New concepts and techniques for the development of high-efficiency concentrating photovoltaic modules
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(7) Abstract A renewed interest in concentrating photovoltaic (CPV) systems has emerged in recent years encouraged by the development of high-efficiency multijunction solar cells based in IIIV semiconductors that have led to CPV module efficiencies which practically double that of flat panel PV and which reach 35% for record modules. This thesis is devoted to the design and experimental implementation of new concepts for obtaining CPV modules that not only achieve high efficiency under standard conditions but also have such a wide tolerance to assembly errors, tracking, temperature and spectral variations, that the energy generated by them throughout the year is maximized. One of the first addressed issues is the design of secondary optical elements whose primary optics is a Fresnel lens and which, for a fixed concentration, allow an increased acceptance angle and tolerance of the system. Several reflective and refractive secondaries have been designed and analyzed using ray tracing. In particular, using nonimaging optics and based on the single-stage design known as ‘dielectric totally internally reflecting concentrator’, a secondary with square output has been designed, fabricated and characterized. Used together with a Fresnel lens, the secondary can simultaneously achieve high efficiency, concentration and acceptance. Furthermore, an alternative method has been proposed and prototyped for the fabrication of the secondary named dome. The optics is manufactured by direct overmolding of silicone over the solar cells. One characteristic that permeates all the work done in this thesis is the holistic approach in the design of CPV modules, meaning that special attention has been paid to the joint design of the solar cell and the optics to ensure that the total system achieves the highest attainable efficiency. In this regard, many optical systems developed in the thesis have been designed, characterized and optimized considering that the current matching among the subcells within the multijunction solar cell beneath the optics must be close to one. Antireflective coating over the cell acts, somehow, as an interface between the optics and the cell. Consequently, a method has been designed to optimize antireflective coatings that takes into account not only the broad wavelength range that multijunction solar cells are sensitive to but also the angular intensity distribution created by the concentrating optics. In addition, the issue of non-uniformity has also been addressed by comparing the spectral and spatial distributions of irradiance created by different optics (simulated by ray tracing and photographed) and the efficiency losses experienced by cells illuminated by those concentrating optics experimentally determined. The effect of temperature on the concentrating optics has also been studied in this thesis. In particular, finite element simulations have been use to analyze the deformations experienced.
(8) by the facets of hybrid (silicon-glass) Fresnel lenses, the change of refractive index with temperature and the influence of both effects on the system performance. A model has been implemented which take into consideration atmospheric variations, mainly temperature and spectral content of the direct normal irradiance, as well as thermal and spectral sensitivities of systems, with the aim of maximizing the energy harvested by a CPV module throughout the year in a particular location. Chapters 5 and 6 of this book are devoted to the design, fabrication, and characterization of a new concentrator concept named FluidReflex and based on a single-stage reflective optics with fluid dielectric. In this new concept, the presence of the fluid provides some significant advantages such as: an increased concentration acceptance angle product (CAP) achievable by surrounding the cell with a medium whose refractive index is greater than one, an improvement of the optical efficiency by reducing losses due to Fresnel reflection at several interfaces, an improvement in heat dissipation as the heat concentrated near the cell is transmitted by natural convection and conduction in the fluid, and an improved electrical insulation. By fabricating and characterizing several elementary-unit prototypes it was shown that there is no fundamental reason that prevents the practical implementation of this theoretical concept reaching high efficiency. Several fluid candidates were investigated proving the existence of at least to fluids that meet all the requirements (including the stability under concentrated light) to become part of the FluidReflex concentrator. Finally, several pre-industrial FluidReflex module prototypes have been designed and fabricated. An optimization process for the manufacturing of the multicavity optics was necessary to attain such an optics quality as the one achieved by the single unit. The module prototypes have been measured, both indoors and outdoors, analyzing the current matching of the solar cells beneath the concentrator for different spectral distribution of the incident irradiance. Additionally, the module showed an excellent thermal performance..
(9) Resumen El interés por los sistemas fotovoltaicos de concentración (CPV) ha resurgido en los últimos años amparado por el desarrollo de células multiunión de muy alta eficiencia basadas en semiconductores de los grupos III-V. Estas células han permitido obtener módulos de concentración con eficiencias que prácticamente duplican las del panel plano y que llegan al 35% en los módulos récord. Esta tesis está dedicada al diseño y la implementación experimental de nuevos conceptos que permitan obtener módulos CPV que no sólo alcancen una eficiencia alta en condiciones estándar sino que, además, sean lo suficientemente tolerantes a errores de montaje, seguimiento, temperatura y variaciones espectrales para que la energı́a que producen a lo largo del año sea máxima. Una de las primeras cuestiones que se abordan es el diseño de elementos ópticos secundarios para sistemas cuyo primario es una lente de Fresnel y que permiten, para una concentración fija, aumentar el ángulo de aceptancia y la tolerancia del sistema. Varios secundarios reflexivos y refractivos han sido diseñados y analizados mediante trazado de rayos. En particular, utilizando óptica anidólica y basándose en el diseño de una sola etapa conocido como ‘concentrador dieléctrico que funciona por reflexión total interna’, se ha diseñado, fabricado y caracterizado un secundario con salida cuadrada que, usado junto con una lente de Fresnel, permite alcanzar simultáneamente una elevada eficiencia, concentración y aceptancia. Además, se ha propuesto y prototipado un método alternativo de fabricación para otro de los secundarios, denominado domo, consistente en el sobremoldeo de silicona sobre células solares. Una de las caracterı́sticas que impregna todo el trabajo realizado en esta tesis es la aproximación holı́stica en el diseño de módulos CPV, es decir, se ha prestado especial atención al diseño conjunto de la célula y la óptica para garantizar que el sistema total alcance la mayor eficiencia posible. En este sentido muchos sistemas ópticos desarrollados en esta tesis han sido diseñados, caracterizados y optimizados teniendo en cuenta que el ajuste de corriente entre las distintas subcélulas que comprenden la célula multiunión bajo el concentrador sea muy próximo a uno. La capa antirreflectante sobre la célula funciona, en cierto modo, como interfaz entre la óptica y la célula, por lo que se ha diseñado un método de optimización de capas antirreflectantes que considera no sólo el amplio rango de longitudes de onda para el que las células multiunión son sensibles sino también la distribución angular de intensidad sobre la célula creada por la óptica de concentración. Además, la cuestión de la falta de uniformidad también se ha abordado mediante la comparación de las distribuciones espectrales y espaciales de irradiancia que crean diferentes ópticas (simuladas mediante trazado de rayos y fotografiadas) y las pérdidas de eficiencia que experimentan las células iluminadas por dichas ópticas de concentración medidas experimentalmente..
(10) El efecto de la temperatura en la óptica de concentración también ha sido objeto de estudio de esta tesis. En particular, mediante simulaciones de elementos finitos se han dado los primeros pasos para el análisis de las deformaciones que sufren los dientes de las lentes de Fresnel hı́bridas (vidrio-silicona), ası́ como el cambio de ı́ndice de refracción con la temperatura y la influencia de ambos efectos sobre el funcionamiento de los sistemas. Se ha implementado un modelo que tiene por objeto considerar las variaciones ambientales, principalmente temperatura y contenido espectral de la radiación directa, ası́ como las sensibilidades térmica y espectral de los sistemas CPV, con el fin de maximizar la energı́a producida por un módulo de concentración a lo largo de un año en un emplazamiento determinado. Los capı́tulos 5 y 6 de este libro están dedicados al diseño, fabricación y caracterización de un nuevo concepto de módulo fotovoltaico denominado FluidReflex y basado en una única etapa reflexiva con dieléctrico fluido. En este nuevo concepto la presencia del fluido aporta algunas ventajas significativas como son: un aumento del producto concentración por aceptancia (CAP, en sus siglas en inglés) alcanzable al rodear la célula con un medio cuyo ı́ndice de refracción es mayor que uno, una mejora de la eficiencia óptica al disminuir las pérdidas por reflexión de Fresnel en varias interfaces, una mejora de la disipación térmica ya que el calor que se concentra junto a la célula se trasmite por convección natural y conducción en el fluido y un aislamiento eléctrico mejorado. Mediante la construcción y medida de varios prototipos de unidad elemental se ha demostrado que no existe ninguna razón fundamental que impida la implementación práctica del concepto teórico alcanzando una elevada eficiencia. Se ha realizado un análisis de fluidos candidatos probando la existencia de al menos dos de ellos que cumplen todos los requisitos (en particular el de estabilidad bajo condiciones de luz concentrada) para formar parte del sistema de concentración FluidReflex. Por último, se han diseñado, fabricado y caracterizado varios prototipos preindustriales de módulos FluidReflex para lo cual ha sido necesario optimizar el proceso de fabricación de la óptica multicavidad a fin de mantener el buen comportamiento óptico obtenido en la fabricación de la unidad elemental. Los distintos prototipos han sido medidos, tanto en el laboratorio como bajo el sol real, analizando el ajuste de corriente de la célula iluminada por el concentrador FluidReflex bajo diferentes distribuciones espectrales de la radiación incidente ası́ como el excelente comportamiento térmico del módulo..
