Techno-economic optimization of a solar thermal power generator based on parabolic dish collector and micro gas turbine.

Department of Energy Enegineering School of Engineering - ETSI University of Seville Techno-Economic Optimization of a Solar Thermal Power Generator Based on Parabolic Dish and Micro Gas Turbine Giacomo Gavagnin Seville, November 2018 Research work submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy PhD programme in Energy, Chemical and Environmental Engineering Department of Energy Enegineering School of Engineering - ETSI University of Seville Techno-Economic Optimization of a Solar Thermal Power Generator Based on Parabolic Dish and Micro Gas Turbine Author: Giacomo Gavagnin Supervisor: Prof. David Sánchez, University of Seville Co-Supervisor: Dr. Sergio Rech, University of Padova Seville, November 2018 Research work submitted to the Department of Energy Engineering, School of Engineering, of the University of Seville in partial fulfillment of the requirements for the degree of Doctor of Philosophy No great discovery was ever made without a bold guess. — Isaac Newton To my famiy... Acknowledgements I wish to acknowledge the main supervisor of this thesis, Prof. David Sánchez, for the long time motivation, guidance and help throughout the course of the OMSoP project and doctoral studies. I am also grateful to Dr. Sergio Rech, second supervisor of this thesis, and to Prof. Andrea Lazzaretto for their support from the very beginning of the thesis and, in particular, during the period of doctoral study abroad, at the University of Padua. I would also like to express my appreciation of the academic support received at both the University of Seville and the University of Padua. I wish to acknowledge the European Union and the companies involved for funding the OMSoP project. I am also grateful to the OMSoP project members whom I had the opportunity and the priviledge to meet. They have been a delightful team to work with and a precious help for this thesis. Above all, I am grateful to my family for their continous support and confidence. Finally, I am also thankful to my friends in Spain, in Italy and all over the world. Seville, 12th November 2018 G. G. i Resumen El aprovechamiento de energía solar con un sistema de producción de potencia microtermosolar basado en un colector de disco parabólico y una microturbina de gas resulta prometedor para suministrar electricidad a comunidades remotas no conectadas a red y para, de manera general, incrementar la contribución de las energías renovables al panorama energético mundial. No obstante, el ímpetu investigador surgido a raíz de la crisis del petróleo de los años setenta fue abandonado posteriormente casi por completo debido a la caída de los precios del combustible fósil y a la falta de apoyo institucional. A pesar de alguna actividad ocasional, no fue hasta la llegada del proyecto OMSoP (Optimised Microturbine SOlar Power generator) en 2013, financiado por la Comision Europea a través del Programa Marco VII, cuando se retomó esta solución tecnológica con decisión. Sobre la base de capacidades complementarias en varias áreas tecnológicas, el proyecto pretendió (y consiguió) demostrar la viabilidad tecno-económica del concepto. En este escenario, la presente tesis está centrada en la optimización de un sistema de producción de potencia termosolar formado por un colector de disco parabólico y una microturbina de gas, con el objetivo de proporcionar una respuesta sólida (esperemos que definitiva) a la pregunta planteada originalmente por el proyecto OMSoP: "¿Pueden los sistemas discomicroturbina ser económicamente rentables en el futuro? Y, en caso afirmativo, ¿qué hace falta para conseguir dicha rentabilidad?" Con este objetivo en mente, la tesis se estructura en tres secciones claramente diferenciadas, cada una de las cuales hace uso de metodologías avanzadas, desarrolladas por el autor odisponibles en la literatura, todas ellas integradas en una plataforma de simulación innovadora. El modelo que evalúa el diseño de los componentes y el comportamiento termodinámico del sistema está compuesto por submodelos cero-dimensionales para la mayoría de los componentes principales, dado que estos resultan escalables con el tamaño adecuadamente: colector, receptor solar, intercambiadores de calor, alternador. Estos modelos están validados con datos disponibles en la literatura o con datos experimentales obtenidos durante el desarrollo del proyecto OMSoP. En el caso de las turbomáquinas, no obstante, se sabe que las pérdidas de energía aumentan de manera no lineal cuando el tamaño de la máquina disminuye (menor número de Reynolds, mayores pérdidas intersticiales y de venteo, etc.), aspecto que se indentificó desde un primer momento como una fuente potencial de pérdida de eficiencia que debía ser tenida en cuenta en la investigación. Por ello, se desarrollaron herramientas unidimensionales (códigos de línea media) de diseño y análisis de compresores y turbinas radiales, adaptadas a las especificaciones particulares de OMSoP. El simulador global resultante demostró ser capaz de proporcionar diseños preliminares de las turbomáquinas y de realizar análisis del sistema en condiciones de diseño y fuera de diseño, en operación estacionaria. Se han considerado tres configuraciones de microturbina: ciclo simple regenerativo, ciclo iii Contents 3 Design engineering 41 3.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.2 Components design and off-design modelling . . . . . . . . . . . . . . . . . . . . 42 3.2.1 Dish concentrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.2 Solar receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.2.3 Turbomachinery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2.4 Recuperator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.2.5 Intercooler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.2.6 Combustor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.2.7 Electric generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.3 System models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.3.1 Simple Recuperated Solar-Only system (SR-SO) . . . . . . . . . . . . . . . 54 3.3.2 Intercooled Recuperated Solar-Only System (ICR-SO) . . . . . . . . . . . 59 3.3.3 Recuperated Solar-Only System with Intercooling and Reheat (ICRR-SO) 61 3.3.4 Simple Recuperated Hybrid system with Serial Heating (SR-HS) . . . . . 63 3.3.5 Simple Recuperated Hybrid system with Parallel Heating (SR-HP) . . . . 65 3.3.6 Simple Recuperated Booster system with Serial Heating (SR-BS) . . . . . 67 3.3.7 Simple Recuperated Booster system with Parallel Heating (SR-BP) . . . . 69 3.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3.4.1 Solar-only systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.4.2 Hybrid systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.4.3 Booster systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 3.5 Summary and findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4 Cost engineering 101 4.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4.2 Cost estimation and modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 4.2.1 Dish collector - manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.2.2 Solar receiver - manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.2.3 Microturbine - manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . 114 4.2.4 Balance Of Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.2.5 Transportation, installation and fees . . . . . . . . . . . . . . . . . . . . . 119 4.2.6 Other costs, operation and maintenance . . . . . . . . . . . . . . . . . . . 120 4.2.7 Competing technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4.3 Cost analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4.4 Summary and findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5 Project appraisal 129 5.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5.2 Economic and financial models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.2.1 Metrics of project feasibility and profitability . . . . . . . . . . . . . . . . 135 5.3 Economic and financial analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 5.3.1 Solar-only projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 5.3.2 Hybrid projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 5.4 Summary and findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 x Contents 6 Optimization 143 6.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 6.1.1 Optimization environment . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 6.1.2 Optimizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 6.2 Single objective optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 6.3 Multi objective optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 6.4 Summary and findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 7 Conclusions 157 7.1 Critical review of assumptions and methodology . . . . . . . . . . . . . . . . . . 157 7.2 Conclusions: Is it cost-effective then? . . . . . . . . . . . . . . . . . . . . . . . . . . 159 7.3 Future research activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 7.4 List of publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 A Turbomachinery design models 163 A.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 A.1.1 Thermodynamics and fluid mechanics . . . . . . . . . . . . . . . . . . . . 164 A.1.2 Boundary layer analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 A.1.3 Clearances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 A.2 Radial inflow turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 A.3 Centrifugal compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Bibliography 214 xi List of Figures 1.1 Share of population without access to the grid [1]. . . . . . . . . . . . . . . . . . . 3 1.2 OMSoP project brochure: consortium members, timeline, contacts, webpage and cover. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 OMSoP project brochure: objective, vision and structure. . . . . . . . . . . . . . 9 1.4 Design and optimization of energy systems flowchart [2]. . . . . . . . . . . . . . 11 1.5 Thermal system design flowchart [3]. . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1 Various glass-faceted mirror designs: (a) Infinia Corporation Inc. dish-Stirling system (b) ADVANCO Vanguard dish-Stirling system (c) ANU dish concentrators (d) McDonnell Douglas Aerospace Corporation dish-Stirling system (e) Solar Systems "Dense Array Converters" (f) ANU big dish SG3 (g) SouthWestBraytonEnergy dish system (h) Heliofocus dish Stirling system (i) ANU big dish SG4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2 Various glass-faceted mirror designs: (a) General Electric PDC-1 system (b) Shenandoah system (c) OMNIUM-G system. . . . . . . . . . . . . . . . . . . . . 17 2.3 Schematic of dish system tracking methods: azimunth-elevation (A) and polarequatorial (B). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4 A wall painting from the Uffizi Gallery, Stanzino delle Matematiche, in Florence, Italy, shows the Greek mathematician Archimedes’ mirror burning Roman military ships. Painted in 1600 by Giulio Parigi. . . . . . . . . . . . . . . . . . . . . . . 18 2.5 Stretched membrane dish designs: (a) DISTAL I by SBP (b) SBP dishes installed in Riyadh (c) DISTAL II by SBP (d) Cummins power generation dish-Stirling system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.6 Aperture areas of dish concentrators developed in the past. . . . . . . . . . . . . 21 2.7 Cumulative probability distribution of dish aperture area (based on actual prototypes). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.8 Tubular receiver prototype by University of Roma tre with thermal energy storage integrated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.9 KTH volumetric (left) and impingment (right) receiver prototypes. . . . . . . . 28 3.1 Definition of a parabola [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.2 Schematic layout of the volumetric cavity receiver. . . . . . . . . . . . . . . . . . 47 3.3 Schematic layout of the reheated volumetric cavity receiver. . . . . . . . . . . . 48 3.4 Layout of the intercooler/water cooling subsystem used in the ICR and ICRR systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.5 Non-dimensional performance maps of the alternator: efficiency vs. shaft power (left) and maximum shaft power vs. shaft speed (right). . . . . . . . . . . . . . . 54 xiii List of Figures 3.6 Solar-only layouts: Simple recuperated. . . . . . . . . . . . . . . . . . . . . . . . . 55 3.7 SR-SO system: flowchart of design (left) and off-design (right) models. . . . . . 56 3.8 Solar-only layouts: Intercooled recuperated. . . . . . . . . . . . . . . . . . . . . . 59 3.9 ICR-SO system: flowchart of design (left) and off-design (right) models. . . . . . 60 3.10 ICRR-SO system: flowchart of design (left) and off-design (right) models. . . . . 62 3.11 Solar-only layouts: Recuperated with intercooling and reheat. . . . . . . . . . . 63 3.12 SR-HS system: flowchart of the off-design model. . . . . . . . . . . . . . . . . . . 64 3.13 Hybrid layouts: Simple recuperated with serial (left) and parallel (right) heating. 65 3.14 SR-HP system: flowchart of the off-design model. . . . . . . . . . . . . . . . . . . 66 3.15 SR-BS system: flowchart of the solar subsystem re-design (left) and off design (right) models flowcharts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.16 SR-BP system: flowchart of the solar subsystem re-design (left) and off design (right) models flowcharts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.17 Meridional views of compressors and turbines wheels in the SR solar-only systems. 74 3.18 Meridional views of compressors and turbines wheels in the ICR solar-only system. 75 3.19 Meridional views of compressors and turbines wheels in the ICRR solar-only system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.20 Turbomachinery perfomance maps. SR-I and SR-II systems. . . . . . . . . . . . 77 3.21 Characteristic maps of the low (top) and high (bottom) pressure shaft turbomachinery. ICR system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.22 Characteristic maps of the low (top) and high (bottom) pressure shaft turbomachinery. ICRR system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.23 Off-design strategy of solar-only systems at the rated ambient temperature: net solar-to-electric efficiency (left) and net electric output (right). . . . . . . . . . . 80 3.24 Off-design strategy of solar-only systems at the rated ambient temperature: compressor air flow (left) and shaft rotational speed (right). . . . . . . . . . . . . 80 3.25 Off-design strategy of solar-only systems at the rated ambient temperature: turbine/s inlet and outlet temperatures. . . . . . . . . . . . . . . . . . . . . . . . 81 3.26 Off-design strategy of solar-only systems at the rated ambient temperature: isentropic efficiency of turbomachinery (left) and thermal efficiency of solar receiver and recuperator (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 3.27 Duration curves of hourly DNI (left) and ambient temperature (right) of the three selected locations in a Typical Meteorological Year (provided by SAM). . . 82 3.28 Performance maps of the solar-only SR-I (left) and SR-II (right) systems. . . . . 83 3.29 Running line of thermo-mechanical equilibrium shown in the compressor (left) and turbine maps (right). SR-I and SR-II systems. . . . . . . . . . . . . . . . . . . 85 3.30 Running line of thermo-mechanical equilibrium shown in the compressor (left) and turbine maps (right). ICR-II systems. . . . . . . . . . . . . . . . . . . . . . . . 86 3.31 Running line of thermo-mechanical equilibrium shown in the compressor (left) and turbine maps (right). ICRR-II systems. . . . . . . . . . . . . . . . . . . . . . . 86 3.32 Off-design strategy of pure-hybrid systems at the nominal ambient temperature: net solar-to-electric efficiency (left) and net electric output (right). . . . . . . . . 87 3.33 Off-design strategy of pure-hybrid systems at the nominal ambient temperature: compressor air flow (left) and shaft rotational speed (right). . . . . . . . . . . . . 88 3.34 Off-design strategy of pure-hybrid systems at the nominal ambient temperature: turbine/s inlet and outlet temperatures. . . . . . . . . . . . . . . . . . . . . . . . 88 xiv List of Figures 3.35 Off-design strategy of pure-hybrid systems at the nominal ambient temperature: isentropic efficiencies of turbomachinery (left) and thermal efficiencies of solar receiver and recuperator (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 3.36 Off-design strategy of pure-hybrid systems at the ambient ambient temperature: fuel mass flow (left) and solar share (right). . . . . . . . . . . . . . . . . . . . . . . 89 3.37 Performance maps of the pure-hybrid SR-HS (left) and SR-HP (right) systems. . 90 3.38 Running line of thermo-mechanical equilibrium shown in the compressor (left) and turbine maps (right). SR-HS system. . . . . . . . . . . . . . . . . . . . . . . . 91 3.39 Running line of thermo-mechanical equilibrium shown in the compressor (left) and turbine maps (right). SR-HP system. . . . . . . . . . . . . . . . . . . . . . . . 91 3.40 Off-design strategy of the solar-booster systems at the design ambient temperature: net solar-to-electric efficiency (left) and net electric output (right). . . . . 94 3.41 Off-design strategy of solar-booster systems at the design ambient temperature: compressor air flow (left) and rotational speed (right). . . . . . . . . . . . . . . . 94 3.42 Off-design strategy of solar-booster systems at the design ambient temperature: fuel mass flow (left) and solar share (right). . . . . . . . . . . . . . . . . . . . . . . 95 3.43 Performance maps of the solar-booster eith serial (SR-BS, left) and parallel (SRBP, right) heating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.1 Breakdown of the cost estimation process proposed by NASA. . . . . . . . . . . 103 4.2 Specific cost data of the solar collector as a function of production rate (left) and aperture area (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 4.3 Figure of merit assessing the trade-offs between performance and cost by Truscello. 109 4.4 Relative collector cost as a function of Concentration Ratio (CRre f =3000). . . 110 4.5 Influence of production rate (left) and aperture area (right) on the specific cost of the solar collector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.6 Specific cost data of solar receivers as a function of production rate (left) and net thermal output (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.7 Specific cost function of the volumetric solar receivers as a function of production rate (left) and net thermal output (right). . . . . . . . . . . . . . . . . . . . . 114 4.8 Specific cost of microturbine as a function of production rate (left) and net electric power (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.9 Specific cost of microturbine as a function of mass flow rate (left) and production rate (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.10 Specific cost function of the Balance of Plant. Influence of production rate (left) and aperture area (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.11 Capital cost breakdown for the systems considered. . . . . . . . . . . . . . . . . . 123 4.12 Specific (left) and absolute (right) system PEC. . . . . . . . . . . . . . . . . . . . . 124 4.13 Effect of production volume on specific PEC. . . . . . . . . . . . . . . . . . . . . . 124 4.14 Effect of market size (production volume) on specific PEC. . . . . . . . . . . . . 125 5.1 Comparison of the nominal (left) and real (right) LCoE of the proposed dish-mGT technology and the competing technologies. . . . . . . . . . . . . . . . . . . . . . 139 6.1 Effect of mass flow rate on the main design variables. . . . . . . . . . . . . . . . . 145 6.2 Fitness function results of the single objective optimization. . . . . . . . . . . . 149 6.3 Results of the fitness function in the single objective optimization. . . . . . . . . 150 xv List of Figures 6.4 Additional results of the fitness function in the single objective optimization. . 150 6.5 Results of the fitness functions for multi-objective optimization: SR-BP solarbooster system for 0.1 MWe/year. . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 6.6 Results of the fitness functions for multi-objective optimization (II): SR-BP solarbooster system for 0.1 MWe/year. . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 6.7 Results of the fitness functions for multi-objective optimization (I): SR-HP solarbooster system for 1 MWe/year. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 6.8 Results of the fitness functions for multi-objective optimization (II): SR-HP solarbooster system for 1 MWe/year. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 6.9 Results of the fitness functions for multi-objective optimization (I): SR-II solaronly system for 10-100-1000 MWe/year. . . . . . . . . . . . . . . . . . . . . . . . . 154 6.10 Results of the fitness functions for multi-objective optimization (II): SR-II solaronly system for 10-100-1000 MWel /year. . . . . . . . . . . . . . . . . . . . . . . . 155 A.1 Design flowchart of turbomachinery for single-shaft layouts. . . . . . . . . . . . 163 A.2 Relative clearance (left) and clearance gap (right) as a function of blade height. 168 A.3 Turbine stage radial (left) and meridional (right) views with numbering of the one-dimensional model stations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 A.4 Turbine rotor velocity triangle for the SR-II engine layout. . . . . . . . . . . . . . 170 A.5 Turbine flowcharts for the design model (left) and performance analysis model (right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 A.6 Compressor stage radial (left) and meridional (right) views with numbering of the one-dimensional model stations. . . . . . . . . . . . . . . . . . . . . . . . . . 179 A.7 Compressor impeller velocity triangle for the S-II engine layout. . . . . . . . . . 180 A.8 Compressor flowcharts for the design (left) and performance analysis models (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 xvi List of Tables 1.1 Advantages and disadvantages of photovoltaic systems as reported in literature. 4 1.2 Advantages and disadvantages of dish-Stirling systems as reported in literature [5, 6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Comparison of advantages and disadvantages of photovoltaic, dish-Stirling and dish-microturbine systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1 Timeline of the historical development of small solar-powered devices before 1950. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 Full surface dish concentrator concepts. . . . . . . . . . . . . . . . . . . . . . . . 19 2.3 Glass-faceted dish concepts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4 Strectched-membrane dish concentrator concepts. . . . . . . . . . . . . . . . . . 20 2.5 Active microturbine manufacturers. . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.1 Typical errors of a dish with one standard distribution unit. . . . . . . . . . . . . 45 3.2 Control strategy of the simple recuperated, solar-only system. . . . . . . . . . . 57 3.3 Control strategy of the simple recuperated, hybrid system with serial heating. . 65 3.4 Control strategy of the simple recuperated, hybrid system with parallel heating. 67 3.5 Control strategy of the simple recuperated, booster system with serial heating. 67 3.6 Control strategy of the simple recuperated, booster system with parallel heating. 70 3.7 Constant ambient parameters and system specifications. . . . . . . . . . . . . . 71 3.8 Independent design variables for the various layouts adopted. . . . . . . . . . . 71 3.9 Independent design variables for the various layouts adopted. . . . . . . . . . . 72 3.10 Solar-only systems design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.11 Compressor design specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.12 Turbine design specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.13 Solar-only systems annual performance . . . . . . . . . . . . . . . . . . . . . . . 84 3.14 Solar-only turbines design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.15 Redesigned solar subsystem of the hsolar-booster system. . . . . . . . . . . . . . 93 3.16 Annual performance of the solar-booster systems. . . . . . . . . . . . . . . . . . 97 4.1 Cost correction factors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4.2 Main cost items of the dish-microturbine stand-alone power-only systems. . . 104 4.3 Cost of the solar collector as a function of production rate (or equivalent total aperture area) (I). General Electric/Pioneer engineering dish with 12 meters aperture diameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 xvii List of Tables 4.4 Cost of the solar collector as a function of production rate (or equivalent total aperture area) (II). General Electric/Pioneer engineering dish with 12 meters aperture diameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4.5 Cost data of solar collector provided by Gallup and Kesseli [7]. . . . . . . . . . . 