Percent_solar,Qboiler_n,0); %[Perc_solar] [T1] [T2] [T3] [T4] [Qb_n] [Qsink] [Qsolar] [M_biogas];  % GAS SYSTEMS************************************************************** %WITHOUT SOLAR 135  [Qh_n_burner,Q_gen,n_th] = Gas_30kW(  ); %SOLAR GAS HYBRID SYSTEM (after regenerator) [A_II] = Gas_30kW_II(Percent_solar, Qh_n_burner,0); %[Perc_solar] [T1] [T2] [Tx1] [Tx] [T3] [T4] [Ty] [Qh_n_burner] [Qsolar] [Q_gen] [M_biogas]  %For manuscript fprintf('\nElectricity and Thermal efficiencies steam\n') n_turb_steam Qsink/Qboiler_n fprintf('\nTElectricity and Thermal efficiencies gas\n') n_th Q_gen/Qh_n_burner  % Plots figure plot(Percent_solar,A_II(9,:),'*',Percent_solar,DATA_table_STEAM(6,:),'*','LineWidth',1) set(gca,'fontsize',12) xlabel('Solar utilization') ylabel('Fuel consumption (kW)') legend('Gas turbine II', 'Steam turbine','Location','Best') figure set(gca,'fontsize',12) plot(Percent_solar,A_II(11,:),'*',Percent_solar,DATA_table_STEAM(7,:),'*','LineWidth',1) xlabel('Solar utilization') ylabel('Heat generated(kW)') legend('Gas turbine II', 'Steam turbine','Location','Best') NET CAPACITY FACTOR CF=0:0.05:1;                                                                %[]         Capacity Factor t_d=((24*3600).*CF);                                                        %[s/day]        Time of operation per day n=size(CF); n=n(1,2); %solar use -----> for i=1:n     Er_STEAM_BIOGAS(i,:)=t_d(i).*DATA_table_STEAM(6,:)./1000;              %[MJ/day]       BIOGAS Energy requirement for the specified net capacity factor  (21x21)  solar use ->     Er_GAS_II_BIOGAS(i,:)=t_d(i).*A_II(9,:)./1000;                         %[MJ/day]       BIOGAS Energy requirement for the specified net capacity factor  (21x21) end for i=1:n     Er_STEAM_SOLAR(i,:)=t_d(i).*DATA_table_STEAM(8,:)./1000;               %[MJ/day]       SOLAR Energy requirement for the specified net capacity factor  (21x21)     Er_GAS_II_SOLAR(i,:)=t_d(i).*A_II(10,:)./1000;                         %[MJ/day]       SOLAR Energy requirement for the specified net capacity factor  (21x21) end  for i=1:n     HEAT_STEAM_SOLAR(i,:)=t_d(i).*DATA_table_STEAM(7,:)./1000;             %[MJ/day]       Heat generation for the specified net capacity factor  (21x21)     HEAT_GAS_II_SOLAR(i,:)=t_d(i).*A_II(11,:)./1000;                       %[MJ/day]       Heat generation for the specified net capacity factor  (21x21) 136  end [X,Y]=meshgrid(CF);  figure surf(X,Y,Er_STEAM_BIOGAS) set(gca,'fontsize',12) xlabel('Solar use') ylabel('Capacity Factor') zlabel('Fuel energy requirement (MJ/day)') title('Steam Turbine') figure surf(X,Y,Er_GAS_II_BIOGAS) set(gca,'fontsize',12) xlabel('Solar use') ylabel('Capacity Factor') zlabel('Fuel energy requirement (MJ/day)') title('Gas Turbine') figure surf(X,Y,Er_STEAM_SOLAR) set(gca,'fontsize',12) xlabel('Solar use') ylabel('Capacity Factor') zlabel('Solar energy requirement (MJ/day)') title('Steam Turbine') figure surf(X,Y,Er_GAS_II_SOLAR) set(gca,'fontsize',12) xlabel('Solar use') ylabel('Capacity Factor') zlabel('Solar energy requirement (MJ/day)') title('Gas Turbine') %For manuscript fprintf('\nfull utilization of solar energy, solar energy requirement \n') max(max(Er_STEAM_SOLAR)) max(max(Er_GAS_II_SOLAR))   figure surf(X,Y,HEAT_STEAM_SOLAR) set(gca,'fontsize',12) xlabel('Solar use') ylabel('Capacity Factor') zlabel('Heat generation (MJ/day)') title('Steam Turbine') figure surf(X,Y,HEAT_GAS_II_SOLAR) set(gca,'fontsize',12) xlabel('Solar use') ylabel('Capacity Factor') zlabel('Heat generation (MJ/day)') title('Gas Turbine') BIOGAS REQUIREMENT 137  V_biomethane_STEAM=Er_STEAM_BIOGAS.*(1/HC_biogas);                      %[m3]           biogas volume requirement per day Steam turbine V_biomethane_GAS_II=Er_GAS_II_BIOGAS.*(1/HC_biogas);                    %[m3]           biogas volume requirement per day Gas turbine II  V_reactor_STEAM=V_biomethane_STEAM.*(1/Biogas_p);                       %[m3]           Digester volume Steam turbine V_reactor_GAS_II=V_biomethane_GAS_II.*(1/Biogas_p);                     %[m3]           Digester volume Gas turbine II  figure surf(X,Y,V_reactor_STEAM) set(gca,'fontsize',12) xlabel('Solar use') ylabel('Capacity Factor') zlabel('Reactor Volume (m3)') title('Steam Turbine') figure surf(X,Y,V_reactor_GAS_II) set(gca,'fontsize',12) xlabel('Solar use') ylabel('Capacity Factor') zlabel('Reactor Volume (m3)') title('Gas Turbine')  %For manuscript fprintf('\nMax digester volumes \n') max(max(V_reactor_STEAM)) max(max(V_reactor_GAS_II)) SOLAR COLLECTORS ANALYSIS Lansing=[1, 2238.095 2, 3190.476 3, 3809.524 4, 4460.317 5, 4301.587 6, 4920.635 7, 5079.365 8, 4476.19 9, 4492.063 10, 2841.27 11, 2142.857 12, 2142.857].*0.0036;                              %[MJ/m2·day] <- [Wh/m2·day]    Solar energy per month  Phoenix=[1, 6243.09 2, 6461.265 3, 7212.79 4, 8230.948 5, 8527.565 6, 9169.261 7, 7818.869 8, 7221.375 138  9, 7517.964 10, 7077.358 11, 6621.037 12, 6086.287].*0.0036;                              %[MJ/m2·day] <- [Wh/m2·day]    Solar energy per month Tamb_Lansing=[-4.75 -3.4 1.7 8.55 14.3 19.75 21.95 20.95 16.65 10.15 4.2 -2.05];                                             %[C] Average ambient temperature Tamb_Phoenix=[13.6 15.4 18.4 22.65 27.85 32.65 34.9 34.2 31.3 24.8 17.85 13];                                             %[C] Average ambient temperature T_min_LAN=min(Tamb_Lansing); T_min_PHO=min(Tamb_Phoenix); figure plot(1:12,Lansing(:,2),1:12,Phoenix(:,2),'LineWidth',2) xlabel('Month') ylabel('Direct Solar Radiation (MJ/m2·day)') legend('Lansing','Phoenix','Location','Best') figure plot(1:12,Tamb_Lansing,1:12,Tamb_Phoenix,'LineWidth',2) xlabel('Month') ylabel('Average ambient temperature (°C)') legend('Lansing','Phoenix','Location','Best')  %Minimum solar energy in a year per location min_Lansing=min(Lansing(:,2));            %[MJ/m2·day] min_Phoenix=min(Phoenix(:,2));            %[MJ/m2·day] ENERGY REQUIREMENT FOR HEATING CRITICAL CASE (min temp) Tmanure_LAN=4;                                                              %[C]        Minimum influent temperature Tmanure_PHO=13;                                                             %[C]        Minimum influent temperature                                                                             %[J/kg·C]   Heat capacity of the influent 139  m1=(V_reactor_STEAM./HRT).*rho_inf;                                         %[kg]       Mass of influent per day m2=(V_reactor_GAS_II./HRT).*rho_inf;                                        %[kg]       Mass of influent per day %------------------------->SOLAR USE -----> this direction on the matrix Heat_req_STEAM_LAN=m1.*CpInfluent.*(T_AD-Tmanure_LAN).*(1+0.3)./1e6;          %[MJ/day]   (21x21) ENERGY requirement for AD culture Heat_req_GAS_II_LAN=m2.*CpInfluent.*(T_AD-Tmanure_LAN).*(1+0.3)./1e6;         %[MJ/day]   (21x21) ENERGY requirement for AD culture  Heat_req_STEAM_PHO=m1.*CpInfluent.*(T_AD-Tmanure_PHO).*(1+0.3)./1e6;          %[MJ/day]   (21x21) ENERGY requirement for AD culture Heat_req_GAS_II_PHO=m2.*CpInfluent.*(T_AD-Tmanure_PHO).*(1+0.3)./1e6;         %[MJ/day]   (21x21) ENERGY requirement for AD culture  %For manuscript fprintf('\nMAX thermal energy required by AD \n') max(max(Heat_req_STEAM_LAN)) max(max(Heat_req_GAS_II_LAN)) max(max(Heat_req_STEAM_PHO)) max(max(Heat_req_GAS_II_PHO)) SELECTION OF PLANT CAPACITY FACTOR AND SOLAR USE (For CF=0.5 and SU=0.5) CF_s=0.5;                                       %[]             Selected Net Capacity Factor t_d_s=(24*3600).*CF_s;                          %[s/day]        Time n2=(1/0.05)*CF_s+1;                             %[]             Index location for the CF E_gen_Steam_CF=HEAT_STEAM_SOLAR(n2,n2);         %[MJ/day]       (1x1) Heat generation steam system for CF_s E_gen_Gas_CF=HEAT_GAS_II_SOLAR(n2,n2);          %[MJ/day]       (1x1) Heat generation gas system for CF_s  %SOLAR USE Lansing y1=Heat_req_STEAM_LAN(n2,:); P = polyfit(Percent_solar,y1,1); SU_LAN_STEAM=(E_gen_Steam_CF-P(2))/P(1);        %[]             Solar use Lansing steam system BU_LAN_STEAM=(1-SU_LAN_STEAM);                  %[]             Biogas use use Lansing steam system  y1=Heat_req_GAS_II_LAN(n2,:); P = polyfit(Percent_solar,y1,1); SU_LAN_GAS=(E_gen_Gas_CF-P(2))/P(1);            %[]             Solar use Lansing gas system BU_LAN_GAS=(1-SU_LAN_GAS);                      %[]             Biogas use Lansing gas system  %SOLAR USE Phoenix y1=Heat_req_STEAM_PHO(n2,:); P = polyfit(Percent_solar,y1,1); SU_PHO_STEAM=(E_gen_Steam_CF-P(2))/P(1);        %[]             Solar use Phoenix steam system BU_PHO_STEAM=(1-SU_PHO_STEAM);                  %[]             Biogas use Phoenix steam system  y1=Heat_req_GAS_II_PHO(n2,:); P = polyfit(Percent_solar,y1,1); SU_PHO_GAS=(E_gen_Gas_CF-P(2))/P(1);            %[]             Solar use Phoenix gas system BU_PHO_GAS=(1-SU_PHO_GAS);                      %[]             Biogas use Phoenix gas system 140   %For manuscript fprintf('\n Solar Use \n') SOLAR_USE_CITIES=[SU_LAN_STEAM SU_LAN_GAS SU_PHO_STEAM SU_PHO_GAS]   figure plot(Percent_solar,HEAT_STEAM_SOLAR(n2,:),Percent_solar,Heat_req_STEAM_LAN(n2,:),'-o',Percent_solar,Heat_req_STEAM_PHO(n2,:),'-x') set(gca,'fontsize',12) xlabel('Solar utilization') ylabel('Thermal energy(MJ/day)') legend('Thermal energy generated (Steam turbine)','AD thermal energy requirement LAN (Steam turbine)','AD thermal energy requirement PHO (Steam turbine)','Location','Best') xeq(1) =SOLAR_USE_CITIES(1,1); yeq(1) =HEAT_STEAM_SOLAR(n2,1); xeq(2) =SOLAR_USE_CITIES(2,1); yeq(2) =HEAT_STEAM_SOLAR(n2,1); hold plot(xeq, yeq, 'o', 'MarkerFaceColor', 'k', 'MarkerEdgeColor','k','LineWidth', 1.5, 'MarkerSize', 5) text(xeq(1),yeq(1)+500, 'Solar U. Lansing', 'Color', 'k') text(xeq(2)-0.2,yeq(2)-500, 'Solar U. Phoenix', 'Color', 'k') figure plot(Percent_solar,HEAT_GAS_II_SOLAR(n2,:),Percent_solar,Heat_req_GAS_II_LAN(n2,:),'-o',Percent_solar,Heat_req_GAS_II_PHO(n2,:),'-x') set(gca,'fontsize',12) xlabel('Solar utilization') ylabel('Thermal energy(MJ/day)') legend('Thermal energy generated (Gas turbine)','AD thermal energy requirement LAN (Gas turbine)','AD thermal energy requirement PHO (Gas turbine)','Location','Best') xeq(1) =SOLAR_USE_CITIES(1,2); yeq(1) =HEAT_GAS_II_SOLAR(n2,1); xeq(2) =SOLAR_USE_CITIES(2,2); yeq(2) =HEAT_GAS_II_SOLAR(n2,1); hold plot(xeq, yeq, 'o', 'MarkerFaceColor', 'k', 'MarkerEdgeColor','k','LineWidth', 1.5, 'MarkerSize', 5) text(xeq(1),yeq(1)+500, 'Solar U. Lansing', 'Color', 'k') text(xeq(2)-0.2,yeq(2)-500, 'Solar U. Phoenix', 'Color', 'k')   for i=1:12                                      %[°C] Manure temperature     Tmanure_LAN(i)=Tamb_Lansing(i);     Tmanure_PHO(i)=Tamb_Phoenix(i);     if Tmanure_LAN(i)<4         Tmanure_LAN(i)=4;     end     if Tmanure_PHO(i)<4         Tmanure_PHO(i)=4;     end end 141  LANSING %CRITICAL SELECTION USING CF=0.5 T_amb_LAN=-2.05; %[°C] % STEAM ___________________________________________________________________ vq1=V_reactor_STEAM(n2,:); AD_volumen_steam=interp1(Percent_solar',vq1',SU_LAN_STEAM);                                             %[m3]           AD reactor volume for the specified net capacity factor m1=(AD_volumen_steam/HRT)*rho_inf;                                                                      %[kg]           Mass of influent per day Heat_req_STEAM_LAN=m1.*CpInfluent.*(T_AD-Tmanure_LAN).*(1+0.3)./1e6;                                    %[MJ/day]       (1x12)Heat requirement for AD culture STEAM_Biogas=interp1(DATA_table_STEAM(1,:),DATA_table_STEAM(6,:),SU_LAN_STEAM,'linear')*t_d_s/1000;     %[MJ/day]       BIOGAS Energy requirement for the specified net capacity factor STEAM_Solar=interp1(DATA_table_STEAM(1,:),DATA_table_STEAM(8,:),SU_LAN_STEAM,'linear')*t_d_s/1000;      %[MJ/day]       SOLAR Energy requirement for the specified net capacity factor STEAM_Solar=STEAM_Solar/E_r1;                                                                           %[MJ/day]       Solar energy requirement considering heat exchanger efficiency (Steam) A1=(STEAM_Solar)/((e_o_parabolic*min_Lansing.*percent_Solar_useful_steam_LAN)-(t_collection_Steam_LAN./1e6).*((ems*c_SB/Cr_Parabolic)*(THS_1^4-(T_amb_LAN+273.15)^4)+(UL/Cr_Parabolic)*(THS_1-(T_amb_LAN+273.15))));      %[m2]     Solar collector area steam system considering heat losses in the solar collector (radiation and convection) % GAS _____________________________________________________________________ vq1=V_reactor_GAS_II(n2,:); AD_volumen_gas_II=interp1(Percent_solar',vq1',SU_LAN_GAS);                                              %[m3]           AD reactor volume for the specified net capacity factor m3=(AD_volumen_gas_II/HRT)*rho_inf;                                                                     %[kg]           Mass of influent per day Heat_req_GAS_II_LAN=m3.*CpInfluent.*(T_AD-Tmanure_LAN).*(1+0.3)./1e6;                                   %[MJ/day]       (1x12)Heat requirement for AD culture GAS_II_Biogas=interp1(A_II(1,:),A_II(9,:),SU_LAN_GAS,'linear')*t_d_s/1000;                              %[MJ/day]       BIOGAS Energy requirement for the specified net capacity factor GAS_II_Solar=interp1(A_II(1,:),A_II(10,:),SU_LAN_GAS,'linear')*t_d_s/1000;                              %[MJ/day]       SOLAR Energy requirement for the specified net capacity factor GAS_II_Solar=GAS_II_Solar/E_r2;                                                                         %[MJ/day]       Solar energy requirement considering heat exchanger efficiency (Gas) A2=(GAS_II_Solar)/((e_o_dish*min_Lansing.