(11) Contents 1 INTRODUCTION. 1. 1.1. Background: Concentrating photovoltaics . . . . . . . . . . . . . . . . . . . .. 1. 1.2. Framework of this research . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10. 1.3. Outline of the thesis structure . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13. 2 SECONDARY OPTICAL ELEMENTS FOR FRESNEL LENS BASED CONCENTRATORS 17 2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17. 2.2. Fresnel lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 18. 2.2.1. Theoretical limits of a Fresnel lens . . . . . . . . . . . . . . . . . . . .. 18. 2.2.2. Manufacturing issues . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 28. Secondary Optical Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29. 2.3.1. The truncated inverted pyramid . . . . . . . . . . . . . . . . . . . . .. 30. 2.3.2. The compound parabolic concentrator . . . . . . . . . . . . . . . . . .. 32. 2.3.3. The dielectric totally internally reflecting concentrator (DTIRC) . . .. 34. 2.3.4. The dome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 40. SOE Comparative analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 43. 2.4.1. Optical efficiency and acceptance angle. . . . . . . . . . . . . . . . . .. 44. 2.4.2. Irradiance distribution over the cell . . . . . . . . . . . . . . . . . . . .. 46. Case study. Design of a DTIRC with square output . . . . . . . . . . . . . .. 49. 2.5.1. Ray tracing and experimental characterization of square DTIRC . . .. 51. Silicone SOE overmolded on solar cells . . . . . . . . . . . . . . . . . . . . . .. 53. 2.6.1. Silicone degradation under UV irradiance . . . . . . . . . . . . . . . .. 55. 2.7. Proposed method for designing nonimaging Fresnel lenses with flat entrance .. 59. 2.8. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61. 2.3. 2.4. 2.5 2.6. Appendices. 65. Appendix A Attainable concentration using a Fresnel lens. 65. i.
(12) Contents Appendix B Design of the dome SOE References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 69 71. 3 OPTICS AND SOLAR CELL INTEGRATION FOR HIGH-EFFICIENCY CONCENTRATING PHOTOVOLTAIC SYSTEMS 77 3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 77. 3.2. Optical design for MJ solar cells . . . . . . . . . . . . . . . . . . . . . . . . .. 79. 3.2.1. Current-matching of a MJ solar cell beneath a concentrator . . . . . .. 79. Antireflective coatings for MJ solar cells under wide-angle ray bundles . . . .. 83. 3.3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 83. 3.3.2. Theoretical approach and ARC numerical optimization method . . . .. 84. 3.3.3. Optimized ARC over the cell for the FluidReflex concentrator . . . . .. 87. 3.3.4. Optimized ARC over the cell for a concentrator composed of a Fresnel lens and a SOE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 90. ARC design for the SOE entrance surface . . . . . . . . . . . . . . . .. 92. Spectral and spatial non-uniformity . . . . . . . . . . . . . . . . . . . . . . . .. 95. 3.4.1. Previous approaches to the non-uniformity problem . . . . . . . . . .. 96. 3.4.2. Analysis and characterization techniques developed at IES-UPM . . .. 97. 3.4.3. Improved ray tracing . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 97. 3.4.4. CCD measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 98. 3.4.5. IV curve measurements under variable irradiance, spectra and temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 99. Case Study: Concentrating systems under variable irradiance level and spectral distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 100. 3.5.1. Fresnel lens with bare cell . . . . . . . . . . . . . . . . . . . . . . . . .. 101. 3.5.2. Fresnel lens combined with refractive pyramid . . . . . . . . . . . . . .. 105. 3.5.3. Fresnel lens combined with refractive dome . . . . . . . . . . . . . . .. 107. Energy harvesting based approach. Combined effects of thermal sensitivity and spectral variation on SOG Fresnel lenses . . . . . . . . . . . . . . . . . .. 109. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 115. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 118. 3.3. 3.3.5 3.4. 3.5. 3.6 3.7. 4 TEMPERATURE EFFECTS IN FRESNEL LENS BASED CPV SYSTEMS125 4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 125. 4.2. Experimental results reported in the literature . . . . . . . . . . . . . . . . .. 127. 4.3. Finite elements (FE) modeling of SOG Fresnel lenses . . . . . . . . . . . . . .. 129. 4.3.1. Description of the simulations . . . . . . . . . . . . . . . . . . . . . . .. 129. 4.3.2. Comparison of simulated and experimental results . . . . . . . . . . .. 130. 4.3.3. The silicone over the glass substrate behaves as a membrane . . . . .. 131.
(13) 4.3.4. Analysis of the deformed facets . . . . . . . . . . . . . . . . . . . . . .. 132. 4.4. Implications on the performance of a CPV module . . . . . . . . . . . . . . .. 133. 4.5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 134. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 136. 5 REFLECTIVE CONCENTRATOR WITH FLUID DIELECTRIC. PROOF OF CONCEPT. 139 5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 139. 5.2. Previous experiences in concentrators with optical fluids . . . . . . . . . . . .. 141. 5.3. Dielectric fluids for concentrating photovoltaic systems . . . . . . . . . . . . .. 145. 5.4. Durability of the candidate optical fluids . . . . . . . . . . . . . . . . . . . . .. 148. 5.4.1. Transmittance measurement . . . . . . . . . . . . . . . . . . . . . . . .. 149. 5.4.2. Evaluation of transmittance losses . . . . . . . . . . . . . . . . . . . .. 149. 5.4.3. UV degradation tests results . . . . . . . . . . . . . . . . . . . . . . .. 150. Optical performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 153. 5.5.1. Theoretical limits imposed by étendue conservation . . . . . . . . . . .. 154. 5.5.2. General discussion on the concentrator configuration . . . . . . . . . .. 155. 5.5.3. Elementary unit optical characterization. Experimental results . . . .. 155. 5.5.4. Fluid refractive index dependence with temperature and its influence on the system efficiency . . . . . . . . . . . . . . . . . . . . . . . . . .. 159. Antireflective coating over the solar cell . . . . . . . . . . . . . . . . . . . . .. 161. 5.6.1. Characterization of the antireflective coating . . . . . . . . . . . . . .. 161. Optics manufacturing issues . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 165. 5.7.1. Silver and aluminum mirrors . . . . . . . . . . . . . . . . . . . . . . .. 165. 5.7.2. Plastic injected optics . . . . . . . . . . . . . . . . . . . . . . . . . . .. 167. 5.8. Non-uniformity irradiance effects . . . . . . . . . . . . . . . . . . . . . . . . .. 168. 5.9. Thermal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 171. 5.9.1. Finite elements (FE) modeling . . . . . . . . . . . . . . . . . . . . . .. 171. 5.9.2. Simulated and experimental results . . . . . . . . . . . . . . . . . . . .. 173. 5.9.3. Analysis based on FE modeling . . . . . . . . . . . . . . . . . . . . . .. 175. 5.9.4. Cell receiver optimization . . . . . . . . . . . . . . . . . . . . . . . . .. 176. 5.10 Summary of efficiency losses and applied characterization techniques . . . . .. 177. 5.11 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 179. 5.5. 5.6 5.7. Appendices. 181. Appendix C UV degradation tests chamber. 181. Appendix D Maximum concentration attainable by a parabola immersed in medium with linear refractive index gradient 185.