106 4.6 Cost data of solar collector provided by Heller [8] . . . . . . . . . . . . . . . . . . 107 4.7 Collector cost as a function of aperture area as provided by Innova [9] . . . . . . 107 4.8 Coefficients of the dish cost estimator, Eq. 4.6. . . . . . . . . . . . . . . . . . . . . 111 4.9 Coefficients of the volumetric solar receiver cost function. . . . . . . . . . . . . . 114 4.10 Microturbine technology levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 4.11 Coefficients of the Solar-only and hybrid microturbine cost function. . . . . . . 117 4.12 Cost function coefficients for the BoP equipment. . . . . . . . . . . . . . . . . . . 119 4.13 Summary of transportation costs in a 20" container from Seville, Spain (System PEC is 100000 e). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 4.14 Installation costs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4.15 Maintenance costs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4.16 Costs of dish-Stirling and photovoltaic technologies. . . . . . . . . . . . . . . . . 120 4.17 Costs of the solar-only systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.18 Costs of the hybrid and booster systems. . . . . . . . . . . . . . . . . . . . . . . . 122 5.1 General financial parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 5.2 Financial parameters that are specific to the plant site. . . . . . . . . . . . . . . . 136 5.3 Levelized Cost of Electricity of solar-only systems. . . . . . . . . . . . . . . . . . 137 5.4 Financial metrics of the solar-only systems. . . . . . . . . . . . . . . . . . . . . . 138 5.5 LCoE of alternative small scale solar power generators. . . . . . . . . . . . . . . 138 5.6 LCoE of hybrid systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 5.7 Economic performance of hybrid systems. . . . . . . . . . . . . . . . . . . . . . . 141 6.1 Decision variables and design space of the optimization process. . . . . . . . . . 144 xviii Nomenclature Design engineering - symbols −Ibase technology level (800°C-85%) −I I advanced technology level (900°C-90%) αgglass absorptivity [−] ¯ ymass based specific gas composition [−] δVoff design turbomachinery parameter [−] ˙ mmass flow rate [kg/s] ˙ Qheat flux [kW ] ˙ Vvolumetric flow air [m3/s] ²emissivity [−] ²Voff design turbomachinery parameter [−] ²sun sun’s angular size [mrad] ηefficiency [−] γspecific heats ratio [−] ˆ Pel specific electric power output [kW /(kg/s)] ˆ Psol ar specific solar-to-electric power output [kW /m2] Φtotal radiant flux reflected [W] Ψangle between the incident and reflected beam [mrad] ρdensity [kg/m3] ρgglass reflectivity [−] σconcentration error [mrad] σSte f an Stefan-Boltzmann constant [W/(m2·K4)] τgglass transmittance [−] xix List of Tables O&M,kW capacity-based maintenance costs pay payment real real repay repayment (i.e., excluding interests) Optimization - symbols Foptimization function xdesi gn vector of design decision variables xL desi gn vector of design decision variables lower limits xU desi gn vector of design decision variables upper limits Appendix - symbols αabsolute flow angle [°] α0relative flow angle [°] α∗optimum incident flow angle [°] ¯ ωcompressor total pressure loss [−] ¯ CRdiffuser performance coefficient [−] βblade angle [°] χblade’s camber angle [°] ∆normalized mass defect thickness [−] δboundary layer thickness [mm] δ∗velocity profile displacement thickness [mm] δcl clearance height [mm] ∆di f f diffuser discharge fractional blockage [−] δdi sk clearance between disk and housing [m] ˙ Wpower ²compressor impeller radius ratio [−] γnozzle blade setting angle [°] λimpeller tip distortion factor [−] µviscosity [Pa ·s] xxvi List of Tables νturbine velocity ratio [−] ωrotational speed [rad/s] φangle formed by a tangent to the mean surface and the axial direction [°] σslip factor coefficient [−] σ0slip factor coefficient for radius ratio limit [−] σbase slip factor coefficient base value [−] τmat material shear stress [Pa] Θnormalized momentum defect thickness of surface boundary layer [−] θboundary layer momentum thickness [mm] θcdiffuser divergence angle [°] εturbine rotor radius ratio [−] εdi sk disk relative roughness [−] εrpeak-to-valley surface roughness [µm] ξnormalized meridional distance [−] ξslip slip factor correction parameter [−] di f f diffuser lo blade loading Apassage area [mm2] aspeed of sound [m/s] Aoblade angle distribuion parameter [°/m] ARcompressor impeller area ratio [−] AVvolute design parameter [°] Bfractional area blockage [−] bannular passage height [mm] Boblade angle distribuion parameter [°/m2] BVvolute design parameter [°] BL blade loading coefficient [−] Cflow velocity in the absolute frame of reference [m/s] xxvii List of Tables Coblade angle distribuion parameter [°/m3] cfSkin friction coefficient [−] Crcontraction area ratio [−] C0,is turbine spouting velocity [m/s] Cdi f f ,θdiffuser performance coefficient [−] Cdi f f ,Ldiffuser performance coefficient [−] CMtorque coefficient [−] ch blade’s chord [mm] ddiameter [mm] Ddi f f diffuser diffusion factor [−] dhy flow channel hydraulic diameter [mm] Htotal enthalpy [kJ/kg] H0relative total enthalpy [kJ/kg] Hbl boundary layer shape factor [−] Iwork input coefficient [−] i∗optimum incident blade angle [°] Ibl impeller blade work input coefficient [−] Kdiffuser performance analysis parameter [−] kmaverage mean surface curvature [°] Kbl midpassage hub blade angle parameter [−] Lblade path length [mm] MMach number [−] mmeridional flow path length [mm] M0relative Mach number [−] Nrotational speed [kr pm] Nnnomber of nozzle’s blade [−] Nrnumber of rotor’s blades [−] ns,tspecific speed number [−] xxviii List of Tables othroat height [mm] p0 trelative total pressure [Pa] pvr diffuser velocity-pressure ratio [−] Rrothalpy [k J/kg] rradius [mm] Rol fractional polar angle overlap [°] RedReynolds number [−] ReeReynolds number limit for surface roughness effect [−] RerReynolds limit when disk is fully rough [−] ResReynolds limit when disk roughness effect start [−] sblade pitch [mm] SP volute size parameter [−] tblade thickness [mm] Ublade tangential speed [m/s] Uti p turbine and compressor blades tangential speed [m/s] Wflow velocity in the relative fram of reference [m/s] Yturbine loss coefficient [−] Zddiffuser number of blades [−] Ziimpeller number of blades [−] α∗optimum (minimum incidence) absolute flow angle [°] C∗optimum (minimum incidence) absolute velocity [m/s] Appendix - subscripts θtangential velocity component Llaminar flow mmeridional velocity component ttotal basis 0−5flow path stations of turbine and compressor one-dimensional models avg average xxix List of Tables bl blade surface cl clearance comp compressor d f disk friction di sk impeller/rotor disk hhub id ideal inc incidence leak flow leakage lim limit value lo blade loading mech mechanical mid mid passage mix blade wake mixing recir flow recirculation rot rotor sep separation SF skin friction sonic sonic conditions st stall conditions sub subcritical sshroud ti p turbine and compressor blades tip station T L transition from laminar to turbulent flow T R turbulent fully rough-wall flow TS turbulent smooth-wall flow ts total-to-static basis tt total-to-total basis xxx List of Tables tur b turbine vp vaneless passage wake blade wake wall wall surface xxxi 1Introduction This first chapter presents the general background of the thesis -in terms of sustainable development and energy utilization-, an overview of the OMSoP project in the frame of which the work was developed, the author’s vision and statement of purpose for the thesis, a discussion of the specific objectives of the thesis and the associated general methodology and, finally, a brief description of the dissertation structure. 1.1 Background The general background of the thesis is presented in this section. Subsection 1.1.1 presents the concepts sustainable development and sustainable energy after which Subsection 1.1.2 analyzes the challenges faced by the energy sector. This includes the need for more decentralized and sustainable power systems for grid-distributed and off-grid applications. Finally, a review of the current state of the art of small-scale decentralized solar power technologies (photovoltaic and dish-Stirling) suggests that further research on alternative and innovative high efficiency systems is still needed. A brief comparison with dish-microturbine introduces the benefits of the technology. 1.1.1 Sustainable development and energy The contemporary interpretation of sustainable development was proposed in 1987 by the Brundtland Commission, formally known as World Commission on Environment and Development (WCED) [ 10 ]. According to this, one of the critical aspects of sustainability has to do with energy resources. Thus, a sustainable energy resource would be defined as a primary energy source which is consumed at a rate that does not compromise its supply to future generations (or at least not without undesirable collateral effects). The technologies that promote a sustainable power generation industry are based (i) on solar, wind, wave, hydro, geothermal, bio or tidal power and (ii) on conservation and efficiency of energy generation, transportation and use. These two are the pillars on which sustainable energy is founded. According to the Brundtland Commision, there are two main reasons calling for a sustainable development roadmap. A noteworthy increase in energy consumption worldwide is foreseen due to the ever increasing population in certain areas and to the higher specific demand (energy consumption per capita) worldwide, in particular in developing regions. At the same time, there is a growing concern about the environmental and public health problems caused by conventional power generation technologies based on fossil-fuel. These factors confirm that it is necessary that all the players involved, in particular policy-makers, work jointly to develop a single, common strategy to ensure that the energy needs of future generations will 1 Chapter 1. Introduction be satisfied in a sustainable way. To this aim, the political will and institutional cooperation has to be renovated. The centralized power generation system found in most countries today, born and raised during the last century, is mostly based on fossil resources. This concept requires a technological readjustment that is expected to last for, at least, two decades, in order to increase the environmental and societal sustainability of the interrelated systems. Two routes are devised to achieve this objective: (i) readjustment of the centralized generation system to include more sustainable energy resources in the primary energy mix; and (ii) readjustment of the centralized generation system including more grid-distributed and off-grid power technologies based on renewable energy resources. This last option is considered particularly interesting given the sparse nature of most renewable energy sources and the scalability of the associated energy conversion technologies which adapt well to both grid-distributed and off-grid energy systems. Moreover, the need for off-grid renewable power in developing countries can be addressed without high capital investments for power generation and transportation in a centralized paradigm. 1.1.2 Decentralized generation A decentralised generation system produces electricity (and potentially heat) directly at or close to the consumer. This type of power systems were used since the early ages of electric power, XIX century, to provide electricity to local customers. Nevertheless, the XX century saw a change of paradigm from distributed to centralized power generation, mainly due to the visible benefits brought about by economies of scale. With the advent of the XXI century, decentralized generation systems have gained importance again in the light of some inherent problems of the prevailing power generation system layout [ 11 ]: carbon dioxide and other harmful gases, need for a high integration between generation, trasmission and consumption, depletion of fossil fuel resources, security of supply, very high capital investment costs... Decentralized energy systems feature certain benefits since they couple generation and consumption, they are less dependent upon centralized energy supply networks and can also operate off-grid, and they require lower investments in both research and industrial activities. These characteristics make them especially suitable for solar power systems which are typically characterized by high specific installation costs. A useful discussion on the important aspects of decentralized energy systems is given by Karlsson [12]. Distributed generation is a particular kind of dispersed generation and, even if there is not a universal definition of it, it can be said that it is the electric power generation within distribution networks that is located at the customer end of the network. This general definition given by Ackermann in [ 13 ] is just one amidst other given by organizations like IEA and EPRI, whose main differences are found in the output ranges and the voltage levels of the distribution network to which the generator is interconnected. Pepermans states in [ 14 ] that "there is no consensus on a precise definition as the concept encompasses many technologies and applications". In this reference, the author discusses the five major factors that contribute to the increased interest in distributed generation technologies: (i) development of the technology itself (i.e., distributed power generators are now more efficient), (ii) constraints set on the construction of new transmission lines, (iii) increased demand for highly reliable electricity, (iv) liberalization of the electricity market and (v) concern about climate change. These factors were first listed in the IEA report on distributed generation in liberalized electricity markets [15]. 2 1.1. Background Off-grid generation is an alternative way to produce dispersed power independently from any remote infrastructure (transmission lines or fuel/heat distribution networks). Off-grid systems can work either as stand-alone or connected to mini-grids, typically to produce power for a small community. In many developing countries, the national electricity grid is not still able to provide rural communities with a reliable supply of electricity which is, in turn, provided by off-grid power systems. The market for off-grid systems is big though, since it is estimated that about 1.16 billion people worldwide do not have access to electricity today. The majority of these people (95%) live in sub-Saharan Africa and South and East Asia, with the remainder spread across Middle East, Central Asia and Latin America, as shown in Figure 1.1 [1]. Figure 1.1: Share of population without access to the grid [1]. The fraction of the world’s population that does not have direct access to energy/electricity supply, living primarily in rural areas distant from the existing energy infrastructure, offers a unique opportunity for the energy system to be more reliant on local distributed renewable energy resources at a cost lower than or comparable to the construction of traditional distribution and transmission systems. In developed countries, where state grids supply electricity to billions of people worldwide, mini-grids are also increasingly being considered an option to improve the security of supply, power quality and reliability as well as to avoid power blackouts. In this regard, the distributed nature of most types of renewable energies make these the best candidate to produce power off the grid, directly on-site and in a sustainable way, by adapting the technology of choice to the local environment. In the short to medium terms, the market for off-grid renewable energy systems is expected to increase, mostly through the hybridization of existing fossil-fuel generators with wind, photovoltaics (PV), biomass gasification and small hydropower [16, 17]. The following paragraph discusses the current state-of-the-art of the systems for small-scale decentralized solar power generation. These will set the portofolio of alternatives against which the dish-microturbine technology explored in this research will have to compete: photovoltaic panels and dish-Stirling systems. 3 Chapter 1. Introduction energy sources deals with both problems. Moreover, the modularity of such small-scale systems enables the development, optimization and manufacturing of one single system to be mass-produced, and it may hence reduce the associated costs. Solar energy is one of the most abundant and best distributed primary energy sources on Earth, what brings about additional socio-political implications. Indeed, the last century saw a number of armed conflicts triggered by the aim to control fossil fuel resources (for instance oil). In this background, the development of renewable energy systems based on solar energy would be greatly beneficial for a large fraction of the world’s population with limited or no access to fossil fuels or, simply, wishing to utilize the available natural resources in an environmentally friendly way. In this context, solar dish and microturbine systems have the potential to foster the development of regions where access to energy/electricity is limited whilst, at the same time, they can largely contribute to mitigating global warming in the most developed regions of the world . Modularity and other design features like hybridization and storage set the technology apart from similar systems like those based on Stirling engines. With the above in mind, it is deemed that the technology must be revisited from a global techno-economic perspective incorporating the most recent progress in the field. The valuable work done in the past by renown institutions like NASA and DLR, in spite of which the technology did not meet the market, set the ground for this research which incorporates the following innovative features. First, the boundary conditions are different in the sense that Concentrated Solar Power has become a reality all over the world. Then, the approach to the power conversion unit is more general. Different cycle layouts are considered and, rather than adapting an existing assembly (usually a turbocharger), tailored designs for each engine concept are developed. The corresponding impact on system performance is assessed in the thesis. From an economic standpoint, cost and financial analysis are integrated into a single tool as opposed to being independent items for study. This enables performing global optimization in terms of installation ( e /kW e ) and production ( e /MWh) costs in lieu of design for lowest capital cost. Overall, this yields a fully flexible tool to explore the current potential of the technology in comparison with competing technologies like dish-Stirling and photovoltaic systems. The global engineering approach used in the thesis starts off from the review of the design engineering methods used for commercial and/or research and development projects, which are described, discussed and compared in the following, also graphically via flowcharts. Based on the conclusions from this review, a general methodology to be used for the present technoeconomic appraisal is then selected. 1.4 Objectives and methodology This thesis aims at answering the original questions posed by the OMSoP project: Can dishmicroturbine systems be profitable in the future? And if they do, what is needed to ensure this profitability?. These questions trigger other follow-up questions like How competitive are dish-mGT systems against dish-Stirling and photovoltaic systems? Which are the projects locations with highest potential to be successful? Which is the optimum system size?, etc. Based on this background, the overarching objective of this thesis is to assess the real potential of small-scale solar thermal power generators based on dish collector and microturbine integration to fulfil the needs of small consumers (whether individuals or small communities) in a decentralized power generation scenario or in areas that do not have access to electricity. 10 1.4. Objectives and methodology Figure 1.4: Design and optimization of energy systems flowchart [2]. Achieving this main objective implies appraising both the technical and economic features of the system. This involves the completion of a series of tasks, each of which aims at a specific goal. These tasks are listed comprehensively below: •Task 1 : to appraise the current state of the art of the dish-microturbine technology (components and systems), focusing on the components adopted for the OMSoP project. The particular objective of this task is to provide a wide, updated and renovated overview of dish-microturbine systems in order to set the starting line for the OMSoP project itself. •Task 2 : to build a reliable design and off-design model useful to size and simulate dishmicroturbine systems. This model must be able to analyze the basic arrangements and their annual performances in selected locations. The particular objective is to create the tool upon which all the technical features of the system can be assessed throughout the project, therefore enabling the technical optimization of it. •Task 3 : to build a complete cost model from manufacturing to operation, based on the results from the technical model, on the cost dataset provided by the Consortium partners and on further cost data found in literature. The objective is to create a tool compatible with the technical model with which a complete cost assessment of the system can be done. •Task 4 : to establish real business models for dish-microturbine systems and to build their complete economic and financial model. These models will be used to discuss the economic performances of the systems with the objective to appraise the financial feasibility of the project for the selected locations. •Task 5 : to integrate the complete project appraisal model into a multi-objective optimization tool able with the particular objective to find a global optimal solution. 11 Chapter 1. Introduction •Task 6 : To discuss the conclusions of the previous task and to integrate them, yielding the main conclusions of the thesis and the associated future challenges that remain unsolved. There is no particular objective in this task other than collecting all the information in Tasks 1 to 5 in order to discuss whether or not the main objective has been achieved. One of the most relevant methodologies for the design and optimization of energy systems is provided by Adrian Bejan, George Tsatsaronis and Micheal Moran [ 2 ]. The authors break down the overall design process of an engineering project into five distinct phases: understanding of the project, development of the concept proposed, detailed design, project engineering and, finally, service of the project. Figure 1.4 shows these five main phases of the design engineering process along with the steps required in each phase and the route to iterate or end the project. Figure 1.5: Thermal system design flowchart [3]. Another useful reference for the design of thermal systems is provided by Robert F. Boehm in [ 3 ]. This design process is defined by the author as "the application of concepts from engineering science topics in a generally specified manner coupled with a creative touch". The conceptual steps recognized by this author are shown in the flowchart of Figure 1.5: conception, synthesis, analysis and, finally, optimization. According to the reference, computer-aided engineering is of great value since it enables the combination of different disciplines of engineering (mechanical, electrical, thermal...) and its graphical representation in order to analyze aspects such as mechanical stress, electromagnetic forces and temperature distributions of a system/component. Boehm presents some guidelines in this regard, derived from the pioneering work by Stoecker [ 50 ], which set the motivations for the synthesis and analysis of the thermal system to be designed: • The components of thermal systems can typically be categorized (pumps, heat exchangers, turbines, mixers, etc.). • A large number of single mechanical/electrical components are included in a single thermal system design. 12 1.5. Structure of the dissertation • A very large number of component parameters, proportional to the amount of components, needs to be set. • These parameters usually affect the cost and economic-performance of the project. • Modelling and other engineering activities are often required, even for well-defined or designed system, in order to satisfy the project objectives. • To a large extent, the modelling activities can be systematized. The methodology employed in this thesis is based on the methodologies outlined above. In particular, the integration of the works by Stoecker [ 50 ], Boehm [ 3 ] and Bejan [ 2 ] yields a simplified methodology based on the following four phases: design engineering, cost engineering, project appraisal and optimization. Such simple breakdown is deemed enough to ensure that the objectives set forth above are successfully achieved and, at the same time, it governs the structure of the research. 