*percent_Solar_useful_gas_LAN)-(t_collection_Gas_LAN./1e6).*((ems*c_SB/Cr_Dish)*(THS_2^4-(T_amb_LAN+273.15)^4)+(UL/Cr_Dish)*(THS_2-(T_amb_LAN+273.15))));      %[m2]     Solar collector area steam system considering heat losses in the solar collector (radiation and convection) % Sumary for critical situation ___________________________________________  %For manuscript fprintf('\n SOLAR AREA LANSING \n') SOLAR_Area_LAN=[A1     A2] fprintf('\n Digester VOLUME LANSING \n') DIGESTER_volume_LAN=[AD_volumen_steam     AD_volumen_gas_II] fprintf('\n Biogas productivity LANSING \n') Biogas_volume_LAN=DIGESTER_volume_LAN.*Biogas_p                                    %[m3biogas/day] Biogas daily productivity  142  % Solar energy collection [DRS_S1,DSR_G1,DRS_S_opt1,DSR_G_opt1,DRS_S_ther1,DRS_G_ther1,Potential_solar1] = Solar_collector(Lansing,SOLAR_Area_LAN,Tamb_Lansing,1);  % Operating time___________________________________________________________ %Steam turbine total/total T_time_S_LAN_BIOGAS=((STEAM_Biogas*n_b).*1000)./(Qboiler_n*n_b);                    %[s] T_time_S_LAN_SOLAR=((Potential_solar1(:,1)*E_r1).*1000)./(Qboiler_n*n_b);           %[s] T_time_S_LAN=T_time_S_LAN_BIOGAS+T_time_S_LAN_SOLAR;                                %[s] %Gas turbine total/total SOLAR_EXTRA=Potential_solar1(:,2)-GAS_II_Solar;                                     %[MJ/day] T_time_G_LAN_BIOGAS=((GAS_II_Biogas*e_HC).*1000)./(Qh_n_burner*e_HC);               %[s] T_time_G_LAN_SOLAR=((GAS_II_Solar*E_r2).*1000)./(Qh_n_burner*e_HC);                 %[s] T_time_G_LAN_SOLAR_E=((SOLAR_EXTRA*E_r2).*1000)./(Qh_n_burner*e_HC);                %[s] T_time_G_LAN=T_time_G_LAN_BIOGAS+T_time_G_LAN_SOLAR+T_time_G_LAN_SOLAR_E;           %[s]  %NET CAPACITY FACTORS NCF_1_LAN=(T_time_S_LAN)./(24*3600); NCF_2_LAN=(T_time_G_LAN)./(24*3600);   % SANKEY DIAGRAM STEAM__________________________________________________________ LAN_S_1=zeros(12,1)+STEAM_Biogas;                                                                   %[MJ/day] Energy from biogas LAN_S_2=DRS_S1;                                                                                     %[MJ/day] Direct solar radiation LAN_S_3=Potential_solar1(:,1);                                                                      %[MJ/day] Energy collected in solar field LAN_S_4=Heat_req_STEAM_LAN';                                                                        %[MJ/day] Thermal energy required by AD LAN_S_5=(T_time_S_LAN.*Qsink)./1000;                                                                %[MJ/day] Thermal energy generated by power block LAN_S_6=(LAN_S_5-LAN_S_4);                                                                          %[MJ/day] Thermal energy non used LAN_S_7=(T_time_S_LAN.*30)./1000;                                                                   %[MJ/day] Electrical energy generated LAN_S_8=(1-e_o_parabolic).*LAN_S_2;                                                                 %[MJ/day] Energy loss by optical efficiency LAN_S_9=LAN_S_2-(LAN_S_8+LAN_S_3);                                                                  %[MJ/day] Solar energy non used  (THERMAL LOSSES) LAN_S_10=(LAN_S_1+LAN_S_3)-(LAN_S_7+LAN_S_5);                                                       %[MJ/day] Irreversible losses LAN_S_11=zeros(12,1)+(Biogas_CU_steam*Biogas_volume_LAN(1))+Elec_AD.*AD_volumen_steam.*(1);         %[MJ/day] Electrical energy required by AD (one hour for influent handling) LAN_S_12=LAN_S_7-LAN_S_11;                                                                          %[MJ/day] Electrical energy non used SANKEY_1_LAN=[LAN_S_1 LAN_S_2 LAN_S_3 LAN_S_4 LAN_S_5 LAN_S_6 LAN_S_7 LAN_S_8 LAN_S_9 LAN_S_10 LAN_S_11 LAN_S_12];  % SANKEY DIAGRAM GAS______________________________________________________ LAN_G_1=zeros(12,1)+GAS_II_Biogas;                                                                  %[MJ/day] Energy from biogas LAN_G_2=DSR_G1;                                                                                     %[MJ/day] Direct solar radiation 143  LAN_G_3=Potential_solar1(:,2);                                                                      %[MJ/day] Energy collected in solar field LAN_G_4=Heat_req_GAS_II_LAN';                                                                       %[MJ/day] Thermal energy required by AD LAN_G_5=(T_time_G_LAN.*A_II(11,1))./1000;                                                           %[MJ/day] Thermal energy generated by power block LAN_G_6=(LAN_G_5-LAN_G_4);                                                                          %[MJ/day] Thermal energy non used LAN_G_7=(T_time_G_LAN.*30)./1000;                                                                   %[MJ/day] Electrical energy generated LAN_G_8=(1-e_o_dish).*LAN_G_2;                                                                      %[MJ/day] Energy loss by optical efficiency LAN_G_9=LAN_G_2-(LAN_G_8+LAN_G_3);                                                                  %[MJ/day] Solar energy non used (THERMAL LOSSES) LAN_G_10=(LAN_G_1+LAN_G_3)-(LAN_G_7+LAN_G_5);                                                       %[MJ/day] Irreversible losses LAN_G_11=zeros(12,1)+(Biogas_CU_gas*Biogas_volume_LAN(2))+Elec_AD.*AD_volumen_gas_II.*(1);          %[MJ/day] Electrical energy required by AD (one hour for influent handling) LAN_G_12=LAN_G_7-LAN_G_11;                                                                          %[MJ/day] Electrical energy non used SANKEY_2_LAN=[LAN_G_1 LAN_G_2 LAN_G_3 LAN_G_4 LAN_G_5 LAN_G_6 LAN_G_7 LAN_G_8 LAN_G_9 LAN_G_10 LAN_G_11 LAN_G_12];  MNT_LAN=7;      %[] Month for SANKEY diagram MNT_LAN2=12;    %[] Month for SANKEY diagram fprintf('\n') fprintf('http://sankeymatic.com/\n') fprintf('\n') fprintf('\n') fprintf('Lansing_steam_hot*****\n') formatSpec = 'Biogas [%.0f] PGS\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN,1)) formatSpec = 'DSR [%.0f] SC \n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN,2)) formatSpec = 'SC  [%.0f] PGS\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN,3)) formatSpec = 'SC  [%.0f] Thermal losses\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN,9)) formatSpec = 'SC  [%.0f] Optical losses\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN,8)) formatSpec = 'PGS [%.0f] EG\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN,7)) formatSpec = 'PGS [%.0f] HG\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN,5)) formatSpec = 'PGS [%.0f] Irreversible losses\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN,10)) formatSpec = 'EG [%.0f] Over generation\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN,12)) formatSpec = 'EG [%.0f] AD\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN,11)) formatSpec = 'HG [%.0f] AD\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN,4)) formatSpec = 'HG [%.0f] Non-used\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN,6)) fprintf('Lansing_steam_cold*****\n') formatSpec = 'Biogas. [%.0f] PGS.\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN2,1)) formatSpec = 'DSR. [%.0f] SC. \n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN2,2)) formatSpec = 'SC.  [%.0f] PGS.\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN2,3)) formatSpec = 'SC.  [%.0f] Thermal losses.\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN2,9)) formatSpec = 'SC.  [%.0f] Optical losses.\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN2,8)) formatSpec = 'PGS. [%.0f] EG.\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN2,7)) formatSpec = 'PGS. [%.0f] HG.\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN2,5)) formatSpec = 'PGS. [%.0f] Irreversible losses.\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN2,10)) formatSpec = 'EG. [%.0f] Over generation.\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN2,12)) formatSpec = 'EG. [%.0f] AD.\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN2,11)) formatSpec = 'HG. [%.0f] AD.\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN2,4)) 144  formatSpec = 'HG. [%.0f] Non-used.\n'; fprintf(formatSpec,SANKEY_1_LAN(MNT_LAN2,6)) fprintf('\n') fprintf('\n') fprintf('GLOBAL EFFICIENCIES\n') 100*(SANKEY_1_LAN(MNT_LAN,7)+SANKEY_1_LAN(MNT_LAN,5))/(SANKEY_1_LAN(MNT_LAN,1)+SANKEY_1_LAN(MNT_LAN,2)) fprintf('\n') 100*(SANKEY_1_LAN(MNT_LAN2,7)+SANKEY_1_LAN(MNT_LAN2,5))/(SANKEY_1_LAN(MNT_LAN2,1)+SANKEY_1_LAN(MNT_LAN2,2)) fprintf('\n') fprintf('\n') fprintf('Lansing_Gas_Hot_I*****\n') formatSpec = 'Biogas [%.0f] PGS\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN,1)) formatSpec = 'DSR [%.0f] SC\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN,2)) formatSpec = 'SC [%.0f] PGS\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN,3)) formatSpec = 'SC [%.0f] Thermal losses\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN,9)) formatSpec = 'SC [%.0f] Optical losses\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN,8)) formatSpec = 'PGS [%.0f] EG\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN,7)) formatSpec = 'PGS [%.0f] HG\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN,5)) formatSpec = 'PGS [%.0f] Irreversible losses\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN,10)) formatSpec = 'EG [%.0f] Over generation\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN,12)) formatSpec = 'EG [%.0f] AD\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN,11)) formatSpec = 'HG [%.0f] AD\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN,4)) formatSpec = 'HG [%.0f] Non-used\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN,6)) fprintf('Lansing_Gas_Cold_*****\n') formatSpec = 'Biogas. [%.0f] PGS.\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN2,1)) formatSpec = 'DSR. [%.0f] SC.\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN2,2)) formatSpec = 'SC. [%.0f] PGS.\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN2,3)) formatSpec = 'SC. [%.0f] Thermal losses.\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN2,9)) formatSpec = 'SC. [%.0f] Optical losses.\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN2,8)) formatSpec = 'PGS. [%.0f] EG.\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN2,7)) formatSpec = 'PGS. [%.0f] HG.\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN2,5)) formatSpec = 'PGS. [%.0f] Irreversible losses.\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN2,10)) formatSpec = 'EG. [%.0f] Over generation.\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN2,12)) formatSpec = 'EG. [%.0f] AD.\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN2,11)) formatSpec = 'HG. [%.0f] AD.\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN2,4)) formatSpec = 'HG. [%.0f] Non-used.\n'; fprintf(formatSpec,SANKEY_2_LAN(MNT_LAN2,6)) fprintf('\n') fprintf('\n') fprintf('GLOBAL EFFICIENCIES\n') 100*(SANKEY_2_LAN(MNT_LAN,7)+SANKEY_2_LAN(MNT_LAN,5))/(SANKEY_2_LAN(MNT_LAN,1)+SANKEY_2_LAN(MNT_LAN,2)) fprintf('\n') 100*(SANKEY_2_LAN(MNT_LAN2,7)+SANKEY_2_LAN(MNT_LAN2,5))/(SANKEY_2_LAN(MNT_LAN2,1)+SANKEY_2_LAN(MNT_LAN2,2)) fprintf('\n') fprintf('\n') Phoenix %CRITICAL SELECTION USING CF=0.5 T_amb_PHO=13; %[°C] % STEAM ___________________________________________________________________ vq1=V_reactor_STEAM(n2,:); 145  AD_volumen_steam=interp1(Percent_solar',vq1',SU_PHO_STEAM);                                             %[m3]           AD reactor volume for the specified net capacity factor m1=(AD_volumen_steam/HRT)*rho_inf;                                                                      %[kg]           Mass of influent per day Heat_req_STEAM_PHO=m1.*CpInfluent.*(T_AD-Tmanure_PHO).*(1+0.3)./1e6;                                    %[MJ/day]       (1x12)Heat requirement for AD culture STEAM_Biogas=interp1(DATA_table_STEAM(1,:),DATA_table_STEAM(6,:),SU_PHO_STEAM,'linear')*t_d_s/1000;     %[MJ/day]       BIOGAS Energy requirement for the specified net capacity factor STEAM_Solar=interp1(DATA_table_STEAM(1,:),DATA_table_STEAM(8,:),SU_PHO_STEAM,'linear')*t_d_s/1000;      %[MJ/day]       SOLAR Energy requirement for the specified net capacity factor STEAM_Solar=STEAM_Solar/E_r1;                                                                           %[MJ/day]       Solar energy requirement considering heat exchanger efficiency (Steam) A1=(STEAM_Solar)/((e_o_parabolic*min_Phoenix.*percent_Solar_useful_steam_PHO)-(t_collection_Steam_PHO./1e6).*((ems*c_SB/Cr_Parabolic)*(THS_1^4-(T_amb_PHO+273.15)^4)+(UL/Cr_Parabolic)*(THS_1-(T_amb_PHO+273.15))));      %[m2]     Solar collector area steam system considering heat losses in the solar collector (radiation and convection) % GAS _____________________________________________________________________ vq1=V_reactor_GAS_II(n2,:); AD_volumen_gas_II=interp1(Percent_solar',vq1',SU_PHO_GAS);                                              %[m3]           AD reactor volume for the specified net capacity factor m3=(AD_volumen_gas_II/HRT)*rho_inf;                                                                     %[kg]           Mass of influent per day Heat_req_GAS_II_PHO=m3.*CpInfluent.*(T_AD-Tmanure_PHO).