(14) Contents Appendix E Navier-Stokes equations and dimensional analysis 187 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 6 REFLECTIVE CONCENTRATOR WITH FLUID DIELECTRIC. FROM ELEMENTARY UNIT TO MODULE. 197 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 6.2 Optics manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 6.2.1 Injecting a multi-cavity piece . . . . . . . . . . . . . . . . . . . . . . . 198 6.2.2 Characterization techniques . . . . . . . . . . . . . . . . . . . . . . . . 200 6.3 Industrial module design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 6.4 Indoor module characterization . . . . . . . . . . . . . . . . . . . . . . . . . . 207 6.4.1 Current-matching of the MJ solar cell beneath FluidReflex concentrator 208 6.5 Outdoor performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 6.5.1 Module thermal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 214 6.6 Accelerated degradation tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 6.6.1 Thermal cycling test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 6.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Appendices Appendix F Estimating the distributions of efficiencies elementary units comprising a CPV module F.1 Module mismatch losses . . . . . . . . . . . . . . . . . F.2 Calculation procedure . . . . . . . . . . . . . . . . . . F.3 Case of study . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 223 and alignments of the 223 . . . . . . . . . . . . . 224 . . . . . . . . . . . . . 228 . . . . . . . . . . . . . 229 . . . . . . . . . . . . . 232. 7 CONCLUSIONS 233 7.1 Summary of contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 7.2 Recommendations for future research . . . . . . . . . . . . . . . . . . . . . . . 237.
(15) List of Figures 1.1. Most significant CPV module achievements. . . . . . . . . . . . . . . . . . . .. 4. 1.2. Geometrical concentration Xgeo , and acceptance angle AA90 , of several concentrating optics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5. 1.3. Evolution of PV and CPV prices as a function of the cumulative production.. 8. 1.4. Energy payback time estimated for systems based on silicon flat-panels and CPV systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10. Maximum concentration attainable with a Fresnel lens and a solar cell, both round, for different source angular size and groove widths. . . . . . . . . . . .. 20. Transmission for a square Fresnel lens made of silicone on glass as a function of its f number obtained by ray-tracing simulations. . . . . . . . . . . . . . . .. 22. Ideal acceptance angle for each groove in a Fresnel lens with f = 1.2 as a function of its radial position, x. . . . . . . . . . . . . . . . . . . . . . . . . .. 22. Maximum concentration attainable with different combination of round/square Fresnel lenses and solar cells. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 24. Schemes of an hemispherical source surrounding the solar cell with uniform brightness and a Fresnel lens. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 25. 2.6. Normalized concentration for rotationally symmetric concentrators. . . . . . .. 27. 2.7. Geometry of the facets of a 120 x 120 mm SOG Fresnel lens with f = 1.2, calculated over its diagonal . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29. 2.8. Reflection of rays in a truncated inverted pyramid. . . . . . . . . . . . . . . .. 31. 2.9. Angular transmission curve of a system comprising a Fresnel lens and a reflective pyramid. The bump in the center is caused by the the efficiency drop when the light starts to be reflected off the pyramid walls. . . . . . . . . . . .. 31. 2.10 Reproduced from [11]. Angular transmission curves for 3D-CPC designed for different input angles θin SOE were obtained by Welford and Winston using ray tracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 33. 2.1 2.2 2.3 2.4 2.5. v.
(16) List of Figures 2.11 The conservation of the optical path length, as stated by Fermat’s principle, is assumed to determine the side profile of a bidimensional compound parabolic concentrator, CPC (left) and dielectric totally internally reflecting concentrator, DTIRC (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 35. 2.12 Attainable concentration XSOE , height hSOE , and angle at the DTIRC exit θout SOE for the 3D-DTIRC obtained rotating bidimensional designs where the input angle is fixed (θin SOE = 23◦ ) and the front surface curvature, and thus ϕ, is varied and vice versa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 38. 2.13 Attainable concentration XSOE , height hSOE , and angle at the DTIRC exit θout SOE for the 3D-DTIRC obtained rotating bidimensional designs where the margin of the input angle δ, and the margin for TIR ǫ, are varied. Input angle is θin SOE = 23◦ + δ and curvature at the front surface is imposed by ϕ = 30◦ .. 39. 23◦. 2.14 Family of DTIRCs with the same input angle θin SOE = and several values of ϕ. Angular transmission curves and irradiance distribution of the cells for systems including them . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 40. 2.15 Design of the dome bidimensional profile by imposing the conservation of the optical path length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 41. 2.16 Phase space diagrams of the bidimensional system composed of a Fresnel lens and a dome at the entrance and exit of the system for the extended light source γext . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 42. 2.17 Concentration attainable by a system consisting of a Fresnel lens and a dome A (blue), a dome B (red), and a bare solar cell (black) when the angular size of the extended light source γext = ±1◦ is considered. . . . . . . . . . . . . . .. 43. 2.18 Profiles for the different SOE being compared: reflective (red) and refractive (green) pyramid, dielectric CPC (yellow), dome A (blue) and dome B (orange). 44 2.19 Angular transmission curves for the different secondaries studied. . . . . . . .. 45. 2.20 Annual energy lost due to misalignments for systems at 1000X using different SOEs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 46. 2.21 Irradiance profiles over the solar cell, encircled energy and angular intensity distribution created by a system comprising a Fresnel lens and different SOEs at 1000X. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 48. 2.22 Photograph of the two square DTIRCs manufactured by glass molding. . . .. 50. 2.23 Phase space diagram of the bidimensional Fresnel lens and DTIRCs at different planes perpendicular to the optical axis for the extended light source γext . . .. 51. 2.24 Normalized efficiency η∗, and acceptance angle AA90 , as a function of the primary to cell distance for the systems comprising a SOG Fresnel lens and a DTIRC with square output. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 53. 2.25 Silicone SOE overmolded on a 1. cm2. MJ solar cell. . . . . . . . . . . . . . . .. 54. 2.26 Poly-dimethylsiloxane (PDMS) and Poly-phenyl-methylsiloxane (PPMS) molecules. 54.
(17) 2.27 Silicones absorption coefficient, αλ . . . . . . . . . . . . . . . . . . . . . . . . .. 57. 2.28 Transmittance for PDMS, PPMS A and PPMS B samples. . . . . . . . . . .. 58. 2.29 SOE manufactured by overmolding PPMS A degraded after three days being illuminated by a PMMA Fresnel lens outdoors. . . . . . . . . . . . . . . . . .. 58. 2.30 SOE manufactured by overmolding using PDMS. . . . . . . . . . . . . . . . .. 59. 2.31 Ideal angular acceptance θa , as a function of the radial position x, for Fresnel lenses with different designs. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 60. 2.32 Irradiance distribution over the receiver for a 320 x 320 mm SOG Fresnel lens with f = 1.1, calculated over its diagonal, with a nonimaging and a classic design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61. A.1 Refraction at the second surface of the most exterior groove of a Fresnel lens with flat entrance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 65. 3.1. 3.2. 3.3. 3.4 3.5 3.6 3.7. 3.8 3.9. Evolution of the ratio between photogenerated current of a MJ solar cell and irradiance ‘seen’ by each ‘isotype’ cell (normalized current) as a function of the spectral matching ratio SM R. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 82. Transmittance for different wavelengths and incidence angles on a MJ solar cell when no ARC is used (up-left), the optimized monolayer is used (up-right), the optimized bilayer is used (down-left) and the optimized trilayer is used (downright). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 89. Weighted transmittance Tweighted , normalized to its maximum when, due to manufacturing errors, the different ARC layers optical thickness (physical thickness, ti multiplied by refractive index ni ) are not the optimized values. . . . .. 90. top OMmid. Optical matching ratio due to the ARC as a function of the thicknesses of a Al2 O3 /TiO2 ARC deposited on a MJ solar cell. . . . . . . . . . . . . . .. 92. Simulated spectral transmittance at the entrance surface of the SOE for different thicknesses of the MgF2 layer (continuous lines). . . . . . . . . . . . . . .. 94. Transmission of a MgF2 ARC over the SOE entrance surface, integrated over the bandwidth used by the top and middle subcells in a classic MJ solar cell.. 94. Spectral response SR of the CCD camera silicon sensor filtered by a cold mirror or a heat glass (empty dots) to simulate the SR of middle and top subcells (solid dots). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 99. Optical systems analyzed as a case of study are composed of a PMMA Fresnel lens and three different receivers: bare cell, refractive pyramid and dome. . .. 100. Irradiance profiles PAR caused by a Fresnel lens. . . . . . . . . . . . . . . . .. 101. 3.10 System comprising a PMMA Fresnel lens and a bare cell. Top-subcell photogeneratedcurrent density (first row) and middle-subcell photogenerated-current density (second row). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.