1.5 Structure of the dissertation This thesis is divided into chapters corresponding to the different phases in which the engineering design process is broken down (see last paragraph in previous section). A brief description of the remaining chapters in the dissertation follows: •Chapter 2 - Technology review . This chapter presents a literature review aiming to assess the current state of the art of dish-microturbine components (dish collectors, solar receivers, turbomachinery, bearings, electric generators and electric equipment, combustors and fuel supply elements) and system layouts (solar-only, hybrid). •Chapter 3 - Design engineering . Review of design engineering practices and general description of the techno-economic appraisal methodology adopted in this research. The design models employed for each component and for the integrated system are described (except for compressor and turbine, which are given in the Appendix) along with their corresponding off-design performance models. The model results for a set of different "base-case" systems, based on different layouts, are shown. •Chapter 4 - Cost engineering . Review of cost engineering practices and general description of the methodology adopted. Models are developed to evaluate the manufacturing costs of the components and the integrated system, and estimates are also given for transportation and installation costs. The costs of the systems designed in the previous chapter are estimated and sensitivity analyses are performed as a function of the manufacturing rate. •Chapter 5 - Project appraisal . The different approaches to project appraisal in engineering are reviewed and the business cases considered are presented. These are discussed both for their boundary conditions and for the resulting techno-economic performance. The economic and financial results of the different base-case systems are analyzed and critically compared against the performance of the competing technologies, PV and dish-Stirling. •Chapter 6 - Optimization . A general discussion about optimization techniques is provided prior to selecting the most suitable one for the reference system. The optimizer is then implemented and the results discussed. •Chapter 7 - Conclusions . The main findings of the research are discussed. Suggestions for future work are also given. 13 Chapter 1. Introduction •Appendix - Turbomachinery models . The design and performance models of compressors and turbines are described in detail. 14 2Literature review. State of the art This chapter presents a literature review of the current state of the art of dish-microturbine technology. The individual component are reviewed first: dish collector, solar receiver and microturbine. Then, the layout of the possible assemblies and the associated thermodinamic cycle are studied. 2.1 Dish concentrators Dish collectors are spatial (i.e., bidimensional) concentrators whose geometry resembles a perfect paraboloid, thus enabling the collection and concentration of direct solar radiation very effectively. This particular geometry concentrates the direct sunlight onto its focus where the receiver and heat engine are located. State-of-the-art dish collectors have diameters ranging from 1-2 m to up to 25 m and achieve Geometric Concentration Ratios (GCR) -dish aperture area divided by receiver aperture areabetween 1000 and 4000 suns [ 51 ]. Actually, this is the most interesting feature of parabolic dish collectors since higher concentration ratios imply that higher temperatures are achievable which in turn translates into higher efficiency of the associated heat engine; chemical reactors running on solar energy also benefit from these higher operating temperatures [6]. A dish-based power generator includes several subsystems in addition to the solar receiver and heat engine already mentioned. Thus, one finds the reflective surface, the frame (supporting structure of the dish), sun tracking system, pedestal/foundation and control system. The general technical features and design guidelines have been reviewed by Gunter [52]. The reflective surface can be either a metallized glass or a plastic material. Since a perfect parabolic collector does not exist, it is not possible to have the incoming haze of beams concentrated on a single point (focus). This misalignment from the ideal specular direction is caused by microscopic (specularity) and macroscopic (waviness) irregularities and is responsible for the size of the concentrated sunlight image on the focal position1. Along with micro and macroscopic specularity, responsible for the scattering of the radiation reflected, another important optical characteristic of the collector is the reflectivity of the surface. This property indicates the fraction of incoming solar energy that strikes the surface of the dish and is not reflected but absorbed. The reflectivity of the surface increases rapidly with increasing spread angles: plastics films present a large spreading angle (7-15 mrad), reflecting most of the energy but on a very large spot, whereas glass mirrors have little spreading (<1 mrad) producing a smaller solar image [ 53 ]. Metallized glass reflective surfaces are used 1 It must be acknowledged here that the actual non-negligible size of the sun’s disk has an impact on the size of the spot which cannot be blamed on the dish 15 Chapter 2. Literature review. State of the art Figure 2.1: Various glass-faceted mirror designs: (a) Infinia Corporation Inc. dish-Stirling system (b) ADVANCO Vanguard dish-Stirling system (c) ANU dish concentrators (d) McDonnell Douglas Aerospace Corporation dish-Stirling system (e) Solar Systems "Dense Array Converters" (f) ANU big dish SG3 (g) SouthWest-BraytonEnergy dish system (h) Heliofocus dish Stirling system (i) ANU big dish SG4. to build glass-faceted concentrators whilst plastic reflective surfaces are used instead for stretched membranes technology. The selection of the reflective surface technology is linked to the design conditions (wind speed, sand, etc.) and cost trade-off considerations. These trade-offs are complex since they need to consider factors like surface material and quality, substrate, structure, tracking mechanism and bearings as well as solar receiver cost and design challenges. The main criteria used to design the dish and select the reflective surface are addressed in several references in the open domain [ 53 , 54 , 55 , 56 ]. In this document, a more in-depth discussion about dish concentrators cost optimization is provided in Section 4.2.1. The dish frame is the element that supports the reflective surface and the receiver and power conversion unit ensuring the operability of the system and keeping the original geometry as much as possible under dead weight and variable wind loads. The frame is usually made of a spatial grid of aluminium or steel. The effect of wind loads on parabolic dishes either in single or multiple units arrangement has been studied by Peterka in [ 57 ]. It has been confirmed that the stiffness of the frame that is required to resist wind loads increases quadratically with the aperture area which means that, for very large dishes, the cost of the supporting frame becomes prohibitive. The sun tracking system is the element that ensures the alignment of the dish and the incoming sunbeams, i.e. orthogonality between the incoming direct radiation and the dish aperture plane, thus enabling perfect concentration in two dimensions. There are two different types of sun tracking: • The azimuth-elevation approach. The dish structure rotates in a plane parallel to the 16 2.1. Dish concentrators Figure 2.2: Various glass-faceted mirror designs: (a) General Electric PDC-1 system (b) Shenandoah system (c) OMNIUM-G system. Figure 2.3: Schematic of dish system tracking methods: azimunth-elevation (A) and polarequatorial (B). surface of the Earth and around an axis perpendicular to it. This azimuth-elevation movement gives the collector the required up/down and left/right rotations to follow the sun path. An example of the implementation of this approach is shown in Figure 2.3-A. • The polar-equatorial approach. The dish structure rotates about an axis parallel to the Earth’s axis of rotation at a constant rotational speed of 15 ° /hr, exactly the same angular speed of the Earth. The declination axis is perpendicular to the polar axis. The rotation around this axis is slow and ranges betwen ± 23 . 5 ° at a maximum speed of 0.016 ° /hr. An example of this approach is shown in Figure 2.3-B. The pedestal foundation is the element that supports the frame and keeps it anchored to the ground. Two techniques can be adopted. One implies the use of a special crane to embed/drill a pole directly into the ground, which then supports the system structure. This solution is very expensive if only a few units are to be installed due to the high cost of the crane and the manufacturing of the special tooling, which is very expensive itself. Actually, if the number of units to install is not large, a common concrete foundation should be adopted in order to reduce specific dish manufacturing and installation costs. It must also be noted that this 17 Chapter 2. Literature review. State of the art Figure 2.4: A wall painting from the Uffizi Gallery, Stanzino delle Matematiche, in Florence, Italy, shows the Greek mathematician Archimedes’ mirror burning Roman military ships. Painted in 1600 by Giulio Parigi. element follows the same cost trend already exhibited by the supporting frame since the wind load effects have a direct impact on the duty of the foundation. The control system of a solar power generator, whether a large power station or a small generator, consists of the hardware, software, and facilities needed to operate and monitor the entire power supply system. A central minicomputer or a microprocessor performs the monitoring and control functions during start-up, shutdown, and the operation under normal, intermittent and emergency conditions [58]. The concept of concentrating solar rays to heat a target area has been known for at least 4000 years. In the Mesopotamia’s clay tablet period, polished gold vessels were used to ignite altar fires. Archimedes is said to have saved Syracuse from invasion by burning the Roman fleet with concentrated solar rays reflected from polished metal, as represented in Wall painting from The Uffizi Gallery by Giulio Parigi, shown in Figure 2.4. Experiments to verify the story of Archimedes were performed in the 17th century with polished metal plates [51]. Figure 2.5: Stretched membrane dish designs: (a) DISTAL I by SBP (b) SBP dishes installed in Riyadh (c) DISTAL II by SBP (d) Cummins power generation dish-Stirling system. During the 18 th , century solar furnaces and solar ovens were built for the first time and the 19 th 18 2.1. Dish concentrators Year Name Type of device ca. 100 a.C. Hero of Alexandria Water pump using heated air 1615 Salomon de Caus Water pump using heated air ca. 1631 Kircher Water pump using heated air ca. 1750 Belidor Water pump using heated air 1860 Deliancourt Water pump using heated air 1860-1878 Mouchout Steam engines 1868-1883 Ericsson Air engines and steam engines 1876 Adams Steam engine 1878-1880 Pîfre Steam engine 1881 Schultz Sulphur dioxide engine 1885 Tellier Aqueous-ammonia engine ca. 1898 Krenn Hybrid coal/solar two-tier system 1901-4 Eneas Large steam engine 1902-8 Willsie & Boyle Low boiling-point fluid engines 1906-11 Shuman Low boiling-point fluid and steam engines 1912-13 Shuman & Boys Large steam engine 1920 Harrington Steam engine and pumped storage 1923 Romagnoli Ethyl chloride engine 1925-35 Claude Ocean thermal engine 1930 Delencourt Ethyl chloride engine 1936-38 Abbot Steam engine with flash boilers 1941-46 Molero Steam engine Table 2.1: Timeline of the historical development of small solar-powered devices before 1950. Dish Area [m2]GCR Year References Omnium-G 28 - 1979 [59, 60, 61] General Electric PDC-1 113 - 1980 [62] Shenandoah 38 250 1982 [63, 64] Table 2.2: Full surface dish concentrator concepts. century saw the first steam and hot air engines operating on solar energy. Augustin Mouchot built a series of dish-engine systems as early as 1864, and displayed a dish concentrator at the Universal Exposition in 1878 in Paris [ 65 ]. During the same century, in 1870, Ericsson invented the solar-powered hot air engine based on the Stirling engine [ 66 , 67 ]. Numerous solar engines and solar furnaces were constructed early in the 20 th century. Experimentation continued in the 1930s before languishing as inexpensive fossil fuels, particularly natural gas, became widely available. Table 2.1, adapted from the historical review study by Spencer, shows the activities on small solar-powered heat engines by various researchers before 1950 [ 66 ]. The same author discusses these activities after 1950 for conventional and unconventional engines up to 100 kW e [ 68 , 69 ]. The most interesting invention for the present work is the solar powered open-cycle hot-air engine, using spherical concentrating mirrors, tested by Ericsson in 1872. The engine is said to have run at 420 rpm at noon on a clear day in New York [66]. In the last last 50 years, the most important program aimed at investigating parabolic dish based solar power systems was granted by the United States (US) Government. The US solar energy program was initiated in 1970 as part of the Research Applied to National Needs (RANN) program of the US National Science Foundation and expanded enormously as a result of the oil price shock in the 1970s. The program was later part of the US Department of Energy (DOE) from the 1980s with special focus on long-term high-cost, high-risk research and development. In those years, DOE worked in conjunction with the Jet Propulsion Laboratory (JPL) [ 70 , 71 , 72 , 62 , 73 ], with Garrett Turbine Engine Company [ 74 ], Sanders Associated [ 70 ] and with Pioneer Engineering Company [ 75 ], to study and develop dish systems for application 19 Chapter 2. Literature review. State of the art (SPHER) operated by injecting a very small mass of fine particles into the compressed air flow, a stream that would then enter a transparent heating chamber (caldron) onto which the solar flux was concentrated. The underlaying principle is that the small particles absorb radiation at a very high rate thanks to their very large effective area and, at the same time and for the same reasons, this energy is rapidly released to the surrounding air by convection. The operating temperature of this receiver is determined by the oxidation rate of the particles. Small particles that adapt to this operation are typically carbon particles because the gas reaction rates for various allotropes of carbon vary over many orders of magnitude and, in addition, the combustion product of carbon is mainly carbon dioxide. Moreover, it has to be noted that the amount of small particles is very low and so the carbon consumed is negligible compared to the consumption of a fossil-fuel combustion system. The particle size and the optical constants have to be chosen properly in order to design a highly efficient small particle receiver. Hunt explained that, in order to obtain this effect, the characteristic absorption length for the light passing into the receiver has to be larger than the diameter of the particle. This is why sub-micron particles are used, produced by quenched flame, chemical reaction or high intensity arc. The consequence of this feature is that the receiver is not limited to the conventional operation of a cavity receiver: the combination of the large surface area and the small size of the particles ensures that the temperature difference between air and particles is very low, thus producing a lower radiant temperature in comparison with other receiver configurations. Other advantages of this solution to receive and harness solar energy are: • No need for heavy and complex heat exchanger elements. Thanks to the design, consisting basically of a hollow chamber with a window, the structure can be very light. • No need to pump the gas through pipes or small orifices. The heat exchanger is uniformly distributed throughout the chamber and pressure losses are reduced. • No maintenance of the heat exchanger. The small particle vaporizes during the process. • No upper temperature limitations for the heat exchangers. It can be adapted to different high temperature (solar) thermal process. In addition to this analysis, Hunt and Brown performed experiments with outlet temperatures up to 1000 K [ 157 ]. Based on these works, some small-scale prototypes were built [ 158 , 159 , 160 ] and the University of San Diego is currently developing a research program on small particle receivers for small solar towers [161, 162]. 2.2.4 Volumetric This is a receiver concept that makes use of an absorber material with high specific porosity. The porous media absorber, placed inside the receiver (cavity configuration), absorbs the impinging solar concentrated irradiation and heats up. Nevertheless, thanks to the porosity of the material, this heat diffuses through the absorber bringing about the following two major advantages: the heat transfer area is increased and the local flux density at the absorber surface is reduced, hence reducing the energy loss due to re-radiation from the receiver surface. According to the review of central receivers by Ávila-Marín, candidate materials for the absorber are metals if temperatures are between 800 ° C and 1000 ° C, siliconized silicon carbide (SiSiC) for temperatures up to 1200 ° C and silicon carbide for temperatures up to 1500 ° C [ 163 ]. In a similar review, Ho states that these receivers have potential for instable flow and nonuniform heating in the absorber, leading to overheating and local failures in the material [ 138 , 164 ]. Morover, as stated by Ávila-Marín, the window needed to have the receiver under 26 2.2. Solar receivers pressure poses substantial design challenges due to the limitations in size and to the specific requirements in terms of optical properties, mechanical strenght, highly variable working temperatures, stress-free installation and sealing and cooling capabilities. During the late 1970s, the US government funded a research programme focused on volumetric air receivers suitable for dish-based applications. The unit was made of steel alloys and incorporated high-temperature insulation to reduce heat losses. Solar radiation woud enter the cavity through a quartz window and impinge on a internal ceramic honeycomb absorber. The size of the receiver was around 15 kW t and was designed to work with 620 ° C/925 ° C inlet and outlet temperatures. The main design features and test results at the White Sands Solar Furnace can be found in [165]. In the same decade, NASA developed closed Brayton cycles for application to low orbital space solar power systems [ 166 ] in conjunction with Sanders. General Electric conducted a substantial design effort followed by component testing of a Brayton receiver for NASA [ 167 , 168 , 169 ]. These systems used receivers that would absorb concentrated solar energy from parabolic dish collectors. The Sanders receiver, called Brayton Advanced Direct Absorption Receiver was able to store thermal energy via latent heat (melting) of alkali metal-fluoride. In the concept, the phase change material liquefied at the end of the solar charge period and solified during night energy extraction. In the report by Kesseli, stemmed from the collaboration between NASA and Garrett AiResearch, other four conceptual designs are analyzed: a quartz dome concept, a direct absorption concept, a packet bed matrix concept and a concept based on a lithium sensible storage loop. In 1989, the DLR designed and tested the Pressure Loaded Volumetric Ceramic Receiver with a thermal output of 5 kW t , with a subsequent scale-up to 500 kW t . The absorber was a ceramic foam of Si 3 N 4 (SIRCON) coated with Pyromark. The window was a domed watch-glass type quartz-glass window with a water-cooled frame [ 170 , 171 ]. As stated in [ 163 ], these windows have the advantage of lower reflection losses and higher resistance to pressurization. During the 1990s, the DLR developed and tested two volumetric receivers for dish Brayton systems at their parabolic dish test facility. The first version of the volumetric receiver was called VOlumetric Brayton RECeiver (VOBREC-1) [ 172 ] and consisted of a paraboloidal quartz window and an alumina foam absorber with 92% porosity. The evolution of this design was called VOBREC-2 and incorporated combustion in series, inside the receiver itself. Moreover, emphasis was put on low cost and easy assembly [ 173 ]. Whilst in the first design an alumina foam absorber was installed, the materials tested in this second design were Si 3 N 4 and SiC for their better thermal shock resistance. During the following stages of development of this receiver, two other designs were developed for the Utility Scale Joint Venture Program (USJVP) in collaboration with Cummins Power Generation and the DOE. DLR developed two volumetric receivers to be integrated in two different tests: a first version for the system demonstration taking place in the TBC-2 at Sandia National Laboratories, Albuquerque (SNLA), and a second version for the prototype based on the new dish developed by Cummins [ 38 ]. The volumetric receiver for the first test was named VOBREC-4 and, since the dish was not able to provide the rated heat flux required by the Brayton engine, the test was performed on a hybrid version of this VOBREC-4 receiver incorporating fuel combustion. In this case, solar-only operation occurs only at part-load operation, when the fuel mass flow required falls to zero. For the final CPG solar Brayton system, a larger version called VOBREC-5 was developed by DLR. A different volumetric solar receiver was designed and tested by the Weizmann Insitute of 27 Chapter 2. Literature review. State of the art Figure 2.9: KTH volumetric (left) and impingment (right) receiver prototypes. Science and Rotem Industries in 1992 [ 163 ], called Directly Irradiated Annular Pressurized Receiver (DIAPR) [ 174 , 175 ]. The versions tested were rated at 11 and 30-40 kW t and the absorber elements were made of Pythagoras alumina-silica tubes to form a "Porcupine" structure. A last volumetric receiver that deserves particular attention has been developed by the Royal Institute of Technology of Stockholm (KTH) in the context of the OMSoP project [ 137 , 176 , 177 ]. The volumetric receiver is based on a pressurized design with flat quartz window and foam absorber. In the work by Aichmayer, metal stress and pressure losses requirements are taken into account to show that open (atmospheric) configurations do not meet the specifications of the unit whilst closed (pressurized) configurations are acceptable. Some concerns about the thermal stress on the the cavity and about the oprating temperaure of the quartz window (and the associated thermal stress) are worth noting. 2.2.5 Impingment This last section is dedicated to pressurized cavity receivers based on air impingment on the outer (internal) wall of the cavity to absorb the solar energy striking on the inner (external) wall. This receiver is also of great importance since it is the second design developed by KTH for the OMSoP project. This impingment receiver will actually be mounted on the OMSoP prototype, planned to be sun-fired during the summer of 2017. The design and performance of the receiver was studied by Wang prior to the performance tests carried out on the solar-flux simulator installed at KTH [178, 179, 180, 181, 182]. 2.3 Microturbine engines Microturbines are very small gas turbines whose power output ranges from a few kilowatts to five hundred kilowatts or so [ 41 ]. The operating principle is based on the UK patent no. 1833 deposited by John Barber in 1791 and containing the most important features of what is known today as the gas turbine engine. Interestningly, Barber’s design included a chaindriven, reciprocating gas compressor, a combustion chamber and a turbine. Nevertheless, the working cycle used by microturbines today takes its name from an american engineer who in 1872 developed a piston engine based on contant-pressure heat addition: George Bailey Brayton. 