*(1+0.3)./1e6;                                   %[MJ/day]       (1x12)Heat requirement for AD culture GAS_II_Biogas=interp1(A_II(1,:),A_II(9,:),SU_PHO_GAS,'linear')*t_d_s/1000;                              %[MJ/day]       BIOGAS Energy requirement for the specified net capacity factor GAS_II_Solar=interp1(A_II(1,:),A_II(10,:),SU_PHO_GAS,'linear')*t_d_s/1000;                              %[MJ/day]       SOLAR Energy requirement for the specified net capacity factor GAS_II_Solar=GAS_II_Solar/E_r2;                                                                         %[MJ/day]       Solar energy requirement considering heat exchanger efficiency (Gas) A2=(GAS_II_Solar)/((e_o_dish*min_Phoenix.*percent_Solar_useful_gas_PHO)-(t_collection_Gas_PHO./1e6).*((ems*c_SB/Cr_Dish)*(THS_2^4-(T_amb_PHO+273.15)^4)+(UL/Cr_Dish)*(THS_2-(T_amb_PHO+273.15))));      %[m2]     Solar collector area steam system considering heat losses in the solar collector (radiation and convection) % Sumary for critical situation ___________________________________________ fprintf('\n SOLAR AREA PHOENIX \n') SOLAR_Area_PHO=[A1             A2] fprintf('\n Digester VOLUME PHOENIX \n') DIGESTER_volume_PHO=[AD_volumen_steam             AD_volumen_gas_II] fprintf('\n Biogas productivity PHOENIX \n') Biogas_volume_PHO=DIGESTER_volume_PHO.*Biogas_p                                    %[m3biogas/day] Biogas daily productivity  % Solar energy collection [DRS_S3,DSR_G3,DRS_S_opt3,DSR_G_opt3,DRS_S_ther3,DRS_G_ther3,Potential_solar3] = Solar_collector(Phoenix,SOLAR_Area_PHO,Tamb_Phoenix,2);  % Operating time___________________________________________________________ %Steam turbine total/total T_time_S_PHO_BIOGAS=((STEAM_Biogas*n_b).*1000)./(Qboiler_n*n_b);                    %[s] T_time_S_PHO_SOLAR=((Potential_solar3(:,1)*E_r1).*1000)./(Qboiler_n*n_b);           %[s] 146  T_time_S_PHO=T_time_S_PHO_BIOGAS+T_time_S_PHO_SOLAR;                                %[s] %Gas turbine total/total SOLAR_EXTRA=Potential_solar3(:,2)-GAS_II_Solar;                                     %[MJ/day] T_time_G_PHO_BIOGAS=((GAS_II_Biogas*e_HC).*1000)./(Qh_n_burner*e_HC);               %[s] T_time_G_PHO_SOLAR=((GAS_II_Solar*E_r2).*1000)./(Qh_n_burner*e_HC);                 %[s] T_time_G_PHO_SOLAR_E=((SOLAR_EXTRA*E_r2).*1000)./(Qh_n_burner*e_HC);                %[s] T_time_G_PHO=T_time_G_PHO_BIOGAS+T_time_G_PHO_SOLAR+T_time_G_PHO_SOLAR_E;           %[s]  %NET CAPACITY FACTORS NCF_1_PHO=(T_time_S_PHO)./(24*3600); NCF_2_PHO=(T_time_G_PHO)./(24*3600);  % SANKEY DIAGRAM STEAM__________________________________________________________ PHO_S_1=zeros(12,1)+STEAM_Biogas;                                                                   %[MJ/day] Energy from biogas PHO_S_2=DRS_S3;                                                                                     %[MJ/day] Direct solar radiation PHO_S_3=Potential_solar3(:,1);                                                                      %[MJ/day] Energy collected in solar field PHO_S_4=Heat_req_STEAM_PHO';                                                                        %[MJ/day] Thermal energy required by AD PHO_S_5=(T_time_S_PHO.*Qsink)./1000;                                                                %[MJ/day] Thermal energy generated by power block PHO_S_6=(PHO_S_5-PHO_S_4);                                                                          %[MJ/day] Thermal energy non used PHO_S_7=(T_time_S_PHO.*30)./1000;                                                                   %[MJ/day] Electrical energy generated PHO_S_8=(1-e_o_parabolic).*PHO_S_2;                                                                 %[MJ/day] Energy loss by optical efficiency PHO_S_9=PHO_S_2-(PHO_S_8+PHO_S_3);                                                                  %[MJ/day] Solar energy non used  (THERMAL LOSSES) PHO_S_10=(PHO_S_1+PHO_S_3)-(PHO_S_7+PHO_S_5);                                                       %[MJ/day] Irreversible losses PHO_S_11=zeros(12,1)+(Biogas_CU_steam*Biogas_volume_PHO(1))+Elec_AD.*AD_volumen_steam.*(1);         %[MJ/day] Electrical energy required by AD (one hour for influent handling) PHO_S_12=PHO_S_7-PHO_S_11;                                                                          %[MJ/day] Electrical energy non used SANKEY_1_PHO=[PHO_S_1 PHO_S_2 PHO_S_3 PHO_S_4 PHO_S_5 PHO_S_6 PHO_S_7 PHO_S_8 PHO_S_9 PHO_S_10 PHO_S_11 PHO_S_12];  % SANKEY DIAGRAM GAS______________________________________________________ PHO_G_1=zeros(12,1)+GAS_II_Biogas;                                                                  %[MJ/day] Energy from biogas PHO_G_2=DSR_G3;                                                                                     %[MJ/day] Direct solar radiation PHO_G_3=Potential_solar3(:,2);                                                                      %[MJ/day] Energy collected in solar field PHO_G_4=Heat_req_GAS_II_PHO';                                                                       %[MJ/day] Thermal energy required by AD PHO_G_5=(T_time_G_PHO.*A_II(11,1))./1000;                                                           %[MJ/day] Thermal energy generated by power block PHO_G_6=(PHO_G_5-PHO_G_4);                                                                          %[MJ/day] Thermal energy non used PHO_G_7=(T_time_G_PHO.*30)./1000;                                                                   147  %[MJ/day] Electrical energy generated PHO_G_8=(1-e_o_dish).*PHO_G_2;                                                                      %[MJ/day] Energy loss by optical efficiency PHO_G_9=PHO_G_2-(PHO_G_8+PHO_G_3);                                                                  %[MJ/day] Solar energy non used  (THERMAL LOSSES) PHO_G_10=(PHO_G_1+PHO_G_3)-(PHO_G_7+PHO_G_5);                                                       %[MJ/day] Irreversible losses PHO_G_11=zeros(12,1)+(Biogas_CU_gas*Biogas_volume_PHO(2))+Elec_AD.*AD_volumen_gas_II.*(1);          %[MJ/day] Electrical energy required by AD (one hour for influent handling) PHO_G_12=PHO_G_7-PHO_G_11;                                                                          %[MJ/day] Electrical energy non used SANKEY_2_PHO=[PHO_G_1 PHO_G_2 PHO_G_3 PHO_G_4 PHO_G_5 PHO_G_6 PHO_G_7 PHO_G_8 PHO_G_9 PHO_G_10 PHO_G_11 PHO_G_12];  MNT_PHO=7;      %[] Month for SANKEY diagram MNT_PHO2=12;    %[] Month for SANKEY diagram fprintf('\n') fprintf('\n') fprintf('\n') fprintf('\n') fprintf('Phoenix_steam_hot*****\n') formatSpec = 'Biogas [%.0f] PGS\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO,1)) formatSpec = 'DSR [%.0f] SC \n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO,2)) formatSpec = 'SC  [%.0f] PGS\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO,3)) formatSpec = 'SC  [%.0f] Thermal losses\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO,9)) formatSpec = 'SC  [%.0f] Optical losses\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO,8)) formatSpec = 'PGS [%.0f] EG\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO,7)) formatSpec = 'PGS [%.0f] HG\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO,5)) formatSpec = 'PGS [%.0f] Irreversible losses\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO,10)) formatSpec = 'EG [%.0f] Over generation\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO,12)) formatSpec = 'EG [%.0f] AD\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO,11)) formatSpec = 'HG [%.0f] AD\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO,4)) formatSpec = 'HG [%.0f] Non-used\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO,6)) fprintf('Phoenix_steam_cold*****\n') formatSpec = 'Biogas. [%.0f] PGS.\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO2,1)) formatSpec = 'DSR. [%.0f] SC. \n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO2,2)) formatSpec = 'SC.  [%.0f] PGS.\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO2,3)) formatSpec = 'SC.  [%.0f] Thermal losses.\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO2,9)) formatSpec = 'SC.  [%.0f] Optical losses.\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO2,8)) formatSpec = 'PGS. [%.0f] EG.\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO2,7)) formatSpec = 'PGS. [%.0f] HG.\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO2,5)) formatSpec = 'PGS. [%.0f] Irreversible losses.\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO2,10)) formatSpec = 'EG. [%.0f] Over generation.\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO2,12)) formatSpec = 'EG. [%.0f] AD.\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO2,11)) formatSpec = 'HG. [%.0f] AD.\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO2,4)) formatSpec = 'HG. [%.0f] Non-used.\n'; fprintf(formatSpec,SANKEY_1_PHO(MNT_PHO2,6)) fprintf('\n') fprintf('\n') fprintf('GLOBAL EFFICIENCIES\n') 100*(SANKEY_1_PHO(MNT_PHO,7)+SANKEY_1_PHO(MNT_PHO,5))/(SANKEY_1_PHO(MNT_PHO,1)+SANKEY_1_PHO(MNT_PHO,2)) fprintf('\n') 100*(SANKEY_1_PHO(MNT_PHO2,7)+SANKEY_1_PHO(MNT_PHO2,5))/(SANKEY_1_PHO(MNT_PHO2,1)+SANKEY_1_PHO(MNT_PHO2,2)) 148  fprintf('\n') fprintf('\n') fprintf('Phoenix_Gas_Hot_I*****\n') formatSpec = 'Biogas [%.0f] PGS\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO,1)) formatSpec = 'DSR [%.0f] SC\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO,2)) formatSpec = 'SC [%.0f] PGS\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO,3)) formatSpec = 'SC [%.0f] Thermal losses\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO,9)) formatSpec = 'SC [%.0f] Optical losses\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO,8)) formatSpec = 'PGS [%.0f] EG\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO,7)) formatSpec = 'PGS [%.0f] HG\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO,5)) formatSpec = 'PGS [%.0f] Irreversible losses\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO,10)) formatSpec = 'EG [%.0f] Over generation\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO,12)) formatSpec = 'EG [%.0f] AD\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO,11)) formatSpec = 'HG [%.0f] AD\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO,4)) formatSpec = 'HG [%.0f] Non-used\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO,6)) fprintf('Phoenix_Gas_Cold_I*****\n') formatSpec = 'Biogas. [%.0f] PGS.\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO2,1)) formatSpec = 'DSR. [%.0f] SC.\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO2,2)) formatSpec = 'SC. [%.0f] PGS.\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO2,3)) formatSpec = 'SC. [%.0f] Thermal losses.\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO2,9)) formatSpec = 'SC. [%.0f] Optical losses.\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO2,8)) formatSpec = 'PGS. [%.0f] EG.\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO2,7)) formatSpec = 'PGS. [%.0f] HG.\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO2,5)) formatSpec = 'PGS. [%.0f] Irreversible losses.\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO2,10)) formatSpec = 'EG. [%.0f] Over generation.\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO2,12)) formatSpec = 'EG. [%.0f] AD.\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO2,11)) formatSpec = 'HG. [%.0f] AD.\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO2,4)) formatSpec = 'HG. [%.0f] Non-used.