(18) List of Figures 3.11 Electrical measurements for the different concentrating systems at different primary-to-receiver distances. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 104. 3.12 Irradiance profiles PAR caused by a Fresnel lens and a refractive pyramid. . .. 105. 3.13 System comprising a PMMA Fresnel lens and a glass refractive pyramid. Topsubcell photogenerated-current density (first row) and middle-subcell photogeneratedcurrent density (second row). . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 3.14 Irradiance profiles PAR caused by a system comprising a Fresnel lens and a dome. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 107. 3.15 System comprising a PMMA Fresnel lens and a silicone overmolded dome. Topsubcell photogenerated-current density (first row) and middle-subcell photogeneratedcurrent density (second row). . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 3.16 Irradiation measured in Madrid throughout a year (May 2011 - May 2012) as a function of the ambient temperature and the spectral content quantified by the SM R and measured using a Tri-band Spectro-heliometer IC-3J25. . . .. 111. 3.17 Normalized module efficiency η*, measured indoors for the low (left) and high (right) tolerance systems as a function of the ambient temperature and the spectral content of the incident irradiance. . . . . . . . . . . . . . . . . . . . .. 112. 3.18 Annual energy losses strongly depend on the spectral condition (SMR*) considered for optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 113. top OMmid ,. 3.19 Optical matching ratio normalized efficiency η*, and acceptance angle AA90 , as a function of the primary-to-receiver distance measured indoors for the high-tolerance system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 4.2 4.3. 4.4 4.5. 4.6 4.7. 114. Refractive index variation as a function of temperature for materials that are typically used in Fresnel lenses. . . . . . . . . . . . . . . . . . . . . . . . . . .. 127. FE modeling of the most exterior groove of a SOG Fresnel lens when it experiences a temperature variation of -25◦ C. . . . . . . . . . . . . . . . . . . . . .. 127. An increase on the operation temperature To , causes a decrease on the refractive index and consequently an increase on the optimum f-number of a SOG Fresnel lens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 129. The size of the spot minimizes when the operation temperature To , of a SOG Fresnel lens coincides with the cure temperature Tc , of the silicone. . . . . . .. 129. Attainable concentration experimentally (left) and predicted by FE modeling (right) of the SOG Fresnel lens cured at temperature Tc under different operation temperatures, To . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 131. Von Mises stress distribution predicted by FE modeling of two equivalent lenses with different silicone depth df when Tc − To = 20◦ C. . . . . . . . . . . . . . Slope error of every facet of a SOG Fresnel lens for several temperature differences (To − Tc ) predicted by FE modeling. . . . . . . . . . . . . . . . . . . .. 132 133.
(19) 4.8. Efficiencies at different temperatures for the different generations of the Soitec system comprising a SOG Fresnel lens and for a 475X CPV system with two different configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 134. 5.1. Schemes of the Cassegrain configuration and FluidReflex new concept. . . . .. 140. 5.2. Previous experiences on concentrators using optical fluids at the IES-UPM. .. 142. 5.3. Previous experiences on concentrators using optical fluids in Australia . . . .. 144. 5.4. Refractive indices as a function of wavelength for several dielectric fluids. . .. 145. 5.5. Transmittance T of the fluids as a function of wavelength λ . . . . . . . . . .. 148. 5.6. Transmittance of fluid samples before and after a UV dosage equivalent to 1-3 years exposed outdoors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 151. Evolution of relative top photocurrent as AM1.5D spectrum is filtered by several fluids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 153. 5.8. Main losses in the Cassegrain configuration and FluidReflex new concept. . .. 154. 5.9. FluidReflex elementary-unit prototype. . . . . . . . . . . . . . . . . . . . . . .. 157. 5.10 Measured optical efficiency for different concentration ratios . . . . . . . . . .. 157. 5.11 Angular transmission curves measured using direct and luminescence inverse method for FluidReflex elementary-unit prototype at 636X. . . . . . . . . . .. 158. 5.12 Theoretical acceptance angle θa , and measured experimental acceptance angles AA90 , at different concentration ratios. . . . . . . . . . . . . . . . . . . . . . .. 158. 5.13 System efficiency measured for cell position errors along X, Y, Z axes at a concentration ratio of 584X. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 159. 5.14 Acceptance angle θa as a function of concentration for several f-number and temperature differences within the fluid. . . . . . . . . . . . . . . . . . . . . .. 160. 5.7. ∗ . ηopt. 5.15 Evolution of normalized optical efficiency and temperature drop between the cell, the fluid and the ambient during the initial transient of the FluidReflex elementary-unit prototype. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 161. 5.16 Reflectance at the solar cell entrance for normal incidence measured using a visible-near-infrared spectroradiometer. . . . . . . . . . . . . . . . . . . . . .. 162. 5.17 System optical efficiency ηopt,λi , for different wavelengths λ, measured using 80 nm-wide band-pass filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 164. 5.18 Efficiency for cells with three different ARC structures (bare cell, bilayer and trilayer ARCs) under FluidReflex concentrator system. . . . . . . . . . . . . .. 165. 5.19 Reflectance for the vacuum deposited aluminum and silver mirrors. . . . . . .. 166. 5.20 Encircled energy EE, of the spots cast by machined and injected mirrors. . .. 168. 5.21 Fill Factor losses when comparing IV curve of a MJ solar cell covered by a mask (with uniformity factor U ) and IV curve under uniform illumination. .. 170. 5.22 β dependence on effective concentration Xef f , for a MJ solar cell under uniform illumination and with uniformity factor U = 0.2 (highly non-uniform spot). .. 171.
(20) List of Figures 5.23 Temperature distribution predicted by FE modeling. . . . . . . . . . . . . . .. 174. 5.24 Velocity distribution predicted by FE modeling. . . . . . . . . . . . . . . . . .. 174. 5.25 Elementary unit outdoor measurement . . . . . . . . . . . . . . . . . . . . . .. 174. 5.26 Effect of the prototype tilt angle over the cell temperature, fluid temperature and fluid velocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 175. 5.27 Evolution of the cell temperature Tcell , when one of the fluid parameters is modified an order of magnitude while the others remain unchanged. . . . . .. 176. 5.28 Cell receiver manufactured by bending a copper sheet and using a plastic material to electrically insulate both contacts. . . . . . . . . . . . . . . . . . . .. 177. 5.29 Temperature difference between the solar cell and the fluid and power losses as a function of the height hb , and width wb , of the beam on which the cell is mounted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 177. 5.30 Schematic view of the main uncertainties that relates the theoretical efficiency, the performance of the elementary-unit prototype and the real figures measured with the module prototypes. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 178. C.1 Spectral distribution at the center of the accelerated UV degradation tests chamber measured using a visible spectroradiometer. . . . . . . . . . . . . . .. 182. C.2 Left: Spectral response of the UV ABC and UV C sensors used to characterize the irradiance distribution. Right: UV AB radiation (280-400 nm) across the samples holder in the UV degradation tests chamber. . . . . . . . . . . . . . .. 183. D.1 Paths described by rays reflected by a parabola in a medium with a linear refractive index gradient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 185. 6.1 6.2 6.3. 6.4. Errors distribution across the mirrors array measured after each attempt in the optimization process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 199. Photograph of the injected piece manufactured in PC when illuminated by polarized light. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 201. Photographs of the mirrors spots in the first injected array (left). Irradiance distribution at the foci of the mirrors predicted by ray-tracing simulation of the injected geometry (right). . . . . . . . . . . . . . . . . . . . . . . . . . . .. 202 203. 6.5. Mean error of the foci positions µfoci error , for several injection attempts. . . IV curve measured for the last injection attempt (10-PMMA). . . . . . . . . .. 6.6. FluidReflex industrial module prototype . . . . . . . . . . . . . . . . . . . . .. 206. 6.7. Specific weight measured for several CPV technologies. . . . . . . . . . . . . .. 206. 6.8. IV curve for FluidReflex module prototype F measured indoors. . . . . . . . .. 208. 6.9. Angular transmission curve for FluidReflex module prototype F. . . . . . . .. 208. 204.