28 2.3. Microturbine engines The ideal Brayton cycle is based on four processes: isentropic compression, isobaric heat addition, isentropic expansion and isobaric heat rejection. This Simple Non-Recuperative cycle (SNR) can be implemented either as an open-loop cycle , releasing hot gases to the atmosphere after the expansion process, or as a closed-loop cycle , in which the working fluid is cooled and recirculated back to the compressor. In both cases and under certain circumstances (typically a low pressure ratio), a heat exchanger is installed to transfer heat from the hot gases downstream of the expander to the air delivered by the compressor. This Simple Recuperative cycle (SR) increases the thermal efficiency of the engine as long as low enough pressure ratios in the order of 3-4 are used. The incorporation of intercooling and/or reheat halfway through the compression and expansion processes respectively has the potential to increase the specific output (kWh/kg) and, to a lesser extent, the efficiency of the engine. When these features are incorporated, the resulting compound cycles enable a smaller footprint for a given output. The following list shows the possible layouts along with some interesting advantages and disadvantages. • Simple Non-Recuperative (SNR): low cost and footprint but with low efficiency and high pressure ratios. • Simple Recuperative (SR): low cost and larger footprint but also higher efficiency and at lower pressure ratios. • Intercooled Compression Recuperative (ICR): reduced compression work that increased specific work and efficiency. Some disadvantages to be considered are the added pressure loss in the intercooler, the lower volume flow through the compressor which makes design difficult at low outputs, the more complex two-shaft arrangement which might result challenging. • Reheated Expansion Recuperative (RR): increased expansion work and, therefore, specific work and efficiency of the engine. The inlet to the low pressure side of the recuperator in this engine is at a higher temperature and this might pose sugnificant challenges to the low pressure turbine. Also, the same considerations about the twin-spool arrangement apply here. • Intercooled Compression, Reheated Expansion Recuperative (ICRR): combination of the considerations listed for the ICR and RR cycles. Simple cycles typically make use of single-shaft arrangements where the expander drives the compressor and generator simultaneously. The rotational speed of these engines is around 100,000 revolutions per minute (rpm) which means that the high speed generator produces power at high-frequency AC that is later rectified to DC and inverted back to AC to commercial frequency (50 Hz or 60 Hz) for its use. Compound cycles are frequently assembled in a twin-shaft arrangement whereby a high pressure turbine drives the high pressure compressor and the low pressure expander drives the low pressure compressor and generator. In these engines, the rotating speed of the high pressure shaft is very high whilst the low pressure shaft can be designed for a lower speed, thus yieding higher efficiencies of the expander and generator. Actually, this makes it more likely taht the power turbine be connected to a conventional 60-Hz AC generator through a low-cost, single-stage gearbox. The turbomachineries employed in microturbine engines have quite a few commonalities with the turbochargers used in the automotive industry, with a market volume of about two millions units per year. Also, auxiliary power systems and auxiliary power units used in aviation 29 Chapter 2. Literature review. State of the art Manufacturer Ref. Model ˙ W[kWe]ηth [%] Bearings ωrot [rpm] Capstone [183] C30 30 26 Gas 96000 C65 30 26 Gas 85000 Ingersoll-Rand [184] MT250 30 242 Lube oil - Ansaldo-Turbec [185] T100 100 30 Lube oil - Durr [186] CPS 100 30 - - Bladon jets [187] MTG12 12 26.5 Gas - MTT [188] EnerTwin 3 15 - - ABB [189] MT100 100 30 - 70000 Table 2.5: Active microturbine manufacturers. use micro and small gas turbines. Decades of experience with these applications provide the basis for the engineering and manufacturing technology of emerging microturbine engines. Unfortunately, even if the utilization of microturbines as small-scale power units is growing nowadays thanks to the support received from distributed generation initiatives, a number of companies had to left the market in the past because the total volume was not growing at the expected rate; Elliot Energy Systems and Bowman Power are just some examples. Table 2.5 shows some of the few microturbine manufacturers in operation today along with their main products and some notes about the possible applications/configurations. More details about the thermodynamic cycles that can be used in dish-microturbine systems are given in Chapter 3. A good introduction to the subject can also be found in [ 41 ] along with an overview of the current state of the art and considerations about the market and the economics of the technology; similar information is available in [ 190 ] and [ 191 ]. Colin Rodgers has published a series of studies on micro and small gas turbines during the last fifty years [ 192 , 193 ]. These studies cover various technical and design aspects, for instance the differences between turbocharger and turbogenerator technologies [ 194 , 195 , 196 ], the route to mass-production of turbogenerators, the incorproation of intercooling and reheating in microturbines [ 197 , 198 , 199 ] and the dependence of component and system performances on size [200, 201, 202, 203, 204]. In the following sections, some notes on the main components of microturbine engines are reviewed in order to provide a solid background for the subsequent discussion. 2.3.1 Turbomachinery Most contemporary microturbine engines employ single-stage radial flow compressors and either single or double-stage radial expanders. This is due to the very small volumetric flows that are typically involved, for which radial turbomachinery attains higher efficiency and wider range whilst also enabling easier manufacturing [41]. The selection of turbomachinery for any particular application dependents upon the thermodynamic cycle (pressures, temperatures and working fluid) and rated output (mass flow rates) and rotational speed. The selection and sizing process of a highly efficient and reliable stage was addressed by Balje in [ 205 , 206 , 207 , 208 ] and, more recently, by Barber-Nichols [ 209 ]. This methodology is based on non-dimensional parameters, namely specific speed and diameter and the characteristic Reynolds and Mach numbers, which provide the designer with a fairly good estimate of the efficiency and geometry of the turbomachinery for a given duty. Machines that are equal in all these four parameters (i) are geometrically similar, (ii) are similar in their veolocity diagrams, (iii) have the same ratio of viscous to inertial forces acting in the flow path; and (iv) operate with fluids of equal thermodynamic quality, have the same dynamic characteristics and therefore performance. 30 2.3. Microturbine engines Balje addresses the preliminary design of turbine-compressor systems on single and multishaft arrangements in [ 206 ]. The rotational speeds of these machines are the same , as well as their pressure ratios and flow rates (excluding pressure losses and leakage flows), since they are assembled on the same shaft and interconnected by the open recuperative thermodynamic cycle. Therefore, there exists a relationships between the geometries of compressor and turbine that maximize the overall system efficiency as it will be discussed in Section 3.2.3 in detail. Further to the comments about Rodgers’ works in the previous section, there are many publications by this author dealing with centrifugal compressor design for microturbine applications [ 210 , 211 , 212 , 213 , 214 , 215 , 216 ] and also radial in-flow expanders for the same purpose [217, 218, 219]. 2.3.2 Bearings Bearings ensure that friction losses in the contact points between shaft and housing/support are as low as possible in order to maximize the mechanical efficiency of the system. The selection of bearings is not straightforward since there are different technologies available. These solutions differ from one another in the cost, reliability, power consumption, maintenance, need for lube fluid, etc. During the OMSoP project, a deliverable by the University of Seville assessed the selection of bearings for dish-mGT system [ 220 ]. In this report, and in other works in literature, the selection of bearings for microturbine engines running at very high rotational speed is provided. The choice is based on the specific load and operation of the engine and the designer have the following alternative solutions available. Active mangetic bearings ensure the support of the shaft relying on a magnetic field. The electromagnetic forces can be produced by either permanent magnets or electromagnets. The first type is limited to a certain temperature range while the second enables the active control of the position of the shaft even if at the cost of a higher energy consumption [221, 222, 223]. Dry rubbing bearings and impregnated bearings are suitable for the operation with high loads/pressures and low rotating/sliding speeds [ 224 ] so they are not really useful for microturbines since these are characterized by high speeds and low axial and radial loads [220]. Conformal fluid bearings include both liquid-lubricated and gas-lubricated bearings. In these devices the rotating surface (shaft) and the static surface (housing) are separated by a lubricant fluid film. When the pressure needed to grow this film (wedge) is provided by the motion of the shaft itself, the bearing is called a self-acting or hydrodynamic, while the bearing is called hydrostatic if it is an external device pressurizing the lubricant. According to Soares, floating sleeve valve oil-lubricated bearings are the most common type used in microturbines [ 41 ]. These use high-grade oil lubricant which enables extremely long life, as the risk of oil contamination is minimal. On the other hand, gas-lubricated bearings are becoming more popular since they provide oil-free operation and do not have sealing requirements for the retainment of the lubricant within the bearing enclosure [ 225 ]. They are considered the most appropriate concept for micro gas turbines and they are preferred over rolling-element bearings and oil-bearings, even if the latter find application when the engine is adapted from turbochargers which typically make use of oil bearings taking advantage of the reciprocating engine’s lube oil system [ 226 ]. Within the category of foil bearings, tilting pad bearings are the most used typology in turbomachinery. They work with a number of pads insterted in the gap between shaft and support, with a tilting degree of freedom that enables the operation at the optimal position [ 227 ]. The advantages that this technology offers with respect to rolling 31 Chapter 2. Literature review. State of the art and liquid-lubricated bearings are discussed in [ 228 ], while the concern about the lack of standardization and commercial availability is acknowledged in [229]. Rolling-element bearings are characterized by the shaft and bearing housing being separated by elements in a predominatly rolling motion, typically lubricated by oil or grease. There are several criteria to categorize these bearings according to: mode of operation -ball and roller rotation-, direction of the loadthrust, angular or radial-, nature of the load -steady or dynamic-, geometry -single or double row-. The relative motion, load conditions and properties of the lubricant determine the frictional characteristics. Moreover, the lubricant is sometimes sealed into the bearing assembly but it can also be applied in a mist of fine droplets [224]. The base design of these elements in the OMSoP project was provided by Compower, based on their solution for a 3 kWemicroturbine working at a very high rotational speed of 150,000 rpm. The bearing system was composed by two radial roller bearings placed on each side of the electric generator, with an overhung compressor and turbine. Lubrication relied on an oil spot method working with compressed air to pulverize the grease. This air-oil spray method is also used to effectively reduce the temperature at high speed so no cooling system is required. For the OMSoP prototype mounted on the dish, the final bearing system selected is similar to the base engine with the difference that the turbine is not overhung and that the bearings are made out of ceramic material. Air bearings will most likely become standard in future microturbines. Nevertheless, oil lubrication is still preferred in the short term given that these engines are usually derived from turbocharger technology. The reasons behind the selection of roller bearings for the Compower microturbine and the OMSoP prototype are the low friction, ability to support combined axial and thust loads, low sensitivity to interruption in lubricant supply, absence of self-excited instabilities , cold-start capabilities and easy sealing of the lubricant inside the bearing hoursing. Morover, their performance is not so sensitive to changes in load, speed and operating temperature. On the negative side, rolling-element bearings are not preferred in the mid to long term for their finite fatigue life if subjected to wide fluctuations of the operating conditions -as it is the case in OMSoP-, large space requirements in the radial direction, low damping capacity, higher noise and more strict alignment needs [ 220 ]. Further to this, it is to note that the investment cost of the bearing rises exponentially with the product of design speed and tolerance/accuracy as explained in [230]. A final comment is needed to highlight the fact that most microturbines work stationary at ground level while microturbines mounted on dish systems change their position with respect to the ground. The force of gravity acting on the bearing is thus variable which implies that the dynamic behaviour of the bearing system needs to be assessed. 2.3.3 Heat exchangers There are two types of heat exchangers in dish-microturbine systems: gas-to-gas recuperators and water-to-gas coolers and intercoolers. The recuperator is the most important heat exchanger since it enables the pre-heating of the compressed air by the exhaust turbine gas. This has various implications. As discussed in Section 2.3, the recuperator increases the thermal efficiency of the engine and, at the same time, decreases the pressure ratio at which this peak efficiency is achieved (2-4), thus allowing for single-stage radial compressors to be used. The design drivers of a recuperator are minimum pressure loss on both streams and minimum specific volume per unit thermal duty. This implies minimum volume and cost for the same 32 2.3. Microturbine engines effectiveness, which is critical since this component can contribute up to 30% of the manufacturing microturbine cost. This general design requirements are reviewed by McDonald [ 231 ] who highlights aspects such as low cost, high effectiveness and reliability, low pressure losses, good part-load performance, compactness, minimum complexity, automated fabrication, welded sealing, mass production, lightness, standardization, resistance to thermal cycling, minimum life (50,000 hours for a standard application), flow path compatibility with turbomachinery, no interconnecting and thermal expansion devices, easy removal/replacement, easy overhaul, etc. As an additional recommendation, the author suggests that unit cost does not exceed 1.5 times the material cost. There are different recuperator technologies available for microturbines. Primary surface heat exchangers (PSHEs) are characterized by the same heat transfer area on both sides of the heat exchanger as they do not make use of any secondary surface. The primary surface separating both sides of the recuperator can thus be produced out of metallic sheets that form parallel channels where the gases flow. This enables easier manufacturing [ 232 ] and even different materials to accomodate to different temperature requirements across the heat exchanger [233]. Plate and fin heat exchangers (PFHEs) are of the compact type, characterized by very high specific heat transfer area (m 2 /m 3 ). Thin and flat plates, arranged in cross or counter flow configurations and with extended surfaces in between, separate both flows and act as supporting structure for the heat exchanger. The utilization of extended surfaces increases the total exchange area and also the turbulence of the flow, which in turn helps enhance the heat exchange rate. The structure of the heat exchanger can be annular or planar and in both cases the whole equipment must be brazed in order to ensure good thermal contact and leak-free operation. The main disadvantages of this type of heat exchanger are the sensitivity to fouling and the lower efficiency of the secondary heat transfer area, which increases the weight and cost of the equipment. Tubular heat exchangers , like shell-and-tube, are not appropriate for this application given their larger volumes than any of the previous types. Still some advantages like pressure containment capacity and resistance to thermal cycling [ 231 ] must be acknowledged and thus some microturbine models use very compact tubes, also with fins, with cylindrical or elliptical shapes and very small hydraulic diameters [234, 233]. As a final option for internal heat recovery in the engine, regenerators can be used. In these, heat is not transferred directly through a surface but through a movable heat storage device (typically a solid ceramic matrix). The application of regenerators, even if they are used in automotive applications, suffers from flow leakages and other design and operational problems related to the hot and cold section split in the rotating matrix [235]. Regarding materials, stainless steel is the most common material for PSHE, as it can withstand temperatures of up to 700 ° C and can be manufactured in thin foils [ 236 ]. Superalloys can be used for next generation microturbines up to 900 ° C, beyond which ceramic components are needed [237]. Intercoolers and coolers are used in microturbine engines when pre-cooling of inlet air is required, when a closed cycle is used or when an intercooled layout is adopted. According to Soares, evaporative cooling could be easily applied in microturbines by means of a fine spray of water injected directly into the inlet air stream [ 41 ]. This kind of cooling method would be interesting in cases with low relative humidity and at the expense of the consumption (and cost) of high-quality water. Alternatively, refrigeration cooling could be applied; in this case, 33 Chapter 2. Literature review. State of the art a mechanical compression cooling system could be used and higher pressure losses would have to be expected. A trade-off study is needed to estimate whether or not the pressure losses and cost of the inlet air cooling system are compensated for by the increase in efficiency and specific power. As discussed by Soares, cool thermal storage could also be implemented to cool the inlet air. Intercoolers cool down the working fluid at an intermediate point of the compression process in order to increase the specific output of the engine. An intercooler is often a gas-to-liquid heat exchanger with extended surfaces on the gas side where the thermal resistance is dominant [ 238 ]. Intercooling in microturbines is not common and there is a need for compact designs of this type of heat exchangers. Something similar applies to closed-cycle microturbines which are not even considered in this work. 2.3.4 Generators and power electronics Microturbines produces electric power thanks to a high-speed generator that spins either connected to the single turbo-compressor shaft or to an independent power turbine driving a gearbox that is itself connected to a conventional generator rotating at frequency of 3000 or 3600 rpm [239]. High speed generators are usually made out of a Samarium-Cobalt permanent magnet alternator, and require the conversion of power from high frequency to low frequency 60/50 Hz Alternate Current (AC) for general/commercial use. This power conditioning involves rectifying the high frequency AC to DC and then inverting the Direct Current (DC) to 60 Hz AC. In order to start up a single-shaft engine, the generator acts as a motor turning the turbocompressor shaft to a high enough rotational speed to enable starting the combustor/solar receiver (a battery need to be integrated for off-grid applications). In order to do that, power electronics need to be built into the mechanical-to-electrical conversion subsystem in order to rectify, invert and filter out the harmonic distorsions of the three-phase electric current produced by the microturbine. Electronic components are used also for system operation, start-up, remote monitoring and control. 2.3.5 Combustors and fuels Microturbines running on natural gas need that the fuel be supplied at pressures in the range from 4.4 to 6.2 bars or above. Since most ditribution networks of natural gas for small consumers are below this values, volumetric compressors are used to boost fuel pressure to that needed by the microturbine [41]. As commented by Rodgers, scaling down the combustor of large gas turbine is not possible in microturbines due to geometric and physical effects like surface area/volume change, increased effects of wall quenching, low fuel flows or increased effects of leakage gaps [ 202 ]. The design of the combustor must thus be done with care and even considering alternative design solutions; such is the case of some designs where a single ejector rotating cup fuel atomizer has successfully been used to enable cold starts with very low fuel flows. High Heat Release Rates (HRR) can also be obtained with catalytic combustors but they require the addition of some form of pre-burner up to 430 ° C, plus additional downstream volume to ensure complete combustion. 34 2.4. Solar-only and hybrid integrated systems 2.4 Solar-only and hybrid integrated systems This last section provides a review of the available literature covering dish-Brayton generators tested in the various research and development programmes developed in past years. The review will focus on the integration of various microturbine layouts with both solar-only and hybrid energy supply and special applications will also be reviewed. The contents are presented in chronological order whenever possible. The first dish-Brayton system was operated by Ericsson in 1872. The system was probably an open air Brayton cycle without recuperator, even if no relevant data was found in the scientific literature. After this first system, no further activity in the development of solar dish-Brayton systems seems to have taken place as reviewed by Spencer [ 66 , 68 , 69 ]. The interest in solar-powered Brayton systems was recuperated by NASA in the 1960s for space applications, as reviewed by Mason [ 240 ]. These Brayton systems for space applications were based on closed cycle engines for obvious reasons and they rejected low grade heat into the space. The main activities of NASA in the field have been based on the Brayton Rotating Units program and on the Solar Dynamic Brayton, as dicussed below. The Brayton Rotating Units Project, which ended in 1978, focused on the integration of Brayton systems into different heat sources; isotope, reactor and solar receiver. The power output ranged between 2.25 and 10.5 kW e [ 241 , 242 , 243 ]. In parallel to this program, NASA developed the mini-BRU program to develop systems with outputs ranging from 0.5 to 2.1 kW e [ 244 ]. The program was run between 1974 and 1978. The Solar Dynamic Brayton Project was developed in the mid-1980s for the Freedom project at NASA Space Station [ 245 , 143 ]. The system was integrated into a hybrid configuration with a PV/Solar Dynamic architecture and with a thermal storage system that eliminated the need for batteries during the night. Final designs of this system were produced but a system was not manufactured. NASA was nonetheless able to demonstrate the technology via the Solar Dynamic Ground Test Demonstration [246, 247, 248]. The 1970s did not see tests of solarized Brayton engine systems and the only activity found in literature is in the form of preliminary assessments for the utilization of such technology. In 1977, Arthur D. Little Inc. released a report discussing the result of a program studying the applicability of Brayton-based solar power systems to naval bases [ 249 ]. This application was mobile and relied on a solar-only open cycle with the cavity receiver placed between recuperator and turbine in a classical configuration. In 1979, another preliminary assessment of small point-focusing, solar, terrestrial power generators based on Brayton air and Rankine steam cycles was published by the Jet Propulsion Laboratory JPL [ 250 ]. Two solar-only layouts were proposed in the report: an open-cycle incorporating inlet air cooling and a closed-cycle system, both with the solar receiver located between recuperator and turbine. A similar conceptual study prepared by AiResearch Manufacturing Company for NASA in 1980 investigates potential cycles for solar-only systems [ 251 ] . These cycles are based on three different thermodynamic cycle concepts: open-atmospheric (ABC), open subatmospheric (SABC) and closed-pressurized (CBC). The integration of the solar receiver for these cycles is the same as in the previous systems and hybridization is also conceptually considered by merely integrating a combustor in series with the solar receiver or, alternatively, in a parallel configuration. Regarding this latter configuration, the author states: "Although systems heated by insolation only were considered in this analysis, each cycle type is also suitable for adaptation to hybrid configurations, using a combination of insolation and fossil fuel. Fossil heat addition, by means of a heat exchanger in series or in parallel with the solar receiver is applicable to all 35 Chapter 3. Design engineering dish total concentration error. These variables are also referred to as "decision variables" because their values can be changed in order to explore the design space and find optimal techno-economic solutions. The system design specifications (common for all the systems) are instead shown in Table 3.7. These are constant parameters that are needed to design the system, like the pressure loss factors, the turbine specific speed, the mechanical and electrical efficiencies, etc. The preliminary design of the components is based on both one (1-D) and zero dimensional (0-D) approaches depending on components features: radial turbomachinery (1-D), solar receiver (0-D), recuperator (0-D) and solar dish (0-D). The basic geometry of turbomachinery, which includes the meridional passages and blades geometries, is then used to estimate the corresponding performance maps (i.e., specific enhtalpy change and isentropic efficiency versus corrected mass flow rate and rotational speed), required by the off-design model. Based on the rated specifications and geometries of the components, the off-design model simulates the performance of the system under arbitrary operating conditions. To this end, suitable control strategies are defined to operate in solar-only and hybrid modes under a feasible range of boundary conditions. The performance of the systems in these conditions are summarised in a set of off-design, steady-state performance maps. The performance maps obtained are used to estimate the annual productivity of the systems in specific locations: for the 8760 pairs of DNI and ambient temperature values characterizing the tipycal local annual meteo, an interpolation is made in the maps and all the values of power output along the year are summed. The total annual net electric output of the systems and the corresponding fuel burnt, for the hybrid systems, are calculated with a similar approach. The design model results are inputs of the cost analysis model since they are used to estimate the component and system costs as functions of the corresponding design variables. Similarly, the off-design model outputs are inputs of the project appraisal model since production and cost have to be integrated in the cash flow economic and financial analysis in order to assess the profitability. 