Free-form optics for Fresnel-lens-based photovoltaic concentrators

The Concentrated Photovoltaics (CPV) promise relies upon the use of high-efficiency triple-junction solar cells (with proven efficiencies of over 44%) and upon high-performance optics that allow for high concentration concurrent with relaxed manufacturing tolerances (all key elements for low-cost mass production). Additionally, uniform illumination is highly desirable for efficiency and reliability reasons. All of these features have to be achieved with inexpensive optics containing only a few (in general no more than 2) optical elements. In this paper we show that the degrees of freedom using free-forms allow the introduction of multiple functionalities required for CPV with just 2 optical elements, one of which is a Fresnel lens.

Advanced Fresnel Köhler concentrators for photovoltaic applications

La concentración fotovoltaica (CPV) es una de las formas más prometedoras de reducir el coste de la energía proveniente del sol. Esto es posible gracias a células solares de alta eficiencia y a una significativa reducción del tamaño de la misma, que está fabricada con costosos materiales semiconductores. Ambos aspectos están íntimamente ligados ya que las altas eficiencias solamente son posibles con materiales y tecnologías de célula caros, lo que forzosamente conlleva una reducción del tamaño de la célula si se quiere lograr un sistema rentable. La reducción en el tamaño de las células requiere que la luz proveniente del sol ha de ser redirigida (es decir, concentrada) hacia la posición de la célula. Esto se logra colocando un concentrador óptico encima de la célula. Estos concentradores para CPV están formados por diferentes elementos ópticos fabricados en materiales baratos, con el fin de reducir los costes de producción. El marco óptimo para el diseño de concentradores es la óptica anidólica u óptica nonimaging. La óptica nonimaging fue desarrollada por primera vez en la década de los años sesenta y ha ido evolucionando significativamente desde entonces. El objetivo de los diseños nonimaging es la transferencia eficiente de energía entre la fuente y el receptor (sol y célula respectivamente, en el caso de la CPV), sin tener en cuenta la formación de imagen. Los sistemas nonimaging suelen ser simples, están compuestos de un menor número de superficies que los sistemas formadores de imagen y son más tolerantes a errores de fabricación. Esto hace de los sistemas nonimaging una herramienta fundamental, no sólo en el diseño de concentradores fotovoltaicos, sino también en el diseño de otras aplicaciones como iluminación, proyección y comunicaciones inalámbricas ópticas. Los concentradores ópticos nonimaging son adecuados para aplicaciones CPV porque el objetivo no es la reproducción de una imagen exacta del sol (como sería el caso de las ópticas formadoras de imagen), sino simplemente la colección de su energía sobre la célula solar. Los concentradores para CPV pueden presentar muy diferentes arquitecturas y elementos ópticos, dando lugar a una gran variedad de posibles diseños. El primer elemento óptico que es atravesado por la luz del sol se llama Elemento Óptico Primario (POE en su nomenclatura anglosajona) y es el elemento más determinante a la hora de definir la forma y las propiedades del concentrador. El POE puede ser refractivo (lente) o reflexivo (espejo). Esta tesis se centra en los sistemas CPV que presentan lentes de Fresnel como POE, que son lentes refractivas delgadas y de bajo coste de producción que son capaces de concentrar la luz solar. El capítulo 1 expone una breve introducción a la óptica geométrica y no formadora de imagen (nonimaging), explicando sus fundamentos y conceptos básicos. Tras ello, la integración Köhler es presentada en detalle, explicando sus principios, válidos tanto para aplicaciones CPV como para iluminación. Una introducción a los conceptos fundamentales de CPV también ha sido incluida en este capítulo, donde se analizan las propiedades de las células solares multiunión y de los concentradores ópticos empleados en los sistemas CPV. El capítulo se cierra con una descripción de las tecnologías existentes empleadas para la fabricación de elementos ópticos que componen los concentradores. El capítulo 2 se centra principalmente en el diseño y desarrollo de los tres concentradores ópticos avanzados Fresnel Köhler que se presentan en esta tesis: Fresnel-Köhler (FK), Fresnel-Köhler curvo (DFK) y Fresnel-Köhler con cavidad (CFK). Todos ellos llevan a cabo integración Köhler y presentan una lente de Fresnel como su elemento óptico primario. Cada uno de estos concentradores CPV presenta sus propias propiedades y su propio procedimiento de diseño. Además, presentan todas las características que todo concentrador ha de tener: elevado factor de concentración, alta tolerancia de fabricación, alta eficiencia óptica, irradiancia uniforme sobre la superficie de la célula y bajo coste de producción. Los concentradores FK y DFK presentan