\n'; fprintf(formatSpec,SANKEY_2_PHO(MNT_PHO2,6)) fprintf('\n') fprintf('\n') fprintf('GLOBAL EFFICIENCIES\n') 100*(SANKEY_2_PHO(MNT_PHO,7)+SANKEY_2_PHO(MNT_PHO,5))/(SANKEY_2_PHO(MNT_PHO,1)+SANKEY_2_PHO(MNT_PHO,2)) fprintf('\n') 100*(SANKEY_2_PHO(MNT_PHO2,7)+SANKEY_2_PHO(MNT_PHO2,5))/(SANKEY_2_PHO(MNT_PHO2,1)+SANKEY_2_PHO(MNT_PHO2,2)) fprintf('\n') fprintf('\n')    149  Appendix B: Matlab script functions for turbine modeling  FUNCTION Steam_30kW( ) function [Qboiler_n,Qsink,n_turb_steam] = Steam_30kW( ) m=0.08071;                                  %[kg/s]     Water mass flow 640 lb/hr Pin=10;                                     %[Bar]      Turbine pressure in Pout=0.2;                                   %[Bar]      Turbine pressure out T1=XSteam('Tsat_p',Pout)-2;                 %[°C]       Temperature inlet pump (2°C safety factor) h1=XSteam('hL_T',T1);                       %[kJ/kg]    Enthalpy @ point 1 vf=XSteam('vL_T',T1);                       %[m3/kg]    Specific volume saturated water Wp=vf*(Pin-Pout)*100/0.65;                  %[kJ/kg]    Condensate Pump work (0.65 is the pump efficiency) P_vp=0.500;                                 %[kW]       Power vacuum pump P=30+Wp*m+P_vp;                             %[kW]       Power Output h2=h1+Wp;                                   %[kJ/kg]    Enthalpy @ point 2 T2=XSteam('T_ph',Pin,h2);                   %[°C]       Temperature point 2 T3=200;                                     %[°C]       Temperature inlet turbine s3=XSteam('s_pT',Pin,T3);                   %[kJ/kg·K]  Entropy @ point 3, 10 bar at 200C h3=XSteam('h_pT',Pin,T3);                   %[kJ/kg]    Enthalpy @ point 3, 10 bar at 200C hTout=h3-P/m;                               %[kJ/kg]    Enthalpy @ inmediatly turbine exit T_Tout=XSteam('T_hs',hTout,s3);             %[°C]       Temperature inmediatly turbine exit h4=XSteam('h_ps',Pout,s3);                  %[kJ/kg]    Enthalpy @ condenser pressure T4=XSteam('Tsat_p',Pout);                   %[°C]       Temperature @ condenser condition Qboiler=m*(h3-h2);                          %[kW]       Thermal energy added in the cycle n_b=0.85;                                   %[]         Efficiency boiler Qboiler_n=Qboiler/n_b;                      %[kW]       Net Power boiler n_turb_steam=(((h3-hTout))/((h3-h2)));      %[]         Thermal efficiency n_cond=0.85;                                %[]         Efficiency boiler Qsink=m*(h4-h1)*n_cond;                     %[kW]       Heat generated end     150  FUNCTION Steam_30kW_solar( ) function [ Vect ] = Steam_30kW_solar(varargin) INPUTS Perc_solar=varargin{1};                 %[]         Percent_solar Qboiler_n=varargin{2};                  %[kW]       Qboiler_n Solar_energy=varargin{3};               %[kW]       Qsolar FUNCTION n_b=0.85;                                   %[]         Efficiency boiler Pin=10;                                     %[Bar]      Turbine pressure in Pout=0.2;                                   %[Bar]      Turbine pressure out T1=XSteam('Tsat_p',Pout)-2;                 %[°C]       Temperature inlet pump (2°C safety factor) h1=XSteam('hL_T',T1);                       %[kJ/kg]    Enthalpy @ point 1 vf=XSteam('vL_T',T1);                       %[m3/kg]    Specific volume saturated water Wp=vf*(Pin-Pout)*100/0.65;                  %[kJ/kg]    Condensate Pump work (0.65 is the pump efficiency) Qboiler=Qboiler_n*n_b;                      %[]         Heat boiler m=0.08071;                                  %[kg/s]     Water mass flow 640 lb/hr P_vp=0.500;                                 %[kW]       Power vacuum pump P=30+Wp*m+P_vp;                             %[kW]       Power Output  if Solar_energy == 0 % if solar_energy is zero, the fuction runs the analysis for a vector of solar utilization from 0 to 100 (solar use precentage)     n=size(Perc_solar);     n1=n(1,2);     n2=n(1,1);     if n1>n2         n=n1;     else         n=n2;     end     Solar=Qboiler.*Perc_solar;          %[kW]           Power from solar radiation else     Solar=Solar_energy;     n=1; end  Vect=zeros(10,n); for i=1:n     Qsolar=Solar(1,i);                          %[kW]       Power required solar for phase change     h2=h1+Wp;                                   %[kJ/kg]    Enthalpy @ point 2     T2=XSteam('T_ph',Pin,h2);                   %[°C]       Temperature point 2     T3=200;                                     %[°C]       Temperature inlet turbine     s3=XSteam('s_pT',Pin,T3);                   %[kJ/kg·K]  Entropy @ point 3, 10 bar at 200C     h3=XSteam('h_pT',Pin,T3);                   %[kJ/kg]    Enthalpy @ point 3, 10 bar at 200C      if Qsolar>Qboiler         Qboiler_n=0;                                            %[kW]         Qb_n=0;                                                 %[kW]       Net Power boiler 151          Qsolar_no_used=Qsolar-Qboiler;                          %[kW]       Solar power no used     else         Qboiler_n=m*(h3-h2)-Qsolar;                             %[kW]       Thermal energy added in the cycle         Qb_n=Qboiler_n/n_b;                                     %[kW]       Net Power boiler         Qsolar_no_used=0;                                       %[kW]       Solar power no used     end      hTout=h3-P/m;                               %[kJ/kg]    Enthalpy @ inmediatly turbine exit     T_Tout=XSteam('T_hs',hTout,s3);             %[°C]       Temperature inmediatly turbine exit     h4=XSteam('h_ps',Pout,s3);                  %[kJ/kg]    Enthalpy @ condenser pressure     T4=XSteam('Tsat_p',Pout);                   %[°C]       Temperature @ condenser condition     n_turb_steam=(((h3-hTout))/((h3-h2)));   %[]         Thermal efficiency     n_cond=0.85;                                %[]         Efficiency boiler     Qsink=m*(h4-h1)*n_cond;                     %[kW]       Heat generated       Vect(1,i)=Perc_solar(1,i);     Vect(2,i)=T1;     Vect(3,i)=T2;     Vect(4,i)=T3;     Vect(5,i)=T4;     Vect(6,i)=Qb_n;     Vect(7,i)=Qsink;     Vect(8,i)=Qsolar;     Vect(10,i)=Qsolar_no_used; end end  FUNCTION Gas_30kW( ) function [Qh_n_burner,Q_gen,n_th] = Gas_30kW(  ) Qsolar=0;                                           %[kW]           Heat from solar collectors m=0.31;                                             %[kg/s]         Air mass flow rp=3.2;                                             %[]             Compression ratio gamma=1.4;                                          %[]             Cp/Cv e_L=0.75;                                           %[]             Heat exchanger efficiency e_C=0.818;                                          %[]             Compressor efficiency e_HC=0.98;                                          %[]             Combustion chamber efficiency e_T=0.8164;                                         %[]             Turbine efficiency e_R=0.775;                                          %[]             Regenerator efficiency ac=rp^((gamma-1)/gamma);                            %[]             Parameter related to pressure ratio of the compressor T1=27+273;                                          %[K]            Temperature Inlet compressor T2=T1*(1+(1/e_C)*(ac-1));                           %[K]            Temperature Outlet compressor T3=1113;                                            %[K]            Temperature Inlet turbine T4=912;                                             %[K]            Temperature Outlet turbine Tx=e_R*T4+T2*(1-e_R);                               %[K]            Temperature after regenerator  Ty=e_R*T2+T4*(1-e_R);                               %[K]            Temperature exhaust after 152  regenerator Cp1=airProp2((Tx+T3)/2,'cp')/1000;                  %[kJ/kg·K]      Specific heat at contant pressure Tx1=Tx+(Qsolar)/(m*Cp1);                            %[K]            Temperature after the solar receiver Cp2=airProp2((Tx+T3)/2, 'cp')/1000;                 %[kJ/kg·K]      Specific heat at contant pressure Qh=m*Cp2*(T3-Tx1);                                  %[kW]           Heat addition in the burner Qh_n_burner=Qh/e_HC;                                %[kW]           Heat addition in the burner w/ efficiency  T_final=85+273.15;                                  %[K]            Temperature of exhaust gases after giving heat for digester Cp4a=airProp2((Ty+T_final)/2, 'cp')/1000;           %[kJ/kg·K]      Specific heat at contant pressure Q_gen=e_L*m*Cp4a*(Ty-T_final);                      %[kW]           Heat extracted  n_th=30/Qh_n_burner;                                %[]             Thermal efficiency end  FUNCTION Gas_30kW_II( ) function [A] = Gas_30kW_II(varargin) INPUTS Perc_solar=varargin{1};                                                     %[]             Percent_solar Qh_n_burner=varargin{2};                                                    %[kW]           Qh_n_burner Solar_energy=varargin{3};                                                   %[kW]           Qsolar CONSTANTS global e_HC T_Fin FUNCTION BASE_energy =Qh_n_burner*e_HC;                                          %[kW]           Heat without efficiency if Solar_energy == 0     n=size(Perc_solar);     n1=n(1,2);     n2=n(1,1);     if n1>n2         n=n1;     else         n=n2;     end     Solar=BASE_energy.*Perc_solar;                                      %[kW]           Power from solar radiation else 153      Solar=Solar_energy;     n=1; end m=0.31;                                                                 %[kg/s]         Air mass flow rp=3.2;                                                                 %[]             Compression ratio gamma=1.4;                                                              %[]             Cp/Cv n_th=1-1/(rp^((gamma-1)/gamma));                                        %[]             Thermal efficiency e_L=0.75;                                                               %[]             Heat exchanger efficiency Water-GAS e_C=0.818;                                                              %[]             Compressor efficiency e_T=0.8164;                                                             %[]             Turbine efficiency e_R=0.775;                                                              %[]             Regenerator efficiency ac=rp^((gamma-1)/gamma);                                                %[]             Parameter related to pressure ratio of the compressor T1=27+273;                                                              %[K]            Temperature Inlet compressor T2=T1*(1+(1/e_C)*(ac-1));                                               %[K]            Temperature Outlet compressor T3=1113;                                                                %[K]            Temperature Inlet turbine T4=912;                                                                 %[K]            Temperature Outlet turbine Tx=e_R*T4+T2*(1-e_R);                                                   %[K]            Temperature after regenerator  A=zeros(13,n); for i=1:n     Qsolar=Solar(1,i);                                                  %[kW]     Cp1=airProp2((Tx+T3)/2,'cp')/1000;                                  %[kJ/kg·K]      Specific heat at contant pressure     Tx1=Tx+(Qsolar)/(m*Cp1);                                            %[K]            Temperature after the solar receiver %change this based on heat     if Tx1>T3         Qh_n_burner=0;                                                  %[kW]           Burner capacity         Tx1=T3;     else         Cp2=airProp2((Tx+T3)/2, 'cp')/1000;                             %[kJ/kg·K]      Specific heat at contant pressure         Qh=m*Cp2*(T3-Tx1);                                              %[kJ/kg]        Heat addition in the burner         Qh_n_burner=Qh/e_HC;                                            %[kW]           Heat addition in the burner w/ efficiency     end     %Solar radiation no-used     if Qsolar>Qh_n_burner         QSolar_no_used=Qsolar-Qh_n_burner;     else 154          QSolar_no_used=0;                                               %[kW]           Burner capacity     end     Ty=e_R*T2+T4*(1-e_R);                                               %[K]            Temperature exhaust after regenerator       T_final=85+273.15;                                                  %[K]            Temperature of exhaust gases after giving heat for digester     Cp4a=airProp2((Ty+T_final)/2, 'cp')/1000;                           %[kJ/kg·K]      Specific heat at contant pressure     Q_gen=e_L*m*Cp4a*(Ty-T_final);                                  %[kW]           Heat extracted      %for analysis partial heating using solar up to T_Fin     T_ini=Tx;                                                           %[K]            Temperature before solar energy addition     Q_ad_solar=m.*Cp1.*(T_Fin-T_ini);                                   %[kW]           Heat added in the solar part for partial heating     Q_ad_biogas=((BASE_energy)-Q_ad_solar)./e_HC;                       %[kW]           Heat added in the gas burner for final heating      %Function output     A(1,i)=Perc_solar(1,i);     A(2,i)=T1;     A(3,i)=T2;     A(4,i)=Tx1;     A(5,i)=Tx;     A(6,i)=T3;     A(7,i)=T4;     A(8,i)=Ty;     A(9,i)=Qh_n_burner;     A(10,i)=Qsolar;     A(11,i)=Q_gen;     A(12,i)=QSolar_no_used;     A(13,i)=Q_ad_solar;     A(14,i)=Q_ad_biogas; end end         155  Appendix C: Matlab script function for solar collector modeling  function [DRS_S,DSR_G,DRS_S_opt,DSR_G_opt,DRS_S_ther,DRS_G_ther,Potential_solar] = Solar_collector(Location,SOLAR_Area,T_ambient,nnnn) CONSTANTS global e_o_parabolic e_o_dish ems c_SB Cr_Parabolic Cr_Dish UL E_r1 E_r2 THS_1 THS_2 T_Fin Biogas_CU_steam_N Biogas_CU_gas_N Biogas_CU_steam Biogas_CU_gas global t_collection_Steam_LAN t_collection_Gas_LAN t_collection_Steam_PHO t_collection_Gas_PHO global percent_Solar_useful_steam_LAN percent_Solar_useful_gas_LAN percent_Solar_useful_steam_PHO percent_Solar_useful_gas_PHO  if nnnn==1     percent_Solar_useful_steam=percent_Solar_useful_steam_LAN;     percent_Solar_useful_gas=percent_Solar_useful_gas_LAN;     t_collection_Steam=t_collection_Steam_LAN;     t_collection_Gas=t_collection_Gas_LAN; else     percent_Solar_useful_steam=percent_Solar_useful_steam_PHO;     percent_Solar_useful_gas=percent_Solar_useful_gas_PHO;     t_collection_Steam=t_collection_Steam_PHO;     t_collection_Gas=t_collection_Gas_PHO; end  % DRS_S1        DSR_G1              DIRECT SOLAR RADIATION % DRS_S_opt1    DSR_G_opt1          OPTICAL LOSSES % DRS_S_ther1   DRS_G_ther1         THERMAL LOSSES % Potential_solar1                  ENERGY TRANSFERED TO MOLTEN SALT FUNCTION %DIRECT SOLAR RADIATION DRS_S=Location(:,2).*SOLAR_Area(1);                                 %[MJ/day]       Direct solar radiation Steam DSR_G=Location(:,2).*SOLAR_Area(2);                                 %[MJ/day]       Direct solar radiation Gas %OPTICAL LOSSES DRS_S_opt=(1-e_o_parabolic).*DRS_S; DSR_G_opt=(1-e_o_dish).*DSR_G; %ENERGY COLLECTED IN MOLTEN SALT Potential_solar(:,1)=SOLAR_Area(1).*((e_o_parabolic.*Location(:,2).*percent_Solar_useful_steam)-(t_collection_Steam./1e6).*((ems.*c_SB/Cr_Parabolic).*(THS_1.^4-(T_ambient+273.15).^4)+(UL./Cr_Parabolic).*(THS_1-(T_ambient+273.15))));  %[MJ/day] Potential_solar(:,2)=SOLAR_Area(2).