3.2 Components design and off-design modelling This Section 3.2 presents how the on and off-design performance of each component of the system is modelled. This includes the dish concentrator, solar receiver, heat exchangers (recuperators, intercoolers and radiators) and the electric generator. As already discussed in the Introduction, turbomachinery is modelled with one-dimensional, mean-line codes based on Aungier’s works [ 288 , 289 ]. This is a standard approach that is widely used in literature and hence the models are described in the Appendix and not in the main text of the thesis. 3.2.1 Dish concentrator As described in Section 2.1, the dish collector in a CSP system with a micro gas turbine can have very different designs in terms of tracking system, dish frame and struss concept, foundation, reflective material and surface layout (glass facets, metal sheet and stretched membranes). Nevertheless, the technical model of the dish collector used in this work is general in nature and can thus represent different dish concentrators depending on the initial design inputs supplied. The model is based on the information provided by Stine and Harrigan in [ 4 ] and considers a paraboloidal shape which maintains sunbeams normal to the dish aperture plane at any time. This paraboloid is obtained when a parabola rotates around its axis, the line perpendicular to 42 3.2. Components design and off-design modelling Figure 3.1: Definition of a parabola [4]. the directix that passes through the focus, Figure 3.1. The point where the parabola intersect the axis is called vertex and is, by definition, halfway between focus and directrix. The equation of a parabola with the origin of the axis located at the focus can be written as in Eq. 3.1, where f is the focal length from the parabola’s vertex to the focus. In polar coordinates ( r,θ ), the equation of a parabola with the origin of the axis of symmetry (x) at the vertex can be written as in Eq. 3.2, where θ is the angle between the axis of symmetry xand the radius r. As it is often useful when studying the geometry of solar concentrators, the parabolic curve is defined with its origin at the focus and with the angle Ψ in polar coordinates; that is, the angle being measured clockwise from the axis of symmetry to the radius from the focus (r’). This angle represents the angle between the axis of the parabola and the reflected beam. y2=4·fdi sh ·¡x+fdi sh¢(3.1) sin(θdish)2 cos(θdish)=4·fdi sh r(3.2) A property of the parabola is that, for any line parallel to its axis, the angle ρbeam between this line and a line orthogonal to the surface is the same as the angle between the orthogonal and a line connecting the reflecting and focal points. Since solar rays are essentially parallel and, 43 Chapter 3. Design engineering according to Snell’s law, the angles of reflection and incidence are equal, all rays parallel to the axis are reflected to the focus F; mathematically Ψ=2·ρbeam. The parabola used to define the paraboloid of a dish collector is actually a truncated part of an (ideally) infinite curve. The extension of this truncation is defined by the rim angle Ψr im or by the ratio fdish ddish where ddi sh is the aperture diameter of the dish. The radius of the dish pdi sh and the rim angle can be calculated as in Eqs. 3.3 and 3.4. fdi sh =ddi sh 4tan(Ψr i m/2) (3.3) pdi sh =2fdi sh 1+cos(Ψr i m)(3.4) For a parabolic mirror, the incident, ideally parallel sunbeams with irradiance Ibeam are reflected to the focus F of the parabola. The area of a differential, annular element of such collector can be expressed as in Eq. 3.5, where cr ing is the circumferential length of the differential ring on the surface of the parabolic dish and ds the differential length of the parabola arc. From geometrical considerations, Eq. 3.6 yields the total radiant flux reflected from the differential dish area onto the focal point. This equation is obtained on the assumption that there are no reflectance losses and considering that dΨ is small enough so as to yield sin(dΨi)=dΨi, where Ψiis the angle between the incident and reflected beam. d Adi sh =cr ing ·pdi sh ·dΨi cos(Ψi/2) (3.5) µdΦ dΨdi sh ¶i=d Adi sh,i dΨdi sh,i·Ibeam ·cos(Ψdi sh,i/2) =cr i ng ·pdish ·Ibeam (3.6) The concentrated solar energy that is theoretically supplied to the receiver is initially evaluated under the assumption of a perfect parabola. This is then corrected for the lack of perfect parallelism between the solar beams (sun shape effect) and also to account for the errors of the reflective surface. Solar beams are, actually, not parallel since the sun has a finite angular size ( ²sun ) of about 9.6 mrad. This implies that the beams are not reflected on a single point (the focus) but rather on a larger spot that is, indeed, centred on the focus. The size of the spot on a plane normal to the beams at the focus (focal plane) is calculated as in Eq. 3.7. ∆rimage =2·pdi sh ·tan(²sun/2) (3.7) The spread of the spot due to the sun shape effect is unavoidable and it is later increased by the non-ideal properties and performance of the reflective surface. These other factors are associated to the actual geometry of the mirror (which is not a perfect paraboloid) due to the fact that the reflective surface is not purely specular, to the tracking errors of the collector, the 44 3.2. Components design and off-design modelling Type and source Effective magnitude (1σ)σ2 One-dimensional errors Structure 5 mrad 25 Tracking sensor 2 mrad 4 Tracking drive non-uniformity 2 mrad 4 Receiver alignment 2 mrad 4 Total 1D 6.1 mrad 37 Two-dimensional errors Mirror specular reflectance 0.5 mrad 0.25 Sun’s width 2.8 mrad 7.84 Total 2D 2.8 mrad 8.09 Total effective error Total 6.7 mrad Table 3.1: Typical errors of a dish with one standard distribution unit. misalignment of dish and receiver, etc. The statistical distribution of these errors is assumed random and reported in terms of standard deviation in order to determine their combined effect realistically. Table 3.1 shows typical errors for a one standard distribution unit (68 % of all measurements of the errors fall within the angular deviations noted). One-dimensional errors are those that contribute to the spreading of the beams in the plane of curvature whereas two-dimensional errors arise when an incident beam does not lie on the plane of curvature (as it is the case for non-specular reflection and sun shape effects). The combination of both contributions is given by Eqs. 3.8-3.10. In these, the multiplying factor 2 accompanying σslope in Eq. 3.9 comes from Snell’s law and from the fact that the normal to the reflective surface is affected by the local slope error whereas the position of the receiver remains unchanged. In addition, the error attributed to the sun’s disc image size is smaller than 9.6 mrad due to the fact that a standard distribution on the solar disc image is imposed. Thanks to the definition of the concentration errors in standard distribution units, the size of the focal spot can be expressed as a function of the total error by multiplying the sun’s image ²sun by a certain multiplier of the total error. By using n=4 or n=6, the probability that the incident energy falls within the beam image is 95.45% and 99.73% respectively. The beam image reflected by the dish is then projected onto the aperture plane of the receiver in order to size the corresponding opening. To this end, the rim angle is set to 45 degrees ( Ψr im =45 ° ) in order to maximise the concentration ratio, thus enabling a smaller window/cavity of the solar receiver. For omnidirectional receivers, the concentration ratio increases monotonically with the rim angle and becomes maximum when Ψr im =45 ° in Eq. 3.11. Finally, in order to calculate the solar energy intercepted by the aperture area of the receiver, the dish is divided into a number of finite rings whose collected energy is calculated as shown in Eq. 3.12. In this equation ρdi sh is the specular reflectance of the mirror and Γi is the flux capture fraction calculated with an analytical formula as a function of the size of the receiver window (see [ 4 ] for the analytical function and associated coefficients). σ1D=q¡2·σslope ¢2+(σsensor )2+(σdr i ve )2+¡σali gn¢2(3.8) σ2D=q¡σre f lect ¢2+(σsun)2(3.9) 45 Chapter 3. Design engineering σtot =qσ2 1D+σ2 2D(3.10) wimage =2·pdi sh ·tan(n·σtot /2) cos(Ψ)(3.11) ˙ Qinter = Ψr im X i=3° ρdi sh ·Γi·µdΦ dΨ¶i·∆Ψi(3.12) For what concerns the parabolic dish collector, there is no difference between the design and off-design performance models. This is because the tracking system, with two degrees of freedom, ensures that the aperture plane of the dish is always perpendicular to the solar beams. 3.2.2 Solar receiver The solar receiver considered in this work is a pressurized, volumetric cavity receiver incorporating a foam absorber and quartz glass window. This design is under development at KTH, as discussed in Section 2.2.4. The design and off-design performances are calculated with a simple lumped-volume thermal model proposed by Aichmayer et al. [ 274 ] and modified to introduce the heat transfer equations for grey bodies by Semprini et al. in [ 290 ]. In the latter work, the optical properties of window and absorber are evaluated at a specific wavelength, the convective and radiative losses are included and the conduction heat loss is neglected. The secondary concentrator, which is useful to reduce the size of the dish size and to increase the concentration ratio, is not considered for the present design since the component introduces high costs. Wavelength-weighted values for a 5 mm thick fused silica glass window for the solar and blackbody at 1100 ° C spectra have been taken from [ 291 ]. The ambient radiation and the radiation produced by the glass are treated with absorptivity equal to 0.8, for a surface temperature of 600 K, which is equal to the corresponding emissivity as per Kirchhoff’s law. The model includes energy conservation of the glass window, Eq. 3.13, cavity, Eq. 3.14 and foam absorber, Eq. 3.15. The absorber temperature is fixed by Eq. 3.16 so that the four unknown temperatures can be solved. The convective heat transfer coefficient between window and environment is calculated as a function of the Nusselt number with a heat transfer correlation valid for natural convection flow on inclined planes hconv,DP =f ( Θincl ) [ 292 ]. The inclination angle is kept constant and equal to Θincl = 60 ° whilst energy conservation is expressed in terms of specific intercepted beam power ( IDP =˙ Qint,DP Arec ) and specific air mass flow rate per unit receiver window area (GDP =˙ mrec,DP Arec ). I·αvis +σSte f an ·¡αth ·T4 amb +αin f ·T4 s−2²th ·T4 w¢= =hconv ·(Tw−Tamb)+Uw·(Tw−Tin)(3.13) G·(hm−hout )=I·τvi s +σSte f an ·¡²th ·T4 w−T4 s,DP +ρin f ·T4 s¢(3.14) 46 3.2. Components design and off-design modelling Figure 3.2: Schematic layout of the volumetric cavity receiver. G·(hm−hin)=Uw·(Tw−Tin)(3.15) Ts=Tout +Tm 2(3.16) Since solar-only reheating is also considered in certain engine layouts, the previous model is upgraded to enable this process. The model is modified considering that two air streams at different pressures and temperatures enter the solar receiver with the same mass flow rate and absorb the energy needed to raise their temperatures up to their target TIT which, in the base case, are equal. This condition is valid for the design point condition used to size the solar receiver only. In this case, the inputs are the temperatures, pressures, mass flow rates, impinging solar flux and ambient conditions, as shown in the flow diagram of the model in Figure 3.10. The main design parameter of the model is the ratio of reheating rRH which is the fraction of the total heat input corresponding to the high pressure stream, Eq. 3.17. Figure 3.3 shows the operating principles of the model schematically. The angle αRH =rRH 360° represents the portion of the circumferential area corresponding to the high pressure stream flow path. Energy conservation in the glass window,cavity and foam absorber, Eqs. 3.18-3.20 respectively, is expressed as a function of the ratio of reheating rRH , considering a uniform temperature of the glass window Tw and foam absorber Ts ; this latter temperature is obtained as the average value between the inlet and outlet temperatures of both streams, Eq. 3.21. rRH =˙ m2,DP ·∆h2,DP ˙ m2,DP ·∆h2,DP +˙ m1,DP ·∆h1,DP (3.17) G1·¡hout1−hm1¢+G2·¡hout2−hm2¢=I·τvi s +σ·¡²th ·T4 w+¡ρin f −1¢·T4 s¢(3.18) I·αvis +σ·¡αth ·T4 amb +αin f ·T4 s−2²th ·T4 w¢= =hconv ·(Tw−Tamb)+Uw·¡rRH ·¡Tw−Tin1¢+(1−rRH )·¡Tw−Tin2¢¢ (3.19) 47 Chapter 3. Design engineering Figure 3.3: Schematic layout of the reheated volumetric cavity receiver. G1·¡hm1−hin1¢+G2·¡hm2−hin2¢= =Uw·¡rRH ·¡Tw−Tin1¢+(1−rRH )·¡Tw−Tin2¢¢ (3.20) Ts=rRH ·Tout2+Tm2 2+(1−rRH )·Tout1+Tm1 2(3.21) Two additional constraints introduced with Eqs. 3.22 and 3.23 are required by the model’s system of equations since two different cavity ("m") and outlet ("out") temperatures are calculated for off-design conditions. The first equation constrains the heat exchange between the two streams and the glass window with the ratio of reheating rRH , while the second equation forces proportionality between the outlet and inlet temperature changes with respect to the design point (the mass flow rates also change proportionally in off-design conditions). G1·¡hm1−hin1¢·(1−rRH )=G2·¡hm2−hin2¢·rRH (3.22) G1·¡hout1−hin1¢·(1−rRH )=G2·¡hout2−hin2¢·rRH (3.23) These two models of the simple and reheated solar-only receiver are used for both the definition of the design point and the simulation of off-design performance. Since the inlet mass flow rate and the fluid thermo-physical properties change in off-design operation, additional equations are incorporated to evaluate changes in global heat exchange coefficient. This relationship is shown in Eq. 3.24 whilst the corresponding change in pressure drops is expressed in Eq. 3.25. Uw=Uw,DP ·µ˙ mrcv ˙ mrcv,DP ¶0.8 (3.24) ∆prcv =∆prcv,DP ·µ˙ mrcv ˙ mrcv,DP ¶1.21 ·ρrcv,DP ρrcv (3.25) 48 3.2. Components design and off-design modelling 3.2.3 Turbomachinery Turbomachinery components are sized and simulated through a combination of both onedimensional (meanline) codes and lumped-volume models. The former codes are used for the calculation of the rated isentropic efficiencies and performance maps of compressors and turbines whilst the models in the second group are used to model the thermodynamics of the cycle in design and off-design conditions. These lumped-volume models calculate the ideal (isentropic) and real (actual) outlet state and the net electric output. This is shown in Eqs. 3.26-3.29, used for both the design and off-design conditions. hout,id,c=h¡pout,c,sin,c,¯ yin,c¢(3.26) hout,c=hin,c+hout,id,c−hin,c ηis,c (3.27) hout,id,t=h¡pout,t,sin,t,¯ yin,t¢(3.28) hout,t=hin,t−¡hin,t−hout,t¢·ηis,t(3.29) Pel,net =¡˙ mt·¡hin,t−hout,t¢−˙ mc·¡hout,c−hin,c¢¢·ηm·ηel (3.30) The off-design, lumped-volume turbomachinery models have the same objective as the design codes but they rely on performance maps to estimate the internal efficiencies and to calculate the mass flow rates, pressures and shaft speed. These performance maps are obtained from the particular geometry of each turbomachine and with aid from the onedimensional performance model to explore the complete operating range. Even if the maps calculated are valid for that particular set of boundary conditions, there is no need to calculate a new set of maps; rather, it is enough to non-dimensionalize the map in order to extend its validity to inlet temperatures and pressures different to those for which the characteristic maps are estimated. With these corrected maps, the performance of compressor and turbine is interpolated for each pair of arbitrary mass flow rate and pressure ratio values. The interpolation of performance maps is based on the similarity relations presented in [ 293 , 294 ]. With respect to the standard formulation used to correct turbomachinery maps (valid for thermally perfect gases), Eqs. 3.31-3.33, the equations below introduce some factors accounting for real gas effects (change of specific heats and compressibility factor), Eqs. 3.34-3.36. Vcr =s2·γ γ+1·gc·Z·R·Tin (3.31) θV=µVcr Vcr,DP ¶2 (3.32) 49 Chapter 3. Design engineering ²V=γDP ·µ2 γDP +1¶γDP γDP −1 ·"γ·µ2 γ+1¶γ γ−1#−1 (3.33) Neq =N pθ(3.34) ˙ meq =˙ m·pθ δ·²(3.35) ∆his,eq = ∆his pθ(3.36) 3.2.4 Recuperator The models employed to size and simulate the performance of the recuperator are of the lumped-volume type. Once the thermodynamic boundary conditions are calculated, the heat exchanger is sized in terms of global heat transfer area (number of transfer units) based on the following input variables: mass flow rates, inlet thermo-physical properties, recuperator effectiveness and pressure loss factors. Equations 3.37-3.42 are used to set the outlet conditions, based on the concept of effectiveness that permits the subsequent sizing. hout,max,cold =h(Tin,hot ,pout,cold ) (3.37) hout,min,hot =h(Tin,cold ,pout,hot ) (3.38) ˙ Qmax =min£˙ mhot ·¡hout,max,cold −hin,cold ¢,˙ mcold ·¡hin,hot −hout,min,hot ¢¤ (3.39) ˙ Qrec =˙ Qmax ·εrec (3.40) hout,cold =hin,cold + ˙ Qrcv ˙ mcold (3.41) hout,hot =hin,hot − ˙ Qrcv ˙ mhot (3.42) 50 3.2. Components design and off-design modelling The recuperator design model is based on the well-know ε−NTU approach described in many textbooks [ 295 ]. The rated inlet and outlet conditions are known from the thermodynamic cycle and the global heat exchange coefficient is set to a constant value: Ur,DP =100 W/m 2· K. The hot and cold flow heat capacitances ( ˙ CDP =˙ mDP ·¯ cp,DP ) and the ratio between their minimum and maximum values ( rrec,DP =˙ Cmin,DP ˙ Cmax,DP ) is then calculated and, finally, the design point number of transfer units NTUDP and total exchange area Aex,rec are calculated. The system of equations is presented in Eqs. 3.43-3.44. NTUDP = loge 1−εrec,DP 1−rrec,DP ·εrec,DP ˙ min,rec,DP ·¡hout,rec,DP −hin,rec,DP ¢(3.43) Aex,rec =˙ min,rec,DP ·cp,in,cold,DP +cp,in,hot,DP 2·NTUDP Urec,DP (3.44) Akin to the solar receiver, the global heat exchange coefficient is scaled in off-design conditions with Eq. 3.45. The pressure drops on the hot and cold sides of the heat exchanger are also scaled with Eq. 3.46. Urec =Urec,DP ·µ˙ min,rec ˙ min,rec,DP ¶0.8 (3.45) ∆prec =∆prec,DP ·µ˙ min,rec ˙ min,rec,DP ¶1.21 ·ρin,rec,DP ρin,rec (3.46) 3.2.5 Intercooler The intercooler integrated in the ICR and ICRR systems is an air-water heat exchanger whose design model is very similar to that used in the recuperator. The intercooler subsystem considered comprises the intercooler ("IC"), radiator ("RAD") and water pump ("WP") as shown in Figure 3.4. The first set of equations, analogous to Eqs. 3.37-3.42, establish the thermodynamic boundary conditions of the heat exchanger. On the water side, the fixed outlet temperature is 90 ° C while the inlet temperature results from energy conservation in the radiator. Additional parameters of the water circuit and intercooler are shown in Table 3.7. The intercooler is then sized with the classical ε−NTU approach, shown in Eqs. 3.43-3.44. In order to calculate the power consumed by the pump in design and off-design conditions, an isentropic efficiency of this device is considered along with the pressure loss factors of the water circuit across both the radiator and intercooler; the equations used are analogous to those used to model the compressors (see Eqs. 3.26-3.27). The rated power consumption of the fan ( Pel,f an ) is estimated with Eq. 3.47, considering guessed values of the pressure drop across the radiator ( ∆pf an ) and the efficiency of the fan ( ηf an ). Then, for off-design calculations, corrections based on similarity laws are used, Eqs. 3.48-3.50. In both cases, pump and fan, the electric efficiency of the electric drive is considered (ηmot ). Pel,f an,DP =˙ mair,r ad,DP ·∆pf an,DP ρair,r ad,DP ·ηm,f an ·ηf an (3.47) 51 Chapter 3. Design engineering reach the limiting conditions of the system while the temperature range is wide enough to estimate the performance in very different locations. A sufficiently wide DNI range is also required by the need to escalate the map to different DNIs at the design point. 3. The off-design performance map of the system is used to predict the annual yield in different locations characterized by 8760 hourly ambient conditions (ambient temperature and DNI) taken from the System Advisory Model [ 287 ] database in the form of Typical Metereological Years (TMY). The system off design operation strategy set is summarised in Table 3.2: (a) the system is defocused and shut down for safety reasons when the maximum temperature rise across the solar receiver is reached; (b), the system is de-rated to maintain the system operation under the feasible electric generator mechanical limits, as long as these limits are not reached the system runs smoothly under normal conditions; (c) the system runs in idle as long as there is enough solar heat input, even if the net power output is minimal; (d) the system is shut down when it cannot run self sustained. The off-design simulation of the solar subsystem and integrated engine requires two main loops in order for the final solution to achieve convergence, Figure 3.7: 1. An inner loop for the convergence of the thermodynamic cycle and mechanical balance of the shaft in steady-state operation (grey line). The guessed, calculated and iterated variables are the cycle mass flow rate ˙ m1 , controlled by compressor-expander matching and dependent upon the cycle conditions and turbomachinery performance maps, and the turbine exit temperature T5 which influences the steady-state solution of the thermodynamic cycle. 2. The outer iterative loop (blue arrow) is used to implement the operating strategy of the system in order to maximize system efficiency and avoid non-feasible operating conditions. This is achieved by changing the rotating speed of the shaft in order to maintain the outlet temperature from the receiver at its peak value T4=T ITDP . This control strategy modifies the equilibrium (balance) point of the shaft since it impacts the mass flow rate and pressure ratio of the engine. The enthalpy rise across the receiver is then changed accordingly and so does turbine inlet temperature which can be kept at the maximum value (design point value) until the temperature limit is reached at the outlet from the expander. It is worth noting that the reduction of rotational speed and mass flow rate, given the performance maps of the radial turbomachinery, leads to a reduction in pressure ratio and, thus, to an increase of TOT . When the limiting value is reached, the rotational speed control logic changes to maintain the limiting value of TOT . The second parameter iterated in the outer loop ( kder ) controls the operating conditions of the electric generator when the available solar energy DNI is higher than nominal. The feasible operation of the electric generator is considered to be limited by either the maximum mechanical power that can be produced (calculated as a function of the actual rotational speed) or by the maximum rotational speed (set to 115% the nominal speed); in addition, a lower limit for rotational speed is set to 75% the nominal speed, below which the system would shut down (see Section 3.2.7). When there is an excess of solar radiation and one of these conditions is reached, the control strategy based on variations of rotational speed cannot be applied further and a certain fraction of the 58 3.3. System models compressor mass flow rate must be by-passed to the recuperator outlet section, where it mixes with the fraction of pressurized air that flows through this component. The solar receiver inlet is cooled down accordingly and so is its outlet temperature reduced. The controlled parameter kder =˙ m2a ˙ m2 is the ratio from mass flow rate that flows through the recuperator to total mass flow rate at compressor outlet. This strategy can be mantained until the maximum temperature rise across the receiver (set differently for the different systems between 300 K and 450 K) is reached. Since at this point the solar receiver cannot be cooled safely, the system is defocused and shut down at this stage. 