una configuración de cuatro sectores para lograr la integración Köhler. Esto quiere decir que POE y SOE se dividen en cuatro sectores simétricos cada uno, y cada sector del POE trabaja conjuntamente con su correspondiente sector de SOE. La principal diferencia entre los dos concentradores es que el POE del FK es una lente de Fresnel plana, mientras que una lente curva de Fresnel es empleada como POE del DFK. El concentrador CFK incluye una cavidad de confinamiento externo integrada, que es un elemento óptico capaz de recuperar los rayos reflejados por la superficie de la célula con el fin de ser reabsorbidos por la misma. Por tanto, se aumenta la absorción de la luz, lo que implica un aumento en la eficiencia del módulo. Además, este capítulo también explica un método de diseño alternativo para los elementos faceteados, especialmente adecuado para las lentes curvas como el POE del DFK. El capítulo 3 se centra en la caracterización y medidas experimentales de los concentradores ópticos presentados en el capítulo 2, y describe sus procedimientos. Estos procedimientos son en general aplicables a cualquier concentrador basado en una lente de Fresnel, e incluyen tres tipos principales de medidas experimentales: eficiencia eléctrica, ángulo de aceptancia y uniformidad de la irradiancia en el plano de la célula. Los resultados que se muestran a lo largo de este capítulo validarán a través de medidas a sol real las características avanzadas que presentan los concentradores Köhler, y que se demuestran en el capítulo 2 mediante simulaciones de rayos. Cada concentrador (FK, DFK y CFK) está diseñado y optimizado teniendo en cuenta condiciones de operación realistas. Su rendimiento se modela de forma exhaustiva mediante el trazado de rayos en combinación con modelos distribuidos para la célula. La tolerancia es un asunto crítico de cara al proceso de fabricación, y ha de ser máxima para obtener sistemas de producción en masa rentables. Concentradores con tolerancias limitadas generan bajadas significativas de eficiencia a nivel de array, causadas por el desajuste de corrientes entre los diferentes módulos (principalmente debido a errores de alineación en la fabricación). En este sentido, la sección 3.5 presenta dos métodos matemáticos que estiman estas pérdidas por desajuste a nivel de array mediante un análisis de sus curvas I-V, y por tanto siendo innecesarias las medidas a nivel de mono-módulo. El capítulo 3 también describe la caracterización indoor de los elementos ópticos que componen los concentradores, es decir, de las lentes de Fresnel que actúan como POE y de los secundarios free-form. El objetivo de esta caracterización es el de evaluar los adecuados perfiles de las superficies y las transmisiones ópticas de los diferentes elementos analizados, y así hacer que el rendimiento del módulo sea el esperado. Esta tesis la cierra el capítulo 4, en el que la integración Köhler se presenta como una buena alternativa para obtener distribuciones uniformes en aplicaciones de iluminación de estado sólido (iluminación con LED), siendo particularmente eficaz cuando se requiere adicionalmente una buena mezcla de colores. En este capítulo esto se muestra a través del ejemplo particular de un concentrador DFK, el cual se ha utilizado para aplicaciones CPV en los capítulos anteriores. Otra alternativa para lograr mezclas cromáticas apropiadas está basada en un método ya conocido (deflexiones anómalas), y también se ha utilizado aquí para diseñar una lente TIR aplanética delgada. Esta lente cumple la conservación de étendue, asegurando así que no hay bloqueo ni dilución de luz simultáneamente. Ambos enfoques presentan claras ventajas sobre las técnicas clásicas empleadas en iluminación para obtener distribuciones de iluminación uniforme: difusores y mezcla caleidoscópica mediante guías de luz. ABSTRACT Concentrating Photovoltaics (CPV) is one of the most promising ways of reducing the cost of energy collected from the sun. This is possible thanks to both, very high-efficiency solar cells and a large decrease in the size of cells, which are made of costly semiconductor materials. Both issues are closely linked since high efficiency values are only possible with expensive cell materials and technologies, implying a compulsory area reduction if cost-effectiveness is desired. The reduction in the cell size requires that light coming from the sun must be redirected (i.e. concentrated) towards the cell position. This is achieved by placing an optical concentrator system on top of the cell. These CPV concentrators consist of different optical elements manufactured on cheap materials in order to maintain low production costs. The optimal framework for the design of concentrators is nonimaging optics. Nonimaging optics was first developed in the 60s decade and has been largely developed ever since. The aim of nonimaging devices is the efficient transfer of light power between the source and the receiver (sun and cell respectively in the case of