*((e_o_dish.*Location(:,2).*percent_Solar_useful_gas)-(t_collection_Gas./1e6).*((ems.*c_SB/Cr_Dish).*(THS_2.^4-(T_ambient+273.15).^4)+(UL/Cr_Dish).*(THS_2-(T_ambient+273.15))));                  %[MJ/day] %THERMAL LOSSES DRS_S_ther=  DRS_S -(Potential_solar(:,1)+DRS_S_opt);     %[MJ/day] DRS_G_ther= DSR_G -(Potential_solar(:,2)+DSR_G_opt);      %[MJ/day] end 156  Appendix D: Matlab code for solarbio hybridization for anaerobic digestion and aerobic treatment clear clc close all num = xlsread('LOCATION DATA','Lansing'); num2 = xlsread('LOCATION DATA','PV_Lansing');.  % OR  %num = xlsread('LOCATION DATA _PHO','Phoenix'); %num2 = xlsread('LOCATION DATA _PHO','PV_Phoenix');  % 1 Hour % 2 Month % 3 Day % 4 Direct Solar radiation % 5 Ambient temperature % 6 GHI % 7 DHI n=size(num); n=n(1);  % % Calculation of the Solar Operating Factor % mbj=1;      %counter % mbj_PV=1;   %counter % for i=1:n %     if num(i,4)>0 %         SOF_CSP(mbj,1)=num(i,4); %         mbj=mbj+1; %     end %     if num2(i,2)>0 %         SOF_PV(mbj_PV,1)=num(i,4); %         mbj_PV=mbj_PV+1; %     end % end  global HC_N TURBINE_P PER_METHANE E_heatexchanger E_condenser E_boiler TURBINE_P=325;              %[kWe]      Turbine electrical power output (design conditions) HC_N=23;                    %[MJ/Nm3]   Biogas heating value PER_METHANE=0.60;           %[]         Percentage methane in biogas E_heatexchanger=0.90;       %[]         Efficiency steam generator using solar energy E_condenser=0.85;           %[]         Efficiency thermal energy extraction in the condenser E_boiler=0.8448;                                 %[] Boiler efficiency DWF=76.34;                                              %[m3/day]                   Daily influent flow [E_biogas,V_biogas]=AnaerobicDigester();                %[MJ/day]                   Thermal energy from biogas combustion E_biogas=E_biogas*(1/3.6);                              %[kWh per day]              Thermal energy from biogas combustion 157  Start_hourAE=0; Finish_hourAE=23; Aerobic_influent=10161.95/2;                            %[m3/day]                   Aerobic influent Air_flow_ref_1=9.375;                                   %[m3air/m3influent]         Biological treatment processes PAG 226 Aerobic_time_op=12;                                     %[h]                        Operating time for aerobic digestion Air_flow_ref=Air_flow_ref_1/(Aerobic_time_op*60);       %[m3air/min·m3influent]     Aeration rate recommended to maintain Dissolved oxygen at 2 mg/L Air_flow=Air_flow_ref*Aerobic_influent/60;              %[m3air/s] Inlet_P=101000;                                         %[Pa]                       Compressor inlet pressure Outlet_P=303000;                                        %[Pa]                       Compressor outlet pressure alpha=(1.4/(1.4-1))*Inlet_P*((Outlet_P/Inlet_P)^((1.4-1)/1.4)-1); %[]               constant Compr_eff=0.90;                                         %[]                         Compressor efficiency Power_AeD_aeration=((alpha*Air_flow)/1000)/Compr_eff;   %[kW]                       Electrical power required for air compression Power_AeD=Power_AeD_aeration;                           %[kW]                       Electrical power required for aeration  %Biogas scrubbing Start_hourBS=0; Finish_hourBS=23; E_BS_v=0.275;                               %[kWh/Nm3biogas] E_BS_v=E_BS_v*(3.6/1);                      %[MJ/Nm3biogas] T_biogas=273.15+40;                         %[K] Biogas temperature E_BS_v=E_BS_v/((1.0074/1)*(288.15/T_biogas));%[MJ/m3biogas] E_BS=E_BS_v*V_biogas;                       %[MJ] E_BS=E_BS*1000;                             %[kJ]  %Cryogenic separation Start_hourCS=0; Finish_hourCS=23; E_CS_v=0.35;                               %[kWh/Nm3biogas] E_CS_v=E_CS_v*(3.6/1);                      %[MJ/Nm3biogas] E_CS_v=E_CS_v/((1.0074/1)*(288.15/T_biogas));%[MJ/m3biogas] E_CS=E_CS_v*V_biogas;                       %[MJ] E_CS=E_CS*1000;                             %[kJ]  t_BS=(Finish_hourBS-Start_hourBS)*3600;     %[s] Power_BS=E_BS/t_BS+E_CS/t_BS;                         %[kW] including cryogenic  %Influent handling Start_hourIH=0; Finish_hourIH=23; Power_IH=[33 33 33 55 55 55 158  55 55 55 56 56 64 110 50 50 72 72 72 55 55 33 33 33 33];  Elec=Power_IH+Power_BS+Power_AeD; Elec_load=zeros(n,1);                       %[kW] Electrical load required for i=1:n     if num(i,1)==0         Elec_load(i:i+23,1)=Elec;     end end Area=500000; %[m2] Collection area  (6757 with storage) Area_SCA=6;                                             %[m2] Area of the solar collector assembly Area=round(Area/6)*6;                                   %[m2] Collection area considering the area of inividual parabolic trough collectors % Area1=0;                                              %[m2] Collection area for iteration % Area2=40000;                                           %[m2] Collection area for iteration % ZZ=1000; % ZZZZZ=ZZ+1; % nnnn=0; % while ZZZZZ>ZZ || ZZZZZ<0 % nnnn=nnnn+1                                           %[]   iteration counter  QfromBiogas=zeros(n,1);                                 %[kW] Power from biogas  %----------FIRST, THE ELECTRICITY GENERATED USING JUST SOLAR ENERGY for i=1:n     [W,X,Y,Z,QdesignB]=turbine(num(i,4)/1000,Area,num(i,5));     QSolarCollected(i,1)=W;                             %[kW] Heat collected     Eelectrical(i,1)=X;                                 %[kW] Electrical energy generated     Qstored(i,1)=Y;                                     %[kW] Thermal energy stored from solar     E_thermal_Condenser(i,1)=Z;                         %[kW] Thermal energy extracted from condenser     if QSolarCollected(i,1)<0         QSolarCollected(i,1)=0;     end  159  end  % Calculation of the Solar Operating Factor mbj=1;      %counter for i=1:n     if Eelectrical(i,1)>0         SOF_CSP(mbj,1)=Eelectrical(i,1);         mbj=mbj+1;     end end  %Daily thermal energy stored ii=1; for i=1:n     if num(i,1)==0         Qstored_THERMAL_TANK(ii,1)= sum(Qstored(i:i+23,1));                    %[kWh]         ii=ii+1;     end end  QstoredDaily=Qstored_THERMAL_TANK.*0; % Multiply by 0 to run analysis without thermal storage   %----------SECOND, THE ELECTRICITY GENERATED USING HEAT STORED, THEN USING BIOGAS for i=1:n     if Eelectrical(i,1)<Elec_load(i,1)         %+++++_____++++%                                        This lines calculates how much thermal energy is required to generate the electricity (tempo2)         [Z1,Z2,Pmin,Pmax] = turbine_biogas(Elec_load(i,1),2);         Eelectrical(i,1)=Z1;                                    %[kW] TOTAL Electrical energy generated         tempo2=Z2(1);                                           %[kW] Thermal energy required to generate the power load (No efficiencies included on this number)         E_thermal_Condenser(i,1)=Z2(2);                         %[kW] Thermal energy extracted from condenser         %+++++_____++++%          DAY_number=ceil(i/24);                                  %[]   Day number corresponding to studied hour         if DAY_number==1                                        %Conditional just for January 1             DAY_number=366;         end           if QstoredDaily(DAY_number-1,1)>(tempo2-QSolarCollected(i,1)*E_heatexchanger)                                   % Compares the energy stored the day before, with the requirement in the specified hour             QstoredDaily(DAY_number-1,1)=QstoredDaily(DAY_number-1,1)-(tempo2-QSolarCollected(i,1)*E_heatexchanger);    % Takes from the energy storage the energy use, for the next iteration             QfromBiogas(i,1)=0;         else             QfromBiogas(i,1)=(tempo2-(QSolarCollected(i,1)*E_heatexchanger)+QstoredDaily(DAY_number-1,1))/E_boiler;      %[kW] Thermal energy required to generate the power load from biogas 160              QstoredDaily(DAY_number-1,1)=0;                                                                              % Takes from the energy storage the energy use, for the next iteration         end     end      % Conditional to calculate electricity over generated     if Elec_load(i,1)<Eelectrical(i,1)         Over_Generation(i,1)=Eelectrical(i,1)-Elec_load(i,1);               %[kW] Extra electrical energy generated     else         Over_Generation(i,1)=0;     end end  % Daily analysis ii=1; for i=1:n     if num(i,1)==0      QfromBiogasDaily(ii,1)= sum(QfromBiogas(i:i+23,1));                    %[kWh]      E_thermal_CondenserDaily(ii,1)= sum(E_thermal_Condenser(i:i+23,1));    %[kWh]      Over_Generation_Daily(ii,1)=sum(Over_Generation(i:i+23,1));            %[kWh]      DNI_Daily(ii,1)= sum(num(i:i+23,4))/1000;                              %[kWh/m2]      DNI_Daily_standard_dev(ii,1)= std(num(i:i+23,4))/1000;                 %[kWh/m2]      GHI_Daily(ii,1)= sum(num(i:i+23,6))/1000;                              %[kWh/m2]      Tamb_Daily(ii,1)= mean(num(i:i+23,5));                                 %[°C]      ii=ii+1;     end end  % Heat requirement E_thermal_CondenserDaily=E_thermal_CondenserDaily.*(3.6); %[MJ] HRT=20;                         %[days]Hydraulic Retention Time V_reactor=DWF*HRT;              %[m3]Reactor volumen TAD=40;                         %[°C]AD culture temperature rho_inf=1100;                   %[kg/m3] Cp_influent=4120;               %[J/kg·°C] for i=1:365     if Tamb_Daily(i,1)<4         Tamb=4;     else         Tamb=Tamb_Daily(i,1);     end     E_heating_Daily(i,1)=((V_reactor/HRT)*rho_inf*Cp_influent*(TAD-Tamb)*(1+0.30))/(1e6); %[MJ/day] end  % Monthly data DNI_Monthly=daily_monthly(DNI_Daily,1);                                     %[kWh/m2] Direct Normal Irradiance GHI_Monthly=daily_monthly(GHI_Daily,1);                                     %[kWh/m2] Global Tamb_Monthly=daily_monthly(Tamb_Daily,2);                                   %[°C] Ambient temperature E_heating_Monthly=daily_monthly(E_heating_Daily,1);                         %[MJ] Thermal energy required for heating 161  E_thermal_CondenserMonthly=daily_monthly(E_thermal_CondenserDaily,1);       %[MJ] Thermal energy extracted in the condenser for heating Over_Generation_Monthly=daily_monthly(Over_Generation_Daily,1);             %[kWh] Electrical energy generated non used  % Biogas balance BIOGAS_balance=E_biogas-QfromBiogasDaily;               %[kWh] Energy requirement from biogas HC=HC_N*(1/3.6);                                        %[kWh/m3] Heat of combustion BIOGAS_balance_VOL=BIOGAS_balance./HC;                  %[m3] Biogas volume requirement  %Split Biogas balance into negative and positive for i=1:365    if BIOGAS_balance_VOL(i,1)<0        Negative_volumeBiogasGROSS(i,1)=BIOGAS_balance_VOL(i,1);               %[m3]        Positive_volumeBiogasGROSS(i,1)=0;    else        Negative_volumeBiogasGROSS(i,1)=0;        Positive_volumeBiogasGROSS(i,1)=BIOGAS_balance_VOL(i,1);               %[m3]    end end  Accumulative_biogas=zeros(366,1); Accumulative_biogas(1,1)=0; for i=1:365    Accumulative_biogas(i+1,1)=Accumulative_biogas(i,1)+BIOGAS_balance_VOL(i,1);    %[m3] end  %Biogas compression initial volume Jan 1// Verify the last term [BiogasVolumeCompression_initial,Day_min]=min(Accumulative_biogas); if Accumulative_biogas(end)<0     BiogasVolumeCompression_initial=BiogasVolumeCompression_initial+Accumulative_biogas(end);  %[m3] TOTAL VOLUME OF COMPRESSED BIOGAS end  %Tank storage analysis Tank_Volume=zeros(366,1); Tank_Volume(1,1)=abs(BiogasVolumeCompression_initial); for i=1:365    Tank_Volume(i+1,1)=Tank_Volume(i,1)+BIOGAS_balance_VOL(i,1);    %[m3] end  % %Cryogenic upgrading stage % V_compresed=(abs(sum(Negative_volumeBiogasGROSS))*PER_METHANE);                     %[m3] Biomethane volume to compress % Flow_comp_ref=450;                                                                  %[Nm3/h] Compressor flow at normal conditions FIND REFERENCE!!!!!!!!!!!!!!!!! % P_digester=1.025;                                                                   %[atm] Digester pressure % P_ref=1;                                                                            %[atm] reference pressure % T_biogas=4+273.15;                                                                  %[K] Biogas temperature % T_ref=288.15;                                                                       %[K] reference temperature 162  % Flow_comp=Flow_comp_ref*(T_biogas/T_ref)*(P_ref/P_digester);                        %[m3/h] Cryogenic Compressor flow % t_CS=V_compresed/Flow_comp;                                                         %[h] Operating time % t_CS=t_CS*3600;                                                                     %[s] Operating time % %Biogas cryogenic separation % E_CS_v=0.45;                                                                        %[kWh/Nm3biogas] From reference % E_CS_v=E_CS_v*(3.6/1);                                                              %[MJ/Nm3biogas] % T_biogas=(4+273.15);                                                                %[K] % E_CS_v=E_CS_v/((1.025/1)*(288.15/T_biogas));                                        %[MJ/m3biogas] % E_CS=E_CS_v*V_compresed;                                                            %[MJe] Electrical energy required to cryogenically treat biogas % E_CS=E_CS*1000;                                                                     %[kJe] Energy required to compress % Pcompr=0*E_CS/t_CS;                                                                   %[kW] Cryogenic separation electrical power % [Eelectricalcomp,E_thermalcomp,PminComp,PmaxComp] = turbine_biogas(Pcompr,2);       %[] Use of steam turbine to power compressor % ThermalEneg_biogas_compression=E_thermalcomp(1);                                    %[kWt] Thermal Power required by the compressor including boiler eff % Energy_biogas_compression=ThermalEneg_biogas_compression*t_CS*(1/1000);             %[MJ] Thermal Energy required from biogas % Biogas_vol_compression=Energy_biogas_compression/HC_N;                              %[m3] Biogas volume required to compress biogas % ZZZZZ=abs(sum(Positive_volumeBiogasGROSS))-abs(sum(Negative_volumeBiogasGROSS))-Biogas_vol_compression; %[m3] Rest biogas after compression, must be equal or greater than zero  ZZZZZ=abs(sum(Positive_volumeBiogasGROSS))-abs(sum(Negative_volumeBiogasGROSS));        %[m3] Rest biogas after compression, must be equal or greater than zero  TANK_SIZE_STORAGE=max(Tank_Volume)*PER_METHANE; %[m3] %Conditionals to break iteration % if ZZZZZ >ZZ %     Area2=Area; %     Area=(Area+Area1)/2; %     Area1=Area1; % end % if ZZZZZ <0 %     Area1=Area; %     Area=(Area+Area2)/2; %     Area2=Area2; % end % if ZZZZZ>0 && ZZZZZ<ZZ %     break % end % ZZZZZ % end (ZZZZZ/TANK_SIZE_STORAGE)*100  figure 163  plot(1:n,Eelectrical) xlabel('Hour') ylabel('Electricity generated (kW)') title('ELECTRICITY GENERATED') figure plot(1:365,E_thermal_CondenserDaily,1:365,E_heating_Daily) xlabel('Day') ylabel('Energy (kWh)') legend('Thermal energy generated','Thermal energy required') title('Thermal ENERGY') figure plot(1:365,BIOGAS_balance) xlabel('Day') ylabel('Energy (kWh)') title('BIOGAS BALANCE') figure plot(1:365,BIOGAS_balance_VOL) xlabel('Day') ylabel('Energy (m3)') title('BIOGAS BALANCE') figure plot(1:366,Accumulative_biogas) xlabel('Day') ylabel('Volume (m3)') title('ACUMMULATIVE BIOGAS VOLUME') figure plot(1:366,Tank_Volume) xlabel('Day') ylabel('Volume (m3)') title('BIOGAS TANK VOLUME') PfromBiogasPV=zeros(n,1);                                                   %[kWe] Power from biogas EelectricalPV=zeros(n,1); E_thermal_biogas=zeros(n,1);   %----------FIRST, THE ELECTRICITY GENERATED USING JUST SOLAR ENERGY for i=1:n     EelectricalPV(i,1)=num2(i,2);                                           %[kWe] TOTAL Electrical energy generated     E_thermal2_Condenser(i,1)=0;                                            %[kW] Thermal energy extracted in the condenser     if EelectricalPV(i,1)>Elec_load(i,1)         Qstored_Batteries(i,1)=EelectricalPV(i,1)-Elec_load(i,1); %[kWe] Potential energy that can be save in baterries, or electricity over generated from PV     else         Qstored_Batteries(i,1)=0;     end end  %Daily electrical energy stored ii=1; for i=1:n 164      if num(i,1)==0         Qstored_ELEC_BATTERY(ii,1)= sum(Qstored_Batteries(i:i+23,1));                    %[kWh]         ii=ii+1;     end end QstoredDailyPV=Qstored_ELEC_BATTERY; % Multiply by 0 to run analysis without battery storage   %For storage: max(Qstored_Batteries)/2=234.9591 from the simulation Batt_max=max(QstoredDailyPV)/2; %[kWhe] Battery bank capacity  for i=1:365  % this conditional limits the amount of energy that can be stored     if QstoredDailyPV(i,1)>Batt_max         QstoredDailyPV(i,1)=Batt_max;     end end  %----------SECOND, THE ELECTRICITY GENERATED USING batteries, THEN USING BIOGAS for i=1:n     if EelectricalPV(i,1)<Elec_load(i,1)         DAY_number=ceil(i/24);                                  %[]   Day number corresponding to studied hour         if DAY_number==1                                        %Conditional just for January 1             DAY_number=366;         end         %***************         tempo2=Elec_load(i,1)-EelectricalPV(i,1); % short of electricyty for the specified hour         if QstoredDailyPV(DAY_number-1,1)>(tempo2)                                   % Compares the energy stored the day before, with the requirement in the specified hour             QstoredDailyPV(DAY_number-1,1)=QstoredDailyPV(DAY_number-1,1)-(tempo2);    % Takes from the energy storage the energy use, for the next iteration             QfromBiogas(i,1)=0;             EelectricalPV(i,1)=Elec_load(i,1);         else             if tempo2<Pmin                                          % If the electrical power is lower than the minimum, the turbine doesnt work, so, the power is set as Pmin                 tempo2=Pmin;             end             [XX,Z,Pmin,Pmax] = turbine_biogas(tempo2,2);             EelectricalPV(i,1)=XX+EelectricalPV(i,1);                                            %[kWe] TOTAL Electrical energy generated             E_thermal_biogas(i,1)=Z(1);                                         %[kW] Thermal energy required from biogas to generated X             E_thermal2_Condenser(i,1)=Z(2);                                     %[kW] Thermal energy extracted in the condenser         end     end     % Conditional to calculate electricity over generated     if Elec_load(i,1)<EelectricalPV(i,1)         Over_GenerationPV(i,1)=EelectricalPV(i,1)-Elec_load(i,1);                    %[kW] Extra electrical energy generated     else         Over_GenerationPV(i,1)=0;     end 165  end  %Daily biogas consumption requirement ii=1; for i=1:n     if num(i,1)==0      QfromBiogasDailyPV(ii,1)= sum(E_thermal_biogas(i:i+23,1));                 %[kWh] Thermal energy required from biogas to generated X      Over_Generation_DailyPV(ii,1)=sum(Over_GenerationPV(i:i+23,1));            %[kWh] Extra electrical energy generated      E_thermal_Condenser_DailyPV(ii,1)=sum(E_thermal2_Condenser(i:i+23,1));     %[kWh] Thermal energy extracted in the condenser      ii=ii+1;     end end  % Heat requirement E_thermal_Condenser_DailyPV=E_thermal_Condenser_DailyPV.*(3.6);                 %[MJ] Thermal energy extracted in the condenser  % Monthly data E_thermal_Condenser_MonthlyPV=daily_monthly(E_thermal_Condenser_DailyPV,1);     %[MJ] Thermal energy extracted in the condenser Over_Generation_MonthlyPV=daily_monthly(Over_Generation_DailyPV,1);             %[kWh] Extra electrical energy generated   % Biogas balance BIOGAS_balancePV=E_biogas-QfromBiogasDailyPV;                                   %[kWh] Energy requirement from biogas   HC=HC_N*(1/3.6);                                                                %[kWh/m3] Heat of combustion BIOGAS_balance_VOL_PV=BIOGAS_balancePV./HC;                                     %[m3] Biogas volume requirement   %Split Negative and positive for i=1:365    if BIOGAS_balance_VOL_PV(i,1)<0        Negative_volumeBiogasGROSSPV(i,1)=BIOGAS_balance_VOL_PV(i,1);            %[m3]        Positive_volumeBiogasGROSSPV(i,1)=0;    else        Negative_volumeBiogasGROSSPV(i,1)=0;        Positive_volumeBiogasGROSSPV(i,1)=BIOGAS_balance_VOL_PV(i,1);            %[m3]    end end  Accumulative_biogasPV=zeros(366,1); Accumulative_biogasPV(1,1)=0; for i=1:365     Accumulative_biogasPV(i+1,1)=Accumulative_biogasPV(i,1)+BIOGAS_balance_VOL_PV(i,1); %[m3] end 166    %Biogas compression initial volume Jan 1// Verify the last term [BiogasVolumeCompression_initial_PV,Day_min_PV]=min(Accumulative_biogasPV); if Accumulative_biogasPV(end)<0     BiogasVolumeCompression_initial_PV=BiogasVolumeCompression_initial_PV+Accumulative_biogasPV(end);  %[m3] TOTAL VOLUME OF COMPRESSED BIOGAS end  %Tank storage analysis Tank_VolumePV=zeros(366,1); Tank_VolumePV(1,1)=abs(BiogasVolumeCompression_initial_PV); for i=1:365    Tank_VolumePV(i+1,1)=Tank_VolumePV(i,1)+BIOGAS_balance_VOL_PV(i,1);    %[m3] end   % %Cryogenic upgrading stage % %Same as CSP % V_compresed_PV=(abs(sum(Negative_volumeBiogasGROSSPV))*PER_METHANE); % t_CS_PV=V_compresed_PV/Flow_comp;                                                         %[h] Operating time % t_CS_PV=t_CS_PV*3600; % %Biogas cryogenic separation % %Same as CSP % Energy_biogas_compressionPV=ThermalEneg_biogas_compression*t_CS_PV*(1/1000);  %[MJ] Thermal Energy required from biogas % Biogas_vol_compressionPV=Energy_biogas_compressionPV/HC_N;                                %[m3] Biogas volume required to compress biogas % ZZZZZ_PV=abs(sum(Positive_volumeBiogasGROSSPV))-abs(sum(Negative_volumeBiogasGROSSPV))-Biogas_vol_compressionPV; %[m3] Rest biogas after compression, must be equal or greater than zero   ZZZZZ_PV=abs(sum(Positive_volumeBiogasGROSSPV))-abs(sum(Negative_volumeBiogasGROSSPV)); %[m3] Rest biogas after compression, must be equal or greater than zero   TANK_SIZE_STORAGE_PV=max(Tank_VolumePV)*PER_METHANE; %[m3]   (ZZZZZ_PV/TANK_SIZE_STORAGE_PV)*100  figure plot(1:n,EelectricalPV) xlabel('Hour') ylabel('Electricity generated (kW)') title('ELECTRICITY GENERATED') figure plot(1:365,BIOGAS_balancePV) xlabel('Day') ylabel('Energy (kWh)') title('BIOGAS BALANCE') figure 167  plot(1:365,BIOGAS_balance_VOL_PV) xlabel('Day') ylabel('Energy (m3)') title('BIOGAS BALANCE') figure plot(1:366,Accumulative_biogasPV) xlabel('Day') ylabel('Volume (m3)') title('ACUMMULATIVE BIOGAS VOLUME PV') figure plot(1:366,Tank_VolumePV) xlabel('Day') ylabel('Volume (m3)') title('BIOGAS TANK VOLUME PV')         168  Appendix E: Matlab sub-functions for solarbio hybridization for anaerobic digestion and aerobic treatment  FUNCTION AnaerobicDigester( ) function [E_thermal,V_biogas] = AnaerobicDigester() %% ANAEROBIC DIGESTION global HC_N V_biogas=2919.96;               %[m3/day] Biogas productivity E_thermal=V_biogas*HC_N;        %[MJ/day]Thermal energy available end   FUNCTION turbine(Qin,AreaC,Tamb ) function [QSolarCollected, Eelectrical, Qstored,E_thermal,QdesignB] = turbine( Qin,AreaC,Tamb ) %% TURBINE PARAMETERS global TURBINE_P E_heatexchanger E_condenser E_boiler   MinTurbOp=0.25;                                 %[] Minimum turbine operation    MaxTurbOp=1.20;                                 %[] Maximum turbine operation F0=-0.0572;                                     %[] Constant F1=1.0041;                                      %[] Constant F2=0.1255;                                      %[] Constant F3=-0.0724;                                     %[] Constant Ef_Turbine=0.35;                                %[] Turbine thermal efficiency   Pdesign=TURBINE_P;                              %[kW] Turbine power design Qdesign=Pdesign/Ef_Turbine;                     %[kW] Turbine heat design Qheat=0.5*Qdesign;                              %[kW] Heat recovered in the condenser Pmin=Pdesign*MinTurbOp;                         %[kW] Minimum turbine power output Pmax=Pdesign*MaxTurbOp;                         %[kW] Maximum turbine power output Qmin_Th=fzero(@(x)((F0+F1*(x/Qdesign)^1+F2*(x/Qdesign)^2+F3*(x/Qdesign)^3)*Pdesign)-Pmin,Qdesign*0.5);    %[kW] Min Thermal input including boiler eff   Qmax_Th=fzero(@(x)((F0+F1*(x/Qdesign)^1+F2*(x/Qdesign)^2+F3*(x/Qdesign)^3)*Pdesign)-Pmax,Qdesign*1.5);    %[kW] Max Thermal inputincluding boiler eff Eelectrical_par=Pdesign*0.05;                              %[kW] Parasitic electrical energy QdesignB=Qdesign/E_boiler;                     %[kW] Turbine heat design with boiler eff. %% OPTICAL EFFICIENCY REFRACTORS Ef_1=0.99;                                          %[] Tracking error and twist 169  Ef_2=0.968;                                         %[] Geometric Accuracy                                           Ef_3=0.925;                                         %[] surface reflectance Ef_4=0.97;                                          %[] Concentration factor Ef_5=1;                                             %[] Cleanliness factor Ef_7=0.98;                                          %[] Dust Ef_6=Ef_1*Ef_2*Ef_3*Ef_4*Ef_5*Ef_7;                 %[] SCA field error Ef_8=1;                                             %[] Fraction of field Ef_9=0.95;                                         %[] Shadow Ef_10=0.963;                                        %[] Transmisivity Ef_11=0.96;                                         %[] Absortivity Ef_12=1;                                            %[] Unaccounted Ef_13=Ef_6*Ef_8*Ef_9*Ef_10*Ef_11*Ef_12;             %[] Optical efficiency   %% PIPING LOSS Q_loss_pipe_ref=10;                                 %[W/m2] Piping heat loss at design temp (316.5 °C) Q_pipe_ref=Q_loss_pipe_ref*AreaC/1000;              %[kW] Piping heat loss at design temp (316.5 °C) PHLTC1=0.001693;                                    %[] Constant PHLTC2=-1.68E-05;                                   %[] Constant PHLTC3=6.78E-08;                                    %[] Constant Tin_WF=300;                                         %[°C] Working fluid temp Solar field inlet Tout_WF=350;                                        %[°C] Working fluid temp Solar field outlet Tavg_WF=(Tin_WF+Tout_WF)/2;                         %[°C] Average working fluid temp Q_pipe=(PHLTC3*(Tavg_WF-Tamb)^3+PHLTC2*(Tavg_WF-Tamb)^2+PHLTC1*(Tavg_WF-Tamb))*Q_pipe_ref;        %[kW] Heat loss in the pipe system   %% THERMAL ENERGY FOR TURBINE Q_rec_loss=6.60896;                                                           %[W/m2] Receiver heat loss QSolarCollected=(Qin*AreaC*Ef_13)-(Q_rec_loss*AreaC/1000)-(Q_pipe);         %[kW] Heat collected     QSolarCollected=QSolarCollected.