(21) 6.10 Evolution of the ratio between photogenerated current of MJ solar cells illuminated by the concentrator and irradiances ‘seen’ by each ‘isotype’ solar cell (normalized currents), for different combination of materials within FluidReflex module. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.11 Current generated by the module prototype A at 1000W/m2 for different spectral content. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . top 6.12 Normalized currents for the module operation outdoors as a function of SM Rmid mid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . and SM Rbot 6.13 Evolution of the temperatures in FluidReflex module prototype A under outdoor operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.14 Infrared image of the 3x3 module prototype under outdoor operation. . . . . 6.15 Equivalent circuit representing the thermal behavior of FluidReflex module. . 6.16 Temperatures drops (Tcell − Twall ) and (Twall − Tamb ) as a function of the 3 , and following variables: DNI, ambient temperature to the third power Tamb time of the measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.17 IV curve for FluidReflex module prototype A measured indoors and outdoors. 6.18 Temperatures (on the thermal chamber, module walls and fluid) and injected current during a thermal cycle. . . . . . . . . . . . . . . . . . . . . . . . . . . F.1 IV curve for the ideal (top) and real (bottom) modules. . . . . . . . . . . . . F.2 Probability density function (pdf) and cumulative density function (cdf) of the efficiencies of the elementary units where µef = 1 and an unknown σef have been assumed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F.3 Probability density function (pdf) and cumulative density function (cdf) of the angular misalignments of elementary units where µmis = 0 and an unknown σmis have been assumed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F.4 Angular transmission curve of the elementary unit. . . . . . . . . . . . . . . . F.5 Module mismatch losses, M Lexp (θtr ) measured for prototype A. . . . . . . . .. 210 212 213 215 215 216. 218 219 221 225. 226. 227 228 230.
(22) List of Figures.
(23) List of Tables 2.1. Maximum attainable concentration X (and f-number f , where it occurs) for a Fresnel lens and two different source angular size γs . A groove width wg = 0.4 mm, and a temperature variation ∆T = 30◦ C are assumed. . . . . . . . . . .. 21. Maximum concentration attainable with different combination of round/square Fresnel lenses and solar cells. Refractive index varies from 1.4309 (λ=350 nm) to 1.4021 (λ=900 nm). Groove width assumed is wg =0.4 mm. . . . . . . . . .. 24. Maximum concentration attainable with different two-stage concentrators with rotational symmetry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 27. 2.4. Reflective and refractive SOE general comparison. . . . . . . . . . . . . . . .. 30. 2.5. Optical efficiency for a system at 1000X using the same primary lens and different SOEs. θ90% and θ98% are deviation angles for an optical efficiency equal to 90% and 98% of the maximum. . . . . . . . . . . . . . . . . . . . . .. 45. 2.6. Main parameters of tested silicones candidate for overmolding SOE. . . . . .. 55. 3.1. Ideal refractive indices for 1, 2 and 3 layers ARC when the solar cell is surrounded by air and by a material with nmedium = 1.5. Dielectric materials whose refractive indices are close to the ideal values are also indicated. . . . .. 86. 3.2. Thicknesses, in nm, and weighted transmittances Tweighted [% . . . . . . . . .. 88. 3.3. Al2 O3 /TiO2 bilayer ARC optimized results for a MJ solar cell to be illuminated by a system composed of a Fresnel lens and different SOEs. . . . . . . . . . .. 91. 3.4. Atmospheric losses for different SOG Fresnel lens based systems. . . . . . . .. 113. 4.1. Physical parameters of the silicone assumed for the FE modeling. . . . . . . .. 130. 5.1. Physical properties of the dielectric fluid candidates. . . . . . . . . . . . . . .. 147. 5.2. Relative photogenerated current for top, middle, classic bottom and new bottom subcells when reference spectrum AM1.5D is filtered by each fluid. . . .. 152. Simulated and measured parameters and results. . . . . . . . . . . . . . . . .. 175. E.1 Main properties and dimensionless numbers for four fluids of interest. . . . .. 190. 2.2. 2.3. 5.3. xiii.
(24) List of symbols and acronyms 6.1 6.2. Summary of the different variations attempted process. . . . . . . . . . . . . . . . . . . . . . . Summary of the main characteristics of the six manufactured. . . . . . . . . . . . . . . . . . . .. throughout the optimization . . . . . . . . . . . . . . . . . industrial module prototypes . . . . . . . . . . . . . . . . .. F.1 Estimated and measured values for two module prototypes comprising 24 solar cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 198 207. 230.
(25) List of symbols and acronyms α. facet slope. αT. short-circuit current dependence on temperature. αw. side wall angle. αλ. absorption coefficient. αbest. alignment of the best unit. αworst. alignment of the worst elementary unit. f¯B. body forces. v̄. flow velocity. βv. volumetric coefficient of thermal expansion. ∆n0. intrinsic birefringence. δ. margin at the SOE entrance. q̇elec. flux transformed into electricity. q̇inc. incident energy flux. ǫrad. emissivity. ∗ ηopt. normalized optical efficiency. ηbest. efficiency of the best performing elementary unit. ηelect (T, SM R). electrical efficiency. ηopt. optical efficiency. ηworst. efficiency of the worst elementary unit. γs. source angular size xv.
(26) List of symbols and acronyms γext. extended light source. γsun. sun angular size. κ. thermal conductivity. κ0. thermal conductivity at the reference temperature. κλ. extinction coefficient. λ. wavelength. λ. wavelength. λd. design wavelength. µ. viscosity. µ0. viscosity at the reference temperature. µfoci error. mean error in foci position. µef. mean of the pdf of efficiencies. µmis. mean of the pdf of misalignments. ν. Poisson’s ratio. Φv. friction thermal dissipation. ρ. density. ρ0. density at the reference temperature. σ. SB. Stefan-Boltzmann constant. σreverse bias. standard deviation of the pdf of elementary units efficiencies directly measured. σθ. standard deviation of the tracker error distribution. σcells. standard deviation of the pdf of efficiencies of solar cells singly measured. σcells. standard deviation of the solar cells efficiencies. σef. standard deviation of the efficiency of elementary units within a module. σef. standard deviation of the pdf of elementary unit efficiencies.
(27) σmis. standard deviation of the angular misalignment of elementary units within a module. σmis. standard deviation of the pdf of misalignments. τ. friction force. θa. ideal acceptance angle. θi. angle of incidence. θr. angle of refraction. θT. temperature drop. θin. SOE. θout. SOE. maximum angle of the rays entering the SOE maximum angle of the rays exiting the SOE. θcell. extreme ray at the exit. θdev. deviation angle. θtr. tracking error. ñ(λ). complex refractive index. ϕ. curvature at the entrance. Aw. wet area. Arad. area radiating energy. AA90. acceptance angle. AEL. annual energy losses. BM adrid (T, SM R) irradiance distribution throughout the year c. speed of light in vacuum. cp. specific heat. CM. current-matching ratio. D. lens diameter. d. diameter of the light spot. d′. short axis of the ellipse of light.
(28) List of symbols and acronyms df. depth of the silicone film between the lens and the glass substrate. E. Young’s Modulus. EAM 1.5D. reference spectral distribution. Esimulator. simulator spectral distribution. EQE. external quantum efficiency. F. focal distance. f. f-number. g. acceleration of gravity. Gr. Grashof number. h. Planck’s constant. hb. beam height. hconv. convection coefficient. Imp. current at the maximum power point. Isc. short-circuit current. ∗ Jsc i. photogenerated current density of subcell i. Jsc. short-circuit current density. L(θ). angular intensity distribution. l0. characteristic length. ML. mismatch losses. M Lef. mismatch losses caused by dispersion in efficiencies. M Lexp. mismatch losses experimentally measured. M Lmis. mismatch losses caused by dispersion in alignments. N. elementary units within a module. N (Isc ). elementary units forward biased when the module is short circuited. n2. refractive index at the exit. nARC. refractive index of the antireflective coating material.