3.3.2 Intercooled Recuperated Solar-Only System (ICR-SO) The compound, recuperated Brayton cycle incorporating an intercooled compression process and based on solar-only operation is shown in Figure in 3.8. Figure 3.8: Solar-only layouts: Intercooled recuperated. This layout is aimed at increasing cycle work (compression work is reduced) and can, if the operating conditions are selected appropriately, also enable higher efficiency. The system works as follows: ambient air is compressed by a first centrifugal compressor stage C1 and then cooled down in an air-water intercooler IC. The cooled, pressurized air stream is again compressed in a second radial compressor stage C2 downstream of which it flows into the high pressure side of the recuperator Rc. In this component, the temperature of air is increased thanks to heat that is recuperated from the hot gas stream exiting the expansion process. Downstream of the recuperator, this high pressure flow is sent to the SR where it is further heated up to the specified TIT. The gas leaving the solar receiver flows into a first, high pressure, radial inflow turbine stage T2 where it produces work to drive the high pressure compressor C2. The exhaust gas from the high pressure turbine flows into the low pressure, 59 Chapter 3. Design engineering radial inflow turbine T1 where it is expanded down to atmospheric pressure (plus the inevitable pressure loss across recuperator and exhaust duct), producing work to drive the low pressure compressor and electric generator. Figure 3.9: ICR-SO system: flowchart of design (left) and off-design (right) models. The pressure ratio split for the compressors is chosen in order to minimize the compression 60 3.3. System models work whilst, for the turbines, this comes determined by the mechanical work balance of the high pressure shaft arrangement. The exhaust gas leaving the low pressure turbine is still at high temperature so it is sent to the low pressure side of the recuperator Rh where it is cooled down and then released to the atmosphere. As it was the case before, stream 2b is needed in off-design operation only, when the solar energy supply to the receiver is too high; in such case, the recuperator would be by-passed through 2b and the receiver cooled down to a safe outlet temperature (not exceeding the design point TIT). The flowchart of the design and off-design models is shown in Figure 3.9. The control strategy of the ICR-SO’s design and off-design models are similar to those already discussed for the SR-SO system. As noted in the design flowchart on the left hand side of Figure 3.9, there is an additional internal loop between the preliminary and final thermodynamic solutions, which includes the simulation of the turbomachinery. This loop is required to calculate the pressure ratio split across the expansion process, which depends upon the isentropic efficiency of turbomachinery. For what concerns the off-design simulation, the steady-state equilibrium of the thermodynamic cycle is obtained by iterating the mass flow rate, the inlet temperature to the hot side of the recuperator and the rotational speed of the high pressure shaft, as shown in the inner loop of the off-design flowchart in Figure 3.9. These parameters are obtained through energy conservation in the high and low pressure shafts along with the thermodynamic features of the recuperated Brayton cycle. The control strategy in this case is analogous to the strategy adopted in the SR-SO system: the speed of the low pressure shaft is varied to control the mass flow rate whereas TIT is changed by reducing or increasing the heat exchange in the solar receiver. The derating control parameter works as described before for the SR-SO system; the limits of shaft speed in the control range are also the same as well as the strategy to control TOT when the pressure ratio is reduced and the inlet temperature to the hot side of the recuperator gets to the maximum value. 3.3.3 Recuperated Solar-Only System with Intercooling and Reheat (ICRR-SO) The compound, recuperated system with intercooling and reheat for solar-only applications, termed ICRR-SO, is shown in Figure 3.11. The adoption of the intercooled compression provides the advantages already discussed for the ICR cycle, whereas using reheat increases the expansion (and cycle) work, thus increasing the specific power output and, potentially, thermal efficiency. The thermo-mechanical processes in the gas path between the inlet to the compressor and the inlet to the (high pressure) turbine are the same as in the ICR system. There are two main differences in the hot gas path though. First, the expansion process is split in two: high pressure and low pressure turbines (T2 and T1 respectively). In between of the turbines, the gas flows through the receiver again in order to increase its temperature again at ideally constant total pressure. The inlet temperature to both turbines, in rated conditions, is the same. The high pressure turbine T2 drives the high pressure compressor C2 whereas the low pressure expander T1 drives both the low pressure compressor C1 and the electric generator G. Downstream of the second turbine T1, the hot exhaust gases are directed towards the low pressure side of the recuperator where they are used to heat up the air stream delivered by the high pressure compressor C2. The pressure ratio split across the compression process is determined in order to minimize the total compression work. This rationale also determines the expansion ratio split between the turbines. Indeed, the exhaust pressure of T2 comes 61 Chapter 3. Design engineering determined by energy conservation in the high pressure shaft. Figure 3.10: ICRR-SO system: flowchart of design (left) and off-design (right) models. The model flowchart is shown in Figure 3.10. The rationale of the model is similar to both the SR-SO and ICR-SO systems. The logic of the design model is the same adopted for the ICR-SO system with one main difference: while for the ICR-SO cycle the exhaust pressure 62 3.3. System models Figure 3.11: Solar-only layouts: Recuperated with intercooling and reheat. and temperature of the high pressure turbine are both iterated, only pressure is iterated in the ICRR-SO system inasmuch as temperature is raised by the reheater to the TIT again. This saves time in the calculations of the preliminary thermodynamic cycle block. The off-design model is also analogous to the ICR-SO system. The thermodynamic cycle and matching of turbomachinery is obtained in a similar manner with the difference that an additional internal loop (red arrow) is necessary due to the reheated nature of the thermodynamic cycle. Hence, in order to simulate the solar receiver properly, the outlet temperature of the high pressure turbine is iterated until convergence between the assumed and calculated values. Regarding the control strategy in off-design operation, the main issue is that the inlet temperature to both turbines cannot be kept at the rated TIT level. Accordingly, the rotational speed of the low pressure shaft is changed so as to ensure that at the higher of the two temperatures is equal to the specified TIT. 3.3.4 Simple Recuperated Hybrid system with Serial Heating (SR-HS) The layout of the simple recuperated hybrid system with serial heating SR-HS system is shown on the left hand side of Figure 3.13. It is pretty much the same described for the SR-SO system except for the combustor connected in series downstream of the solar receiver (therefore serial heating). The SR-HS system is regarded a pure hybrid system inasmuch as the combustor does not burn fuel when the system is running at the rated conditions. Whilst this introduces an additional pressure loss, hence efficiency drop, in the design point, it enables additional heat addition (fossil fuel) to make up for the lack of solar energy when DNI decreases to low values. Figure 3.12 shows the flowchart of the models used to calculate the design conditions and off-design performance of the SR-HS system. The flowchart shows that the microturbine 63 Chapter 3. Design engineering is simulated with the new combustor in series: the inner grey loop iterates the matching of turbomachinery and the thermodynamic cycle, while the outer red loop iterates on the rotational speeds that yield the target value of TIT ( T ITDP ). The fuel mass flow rate is set to zero at design point, while its flow is controlled by the system strategy in off-design. Figure 3.12: SR-HS system: flowchart of the off-design model. Equilibrium in off-design is sought with the same loop used for the design point definition, even if with a different operating strategy. The strategy to derate the system when the solar heat input is too high is the same as for the solar-only system. The control of shaft speed is also the same until this parameter reaches the minimum value (75% the rated speed). When this limit is achieved, the speed is set equal to the minimum value and the additional heat required by the system to apply the default operational strategy (constant TIT or TOT depending on the expansion ratio). Table 3.3 shows the controls and strategy applied to the system for different DNI levels with respect to the known rated conditions. The difference with the strategy proposed for the solar-only systems is that, when the limiting minimum rotational 64 3.3. System models Figure 3.13: Hybrid layouts: Simple recuperated with serial (left) and parallel (right) heating. speed is reached, the system works at constant speed by adding the required additional heat in the combustor (d). Controls Defocus Derate Speed Fuel Strategy (a) Very high DNI kde f =0 - - - ∆Trcv <Tr cv,max (b) High DNI kde f =1kder ≤1N≤Nmax ˙ mf uel =0 Pm≤Pm,max T IT ≤T ITDP TOT ≤TOTmax (c) Low DNI kde f =1kder =1 N≥Nmin ˙ mf uel =0 T IT ≤T ITDP TOT ≤TOTmax (d) Very low DNI kde f =1kder =1 N=Nmin ˙ mf uel >0 T IT ≤T ITDP TOT ≤TOTmax Table 3.3: Control strategy of the simple recuperated, hybrid system with serial heating. 3.3.5 Simple Recuperated Hybrid system with Parallel Heating (SR-HP) The simple recuperated hybrid system with parallel heating SR-HP is shown on the right hand side of Figure 3.13. Again, the system behaviour is similar to the SR-SO and SR-HS systems with the main difference that the fuel combustor is now located in parallel with the solar receiver. In this case, the system is regarded as a pure-hybrid system, i.e. no fuel is burnt at design conditions and the dish and receiver sizes (and also the core engine) are the same designed for the solar-only SR-SO system. Since SR-HP and SR-SO are actually the same system but with an additional component in the former layout, there is no need to re-design any component 65 Chapter 3. Design engineering of the system. Figure 3.14: SR-HP system: flowchart of the off-design model. The only flowchart proposed, shown in Figure 3.14, is used to simulate the off-design behaviour with the new layout. At the rated ambient conditions, the system behaviour is identical to that of the SR-SO system since no fuel is burnt and no additional pressure losses are to be accounted for. The off-design strategy, shown in Table 3.4, includes the control of shaft speed (analogous to the solar-only system), fuel and mass flow rate across the receiver (valve). The standard control of shaft speed is kept identical to the solar-only system until the limiting value of rotational speed in reached. Starting from this condition and down to null DNI, shaft speed is kept constant and some air mass flow rate is diverted from the inlet to the solar receiver to the combustor by means of the control valve. The fuel mass flow rate injected in the combustor is calculated in order as to achieve the same temperature in both streams merging at turbine inlet (i.e., compressor and receiver outlet temperatures are equal to the target turbine inlet temperature). When DNI is null, the mass flow rate of air delivered by the high pressure side of the recuperator is completely diverted 66 3.3. System models towards the combustor. Controls Defocus Derate Speed Fuel Parallel Strategy Very high DNI kde f =0 - - - - ∆Trcv <Tr cv,max High DNI kde f =1kder ≤1N≤Nmax ˙ mf uel =0 kval ve=1 Pm≤Pm,max T IT ≤T ITDP TOT ≤TOTmax Low DNI kde f =1kder =1 N≥Nmin ˙ mf uel =0 kval ve=1 T IT ≤T ITDP TOT ≤TOTmax Very low DNI kde f =1kder =1 N=Nmin ˙ mf uel >0 0<kval ve<1 T IT ≤T ITDP TOT ≤TOTmax Table 3.4: Control strategy of the simple recuperated, hybrid system with parallel heating. 3.3.6 Simple Recuperated Booster system with Serial Heating (SR-BS) The simple recuperated booster system with serial heating SR-BS is the hybrid solar-booster version of the previous purely-hybrid SR-HS system presented. The integration layout, shown in Figure 3.13, is the same described in the previous paragraph and it will not be described again. When the solar receiver and fuel combustor are in series, the fuel booster of a solar system can be obtained by selecting two different outlet temperatures for the two components: a smaller dish is thus integrated and a certain amount of fuel is burnt at design point conditions to reach the design TIT (900 ° C) from a lower receiver outlet temperature ROT (800 ° C). The new design point conditions are therefore influenced not only by the combustor pressure loss but also by the changes in the turbine mass flow rate and composition of the working fluid. It is easily deduced that the main difference between the booster and hybrid versions of the same layout is that, in rated conditions, the former keeps the combustor in operation whereas the later does not. Controls Defocus Derate Speed Fuel Strategy Very high DNI kde f =0 - - - ∆Trcv <Tr cv,max High DNI kde f =1kder ≤1N≤Nmax ˙ mf uel >0 Pm≤Pm,max ROT =ROTDP T IT ≤T ITDP TOT ≤TOTmax Low DNI kde f =1kder =1 N≥Nmin ˙ mf uel >0 ROT =ROTDP T IT ≤T ITDP TOT ≤TOTmax Very low DNI kde f =1kder =1 N=Nmin ˙ mf uel >0 ROT ≤ROTDP T IT ≤T ITDP TOT ≤TOTmax Table 3.5: Control strategy of the simple recuperated, booster system with serial heating. The flowchart used to simulate this new design point conditions is shown on the left of Figure 3.15. As for the other systems, an inner iterative loop seeks convergence of the system in terms of thermo-mechanical equilibrium whilst an outer loop sets the control strategy. The control strategy for the new rated conditions is to maintain the design speed whilst changing the fuel flow rate burnt in order to achieve the target TIT. The design point simulation, unlike in the 67 Chapter 3. Design engineering The rotational speed of the single shaft arrangment for both systems is around 130 krpm. This variable is influenced by the specific speed of the turbine which depends itself on the isentropic enthalpy drop of the expansion process and the volumetric flow rate through the machine, which are equal for both systems (excluded the effect of a different TIT). A visible difference between the two systems is the size of the recuperator: the exchange area and NTU as these are almost 60% higher in the SR-II case. This is due to the higher internal heat recuperation of the SR-II systems due to both higher cycle TIT and higher recuperator effectiveness. The calculated isentropic efficiencies of turbomachinery values are around 82% for the turbine and 76% for the compressor, the differences being due to the different TIT and calculated rotational speeds. The solar receiver efficiencies lays around 82%, with an higher value for the SR-I system, due to the lower glass and absorber temperatures thanks to the lower gas temperature. These two lower temperatures enable the reduction of re-radiation and convection losses of the solar receiver. The solar-to-electric efficiency of the SR-I system results in 17.8%, while that of the SR-II system results in 21.6%, 20% higher than in the former. Finally, dish concentrator efficiencies are the same for both systems. Figure 3.17: Meridional views of compressors and turbines wheels in the SR solar-only systems. The advanced solar-only layouts (ICR-II and ICRR-II) provide much higher power output than the SR-II system, around 13.5 kW e and 15 kW e respectively. The difference with the SR-II system, which is even larger with respect to the SR-I system, is not due to a size effect, since the mass flow rate specified is the same for all systems, but to the increase in specific power output and engine thermal efficiency. This is thanks to the adoption of advanced cycles characterized by intercooled compression and reheated expansion. The rotational speeds are around 150 krpm and 130 krpm for the low and high pressure shafts respectively. 74 3.4. Simulations The differences between the advanced and simple layouts are due to the difference in specified compression ratio (6 vs. 3) which provides higher pressure at the turbines inlet and so a reduced volumetric flow that yields a higher rotational speed. The required dish area is 73.3 m 2 and 78.3 m 2 , a difference of only 6%. It is interesting to note that also the receiver dimension changes: while a 244 cm 2 aperture receiver is calculated for the ICR-II, the ICRR-II requires 260 cm 2 aperture area, again 6% higher. The Geometrical Concentration Ratio, calculated as the ratio between dish and receiver aperture areas, is in the order of 3000 suns for all the systems. Figure 3.18: Meridional views of compressors and turbines wheels in the ICR solar-only system. The recuperator exchange area and NTU are slightly lower for the ICRR-II system but they are comparable, while the exchange area and NTU of the intercooler heat exchanger are exactly the same for both systems. The calculated turbomachinery efficiencies are similar for both systems but different for each shaft. Hence, while the isentropic efficiencies of the low pressure shaft turbines and compressors are around 83% and 80% respectively, these are around 87% and 76% in the high pressure shaft. The comments done for the receiver and dish efficiencies for the SR systems are still valid for the advanced layouts. The calculated solar-to-electric efficiencies are 22.4% for the ICR-II and 23.5% for the ICRR-II, 5% and 10% higher than the SR-II system. "Base-case" turbomachinery design The results of the turbomachinery designs, obtained with the one-dimensional approaches presented in the Appendix, are discussed in the following. The main variables of the centrifugal compressor design are shown in Table 3.11 for the solar-only systems. The main compressors 75 Chapter 3. Design engineering in the SR system, which provide a pressure ratio of 3, have similar characteristics. They in fact have the same inlet and outlet conditions, but operate at different shaft speeds, imposed by the different TIT. The compressors of the advanced ICRR and ICR layouts provide a pressure ratio of 2.45. They have different characteristics for the high and low pressure shafts, determined by the rotational speed imposed by the corresponding driver turbine. The total-to-total isentropic efficiencies of the compressor stages are around 76%-77% except that of the low pressure shafts of the advanced layout: they present a higher efficiency, around 80%, thanks to the higher rotational speed of the associated power turbine (which enables a higher specific speed number of the compressor). Total-to-static efficiencies present the same trend but with values that are 4-5 percentage point lower. Figure 3.19: Meridional views of compressors and turbines wheels in the ICRR solar-only system. The main design variables of the radial inflow turbines are shown in Table 3.12. The design expansion ratio of the turbines in the SR layout is 2.72 and their main difference is in TIT and, accordingly, rotational speed. The different inlet gas density also influences the design of the flow path. The low pressure turbines in the ICR and ICRR layouts have an expansion ratio of 3.39 and 3.25 respectively: the resulting designs present different efficiencies, rotational speeds and meridional gas path. The high pressure turbines of the ICR and ICRR have the same inlet conditions and hence very similar designs are obtained. The meridional views of the wheels of compressors and turbines mounted on the same shaft are presented in Figure 3.17 for the simple cycle systems and in Figures 3.18 and 3.19 for the advanced ones. 76 3.4. Simulations "Base-case" turbomachinery maps The intermediate step between system design and off-design is the characterization of component performance. The behaviour of most components is simulated through analytical correlations but turbomachinery requires a higher degree of fidelity/accuracy, which in this case is provided by the one-dimensional models used to design the compressors and turbines. The performance analysis is used to produce a so called "characteristic map" of the turbomachinery that will be integrated into the off-design model. The model that produces the map is the same used for the one-dimensional design but, in this case, the input/output variable sets change. Similarity relationships allow to finally simulate the turbomachinery in off-design conditons, as explained in Section 3.2.3. Figure 3.20: Turbomachinery perfomance maps. SR-I and SR-II systems. The characteristic maps obtained for the solar-only systems turbomachinery are shown in Figure 3.20 for the simple cycles and in Figures 3.21 and 3.22 for the advanced cycles. 