*E_heatexchanger;   if QSolarCollected<0     QSolarCollected=0; end   if QSolarCollected<Qmin_Th     QSolarUseful=0;                                                         %[kW] Thermal energy for turbine     Qstored=QSolarCollected;                                                %[kW] Thermal energy for storage else     if QSolarCollected>Qmax_Th         QSolarUseful=Qmax_Th;         Qstored=QSolarCollected-Qmax_Th;     else         QSolarUseful=QSolarCollected;         Qstored=0;     end 170  end   Eelectrical=(F0+F1*(QSolarUseful/Qdesign)^1+F2*(QSolarUseful/Qdesign)^2+F3*(QSolarUseful/Qdesign)^3)*Pdesign; %[kW] Electrical power generated Eelectrical=Eelectrical-Eelectrical_par;     if Eelectrical<0     Eelectrical=0; else     Eelectrical=Eelectrical; end   E_thermal=(F0+F1*(QSolarUseful/Qdesign)^1+F2*(QSolarUseful/Qdesign)^2+F3*(QSolarUseful/Qdesign)^3)*Qheat*E_condenser; %[kW] Heat extracted in the condenser   if E_thermal<0     E_thermal=0; else     E_thermal=E_thermal; end end   FUNCTION turbine_biogas(Qin,n) function [Eelectrical,E_thermal,Pmin,Pmax] = turbine_biogas(Qin,n) %Qmin_Th < Qin < Qmax_Th % if n=1, the input value must be Thermal energy to calculate electrical power % If n=2, the input value must be Electrical power to calculate thermal energy % Input energy in [kW]   %% TURBINE PARAMETERS global TURBINE_P E_heatexchanger E_condenser E_boiler         MinTurbOp=0.25;                                 %[] Minimum turbine operation         MaxTurbOp=1.20;                                 %[] Maximum turbine operation         F0=-0.0572;                                     %[] Constant         F1=1.0041;                                      %[] Constant         F2=0.1255;                                      %[] Constant         F3=-0.0724;                                     %[] Constant         Ef_Turbine=0.35;                                 %[] Turbine thermal efficiency         Pdesign=TURBINE_P;                              %[kW] Turbine power design         Qdesign=Pdesign/Ef_Turbine;                     %[kW] Turbine heat design         Qheat=0.5*Qdesign;                              %[kW] Heat recovered in the condenser 171          QdesignB=Qdesign/E_boiler;                     %[kW] Turbine heat design with boiler eff.         Pmin=Pdesign*MinTurbOp;                         %[kW] Minimum turbine power output         Pmax=Pdesign*MaxTurbOp;                         %[kW] Maximum turbine power output         Qmin_Th=fzero(@(x)((F0+F1*(x/QdesignB)^1+F2*(x/QdesignB)^2+F3*(x/QdesignB)^3)*Pdesign)-Pmin,QdesignB*0.5);    %[kW] Min Thermal input including boiler eff         Qmax_Th=fzero(@(x)((F0+F1*(x/QdesignB)^1+F2*(x/QdesignB)^2+F3*(x/QdesignB)^3)*Pdesign)-Pmax,QdesignB*1.5);    %[kW] Max Thermal inputincluding boiler eff         Eelectrical_par=Pdesign*0.05;                              %[kW] Parasitic electrical energy                            switch n             case 1      %To calculate power given heat                 if Qin<0                     Qin=0;                 end                                  if Qin<Qmin_Th                     QSolarUseful=0;                                                       %[kW] Thermal energy for turbine                     Qstored=0;                                                            %[kW] Thermal energy for storage non use for biogas input                 else                     if Qin>Qmax_Th                         QSolarUseful=Qmax_Th;                         Qstored=Qin-Qmax_Th;                     else                         QSolarUseful=Qin;                         Qstored=0;                     end                 end                                                                                                                                                             %[kWt] Thermal energy for turbine                 Eelectrical=(F0+F1*(QSolarUseful/QdesignB)^1+F2*(QSolarUseful/QdesignB)^2+F3*(QSolarUseful/QdesignB)^3)*Pdesign-Eelectrical_par;            %[kWe] Electrical power generated                 E_thermal=(F0+F1*(QSolarUseful/QdesignB)^1+F2*(QSolarUseful/QdesignB)^2+F3*(QSolarUseful/QdesignB)^3)*Qheat*E_boiler;                      %[kWt] Thermal energy extracted in the condenser                          case 2      %To calculate thermal energy given electrical power (Qin is here, the electrical power)                                 Eelectrical=Qin+Eelectrical_par;%[kW] Electrical power desired                                   if Eelectrical>Pmin && Eelectrical<Pmax                                         E_thermal(1)=(fzero(@(x)((F0+F1*(x/QdesignB)^1+F2*(x/QdesignB)^2+F3*(x/QdesignB)^3)*Pdesign)-Eelectrical,QdesignB))/E_boiler;              %[kWth] Thermal energy required for the specified electrical power with boiler eff. 172                      E_thermal(2)=(F0+F1*(E_thermal(1)/QdesignB)^1+F2*(E_thermal(1)/QdesignB)^2+F3*(E_thermal(1)/QdesignB)^3)*Qheat*E_condenser;                   %[kW] Thermal energy extracted in the condenser                     Eelectrical=Eelectrical-Eelectrical_par;                                                                                                    %[kW] NET Electrical power generated                 else                     E_thermal(1)=0;                     E_thermal(2)=0;                     Eelectrical=0;                 end             otherwise                 disp('other value for function MAE')         end end  FUNCTION daily_monthly( B,z ) function [ A,AA ] = daily_monthly( B,z ) % z=1  sum % z=2  mean %% function to add daily values into monthly cells n=size(B); n=n(1);  %Accumulative days D=[31     59     90     120     151     181     212     243     273     304     334     365]; switch z     case 1         tempo=1;         for i=1:12             A(i,1)=sum(B(tempo:D(i,1),1));             AA=0;             tempo=1+D(i,1);         end     case 2         tempo=1;                 for i=1:12             A(i,1)=mean(B(tempo:D(i,1),1));             AA(i,1)=std(B(tempo:D(i,1),1));             tempo=1+D(i,1);         end             otherwise         disp('other value for function MAE') end  173  Appendix F: Additional figures for a two-module Fresnel lens solar thermal collector    Figure VII-1. Bipolar parallel connection to connect stepper motor to drive   (a)                                                 (b)                                          (c)  (d)                                                 (e)                                           (f)  (g)                                                (h)                                            (i)  Figure VII-2. Temperature profiles obtained using FEM simulation* 174  Figure VII-2.  *: (a) 1451 mm2 absorber area and 256 CR; (b) 1451 mm2 absorber area and 576 CR; (c) 1451 mm2 absorber area and 1000 CR; (d) 2580 mm2 absorber area and 256 CR; (e) 2580 mm2 absorber area and 576 CR; (f) 2580 mm2 absorber area and 1000 CR; (g) 4032 mm2 absorber area and 256 CR; (h) 4032 mm2 absorber area and 576 CR; (i) 4032 mm2 absorber area and 1000 CR       175  Appendix G: Astronomical algorithm for solar tracking system   %This script receives minute, second, day, month, year, hour, observer %time, latitude, longitud and elevation to calculate the topocentric %position of the sun P=820; %millibars    annual average local pressure T=11; %C  annual average local temperature JULIAN CALCULATION if(month == 1 || month == 2)     Year=year-1;     Month=month+12; else     Year=year;     Month=month; end ut_time = ((hour - UTC)/24) + (minute/(60*24)) + (second/(60*60*24)); D = day + ut_time; if(year == 1582)     if(month == 10)         if(day <= 4) % The Julian calendar ended on October 4, 1582             Earth_heliocentric_position_latitude = 0;         elseif(day >= 15) % The Gregorian calendar started on October 15, 1582             A = floor(Year/100);             Earth_heliocentric_position_latitude = 2 - A + floor(A/4);         else             disp('This date never existed!');             month = 10;             day = 4;             Earth_heliocentric_position_latitude = 0;         end     elseif(month<10) % Julian calendar         Earth_heliocentric_position_latitude = 0;     else % Gregorian calendar         A = floor(Year/100);         Earth_heliocentric_position_latitude = 2 - A + floor(A/4);     end  elseif(year<1582) % Julian calendar     Earth_heliocentric_position_latitude = 0; else     A = floor(Year/100); % Gregorian calendar     Earth_heliocentric_position_latitude = 2 - A + floor(A/4); end POLYNOMIAL EXPRESSION FOR DELTA T (DT) yy=year+(month-0.5)/12; tt=yy-2000; DT=62.92+0.32217*tt+0.005589*tt^2; %the difference between the Earth rotation time and the Terrestrial Time(TT) 176  %valid for years between 2005 - 2050 delta_t =DT;  Julian_day = floor(365.25*(Year+4716)) + floor(30.6001*(Month+1)) + D + Earth_heliocentric_position_latitude - 1524.5; Julian_ephemeris_day = Julian_day + (delta_t/86400); Julian_century = (Julian_day - 2451545) / 36525; Julian_ephemeris_century = (Julian_ephemeris_day - 2451545) / 36525; Julian_ephemeris_millenium = Julian_ephemeris_century / 10;  L0table = [175347046.0 0 0  3341656.0 4.6692568 6283.07585  34894.0 4.6261 12566.1517  3497.0 2.7441 5753.3849  3418.0 2.8289 3.5231  3136.0 3.6277 77713.7715  2676.0 4.4181 7860.4194  2343.0 6.1352 3930.2097  1324.0 0.7425 11506.7698  1273.0 2.0371 529.691  1199.0 1.1096 1577.3435  990 5.233 5884.927  902 2.045 26.298  857 3.508 398.149  780 1.179 5223.694  753 2.533 5507.553  505 4.583 18849.228  492 4.205 775.523  357 2.92 0.067  317 5.849 11790.629  284 1.899 796.298  271 0.315 10977.079  243 0.345 5486.778  206 4.806 2544.314  205 1.869 5573.143  202 2.4458 6069.777  156 0.833 213.299  132 3.411 2942.463  126 1.083 20.775  115 0.645 0.98  103 0.636 4694.003  102 0.976 15720.839  102 4.267 7.114  99 6.21 2146.17  98 0.68 155.42  86 5.98 161000.69  85 1.3 6275.96  85 3.67 71430.7  80 1.81 17260.15  79 3.04 12036.46  71 1.76 5088.63  74 3.5 3154.69  74 4.68 801.82  70 0.83 9437.76 177   62 3.98 8827.39  61 1.82 7084.9  57 2.78 6286.6  56 4.39 14143.5  56 3.47 6279.55  52 0.19 12139.55  52 1.33 1748.02  51 0.28 5856.48  49 0.49 1194.45  41 5.37 8429.24  41 2.4 19651.05  39 6.17 10447.39  37 6.04 10213.29  37 2.57 1059.38  36 1.71 2352.87  36 1.78 6812.77  33 0.59 17789.85  30 0.44 83996.85  30 2.74 1349.87  25 3.16 4690.48];  L1table = [628331966747.0 0 0  206059.0 2.678235 6283.07585  4303.0 2.6351 12566.1517  425.0 1.59 3.523  119.0 5.796 26.298  109.0 2.966 1577.344  93 2.59 18849.23  72 1.14 529.69  68 1.87 398.15  67 4.41 5507.55  59 2.89 5223.69  56 2.17 155.42  45 0.4 796.3  36 0.47 775.52  29 2.65 7.11  21 5.34 0.98  19 1.85 5486.78  19 4.97 213.3  17 2.99 6275.96  16 0.03 2544.31  16 1.43 2146.17  15 1.21 10977.08  12 2.83 1748.02  12 3.26 5088.63  12 5.27 1194.45  12 2.08 4694  11 0.77 553.57  10 1.3 3286.6  10 4.24 1349.87  9 2.7 242.73  9 5.64 951.72  8 5.3 2352.87  6 2.65 9437.76 178   6 4.67 4690.48];  L2table = [52919.0 0 0  8720.0 1.0721 6283.0758  309.0 0.867 12566.152  27 0.05 3.52  16 5.19 26.3  16 3.68 155.42  10 0.76 18849.23  9 2.06 77713.77  7 0.83 775.52  5 4.66 1577.34  4 1.03 7.11  4 3.44 5573.14  3 5.14 796.3  3 6.05 5507.55  3 1.19 242.73  3 6.12 529.69  3 0.31 398.15  3 2.28 553.57  2 4.38 5223.69  2 3.75 0.98];  L3table =[289.0 5.844 6283.076  35 0 0  17 5.49 12566.15  3 5.2 155.42  1 4.72 3.52  1 5.3 18849.23  1 5.97 242.73];  L4table = [114.0 3.142 0  8 4.13 6283.08  1 3.84 12566.15];  L5table = [1 3.14 0];   A0=L0table(:,1); B0=L0table(:,2); C0=L0table(:,3); A1=L1table(:,1); B1=L1table(:,2); C1=L1table(:,3); A2=L2table(:,1); B2=L2table(:,2); C2=L2table(:,3); A3=L3table(:,1); B3=L3table(:,2); C3=L3table(:,3); A4=L4table(:,1); B4=L4table(:,2); C4=L4table(:,3); A5=L5table(:,1); 179  B5=L5table(:,2); C5=L5table(:,3);  L0 = sum(A0 .* cos(B0 + (C0 * Julian_ephemeris_millenium))); L1 = sum(A1 .* cos(B1 + (C1 * Julian_ephemeris_millenium))); L2 = sum(A2 .* cos(B2 + (C2 * Julian_ephemeris_millenium))); L3 = sum(A3 .* cos(B3 + (C3 * Julian_ephemeris_millenium))); L4 = sum(A4 .* cos(B4 + (C4 * Julian_ephemeris_millenium))); L5 = sum(A5 .* cos(B5 + (C5 * Julian_ephemeris_millenium)));  %Earth heliocentric position longitude L Earth_heliocentric_position_longitude=(L0+L1*Julian_ephemeris_millenium+L2*Julian_ephemeris_millenium^2+L3*Julian_ephemeris_millenium^3+L4*Julian_ephemeris_millenium^4+L5*Julian_ephemeris_millenium^5)/1e8; %RADS Earth_heliocentric_position_longitude=Earth_heliocentric_position_longitude*180/pi;%DEG  %Limiting Earth_heliocentric_position_longitude to 360°interval Earth_heliocentric_position_longitude = Earth_heliocentric_position_longitude - 360 * floor(Earth_heliocentric_position_longitude/360); if(Earth_heliocentric_position_longitude<0)     Earth_heliocentric_position_longitude = Earth_heliocentric_position_longitude + 360; end  %^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ B0table = [280.0 3.199 84334.662  102.0 5.422 5507.553  80 3.88 5223.69  44 3.7 2352.87  32 4 1577.34];  B1table = [9 3.9 5507.55  6 1.73 5223.69];  A0=B0table(:,1); B0=B0table(:,2); C0=B0table(:,3); A1=B1table(:,1); B1=B1table(:,2); C1=B1table(:,3);  L0=sum(A0 .* cos(B0 + (C0 * Julian_ephemeris_millenium))); L1=sum(A1 .