(29) ncell. refractive index of the solar the cell. nmedium. refractive index of the medium surrounding the cell. OM. optical matching ratio. p. pressure. Pl. Plank number. Pr. Prandtl number. Q. external energy output. q. charge of a single electron. r. distance from the groove to the center of the receiver. RRMS. roughness (root mean square). Ra. Rayleigh number. Re. Reynolds number. SA. hardness shore A. SAM 1.5D (λ). artificial reference spectrum. SM R. spectral matching ratio. SM R*. spectral matching ratio that minimizes AEL. SR. spectral response. T. temperature. t. layer thickness. t∗. layer thickness for oblique incidence. T0. reference temperature. Tc. cure temperature. To. operation temperature. Tamb. ambient temperature. Tcell. temperature at the cell. Topt (λ, θ). optics transmittance.
(30) List of symbols and acronyms Twall. temperature at the wall. Tweighted. weighted transmittance. Vγ. voltage of the bypass diode. Vmp. voltage at the maximum power point. wb. beam width. wg. groove width. X. concentration ratio. x. radial position. x. radial position. AM. air mass. APE. average photon energy. ARC. antireflective coating. BMC. bulk material compound. CAD. computer-assisted design. CAP. concentration acceptance angle product. CCD. charge-coupled device. cdf. cumulative density function. cdf. cumulative density function. CPC. compound parabolic concentrator. CPV. concentrating photovoltaics. CSTC. concentrator standard test conditions. CTE. coefficient of thermal expansion. DNI. direct normal irradiance. DTIRC. dielectric totally internally reflecting concentrator. DUT. device under test. EE. encircled energy.
(31) FE. finite elements. IES-UPM. Instituto de Energı́a Solar - Universidad Politécnica de Madrid. ISI. Instruments and Systems Integration. LED. light emitting diode. MJ. multijunction. NURBS. non-uniform rotational b-spline. PAR. peak to average ratio. PC. polycarbonate. pdf. probability density function. PMMA. polymethyl methacrylate. POE. primary optical element. RMS. root mean square. SOE. secondary optical element. SOG. silicone on glass. STD. standard deviation. STD. standard deviation. SWR. solar weighted reflectance. TIR. total internal reflection.
(32) List of symbols and acronyms.
(33) Chapter 1. INTRODUCTION 1.1. Background: Concentrating photovoltaics. Concentrating photovoltaics (CPV) is one of the technologies proposed to obtain cheap solar electricity. The idea behind concentration consists in taking advantage of high-efficiency solar cells and using optical systems to concentrate light over them. Although high-efficiency devices are more expensive, if the concentration level is high enough and the optics is affordable enough, the final system becomes cost competitive. Concentration is key to achieve high-efficiency photovoltaics. From a theoretical point of view, one of the strategies to match the angle of incidence of the light to the angle of emission of a solar cell, and thus to maximize the efficiency limit of the device is, in point of fact, to increase the angle of incidence of the light by using concentrating optics. The well-known Shockley-Queisser limit for single junction solar cells increases from 30.5% to 40.7% if, instead of the sun angular size, isotropic illumination over the cell is assumed [1, 2]. Furthermore, from a practical point of view, concentration enables the use of solar cells based on novel concepts by reducing the influence of their cost on the total system cost. CPV was proposed several decades ago mainly based on high-efficiency silicon solar cells; during years several research centers have been working on this technology and significant results have been achieved [3]. Nowadays, the recent development of multijunction (MJ) solar cells, whose efficiencies reach up to 44.4% [4], together with the new situation in the energy generation markets worldwide brings a renewed interest in CPV. A wide variety of systems with different concentration levels and optical designs, based on both lenses and mirrors, have been proposed and developed throughout the last twenty five years. The existence of such a wide variety of concepts currently under development shows that no single architecture has yet emerged as the most cost competitive. However, concentrators based in Fresnel lenses are the ones that seem to have more chances of ‘winning’, on the basis of the number of systems. 1.
(34) Chapter 1 using this configuration. In fact, the company with the greatest development plans for the short-term, Soitec, make use of Fresnel lenses. Soitec will provide CPV modules for several utility-scale projects in California that, under several PPAs1 , will be installed in the coming years and account for 300MWp [5]. In order to provide a general overview of the variety of high-concentration PV modules developed in the recent years a thorough literature research was conducted and the gathered information has been summarized in figures 1.1 and 1.2. The graphs only include concentrators whose architecture is based on a module comprising an array of point-focus elementary units. That is, for the sake of clarity, concentrators with linear geometries and those composed of a single large optics and a densely packed array are omitted. Some of the systems were developed by companies that are no longer in the CPV business but nevertheless they are included since those modules are considered a significant milestone in the history of CPV (because of the performance attained by the module at the time when it was reported or because of the amount of watts peak manufactured by the company). In addition, to perform a fair comparison, only reported values for the measured efficiency and acceptance of the entire module are included in figures 1.1 and 1.2, that is, neither simulated values nor results reported for elementary-unit systems are included. For those technologies whose acceptance angle has only been reported for the elementary-unit concentrator the reported value has been multiplied by 0.9 to account for losses in acceptance when transitioning from the elementary unit to the module. For the same reason, when only the efficiency of the elementary unit was available, it was multiplied by 0.95 to account for losses due to inaccuracies on the module assembly. Most of the values included in the graphs can be found in the references at the end of this chapter. Additionally, some results measured at the IES-UPM laboratories and only reported internally to the private companies are included. Figure 1.1 depicts the historical evolution of CPV module efficiencies. The efficiency values reported at operating conditions have not been corrected and the atmospheric conditions at the moment of the measurement can be found in the corresponding reference. For the modules measured at IES-UPM the efficiency at concentrator standard test conditions (CSTC)2 is reported. This may cause a certain error when comparing the efficiency attained by two particular modules, but the general overview is still valid. It should be noticed that the historical increase in efficiency that can be appreciated in figure 1.1 has been mainly obtained thanks to improvements in the high-efficiency solar cells that make part of the concentrator, 1. A Power Purchase Agreement (PPA) is a contract signed between an electric utility and an Independent Power Producer (IPP) for which the utility is committed to buy all the electricity produced by the IPP during a given period of time, i.e. 15-20 years. 2 Concentrator standard test conditions (CSTC) imply an irradiance level of 1000 W/m2 , reference spectrum AM1.5D G173-03, and cell temperature equal to 25◦ C.. 2.
(35) Introduction but it should also be remarked that the optics has been adapting to illuminate the prevailing high-efficiency device. The first CPV modules were developed in the eighties and nineties to illuminate highefficiency silicon solar cells. Prominent among them are the Martin Marietta concentrator built by Sandia Labs [6], the Ramon Areces system at the IES-UPM [7], the concentrator known as Sandia Concept-90 which was industrially developed by the company Alpha Solarco [8, 9], and the Amonix first modules illuminating high-efficiency back-point contact silicon solar cells [10]. During the first years of the decade of the 2000s, the development of MJ solar cells brought a renewed interest in concentrating systems. Isofoton worked on the TIR-R concentrator trying to get advantage of the high concentration achieved by nonimaging optics on small solar cells [11]. At the same time, researchers at the Ioffe Institute in San Petersburg and Fraunhofer Institute in Freiburg (Germany) developed the all-glass module using silicone on glass (SOG) Fresnel lenses [12]. The module, named Flatcon, was subsequently transfered to the industry and it is actually been fabricated by Soitec. They should also be mentioned here the Daido concentrator based on dome-shaped Fresnel lenses [13] and the two-stage reflective concentrator by SolFocus [14]. Finally, a myriad of CPV modules started to emerge in the last years. As early mentioned, there is not a single architecture but a wide variety of concentration ratios, solar cell sizes and optical designs coexist. Some of them include InGaP/GaAs/InGaAs solar cells and have recently reported efficiency values higher than 35% [22–25]. When looking at figure 1.1 we should keep in mind that differences in efficiency values shown from 2010 are caused not only by differences in the optical efficiency and assembly accuracy of the modules but also by different reporting conditions and, what is more important, by different efficiencies of the solar cells included in them. Nevertheless, with the mentioned caveats, figure 1.1 shows that there is a wide range of concentrators which have already attained or have the potential of attaining more than 30% efficiency, that is, a very significant efficiency increase when compared with classic flat panel PV.. 3.