77 Chapter 3. Design engineering Figure 3.21: Characteristic maps of the low (top) and high (bottom) pressure shaft turbomachinery. ICR system. "Base-case" off-design and performance maps This paragraph presents the next step in the characterization of the system which is the offdesign performance model of the complete system, made up of the models of the individual components and the global operating strategy. First, the operating strategies of the solar-only systems are discussed. Then the off-design performance matrix for each of the systems is shown, together with the generation of electricity of the system in selected locations. In order to show the control strategy and to compare the performance of the various solar-only layouts, off-design operation is presented for the design ambient temperature only. The complete off-design performance matrix for other ambient temperatures will be shown. The solar-to-electric efficiency and the net electric output of the SR, ICR and ICRR solar-only systems are compared in Figure 3.23. The solar-to-electric efficiency curves of Figure 3.23 show that the four systems present different operational limits: the largest operative range is that of the SR-II system, while the shortest is that of the ICR-II. These differences in the characteristics are due to the combination of various effects: • Different turbomachinery maps, specifically calculated for the design point conditions 78 3.4. Simulations of each of the systems. • The ICR-II and ICRR-II systems has a two-shafts arrangement. The variation of rotational speeds that is necessary to increase/reduce the mass flow rate through the engine is larger, thus reducing the operating range. • Each system makes use of a different thermodynamic cycle. Figure 3.22: Characteristic maps of the low (top) and high (bottom) pressure shaft turbomachinery. ICRR system. The operating strategy is discussed in more detail with the aid of the next figures. Figure 3.24 shows the variation of rotational speed and mass flow rate during off-design operation, as a function of DNI, for the nominal ambient temperature. When solar radiation decreases, the air mass flow rate is reduced through the control of rotational speed, until its lower limit is reached and the dish is defocused; when solar radiation is in excess, the rotational speed control increases the mass flow through the solar receiver until the upper limit of either rotational speed or generator mechanical power is reached. At this point, the limiting value of rotational speed is maintained by de-rating the internal heat recuperated by the cycle 79 Chapter 3. Design engineering (recuperator by-pass control), until the maximum temperature difference across the solar receiver is met. Indeed, by de-rating the system, the amount of heat recuperated and so the receiver inlet temperature are reduced, hence increasing the temperature rise across this component. Figure 3.23: Off-design strategy of solar-only systems at the rated ambient temperature: net solar-to-electric efficiency (left) and net electric output (right). Figure 3.24: Off-design strategy of solar-only systems at the rated ambient temperature: compressor air flow (left) and shaft rotational speed (right). Figure 3.25 shows the effect of the operating strategies on the turbines inlet/outlet temperatures. In general, the control strategy for all the systems is set to maintain TIT, while TOT varies as a consequence of the changes in expansion ratio. TIT is maintaned for the SR-I system in all the operating range since the maximum inlet temperature on the hot side of the recperator (675 ° C) is not reached; the same cannot be said for the SR-II system which, despite a much higher allowable TOT (750 ° C), needs to decrease TIT at low DNI (lower than 400 W/m 2 ). For what concerns the ICR-II system, TIT is kept constant as well as TOT of the high pressure turbine; the low pressure turbine TOT varies but at a temperature much lower than the recuperator hot side limit. The ICRR-II system, due to the nature of the reheated solar receiver, is not able to maintain both TIT (low and high pressure turbines) constant at the 80 3.4. Simulations optimal rated value. For this, the operating strategy is to keep these two temperatures as close to their rated value as possible. Figure 3.25: Off-design strategy of solar-only systems at the rated ambient temperature: turbine/s inlet and outlet temperatures. As shown, the high pressure turbine TIT is maintained for DNI lower than the design point and viceversa. This effect is due to the change in solar receiver inlet temperature of the reheated stream, as a consequence of the change in expansion ratio of the high pressure turbine. The low pressure TOT, which is the inlet temperature to the hot side of the recuperator, increases for DNI lower than the rated value, even if the low pressure shaft TIT is slightly reduced due to the effect of pressure ratio variations. Nevertheless, this critical temperature for the system does not reach the limiting temperature of 750 ° C. Figure 3.26 highlights the performance of the different components. Turbomachinery efficiencies decrease with respect to the design point, but with small changes thanks to the rotational speed/mass flow rate/pressure ratio control. The efficiency of the solar receiver also presents small efficiency penalties at offdesign conditions. The effectiveness of the recuperator increases for DNI lower than the rated value and viceversa, except for the the range of system de-rating (recuperator by-pass), for which the effectiveness increases again. Figure 3.28 shows the maps of the simple and advanced solar-only systems respectively. The maps are calculated in a wide range of DNIs for six ambient temperatures ranging from 0 ° C to 50 ° C. Finally the operatating range of the solar-only systems is drawn in the characteristic maps (only the low pressure shaft for the advanced layouts) in order to visualize the stability of 81 Chapter 3. Design engineering the operation (i.e., avoidance of stall and choke of the compressor). Figures 3.29-3.31 show the off-design characteristic maps of turbomachinery and the operating points calculated for the reference operating range. As explained in Section 3.2.3, the turbine characteristic maps are modified in order to enable a more precise interpolation when the turbine approaches choke (constant mass flow rate). To do so, the vector containing the mass flow rate is multiplied by the corresponding rotational speed to obtain modified maps. This is shown in the following. Figure 3.26: Off-design strategy of solar-only systems at the rated ambient temperature: isentropic efficiency of turbomachinery (left) and thermal efficiency of solar receiver and recuperator (right). "Base-case" annual operation This section explores the annual performance of the solar-only systems. The performance maps shown in the previous Section 3.4.1 are used to estimate (by means of interpolation) the net electric energy produced by the system during the entire year on a hourly basis. The locations are in fact characterized by a Typical Meteorological Year (TMY) series of hourly data of DNI and ambient temperature, which are inputs of the interpolation. Beyond the limits of the performance maps, the system cannot operate stably and hence the net electric output zero. Figure 3.27: Duration curves of hourly DNI (left) and ambient temperature (right) of the three selected locations in a Typical Meteorological Year (provided by SAM). 82 3.4. Simulations Figure 3.28: Performance maps of the solar-only SR-I (left) and SR-II (right) systems. 83 Chapter 3. Design engineering efficiency when DNI approaches zero, for both the SR-HP and SR-HS systems. Finally, the fuel mass flow rate and solar share are shown. As explained before, no fuel is burnt above the lower limit of rotational speed and this can be observed in the 100% solar share and zero fuel mass flow rate. Below this limit, fuel mass flow rate increases linearly as DNI decreases, while solar share decreases linearly to zero. Figure 3.37: Performance maps of the pure-hybrid SR-HS (left) and SR-HP (right) systems. The performance maps of the SR-HP and SR-HS systems, obtained in the full range of ambient conditions, are shown in Figure 3.37. These systems need two maps for the complete interpolation: the net electric power output map and the corresponding fuel mass flow rate 90 3.4. Simulations map. Two interpolations are thus required to estimate the production of electricity and fuel consumption. The operating point of the SR-HS and SR-HP systems on the SR-II turbomachinery maps are shown in Figures 3.38 and 3.39, confirming that the turbomachineries operate in the stable region, far from the compressor stall and choke limits. Figure 3.38: Running line of thermo-mechanical equilibrium shown in the compressor (left) and turbine maps (right). SR-HS system. Figure 3.39: Running line of thermo-mechanical equilibrium shown in the compressor (left) and turbine maps (right). SR-HP system. "Base-case" annual operation This last paragraph presents the annual performance which is summarized in Table 3.14. Some additional figures of merit are included: fuel het input Qf uel , fuel flow Vf uel(5bar ) and solar share fsol ar . This last parameter is the ratio between the solar heat input to the system Qsol , defined above, and the total heat input (solar and fuel), as shown in Eq. 3.61. fshare =Qsol Qsol +Qf uel (3.61) The system conversion efficiency (different from the previous solar efficiency) is defined by the ratio of the net electric ouput and the total heat input (solar and fuel), as shown in Eq. 3.62. 91 Chapter 3. Design engineering ηannual =Eel,net Esol +Qf uel (3.62) As far as operation is concerned, hybrid system are fully dispatchable in the sense that the possibility to run on fuel only enables system operation at any time (for example during the night). This is in contrast with solar-only systems which work only when DNI is within a certain range. For this reason, two different operation strategies have been set for the hybrid and solar-booster systems. • Strategy A: the system runs non-stop (24 hours/day), at full capacity during sun hours and at the a minimum stable load at night. • Strategy B the system runs from 7 a.m. to 10 p.m. only; i.e., when the electricity demand and solar radiation are both high, fuel addition is used to compensate for the fluctuations of DNI. Fuel is also used to get the system ready for the solar start-up in the morning and to extend operation beyond sunset in the evening. Table 3.14 summarizes the annual operation for the two pure-hybrid systems in different locations and for the two different operating strategies. Beijing Strategy A Strategy B SR-HS SR-HP SR-HS SR-HP Esol [MW h] 61.2 61.2 61.2 61.2 Qf uel [MW h] 111.4 96.7 56.0 49.5 Eel,net [MW h] 29.1 31.2 20.2 21.5 Vf uel [m3]5bar 2148 1864 1079 955 ηannual 16.8% 19.8% 17.2% 19.4% fsol ar 33.3% 36.5% 49.9% 52.9% fcapaci t y 37.2% 40.0% 25.9% 27.6% fCO2[g[CO2]/kW h] 671 542 486 403 Casablanca Strategy A Strategy B SR-HS SR-HP SR-HS SR-HP Esol [MW h] 81.5 81.5 81.5 81.50 Qf uel [MW h] 135.4 116.9 60.2 53.0 Eel,net [MW h] 38.3 40.9 26.2 27.7 Vf uel [m3]5bar 2610 2254 1161 1021 ηannual 17.6% 20.6% 18.5% 20.6% fsol ar 37.6% 41.1% 57.5% 60.6% fcapaci t y 49.0% 52.4% 33.6% 35.5% fCO2[g/kW h] 620 501 402 335 Cape Town Strategy A Strategy B SR-HS SR-HP SR-HS SR-HP Esol [MW h] 99.1 99.1 99.1 99.1 Qf uel [MW h] 131.2 112.9 55.8 48.8 Eel,net [MW h] 41.7 44.2 29.6 31.0 Vf uel [m3]5bar 2529 2176 1075 940 ηannual 18.1% 20.8% 19.1% 21.0% fsol ar 43.0% 46.7% 64.0% 67.0% fcapaci t y 53.4% 56.6% 37.9% 39.7% fCO2[g/kW h] 551 448 331 276 Table 3.14: Solar-only turbines design 92 3.4. Simulations In general, the SR-HP system produces a higher amount of electricity, thus having a higher capacity factor than the SR-HS system. The solar share is also higher for the SR-HP system. In terms of operating strategies, Stategy A produces a larger amount of eletricity (around 50% more), as expected, for it makes use of a large amount of fuel with respect to the solar energy available. The attainable solar shares with this strategy are in fact between 33% in China and 47% in South Africa, but with capacity factors ranging 37%-57%. If Strategy B is considered, the capacity factor is reduced to values between 26% and 40%, depending on the location, but higher solar shares in the range of 50%-67% are also obtained. For all the systems and strategies, the annual system efficiency lies between 17% and 21%. The best performance is again obained in Cape Town: highest electricity production, solar share and capacity factor. 3.4.3 Booster systems This section discusses the design and performance of the solar-booster systems. As for hybrid systems, these booster systems are based on the SR-II solar-only engine. In this case thogh, the difference is that solar sub-system of the booster system has to be re-designed to match the new solar thermal power required by the hybrid engine. This is why this secton includes an additional sub-section where the re-design of the solar dish and receiver are discussed. "Base-case" design The hybrid-boster systems, as well as the pure-hybrid systems, is based on the microturbine engine designed for the SR-II solar-only system, whose design was already presented in Section 3.4.1. Nevertheless, unlike the latter, the booster systems make use of fuel combustion at the design point, thus reducing the required solar heat input from the parabolic dish. The solar subsystem (dish and solar receiver) of the SR-II solar-only system is re-designed in accordance with the new conditions, as also explained in Section 3.3.6 and 3.3.7, yielding the dimensions and efficiencies that are shown in Table 3.15. The dish collectors in the hybrid-booster systems have half the aperture area of their solar-only and pure-hybrid counterparts for the same electric output, this being proportional to the corresponding solar share. The solar receivers are also smaller given the reduced solar spot of the concentrated solar energy haze. Since the concentration error is not changed, the Geometrical Concentration Ratio remains constant. SR-BS SR-BP Adi sh £m2¤31.5 25.7 ddi sh [m]6.3 5.7 Arcv £cm2¤105 86 drcv [cm]11.6 10.4 CR [−]3003 3003 ηdi sh,DP [−] 90.4% 90.3% ηrec,DP [−] 82.4% 82.0% Table 3.15: Redesigned solar subsystem of the hsolar-booster system. "Base-case" off-design and performance maps The off-design control strategy and the overall performance maps of the hybrid-booster SR systems are discussed now. Figure 3.40 shows the global efficiency and net electric power of the serial (SB-BS) and parallel (SB-BP) booster systems at the design ambient temperature. The SR-BS system works akin to the SR-HS system but with a wider operating range for DNI>DNI DP due to the lower temperture rise across the solar receiver at the design point. The limiting 93 Chapter 3. Design engineering value is, in this case, reduced to ∆ T max,rcv =300 ° C. The SR-BP also has a wider operating range for DNI>DNI DP because de-rating is performed in the solar receiver line of the parallel heater configuration, while the inlet to the combustor side is not cooled down. The corresponding limit is in this case set to ∆Tmax,r cv =350°C. Figure 3.40: Off-design strategy of the solar-booster systems at the design ambient temperature: net solar-to-electric efficiency (left) and net electric output (right). Figure 3.41 shows the corresponding variations of mass flow rate and rotational speed. As discussed already, the control system of the SR-BP system enables a slower decrease of rotational speed and mass flow rate, since the air flow through the combustor remains constant all the way down to the lower limit of rotational speed. The SR-BS system has instead a faster decrease of rotational speed and mass flow rate (though slower than for the SR-II solar-only system) given that any change in air mass flow rate across the solar receiver is transferred to the compressor directly. As for the dependence of turbine inlet/outlet temperatures and component efficiencies, these are not presented because the results are analogous to those discussed for the hybrid systems. Figure 3.41: Off-design strategy of solar-booster systems at the design ambient temperature: compressor air flow (left) and rotational speed (right). The main difference between pure-hybrid and solar-booster systems is visualized in Figure 94 3.4. Simulations 3.42. The fuel mass flow rate is not null in the latter, not even at the design point. Amongst the two possible configurations, the SR-BP system has a much higher fuel flow, for the aforesaid reasons, and hence a lower solar share. Then, both systems exhibit similar performance as DNI approaches zero. The performance maps of the solar-booster systems are shown in Figure 3.43, where the running lines are not overlaid on the turbomachinery maps for their close similarity to those shown earlier for the hybrid systems. Figure 3.42: Off-design strategy of solar-booster systems at the design ambient temperature: fuel mass flow (left) and solar share (right). "Base-case" annual operation Following the presentation made for the hybrid systems, the booster systems annual performance is shown. Two operation strategies are considered, equal to the ones used for the pure-hybrid operation: a strategy (Strategy A) for the operation 24 hours a day and another (Strategy B) for the operation between 7 a.m. and 10 p.m. when solar radiation is expected to be intense. Table 3.16 summarizes the annual operation for the two solar-booster systems by considering the two different operating strategies. The SR-BP system produces more electricity, thus has higher capacity factor than the SR-BS system as it was als the case for the hybrid systems. The solar share is on the contrary a few percentages lower for parallel than for serial heating. In terms of operation strategies, Stategy A brings about a higher yield (around 50% higher) as a consequence of the heavier firing with respect to the solar energy available. The attainable solar share with this strategy is in fact low, between 22% in China and 28% in South Africa, but with capacity factors ranging from 39% to 56%. If Strategy B is considered, the capacity factor is reduced to values of 28%-41% depending on the system and location, but with higher solar shares in the range of 25%-40%. It is to note that the differences in performance between the two systems increase with the second strategy, for which the SR-BS system presents much higher solar-share and lower capacity factor than the SR-BP system. Again, for all the systems and strategies, the annual efficiency lies between 19% and 21%. The location exhibiting best performance is again Cape Town which achieves highest yield, solar share and capacity factor. 95 Chapter 3. Design engineering Figure 3.43: Performance maps of the solar-booster eith serial (SR-BS, left) and parallel (SR-BP, right) heating. 3.5 Summary and findings This chapter presents the general methodology employed during the design engineering phase, which is the crucial step incorporating most of the risk in the race for business success. The design models of each major component are described in detail, based on the technology review presented in Chapter 2, and the same applies at the system integration level where control and operating strategies are also assessed for the layouts of interest: solar-only, hybrid and solar-booster; simple recuperated, intercooled and intercooled-reheated. These models concern either design or off-design performance analysis and include diagrams to facilitate the 96 3.5. Summary and findings visualization of the algorithm and process flows. Within this frame, the following paragraphs summarize the main findings of the chapter. Beijing Strategy A Strategy B SR-BS SR-BP SR-BS SR-BP Esol [MW h] 37.5 30.5 37.5 30.5 Qf uel [MW h] 120.1 125.6 72.6 82.2 Eel,net [MW h] 31.1 32.0 21.9 23.4 Vf uel [m3]5bar 2314 2421 1400 1584 ηannual 19.7% 20.5% 19.9% 20.7% fsol ar 22.1% 18.1% 32.0% 25.3% fcapaci t y 39.8% 41.0% 28.0% 30.0% fCO2[g/kW h] 677 688 582 616 Casablanca Strategy A Strategy B SR-BS SR-BP SR-BS SR-BP Esol [MW h] 49.9 40.6 49.9 40.6 Qf uel [MW h] 149.7 155.7 85.3 96.8 Eel,net [MW h] 40.6 40.9 28.1 29.2 Vf uel [m3]5bar 2885 3002 1644 1865 ηannual 20.3% 20.8% 20.8% 21.2% fsol ar 25.0% 20.7% 36.9% 29.6% fcapaci t y 52.0% 52.3% 36.0% 37.3% fCO2[g/kW h] 647 669 534 582 Cape Town Strategy A Strategy B SR-BS SR-BP SR-BS SR-BP Esol [MW h] 60.6 49.4 60.6 49.4 Qf uel [MW h] 152.0 158.2 87.5 99.2 Eel,net [MW h] 43.9 43.8 31.3 32.0 Vf uel [m3]5bar 2930 3050 1685 1912 ηannual 20.6% 21.1% 21.2% 21.6 fsol ar 28.5% 23.8% 40.9% 33.2 fcapaci t y 56.2% 56.1% 40.1% 41.0 fCO2[g/kW h] 607 633 489 543 Table 3.16: Annual performance of the solar-booster systems. A set of independent design variables and fixed system specifications have been proposed to size the "base-case" systems. This is done for two different technology levels, each one of which is defined by fixed values of turbine inlet temperature and recuperator effectiveness. These two parameters are considered as the main drivers for the overall system assessment. The "base-case" systems are powered by solar dishes with aperture areas (size) in the range from 25 to 80 m 2 and concentration ratios of around 3000 suns. High values of solar dish efficiency (slightly higher than 90%) are obtained by a zero-dimensional model. The main design driver recognized for this component is the total error incurred in concentrating solar energy on the focus, as this has a strong impact on the size of the solar spot on the receiver: the concentration ratio achieved increases as the concentration error decreases thanks to the better quality of the dish. The impacts of dish size and quality on the cost of the collector will be assessed in Chapter 4. The solar dish is coupled to either simple or reheated solar receivers, located at the focus of the dish and connected to the microturbine engine; the relatively small dimensions of the receiver, in the order of 10-20 cm in diameter, poses a design challenge in order to a realiable and efficient operation of the overall system. These components are studied with zero-dimensional models describing the energy exchange along the air flow path, hence 97 Chapter 3. Design engineering yielding temperatures and pressures for the cases considered. The inclusion of reheat is aimed at assessing the potential of reheated cycles in systems with multi-shaft arrangements. A very similar receiver efficiency, in the order of 82%, was calculated for both receivers (reheat and non-reheat) at design conditions. The off-design operation of the receiver is considered feasible under the operating conditions imposed by the control strategies of each system: the outlet temperature is controlled by means of variations of mass flow rate and turbine inlet temperature whilst, at the same time, the maximum temperature difference across the solar receiver is also checked for safetyand mechanical-integrity purposes. The energy conversion from thermal to electrical was considered with various microturbine layouts: a simple-recuperated cycle in a single shaft arrangement and intercooled or intercooled-reheated cycles in a twin-shaft layout. The efficiency of microturbines based on the simpler configuration shows the expected trend, with higher TIT and recuperator effectiveness yielding better performance. And the advanced cycles also shows the expected trend, providing higher efficiency even when the additional consumption due to the auxiliary systems in the cooling water subsystem and the additional pressure losses in the reheating process are accounted for. This is thanks to the superior performance of the working cycle. Overall, the so-called technology levels turn out as the main drivers of performance for the solar-assisted microturbine. A classical hybridisation scheme with the combustor in series with the solar receiver was considered in order to support off-design operation in conditions with low radiation. This was also checked against a parallel arrangement to verify the advantages of the former configuration. Both arrangements showed similar off-design fuel-aided performance curves: the first layout is slightly more efficient than the second at very high DNI and vice versa for very low DNI. Overall, the parallel scheme shows a better conversion efficiency and solar share when the annual performance is computed. The possibility to incorporate fuel combustion in rated (design) operation was also investigated through the solar-booster systems, with the main aim of decreasing the required dish area per unit electric output (m 2 /kW). These solar-boosters are characterized by lower solar shares and higher specific CO 2 emissions. Their advantage is nevertheless their higher electric output for a given dish size (or viceversa) which can make the system more compact and less costly. As far as the main equipment is concerned, various design features can be highlighted: • Classical, simple heat exchangers models were used to size these devices. For the recuperator, which is the biggest and most expensive heat exchanger, two different technology levels were considered based on their effectiveness. As expected, better solar-to-electric performance of the system was obtained for the most effective heat exchanger. The preliminary design of the intercooler and the integrated heat rejection subsystem was also investigated for the multi-shaft system. Considering the effectiveness of these components and their respective pressure losses provides a sense of their impact on the overall performance of the system. According to this analysis, the incorporation of these layouts is considered feasible. Limits on the operation of these devices were checked in terms of maximum air inlet temperatures. In addition, an innovative control scheme for the recuperator by-pass line was included in order to increase the safe operational range of the systems. The by-pass enables the system to produce power even if DNI exceeds the maximum value allowed by the limits of the electric generator. This implies a higher production of electricity and 98 3.5. Summary and findings ensures the safe operation without the need to de-focus the dish during high production periods. • One-dimensional models of radial turbomachinery have been integrated in the overall design model. This choice was made considering the large impact of their efficiency on the performance of the prime mover and also considering that, due to their reduced size, the efficiencies calculated with classical lumped-volume approaches would be much more uncertain. For pressure ratios in the range 2.5-3.5, the calculated efficiencies are between 75%-79% and 81%-87% for compressors and turbines respectively. Also, these models permit the estimation of preliminary geometries and, on this basis, of their specific off-design performance maps. This new integration approach characterizes systems with compressors and turbines with different rotational speeds, inlet conditions, number of shafts, etc., thus enabling a wide use of the design tool. The preliminary geometries obtained show very small dimensions of the rotating parts of the microturbine, as shown in the numerous meridional views of compressors and turbines provided in the thesis. For the base-case systems, feasible meridional contours of the air path were drawn. For the advanced cycles, the turbomachinery in the low pressure shaft shows feasible meridional flow passages; the high pressure shafts’ compressors show a very narrow meridional passage and the turbines are very short and small. Out of these results, it is envisaged that a bigger system size (electric output) than the base-case should be considered for the advanced cycles. The performance maps calculated for the base-case systems show that compressors design point is more distant to the surge line while it is closer to the choke limit. The compressors in the advanced cycles show instead a design point located in the central region of the map. The low pressure turbines are characterized by a design point very close to the choke conditions while high pressure turbines are far from this operation. Similarity laws including real gas parameters were used to match the operation of these components in the off-design simulations of the overall system. The operating points in equilibrium, for the various systems, were visualized on the characteristic maps and they were found to be sufficiently far from the unstable working conditions, i.e. compressor choke and surge. • A non-dimensional (lumped-volume) electric generator model, based on the specifications of a real component used for the OMSoP system prototype, was used to both simulate the mechanical-to-electric conversion efficiency and to estimate the operational limits in terms of mechanical power absorbed and maximum rotational speed. This was found useful to set the control of the systems. From a global standpoint, the main finding of the solar-only system is that dish-microturbine systems are able to attain fairly high solar-to-electric efficiencies. Thus, the performance achieved by an SR-II system located in Cape Town, South Africa, was 21.6% design point efficiency and 18.9% average annual efficiency. For the more advanced cycles, the recuperated system incorporating intercooling and reheat achieved highest rated and annual conversion efficiencies in the same location, 23.5% and 19.5% respectively. These efficiencies lie in between those of dish-Stirling and PV technologies. 