* cos(B1 + (C1 * Julian_ephemeris_millenium)));  %Earth heliocentric position latitude B Earth_heliocentric_position_latitude=(L0+L1*Julian_ephemeris_millenium)/100000000; Earth_heliocentric_position_latitude=Earth_heliocentric_position_latitude*180/pi; %DEG  %^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^  % R terms from the original code R0table = [ 100013989.0 0 0  1670700.0 3.0984635 6283.07585 180   13956.0 3.05525 12566.1517  3084.0 5.1985 77713.7715  1628.0 1.1739 5753.3849  1576.0 2.8469 7860.4194  925.0 5.453 11506.77  542.0 4.564 3930.21  472.0 3.661 5884.927  346.0 0.964 5507.553  329.0 5.9 5223.694  307.0 0.299 5573.143  243.0 4.273 11790.629  212.0 5.847 1577.344  186.0 5.022 10977.079  175.0 3.012 18849.228  110.0 5.055 5486.778  98 0.89 6069.78  86 5.69 15720.84  86 1.27 161000.69  85 0.27 17260.15  63 0.92 529.69  57 2.01 83996.85  56 5.24 71430.7  49 3.25 2544.31  47 2.58 775.52  45 5.54 9437.76  43 6.01 6275.96  39 5.36 4694  38 2.39 8827.39  37 0.83 19651.05  37 4.9 12139.55  36 1.67 12036.46  35 1.84 2942.46  33 0.24 7084.9  32 0.18 5088.63  32 1.78 398.15  28 1.21 6286.6  28 1.9 6279.55  26 4.59 10447.39];  R1table = [ 103019.0 1.10749 6283.07585  1721.0 1.0644 12566.1517  702.0 3.142 0  32 1.02 18849.23  31 2.84 5507.55  25 1.32 5223.69  18 1.42 1577.34  10 5.91 10977.08  9 1.42 6275.96  9 0.27 5486.78];  R2table = [4359.0 5.7846 6283.0758  124.0 5.579 12566.152  12 3.14 0  9 3.63 77713.77 181   6 1.87 5573.14  3 5.47 18849];  R3table = [145.0 4.273 6283.076  7 3.92 12566.15];  R4table = [4 2.56 6283.08];  A0 = R0table(:,1); B0 = R0table(:,2); C0 = R0table(:,3);  A1 = R1table(:,1); B1 = R1table(:,2); C1 = R1table(:,3);  A2 = R2table(:,1); B2 = R2table(:,2); C2 = R2table(:,3);  A3 = R3table(:,1); B3 = R3table(:,2); C3 = R3table(:,3);  A4 = R4table(:,1); B4 = R4table(:,2); C4 = R4table(:,3);  % Compute the Earth heliocentric radius vector L0 = sum(A0 .* cos(B0 + (C0 * Julian_ephemeris_millenium))); L1 = sum(A1 .* cos(B1 + (C1 * Julian_ephemeris_millenium))); L2 = sum(A2 .* cos(B2 + (C2 * Julian_ephemeris_millenium))); L3 = sum(A3 .* cos(B3 + (C3 * Julian_ephemeris_millenium))); L4 = A4 .* cos(B4 + (C4 * Julian_ephemeris_millenium));  % Units are in AU earth_heliocentric_position_radius = (L0 + (L1 * Julian_ephemeris_millenium) + (L2 * Julian_ephemeris_millenium^2) + (L3 * Julian_ephemeris_millenium^3) + (L4 * Julian_ephemeris_millenium^4)) / 1e8; GEOCENTRIC LONGITUDE AND LATITUDE %Geocentric Longitude Geocentric_longitude=Earth_heliocentric_position_longitude+180; %deg %Limiting Geocentric_longitude to 360°interval Geocentric_longitude = Geocentric_longitude - 360 * floor(Geocentric_longitude/360); if(Geocentric_longitude<0)     Geocentric_longitude = Geocentric_longitude + 360; end %Geocentric latitude Geocentric_latitude=-Earth_heliocentric_position_latitude; %deg THE NUTATION IN LONGITUDE AND OBLIQUITY 182  %mean elongation of the moon from the sun X0=297.85036+445267.11148*Julian_ephemeris_century-0.0019142*Julian_ephemeris_century^2+(Julian_ephemeris_century^3)/189474; %the mean anomaly of the sun (Earth) X1=357.52772+35999.05034*Julian_ephemeris_century-0.0001603*Julian_ephemeris_century^2-(Julian_ephemeris_century^3)/300000; %the mean anomaly of the moon X2=134.96298+477198.867398*Julian_ephemeris_century+0.0086972*Julian_ephemeris_century^2+(Julian_ephemeris_century^3)/56250; s argument of latitude X3=93.27191+483202.017538*Julian_ephemeris_century-0.0036825*Julian_ephemeris_century^2+Julian_ephemeris_century^3/327270; mean equinox of the date X4=125.04452-1934.136261*Julian_ephemeris_century+0.0020708*Julian_ephemeris_century^2+Julian_ephemeris_century^3/450000;  PTFNLO=[0 0 0 0 1 -171996 -174.2 92025 8.9 -2 0 0 2 2 -13187 -1.6 5736 -3.1 0 0 0 2 2 -2274 -0.2 977 -0.5 0 0 0 0 2 2062 0.2 -895 0.5 0 1 0 0 0 1426 -3.4 54 -0.1 0 0 1 0 0 712 0.1 -7 0 -2 1 0 2 2 -517 1.2 224 -0.6 0 0 0 2 1 -386 -0.4 200 0 0 0 1 2 2 -301 0 129 -0.1 -2 -1 0 2 2 217 -0.5 -95 0.3 -2 0 1 0 0 -158 0 0 0 -2 0 0 2 1 129 0.1 -70 0 0 0 -1 2 2 123 0 -53 0 2 0 0 0 0 63 0 0 0 0 0 1 0 1 63 0.1 -33 0 2 0 -1 2 2 -59 0 26 0 0 0 -1 0 1 -58 -0.1 32 0 0 0 1 2 1 -51 0 27 0 -2 0 2 0 0 48 0 0 0 0 0 -2 2 1 46 0 -24 0 2 0 0 2 2 -38 0 16 0 0 0 2 2 2 -31 0 13 0 0 0 2 0 0 29 0 0 0 -2 0 1 2 2 29 0 -12 0 0 0 0 2 0 26 0 0 0 -2 0 0 2 0 -22 0 0 0 0 0 -1 2 1 21 0 -10 0 0 2 0 0 0 17 -0.1 0 0 2 0 -1 0 1 16 0 -8 0 -2 2 0 2 2 -16 0.1 7 0 0 1 0 0 1 -15 0 9 0 -2 0 1 0 1 -13 0 7 0 0 -1 0 0 1 -12 0 6 0 0 0 2 -2 0 11 0 0 0 2 0 -1 2 1 -10 0 5 0 2 0 1 2 2 -8 0 3 0 183  0 1 0 2 2 7 0 -3 0 -2 1 1 0 0 -7 0 0 0 0 -1 0 2 2 -7 0 3 0 2 0 0 2 1 -7 0 3 0 2 0 1 0 0 6 0 0 0 -2 0 2 2 2 6 0 -3 0 -2 0 1 2 1 6 0 -3 0 2 0 -2 0 1 -6 0 3 0 2 0 0 0 1 -6 0 3 0 0 -1 1 0 0 5 0 0 0 -2 -1 0 2 1 -5 0 3 0 -2 0 0 0 1 -5 0 3 0 0 0 2 2 1 -5 0 3 0 -2 0 2 0 1 4 0 0 0 -2 1 0 2 1 4 0 0 0 0 0 1 -2 0 4 0 0 0 -1 0 1 0 0 -4 0 0 0 -2 1 0 0 0 -4 0 0 0 1 0 0 0 0 -4 0 0 0 0 0 1 2 0 3 0 0 0 0 0 -2 2 2 -3 0 0 0 -1 -1 1 0 0 -3 0 0 0 0 1 1 0 0 -3 0 0 0 0 -1 1 2 2 -3 0 0 0 2 -1 -1 2 2 -3 0 0 0 0 0 3 2 2 -3 0 0 0 2 -1 0 2 2 -3 0 0 0 ];  for i=1:63 PTFNLO(i,10)=PTFNLO(i,1)*X0+PTFNLO(i,2)*X1+PTFNLO(i,3)*X2+PTFNLO(i,4)*X3+PTFNLO(i,5)*X4; PTFNLO(i,11)=(PTFNLO(i,6)+PTFNLO(i,7)*Julian_ephemeris_century)*sin(PTFNLO(i,10)*pi/180); PTFNLO(i,12)=(PTFNLO(i,8)+PTFNLO(i,9)*Julian_ephemeris_century)*cos(PTFNLO(i,10)*pi/180); end  %the nutation in longitude Nutation_longitude=sum(PTFNLO(:,11))/36000000;%deg %the nutation in obliquity Nutation_obliquity=sum(PTFNLO(:,12))/36000000;%deg   THE TRUE OBLIQUITY OF THE ECLIPTIC U=Julian_ephemeris_millenium/10; %the mean obliquity of the ecliptic mean_obliquity_ecliptic=84381.448-4680.93*U-1.55*U^2+1999.25*U^3-51.38*U^4-249.67*U^5-39.05*U^6+7.12*U^7+27.87*U^8+5.79*U^9+2.45*U^10; %arc seconds %the true obliquity of the ecliptic true_obliquity_ecliptic=mean_obliquity_ecliptic/3600+Nutation_obliquity; %deg THE ABERRATION CORRECTION 184  %Aberration_correction Aberration_correction=-20.4898/(3600*earth_heliocentric_position_radius); %deg THE APPARENT SUN LONGITUDE Apparent_sun_longitude=Geocentric_longitude+Nutation_longitude+Aberration_correction;%deg THE APPARENT SIDEREAL TIME AT GREENWICH AT ANY GIVEN TIME %Apparent_sidereal_time Apparent_sidereal0_time=280.46061837+360.98564736629*(Julian_day-2451545)+0.000387933*Julian_century^2-Julian_century^3/38710000;  %Limiting Apparent_sidereal_time to 360°interval Apparent_sidereal0_time = Apparent_sidereal0_time - 360 * floor(Apparent_sidereal0_time/360); if(Apparent_sidereal0_time<0)     Apparent_sidereal0_time = Apparent_sidereal0_time + 360; end  %the apparent sidereal time at Greenwich Apparent_sidereal_time_greenwich=Apparent_sidereal0_time+Nutation_longitude*cos(true_obliquity_ecliptic*pi/180);%deg THE GEOCENTRIC SUN RIGHT ASCENSION Y = (sin(Apparent_sun_longitude * pi/180) * cos(true_obliquity_ecliptic * pi/180)) - (tan(Geocentric_latitude * pi/180) * sin(true_obliquity_ecliptic * pi/180)); X = cos(Apparent_sun_longitude * pi/180);  sun_right_ascension = atan2(Y, X);  sun_right_ascension =sun_right_ascension*180/pi; %degrees  %Limiting sun_right_ascension to 360°interval sun_right_ascension = sun_right_ascension - 360 * floor(sun_right_ascension/360); if(sun_right_ascension<0)     sun_right_ascension = sun_right_ascension + 360; end THE GEOCENTRIC SUN DECLINATION Geocentric_sun_declination=asin(sin(Geocentric_latitude* pi/180)*cos(true_obliquity_ecliptic*pi/180)+cos(Geocentric_latitude*pi/180)*sin(true_obliquity_ecliptic*pi/180)*sin(Apparent_sun_longitude*pi/180))*180/pi; %where it is positive or negative if the sun is north or south of the celestial equator,respectively THE OBSERVER LOCAL HOUR ANGLE Observer_local_hour_angle=Apparent_sidereal_time_greenwich+longitude-sun_right_ascension;  %Limiting H to 360°interval Observer_local_hour_angle = Observer_local_hour_angle - 360 * floor(Observer_local_hour_angle/360); if(Observer_local_hour_angle<0) 185      Observer_local_hour_angle = Observer_local_hour_angle + 360; end THE TOPOCENTRIC SUN RIGHT ASCENSION %the equatorial horizontal parallax of the sun Equatorial_horizontal_parallax=8.794/(3600*earth_heliocentric_position_radius); %deg  %the term u latitude=latitude*pi/180; Term_u=atan(0.99664719*tan(latitude));  %the term x Term_x=cos(Term_u)+(elevation/(6378140))*cos(latitude*pi/180);  %the term y Term_y=0.99664719*sin(Term_u)+(elevation/6378140)*sin(latitude*pi/180);  %the parallax in the sun right ascension Parallax_sun_right_ascension=atan2((-Term_x*sin(Equatorial_horizontal_parallax*pi/180)*sin(Observer_local_hour_angle*pi/180)),(cos(Geocentric_sun_declination*pi/180)-Term_x*sin(Equatorial_horizontal_parallax*pi/180)*cos(Observer_local_hour_angle*pi/180))); Parallax_sun_right_ascension=Parallax_sun_right_ascension*180/pi;   %the topocentric sun right ascension topocentric_sun_right_ascension=Parallax_sun_right_ascension+sun_right_ascension;  %the topocentric sun declination topocentric_sun_declination=atan(((sin(Geocentric_sun_declination*pi/180)-Term_y*sin(Equatorial_horizontal_parallax*pi/180))*cos(Parallax_sun_right_ascension*pi/180))/(cos(Geocentric_sun_declination*pi/180)-Term_x*sin(Equatorial_horizontal_parallax*pi/180)*cos(Observer_local_hour_angle*pi/180))); topocentric_sun_declination=topocentric_sun_declination*180/pi; %degrees THE TOPOCENTRIC LOCAL HOUR ANGLE Topocentric_local_angle=Observer_local_hour_angle-Parallax_sun_right_ascension;%deg THE TOPOCENTRIC ZENITH ANGLE %the topocentric elevationation angle without atmospheric refraction correction topocentric_elevation_angle_Wo_atm_refract_correct=asin(sin(latitude)*sin(topocentric_sun_declination*pi/180)+cos(latitude)*cos(topocentric_sun_declination*pi/180)*cos(Topocentric_local_angle*pi/180)); topocentric_elevation_angle_Wo_atm_refract_correct=topocentric_elevation_angle_Wo_atm_refract_correct*180/pi; %degrees  %the atmospheric refraction correction atmosferic_refraction_correction=(P/1010)*(283/(273+T))*(1.02/(60*tan((topocentric_elevation_angle_Wo_atm_refract_correct+10.3/(topocentric_elevation_angle_Wo_atm_refract_correct+5.11))*pi/180)));   186  %the topocentric elevationation angle topocentric_elevation_angle=topocentric_elevation_angle_Wo_atm_refract_correct+atmosferic_refraction_correction;%degrees Topocentric_zenith_angle=90-topocentric_elevation_angle; %degress THE TOPOCENTRIC AZIMUTH ANGLE %topocentric astronomers azimuth angle topocentric_astronomers_azimuth_angle=atan2((sin(Topocentric_local_angle*pi/180)),(cos(Topocentric_local_angle*pi/180)*sin(latitude)-tan(topocentric_sun_declination*pi/180)*cos(latitude)));%rad topocentric_astronomers_azimuth_angle=topocentric_astronomers_azimuth_angle*180/pi; %deg  %Limiting to 360°interval topocentric_astronomers_azimuth_angle = topocentric_astronomers_azimuth_angle - 360 * floor(topocentric_astronomers_azimuth_angle/360); if(topocentric_astronomers_azimuth_angle<0)     topocentric_astronomers_azimuth_angle = topocentric_astronomers_azimuth_angle + 360; end  %the topocentric azimuth angle Topocentric_azimuth_angle=topocentric_astronomers_azimuth_angle+180;  %Limiting F to 360°interval Topocentric_azimuth_angle = Topocentric_azimuth_angle - 360 * floor(Topocentric_azimuth_angle/360); if(Topocentric_azimuth_angle<0)     Topocentric_azimuth_angle = Topocentric_azimuth_angle + 360; end Script output taa=Topocentric_azimuth_angle; tza=Topocentric_zenith_angle;     187  Appendix H: LabVIEW screenshots for control in solar tracking system  The user enters the information about location, desired focal length (for concentration ratio). The interface shows the topocentric azimuth and zenith angle, before and after the filter (round up or down), number of steps for motors, and error dialogs (Figure VII-3).    Figure VII-3. User interface for the solar tracking system        188   the astronomical algorithm sub-VI. After the calculation of the topocentric azimuth and zenith angles, the script compares those values to the permissible range of movement for the unit (Figure VII-4).   Figure VII-4. Main LabView script. Part 1 (including Sub-VI astronomical algorithm)      189  The topocentric zenith and azimuth angle values enter in a loop that runs each 30 seconds (Elapsed time), where are converted into number of steps for the motors. Data such as number of steps and position are stored in an Excel file. The number of steps are used for a movement sequence (one for each motor) for the lens adjustment (Figure VII-5).   Figure VII-5. Main LabView script. Part 2 (including Sub-VI Motor steps calculations and Motor sequence)         190  Figure VII-5.                 191  The sub-VI calculates the topocentric zenith and azimuth angles using a Matlab script. The sub-Vi requires location and time values for the calculation (Figure VII-6).    Figure VII-6. Sub-VI astronomical algorithm          192  The Sub-VI for steps calculations depends on the geometrical characteristics of the bench scale unit. The topocentric angles are converted into steps based on gearbox reduction ratio and linear displacement of the mechanical actuators (Figure VII-7).    Figure VII-7. Sub-VI Motor steps calculations          193  The motor sequence include the reading od velocity, acceleration, deceleration, number of steps, and the specific command in SCL language (Figure VII-8).    Figure VII-8. Sub-VI Motor sequence. 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