(36) Chapter 1. CPV module historical achievements. 40. Amonix [24-25]. CPV module efficiency [%]. 35. Semprius a. LPI-Boeing. [22-23] [15-16] Soitec [21]. 30. Heliotrop [20] Daido Steel [13]. Sumitomo. Concentrix/ Soitec [12]. 25. FluidReflex. SolFocus [14] Sandia/Alpha. 20. Solarco [8-9] IES/Ramón. Fotón. Areces[7]. Amonix [10]. HC. 15. IES/ Martifer [17] UPM-LPI /. 10. a. Fresnel Köhler. [18]. Sandia/ Martin Marietta [6]. 5. 1980. 1985. 1990. 1995. 2000. 2005. 2010. 2015. 2020. Figure 1.1: Most significant CPV module achievements. Values depicted in the graph were either reported at the references included in this chapter or measured at the IES-UPM laboratories. The color code is as follows: blue, systems including silicon solar cells and Fresnel lenses; red, systems including Ge-based triplejunction (3J) solar cells and Fresnel lenses; green, systems including Ge-based 3J solar cells and reflective optics; yellow, systems including 3J solar cells based on a GaAs substrate and Fresnel lenses. a For this concentrators only the elementary unit efficiency was reported. Thus, 95% of that value has been assumed to be attainable by the entire module.. Figure 1.2 depicts the previously mentioned CPV modules as a function of the concentration ratio and the acceptance angle3 achieved by them. Concentration and acceptance angle are two significant figures of merit to evaluate the optics. The two values, together with the efficiency, inform on the potential of the module. Obviously the higher the efficiency, the greater its capacity to attain low cost but, in addition, the larger the concentration ratio, the smaller the influence of the cell cost in the total system cost. Furthermore, a wide acceptance angle may imply a significant cost reduction due to an increased tolerance in the assembly and tracking. Figure 1.2 also shows the maximum combination of values imposed by the conservation of étendue for a cell surrounded by air and for a system in which a medium 3. Acceptance angle AA90 , is defined as the deviation angle such that efficiency of the system is 90% of its maximum.. 4.
(37) Introduction with refractive index 1.5 surrounds the cell, i.e. glass or silicone. It can be clearly seen how the reflective optics (in green) approach closest to the theoretical limits as they do not suffer chromatic aberration. Among the refractive optics (in red), those making use of nonimaging designs (Martifer [17], Fresnel-Köhler [18] and TIR-R [11]) are also closer to the theoretical limit.. 3.0 ideal system (n=1.5). 90. [º]. ideal system (n=1). 2.5. Acceptance angle,. 2.0 Sandia/ Martin. FluidReflex. Marietta. 1.5. a. Sol Focus [14]. [6] IES/. b. Martifer [17]. LPI-Boeing. [15-16]. IES/Ramón a. TIR-R Isofoton [11]. UPM-LPI /. Areces [7]. 1.0. b. Sandia/Alpha. Fresnel Köhler. [18] Becar [19]. Daido Steel [13]. Solarco [8-9] Fotón HC. 0.5. Flatcon/ Amonix [10]. 0. 200. Semprius [22-23] Sumitomo. Heliotrop [20]. Soitec [12]. 400. 600. 800. Concentration,. 1000. 1200. 1400. Xgeo. Figure 1.2: Geometrical concentration Xgeo , and acceptance angle AA90 , of several concentrating optics. Values depicted in the graph were either reported at the references included in this chapter or measured at the IES-UPM laboratories. The color code is as follows: blue, systems including silicon solar cells and Fresnel lenses; red, systems including Ge-based 3J solar cells and Fresnel lenses; green, systems including Ge-based 3J solar cells and reflective optics; yellow, systems including 3J solar cells based on a GaAs substrate and Fresnel lenses.The continuous lines represent the theoretical limit of the attainable concentration acceptance angle product (CAP) achievable according to the conservation of étendue, for a system where the cell is surrounded by air (n=1) or a medium whose refractive index is n=1.5, i.e. glass or silicone. a For these early systems measured acceptance angle has not been reported, then a value for the CAP equal to the most similar technology (Amonix ) was assumed. b For this concentrators only acceptance angle for the elementary unit was reported. Thus, 90% of that value has been assumed to be attainable for the entire module.. Let’s return now to the main purpose of CPV, namely the promise of cost-competitive solar 5.
(38) Chapter 1 electricity. On the one hand, CPV modules whose efficiency doubles that of flat panel PV modules have been recently reported which may enable a lower cost of the electricity produced by the formers. On the other hand, flat-panel market has experienced such an exponential growth during the last years that, with more than 100GW installed worldwide by 2012 [26] and prices that have exceeded even optimistic predictions, it seems unbeatable by any other photovoltaic technology. Both technologies can be compared by looking at their ‘learning curves’. This analysis has been proposed to asses a technology potential for cost reduction. The method draws an empirical relationship between cost reduction and volume of manufacturing. If production cost C, of a certain technology is assumed to follow an exponential dependence with cumulative production volume V (equation 1.1), the learning rate LR, is defined as the decrease in cost when cumulative production doubles (equation 1.2). C = aV −b. (1.1). LR = 1 − 2−b. (1.2). Figure 1.3 plots the evolution of the price for flat panel PV modules as a function of the cumulative production reported in [27], as well as the evolution of the price for CPV systems from several market reports gathered in [28]. In both references, the price is used as an approximation for the manufacturing cost, as the later is very difficult to know. Obviously, the two datasets are not directly comparable, mainly because the former refers to module price while the later represents the price for the entire systems. But still, the graph shows some interesting results. The wider dispersion for CPV data, only covering a 6 years period, points out that uncertainties related to CPV are considerably larger. In fact, the cumulative installed CPV power only accounts for 0.1% of total PV deployment, making the future predictions based on its past evolution less reliable. The learning rates that can be obtained from the slopes of the regression lines on figure 1.3 are highly sensitive to the assumptions made for their estimation, i.e. LR varies if yearly mean values are assumed, instead of individual data points, for the CPV system price evolution [28] or if the most recent data for PV panels, that clearly show a different tendency, are considered or not [27]. Nevertheless, the learning rate values estimated are close to LR ≈ 20% for both technologies (the regression lines are almost parallel in figure 1.3), predicting a similar potential for cost reduction for CPV as the one experienced by flat panel PV. The evolution of PV and CPV production costs would be key in determining the future significance of CPV in the electricity generation markets worldwide. However, there are other key issues that may tip the balance one way or the other. Prominent among CPV greatest 6.
(39) Introduction concerns are the doubts regarding its long-term reliability which may be an obstacle for bankability. One of the leader companies in CPV, Soitec, decided to confront this problem by becoming and independent power producer (IPP) who sells the electricity to one of the Californian utilities through a PPA4 [29]. That is, by selling the electricity generated by their systems, instead of their systems, Soitec assumes the risk of reliability by themselves. If, as all signs seem to indicate, they prove to have a reliable CPV technology this could be a great boost for the rest of CPV manufacturers. Furthermore, one of the most significant benefits of CPV when compared to flat panel PV is the low CapEx5 necessary to trigger its deployment. But above all, the fundamental reason supporting CPV is the fact that the levelized cost of electricity6 (LCoE) in locations with high direct normal irradiation (DNI), is lower for CPV utility-scale plants than for those based on flat panel PV.. 4. See footnote 1. Capital expenditures (CapEx) refer to the capital invested to build a manufacturing facility. Since CPV uses a lower proportion of semiconductor per watt peak and since it can take advantage of other industries already developed (i.e. steel, glass, aluminum) the necessary CapEx is significantly lower for CPV than for PV. 6 The levelized cost of electricity (LCoE) estimates the cost of generating electricity at the point of connection, dividing the total lifetime system costs by the total energy produced over the system’s lifetime. Such a calculation is also necessary in order to compare the competitiveness of PV and CPV with that of conventional power generation. 5. 7.