99 Chapter 4. Cost engineering Production rate Material Labor Burden Specific Relative huni ts year i[e] [e] [e] [e/m2] [-] 100 42273 4337 2886 439 1.02 1000 40560 3941 4242 431 1.00 5000 27632 4071 4481 320 0.74 10000 27500 3121 3261 299 0.69 50000 27222 2286 2430 284 0.66 100000 27160 2240 2261 280 0.65 400000 26901 2082 2187 276 0.64 1000000 26812 2063 2166 274 0.64 Table 4.3: Cost of the solar collector as a function of production rate (or equivalent total aperture area) (I). General Electric/Pioneer engineering dish with 12 meters aperture diameter. Production rate Tooling Equipment Assembly Personnel Plant # of plants huni ts year i[Me] [Me]hhr s uni ts i[-] [m2] [-] 100 1.3 11.1 188 18 15 0.07 1000 2.5 17.0 177 108 43 0.21 5000 6.6 44.8 173 553 217 1.00 10000 11.3 72.7 132 825 320 1.47 50000 33.9 272.0 94 2938 1128 5.15 100000 52.9 541.9 87 5438 2066 9.26 400000 143.4 1866 84 21000 7896 35.3 1000000 334.6 4275 84 52500 19530 86.0 Table 4.4: Cost of the solar collector as a function of production rate (or equivalent total aperture area) (II). General Electric/Pioneer engineering dish with 12 meters aperture diameter. A similar approach to that presented in the previous paragraphs was again used by Fortgang to assess the cost of the OMNIUM-G full surface concentrator [ 61 ]. Gallup and Kesseli [ 7 ] also developed in 1994, for Northern Research and Engineering Corp. (NREL) under contract of Sandia National Laboratories, a technical and economic study of a solarized Brayton engine based on turbo-charger technology and integrated with a solar receiver by the German Aerospace Research Establishment (DLR). The manufacturing specific cost reported in this work is considered constant over a range of dish aperture area, i.e. from 67 m 2 to 230 m 2 , and then dependent upon production rate in a range between 100 units/year and 10000 units/year. Table 4.5 shows the data collected after normalization to e2016 , and assuming a 15% profit margin in order to derive the manufacturing cost from the corresponding market prices. Finally, the cost breakdown of an 11 kW e Envirodish dish-Stirling system is presented by Heller in [ 8 ]. Considering the collector only, the expected cost reduction for large production rates (economies of scale) is similar to that observed in other references whilst the main difference with OMSoP is the very large contribution of the Stirling engine as compared to a microturbine. The cost figures correspond in this case to a dish with 60 m 2 aperture area, 12 facets, a reflectivity of 94% and a high concentration ratio of 12730 suns. Table 4.6 summarizes the cost data collected and normalized from the cited reference. Production rate Specific cost Relative cost huni ts year i[e/m2] [-] 100 525 2.00 1000 263 1.00 10000 175 0.67 Table 4.5: Cost data of solar collector provided by Gallup and Kesseli [7]. 106 4.2. Cost estimation and modelling Production rate Specific cost Relative cost huni ts year i[e/m2] [-] 1 901 3.06 10 677 2.30 100 388 1.32 1000 295 1.00 Table 4.6: Cost data of solar collector provided by Heller [8] A further cost dataset for this research was provided by the OMSoP project Consortium partner Innova [ 9 ], applicable to parabolic dish collectors with 90 m 2 aperture area and built upon the company’s commercial experience with smaller collectors for Combined Heat and Power (CHP) Stirling-based units. The information provided considers different production rates from 50 to 10000 units/year but is incomplete with respect to costs breakdown. Therefore, in order to have a more detailed distribution of costs, the data in [ 75 ] have been extrapolated and applied to the dish delivered by Innova through a power function based on size ratio (90 m 2 for Innova and 113 m 2 for Pioneer engineering); this is the usual practice in most cost-estimating references, for instance [ 296 ]. The dependence of labor and burden costs on this scaling factor is assumed linear whilst material costs are scaled with a different exponent depending on whether the reference dish is scaled up or down. This information is provided in Table 4.7 and applied as in Eq. 4.5. cdi sh =cdi sh,re f µAdi sh Adi sh,re f ¶ndi sh (4.5) Area Material Labour Burden Specific Total Exponent nDish [m2] [e] [e] [e] [e/m2] [e] [-] 50 11433 1047 1127 272 13608 0.9 90 19404 1885 2029 259 23319 1 130 29079 2723 2931 267 34733 1.1 170 41625 3561 3833 288 49019 1.2 210 58381 4399 4735 322 67516 1.3 Table 4.7: Collector cost as a function of aperture area as provided by Innova [9] The cost exponents nDi sh indicated in Table 4.7 have been selected with the objective that the dish specific cost increases when departing from the reference aperture area of 90 m 2 . Even if the cost increase is less steep when the size of the collector is reduced (left branch of the parabola), the motivation is to locate the optimum dish size in the region between 50 m2 (corresponding to a diameter of 9 m) and 120 m2 (14 m), as stated in [ 51 ]. Jaffe recognized that the minimum specific cost of parabolic dish collectors lies between 5 (20 m 2 ) and 15 meters (175 m 2 ) of aperture diameter, considering the stiffness requirements of the supporting structure and due to the fact that, for very low dish areas, the specific cost of the tracking system drive increases [ 302 ]. The manufacturing cost datasets obtained after normalization are presented jointly in Figure 4.2. 107 Chapter 4. Cost engineering Figure 4.2: Specific cost data of the solar collector as a function of production rate (left) and aperture area (right). In regards to the dependence of the manufacturing cost on the optical quality of the dish, Truscello defined a figure of merit to obtain the optimum collector design: the ratio from the energy absorbed by the receiver at the specific operating temperature to the cost of the collector. The trade-off between optical quality and specific cost is discussed in [ 53 ], as shown in Figure 4.3 where it is observed that the cost and efficiency of the collector present a more than proportional increase with optical quality. The figure of merit does, on the contrary, incorporates these trade-offs between performance and cost, yielding a global optimum beyond which any further increase in optical quality produces an increase in efficiency but also a more than proportional increase in cost. The same figures provides the functional dependence of the figure of merit, showing that this depends on the reflective surface (reflectivity), substrate fabrication (surface quality) and control and stiffness of the supporting pole (pointing error). The trade-offs when selecting the reflective surface and substrate of the dish have been discussed by Bouquet in [ 54 , 55 ]. This author concluded that there exist three types of reflective mirrors: second-surface silvered (or aluminized) glass, anodized aluminium, and aluminized polymeric film. Following Bouquet’s conclusions, the final selection must rely on specific system requiements: for nominal receiver cavity temperatures between 400 ° C and 1400 ° C, commercial second-surface metalized glass mirrors are preferred; for temperatures above 600 ° C, aluminium reflectors can also compete with the metalized glass mirrors; and for temperatures below 600 ° C, the best cost trade-off is that of aluminized polymeric film surfaces. Lovegrove recognized a number of factors influencing the performance and cost of the parabolic dish collector strongly: optical quality (most of all for high concentration ratios), stiffness of the dish structure under dead weight and wind load, facet alignment, alignment of the absorber along and across the optical axis and, finally, the tracking accuracy when following the sun’s path. Andraka [ 56 ] studied the impact of optical quality on cost and performance of dish reflectors with different surface slope errors, concluding that high precision reflectors pay off in the end even at a relatively high cost. Prof. Bammert studied the economics of large parabolic dish systems coupled with micro gas turbines in 1981 [ 303 ]: an important cost relationship between Concentration Ratio ( CR =Adi sh / Arcv ) and specific collector cost was proposed for various solar concentrating technologies and CR ranging from 108 4.2. Cost estimation and modelling 10 to 10000. Figure 4.4 shows the data proposed by Bammert in relative terms with respect to CRre f = 3000, for the usual range in in which parabolic dish are preferred (between 1000 and 10000 suns). Figure 4.3: Figure of merit assessing the trade-offs between performance and cost by Truscello. Once the available cost datasets found in literature and provided by the industrial partners in OMSoP have been reviewed, it is necessary to identify and discuss the cost drivers in order to set the analytical parametric cost functions for the overall economic analysis. The main drivers of the manufacturing cost of a parabolic dish collector are the dish aperture area (size), annual production rate (economies of scale), optical quality (design quality) and type and structure of the reflective surface. Amongst these, the strongest cost dependences are: • Size (aperture area): the dependence on size incorporates the need to improve/assure the quality of the manufacturing process for larger dishes, hence increasing costs. Larger dishes request better performance of the reflective surface in order to limit spillage; otherwise, there would be lack of proportionality between the sizes of dish (heat input) and engine (electric output). Dish calibration (mounting and canting of facets) is also more expensive if the focal distance increases. The growth in size brings about a more than proportional increase in the cost of the supporting frame and foundation due to the quick rise of wind loads (proportional to aperture area and diameter/height of the dish). A similar effect is experienced by the tracking system (motors and drivers) whose specific cost ( e / ADi sh ) decreases in spite of the higher total cost ( e ). With all this in mind, it is assumed that the specific cost of the dish decreases for increasing aperture area but, from a certain size on, it increases again. This is implemented by means of a quadratic polynomial. • Production rate (number of units manufactured in a year): the specific cost experiences an exponential reduction for large scale manufacturing. Larger productions mean a 109 Chapter 4. Cost engineering reduction in material (coming from mass purchase of large quantities of raw materials) and manufacturing costs (economies of scale applied to automated manufacturing). The estimator considers a power function with three parameters for this driver as it is assumed that the slope of the specific cost function decreases (in absolute value) for larger production volumes. •Optical quality: the dependence on optical quality include the effects of surface reflectivity, of the substrate manufacturing quality and of the stiffness and tracking system of the supporting frame. These influence both the dish cost and performance (efficiency), so that a trade-off between quality and cost exists. In general, high optical quality are preferred for high maximum engine temperatures. The relative cost function selected in this case is a third order polynomial which increases monotonically with concentration ratio (up to 10000). • Dish typology: the type and constituents of the dish collector have a strong influence on its costs, which add up to the influence of size, production rate and optical quality. Accordingly, the cost functions are different for the various types reviewed in Section 2.1. In this case though, only dishes based on second-surface metalized glass mirrors are considered. Figure 4.4: Relative collector cost as a function of Concentration Ratio (CRre f =3000). The resulting specific cost estimator includes the following set of equations, Eqs. 4.6, whose corresponding coefficients are detailed in Table 4.8:            lCMan,Di sh =fL,Di sh ·fCR,Di sh ·cMan,Di sh ·ADish cMan,Dish =aA,Dish ·A2 Di sh +bA,Di sh ·ADi sh +cA,Di sh fL,Di sh =aL,Di sh ·LbL,Di sh Di sh +cL,Di sh fCR,Di sh =aCR,Dish ·CR3 Di sh +bCR,Di sh ·CR2 Di sh +cCR,Di sh ·CRDi sh +dCR,Di sh (4.6) where: 110 4.2. Cost estimation and modelling •CMan,Dish: total manufacturing cost of the solar dish [e]. •cMan,Dish: specific manufacturing cost of the receiver per unit aperture area [e/m2]. •fN,Di sh: correction factor for production rate. •ADi sh: dish aperture area [m2]. •CRDi sh: dish concentration ratio. •aA,Di sh , bA,Di sh , cA,Di sh , aN,Di sh , bN,Di sh , cN,Di sh , aCR,Di sh , bCR,Di sh , cCR,Di sh , dCR,Di sh : cost functions coefficients. •LDi sh: annual production rate [units/year]. Coefficients a b c d xA,Dish +4.7051·10−3-9.0340·10−1+3.0454·102 xL,Dish +3.6100·100-3.0952·10−1+5.3076·10−1 xCR,Di sh +1.1429·10−12 -1.9378·10−8+1.2392·10−4+7.6962·10−1 Table 4.8: Coefficients of the dish cost estimator, Eq. 4.6. Figure 4.5 presents the functional dependence of the cost function upon production rate (left) and aperture area (right), complementing the information about the impact of concentration ratio presented above in Figure 4.4. Figure 4.5: Influence of production rate (left) and aperture area (right) on the specific cost of the solar collector. 4.2.2 Solar receiver - manufacturing The state of art of solar receivers for point-focusing dish collectors was reviewed in Section 2.2, illustrating the various solar receiver typologies that are applicable, either based on tubular, heat pipe, small particle, volumetric absorber and impingment cavity concepts. In this work, a volumetric solar receiver is considered for which simple and reheated configurations working at two different temperatures are considered: 800 ° C and 900 ° C. The manufacturing cost is estimated first and analytical cost functions are then built, based on manufacturing cost data available in literature and on cost data provided by The Royal Institute of Technology in 111 Chapter 4. Cost engineering Stockholm within the development of the OMSoP project. Before using these data though, the costs of various solar receivers reported in literature are reviewed. Amongst the different design alternatives considered in the conceptual study and cost analysis of a solar thermal receiver for solar-dish systems developed by JPL and GE in 1980 [ 141 ], a ceramic tubular pressurized air system operating at 3.1 bar and 1371 ° C outlet temperature (TIT) was eventually adopted. Nonetheless, this information is not deemed useful since the concept, materials and the outlet temperature are different to those considered in this research. In 1981, Pioneer Engineering & Manufacturing Company carried out (for JPL again) an analysis of the manufacturing costs of a similar pressurized air solar receiver that had previously been designed by the AiResearch Division of the Garret Corporation, aimed at being used in solar dish and mGT applications [ 304 ]. The analysis reported manufacturing costs for different production volumes (from 100 to 10000000 units/year). This information is indeed useful for this research since the design adopted is very similar to both the impingment and the volumetric concepts. In fact, it consists of a cavity made out of two concentric cylinders with an insulation between them and ceramic parts were the temperatures are higher. Kesseli and Gallup considered a similar application and evaluated the dependence of receiver cost on size and production volume, providing the price of the solar receiver, mGT and parabolic dish for different system sizes and production rates [ 7 ]. The information in these references is complemented by the dataset provided by Innova, the industrial partner in charge of developing the dish in the OMSoP project. This company used to commercialize a dish Stirling system incorporating a directly illuminated receiver whose costs have been made available to the consortium. The consortium partner responsible for the design and delivery of the solar receiver within the OMSoP project is the Royal Institute of Technology in Stockholm, KTH. The price of the prototype has been provided by this institution and then corrected to manufacturing costs by merely applying a profit margin and the effects of size and economies of scale, as well as cost factors for different outlet temperatures for the simple and reheated configurations. Manufacturing cost estimates were also provided for a 20.5 kW t volumetric receiver with foam absorber. The main cost drivers for this component are the size, production volume, outlet temperature and layout (whether or not a reheated configuration is considered). These dependences are incorporated following the methodology outlined in [ 47 ] for the impingement cavity receiver. Economies of scale are built in using various sources available whereas the dependence on layout and operating temperature is defined as suggested by KTH and Compower. The influence of size has already been discussed by the author in [ 47 ] and relies on the raw data obtained for the 20.5 kW t prototype and a scaling exponent equal to 0.6, as shown in Eq. 4.7. crcv =crcv,re f µPr cv,th Prcv,th,re f ¶0.6 (4.7) All the information gathered from literature, provided by the Consortium partner and obtained by preliminary cost calculations is shown in Figure 4.6. 112 4.2. Cost estimation and modelling Figure 4.6: Specific cost data of solar receivers as a function of production rate (left) and net thermal output (right). Based on the information above, continuous cost functions are developed in order to calculate the cost of the solar receiver for different design specifications. These functions are based on the following cost drivers: • Size (net thermal output): increasing the net output of the receiver brings about a specific cost decrease ( e /kW t ) that affects material, labor and burden costs. This is assumed to be valid for the entire range considered, which extends to about 150 kWt. • Production rate: again, increasing the production volume brings about a transition from craft production to industrial, automated mass production. This results in lower costs. • Technology level (outlet temperature): regarding this parameter, it is commonly acknowledged that increasing the receiver outlet temperature brings with it higher specific costs. This is due to the substitution of more resistant superalloys or even ceramic materials for the standard alloys used in common high temperature units (<800 ° C). A different set of coefficients is used for each outlet temperature, representing the discontinuities in the cost and selection of the solar receiver outlet temperature. • Reheating: a different cost is considered for the reheated solar receiver configuration with respect to the simple configuration. Additional cost are required for the added complexity associated to integrating two different air streams in the same cavity. These three functional dependences have been integrated in the analytical cost functions shown in Eq. 4.8, in conjunction with the set of coefficients provided below.        lCMan,Rcv =cMan,Rcv ·fL,Rcv ·Pth,Rcv cMan,Rcv =aP,Rcv ·PbP,Rcv th,Rcv +cP,Rcv fL,Rcv =aL,Rcv ·LbL,Rcv Rcv +cL,Rcv (4.8) where: •CMan,Rcv : total manufacturing cost of the receiver [e]. 113 Chapter 4. Cost engineering •Pth,Rcv : net heat output [kWt]. •cMan,Rcv : specific manufacturing cost of the receiver per unit heat input [e/kWt]. •fL,Rcv : correction factor for production rate. •aP,Rcv ,bP,Rcv ,cP,Rcv ,aL,Rcv ,bL,Rcv ,cL,Rcv : coefficients. •LRcv : annual production rate [units/year]. A different set of coefficients is calculated and provided for each receiver outlet temperature and configuration. Table 4.9 shows this information for the volumetric receiver whilst the resulting cost functions are plotted in Figure 4.7. Coefficients Technology a b c xP,Rcv 800°C+9.9309·101-2.3634·10−1-1.5429·101 xP,Rcv 900°C+1.1917·102-2.3634·10−1-1.8515·101 xP,Rcv 900°CRH +1.4896·102-2.3634·10−1-2.3144·101 xL,Rcv All +1.4694·101-4.2308·10−1+2.2915·10−1 Table 4.9: Coefficients of the volumetric solar receiver cost function. Figure 4.7: Specific cost function of the volumetric solar receivers as a function of production rate (left) and net thermal output (right). 4.2.3 Microturbine - manufacturing The state of the art of microturbines for power generation was assessed in Section 2.3. In the following, the cost of microturbines for dish applications is estimated based on cost data from literature and manufacturing cost data given by the OMSoP consortium partners, . Following the methodology already familiar to the reader, used for the dish and solar receiver, analytical cost functions correlating specific costs with the main design variables are proposed. Given the received set of cost data by the consortium partner Compower, the assessment of microturbine manufacturing costs covers two different technology levels, characterized by TIT and recuperator effectiveness. 114 4.2. Cost estimation and modelling Figure 4.8: Specific cost of microturbine as a function of production rate (left) and net electric power (right). Fortgang and Mayers provide a very interesting report in [ 305 ], assessing the manufacturing cost and required selling price of an mGT of 20 kW e peak electric output developed by Garrett AiResearch Manufacturing Company of California, for integration into solar dish collectors (the system was an upgrade of a previous 10 kW e design). Another useful reference to estimate the cost of mGTs was provided by Donald Gallup and James Kesseli, containing a breakdown of micro gas turbine costs (engine, lube oil system, gearbox and generator) as a function of size and production volume [ 7 ]. These data confirm that there are evident economies of scale both in terms of production rate and system size. Moreover, such specific cost reductions exhibit a non-linear (more than proportional) behavior, meaning that they are particularly strong for small systems and low annual production volumes. These cost data are presented in Figure 4.8. Many other sources about costs of microturbines in the range from 5 kW e to 50 kW e can be found in literature [ 306 , 201 , 307 , 194 , 308 , 309 ], amongst which the works by Rodgers are particularly interesting [ 306 , 201 , 194 ]. In the latter, the author discusses the design of an mGT, already in the early phase of industrial deployment, in comparison with that of a turbocharger. The same reference provides a discussion about how to reduce costs and increase the performance of the system, showing that the use of recuperators for the singleshaft configuration can easily double the cost (depending on the degree of heat recovery) but brings with it great benefits in terms of efficiency. It is concluded that, as a general rule of thumb, converting a turbocharger into a gas turbine provides little cost advantage unless the costs of the ancillary equipment can be reduced. Finally, in another useful reference, McDonald and Rodgers focus on a 5 kW e personal mGT design and provide a preliminary cost breakdown accompanied by some hints on how to attain substantial cost reductions [ 309 ]. Regarding economies of scale, Myers declares that a widely applicable rule of production economics is that "costs per unit drop in half for a tenfold increase in production quantities per unit time” [ 308 ]. The author provides a comparison of the manufacturing methods to produce turbogenerators in the aerospace and the automotive industries claiming that, although the engines are very similar in concept, the manufacturing methods and the specific costs differ largely due to the very stringent requirements set forth by the aero industry. 115