(40) Chapter 1. 100. 1976. /W]. CPV [28]. 2012. 2010. PV module price [euros. /W]. PV [27]. 1980. 1990. 10. 10 2000. 2007. 2012. 2010. 1. 1. 2012. 0.1 0.1. CPV system price [euros. 100. 0.1 1. 10. 100. 1000. cumulative production,. 10000. 100000. V [MW]. Figure 1.3: Evolution of PV and CPV price as a function of the cumulative production V . Notice that PV dataset refers to the module price [27] while CPV dataset refers to the price for the entire systems [28].. Besides the cost, influenced not only by technological aspects but also by economies of scale, global markets and political decisions, another important metric to evaluate the CPV technology is the energy payback time, EP BT . It is defined as the period that a CPV system requires to generate the same amount of energy that has been used by the system from cradle to grave. Figure 1.4 gathers a comparison of EP BT for flat-panel based systems, including both mono- and poly- crystalline silicon modules, and CPV systems. To estimate the EP BT , the cumulative energy demand method is used to calculate the total amount of energy employed to fabricate the system and to operate it during its complete lifetime. Then, the cumulative energy demand CED, is divided by the electricity generated by the system in one year Eelec . It is also necessary to include a conversion factor Rp−e , between primary energy and electricity that is country-dependent as it is influenced by the electricity generation mix considered. EP BT =. CED Eelec Rp−e. (1.3). There are some uncertainties in the EP BT calculation, prominent among them is the definition of which aspects are included when estimating the CED necessary to fabricate 8.
(41) Introduction and operate the system. In fact, a significant diversity of assumptions can be found in the literature [30–35]. Additionally it should be remarked that the estimated EP BT is highly influenced by both, the irradiance at the location where the system is installed and the Rp−e considered. Data gathered in figure 1.4 have been normalized assuming that every system is installed in Madrid, that is, flat panels are considered to be fixed at their optimum orientation and inclination angle, and thus receiving a global irradiance equal to 2059 kWh/m2 /year. DNI assumed for CPV systems is 2089 kWh/m2 /year [36]. Results in the literature have also been normalized taking into account the conversion factor of primary energy to electricity in Spain Rp−e =2.25 kWh primary energy / kWh electricity [37]. The well-known references by Alsema et al. [30] and Fthenakis and Alsema [31] estimated an EP BT lower than 2 years for systems based on both mono- and poly- crystalline silicon modules. Furthermore, Perpiñán et al. [32] showed how, from the energy payback point of view, adding a tracker is worth it, that is, the EP BT decreases for flat-panel silicon modules on a two-axis tracker compared to fixed modules. For the case of Madrid, EP BT of the 2-axis tracking system will be barely 83% of that of the fixed systems. Figure 1.4 also includes the EP BT estimated for three CPV systems with different module architectures: Soitec [33], Amonix [34] and SolFocus [35]. As previously mentioned, the EP BT values estimated in the literature have been normalized considering the DNI in Madrid. With the aforementioned caveats, and as a general result, we can state that the EP BT for CPV systems is lower than 1.5 years and lower than that estimated for the systems based on silicon flat panels. The key drivers in the energy consumption to manufacture flat-panel systems are the silicon feedstock and the fabrication of the wafers. The former is not necessary in CPV modules while the later has not such an influential role. For the CPV modules, two of the key drivers that can be easily identified are the tracker and the transport. For the Soitec module, the label ‘transport’ includes the necessary energy to deliver the modules manufactured in Germany to Spain where they are assumed to be installed [33]. In the case of the SolFocus and Amonix modules, ‘transport’ also includes the shipping of the elements as they are manufactured in a different location where the module is assembled [35]. We can foresee how, under a different manufacturing scheme, the relative importance of transportation in the EP BT can significantly change. Although it has also been included in the comparative analysis, the split into different concepts for the SolFocus case is radically different to the other two. In fact labels as ‘electricity consumption’ and ‘others’ probably gather most of the concepts that are listed apart in the other modules. Finally, the calculation made for the Amonix module is probably the most comprehensive 9.
(42) Chapter 1. Energy Payback Time,. EPBT [years]. as it gathers inputs as the energy consumptions attributable to ‘operation and maintenance’ (O&M) or the ‘end of life’ (EOL) management of the system. It is noticeable how, for the Amonix system, the relative importance of the wafer and MJ solar cell manufacturing is lower than 1% of the total energy consumption.. 2.0. other. 1.5. electricity a. O&M, EOL transport BOS. 1.0. tracker module cell wafer. 0.5. Si feedstock. 0.0 Si (mono). [30-31]. Si (poly). [30-31]. Soitec. Amonix. SolFocus. CX-75. 7700. SF1100. [33]. [34]. flat-panel. [35]. CPV. Figure 1.4: Energy payback time EP BT , estimated for fixed mono- and multi- crystalline silicon flat panels assuming a global irradiance at the optimum inclination of 2059 kWh/m2 /year and three CPV systems assuming a direct normal irradiance (DNI) equal to 2089 kWh/m2 /year. a O&M stands for operation and maintenance, EOL represents energy consumption at the system end of life.. 1.2. Framework of this research. This thesis has been carried out in the ‘Instruments and Systems Integration’ (ISI) group at the Instituto de Energı́a Solar - Universidad Politécnica de Madrid (IES-UPM). As the unofficial name of the ISI group, concentrating systems, research is devoted to the design, simulation, prototype fabrication, and characterization of these systems, as well as, the development of the necessary tools and methods to measure them properly. The holistic approach in the design and characterization of CPV systems is one of the hallmarks of the group along with the versatility and the wide range of knowledge used in everyday research. This thesis, as it could not be otherwise, is permeated by the spirit of work of the ISI group. Furthermore, it is one of the main motivations of the group to remain close to the industry to help in the development of products that work in reality. Therefore, many of the developments that this book collects have emerged in response to questions or unexpected 10.
(43) Introduction underperforming prototypes from some CPV manufacturers. In addition, some theoretical concepts whose potential is attractive are developed exclusively within the group and, if the results are successful, transferred to industry. In particular, the FluidReflex concentrator, developed in this thesis and reported in chapters 5 and 6, was inspired by previous experiences in the IES-UPM. The realization that, concentrator prototypes that were built long time ago have solar cells which were functioning properly more than twenty years later, led to the proposal of developing a high-efficiency concentrator based on a single-stage mirror and filled with a dielectric fluid. The development of this novel module was enabled by a project funded by the Spanish Ministry of Education and Science and by the 4-years European founded project NACIR (New Applications for Cpv’s: a fast way to Improve Reliability and technology progress) included within the seventh research framework program of the European Commission (FP7). In short, the two main objectives of this thesis can be stated as: 1. Designing and characterizing high-concentrating photovoltaic systems with high efficiency and wide tolerance so the energy produced by them is maximized. For this purpose the following issues are addressed: the design of high-efficiency optical systems, its coupling to multijunction solar cells, and the analysis of thermal effects on the optics. 2. Proving that there is no limitation to the practical realization of the FluidReflex concept: a single-stage reflective concentrator filled with fluid dielectric. Consequently, designing an industrial CPV module based on this concept.. 1.3. Outline of the thesis structure. After this chapter that provides a general introduction and a context for the research carried out, the thesis is divided in five technical chapters. The outline of the thesis is as follows, Chapter 2 is devoted to the optical design including the analysis of several secondary optical elements (SOE) illuminated by a Fresnel lens. Their principles of design are presented and a comparative analysis of equivalent systems comprising any of the SOE are included. Theoretical and experimental analysis of two particular cases of special relevance is included in this chapter: the design of a DTIRC SOE with square output and the dome SOE manufactured by silicone overmolding. Chapter 3 deals with the integration of concentrating optics and multijunction solar cells to attain high-efficiency systems. This includes the study of issues related to the currentmatching of solar cells beneath concentrating optics, the design of antireflective coating particularly optimized for concentrator cells, and the analysis of irradiance distributions over the cells which are not uniform, neither spatially nor spectrally. 11.
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