CPV), disregarding image formation. Nonimaging systems are usually simple, comprised of fewer surfaces than imaging systems and are more tolerant to manufacturing errors. This renders nonimaging optics a fundamental tool, not only in the design of photovoltaic concentrators, but also in the design of other applications as illumination, projection and wireless optical communications. Nonimaging optical concentrators are well suited for CPV applications because the goal is not the reproduction of an exact image of the sun (as imaging optics would provide), but simply the collection of its energy on the solar cell. Concentrators for CPV may present very different architectures and optical elements, resulting in a vast variety of possible designs. The first optical element that sunlight goes through is called the Primary Optical Element (POE) and is the most determinant element in order to define the shape and properties of the whole concentrator. The POE can be either refractive (lens) or reflective (mirror). This thesis focuses on CPV systems based on Fresnel lenses as POE, which are thin and inexpensive refractive lenses able to concentrate sunlight. Chapter 1 exposes a short introduction to geometrical and nonimaging optics, explaining their fundamentals and basic concepts. Then, the Köhler integration is presented in detail, explaining its principles, valid for both applications: CPV and illumination. An introduction to CPV fundamental concepts is also included in this chapter, analyzing the properties of multijunction solar cells and optical concentrators employed in CPV systems. The chapter is closed with a description of the existing technologies employed for the manufacture of optical elements composing the concentrator. Chapter 2 is mainly devoted to the design and development of the three advanced Fresnel Köhler optical concentrators presented in this thesis work: Fresnel-Köhler (FK), Dome-shaped Fresnel-Köhler (DFK) and Cavity Fresnel-Köhler (CFK). They all perform Köhler integration and comprise a Fresnel lens as their Primary Optical Element. Each one of these CPV concentrators presents its own characteristics, properties and its own design procedure. Their performances include all the key issues in a concentrator: high concentration factor, large tolerances, high optical efficiency, uniform irradiance on the cell surface and low production cost. The FK and DFK concentrators present a 4-fold configuration in order to perform the Köhler integration. This means that POE and SOE are divided into four symmetric sectors each one, working each POE sector with its corresponding SOE sector by pairs. The main difference between both concentrators is that the POE of the FK is a flat Fresnel lens, while a dome-shaped (curved) Fresnel lens performs as the DFK’s POE. The CFK concentrator includes an integrated external confinement cavity, which is an optical element able to recover rays reflected by the cell surface in order to be re-absorbed by the cell. It increases the light absorption, entailing an increase in the efficiency of the module. Additionally, an alternative design method for faceted elements will also be explained, especially suitable for dome-shaped lenses as the POE of the DFK. Chapter 3 focuses on the characterization and experimental measurements of the optical concentrators presented in Chapter 2, describing their procedures. These procedures are in general applicable to any Fresnel-based concentrator as well and include three main types of experimental measurements: electrical efficiency, acceptance angle and irradiance uniformity at the solar cell plane. The results shown along this chapter will validate through outdoor measurements under real sun operation the advanced characteristics presented by the Köhler concentrators, which are demonstrated in Chapter 2 through raytrace simulation: high optical efficiency, large acceptance angle, insensitivity to manufacturing tolerances and very good irradiance uniformity on the cell surface. Each concentrator (FK, DFK and CFK) is designed and optimized looking at realistic performance characteristics. Their performances are modeled exhaustively using ray tracing combined with cell modeling, taking into account the major relevant factors. The tolerance is a critical issue when coming to the manufacturing process in order to obtain cost-effective mass-production systems. Concentrators with tight tolerances result in significant efficiency drops at array level caused by current mismatch among different modules (mainly due to manufacturing alignment errors). In this sense, Section 3.5 presents two mathematical methods that estimate these mismatch losses for a given array just by analyzing its full-array I-V curve, hence being unnecessary any single mono-module measurement. Chapter 3 also describes the indoor characterization of the optical elements composing the concentrators, i.e. the Fresnel lenses acting as POEs and the free-form SOEs. The aim of this characterization is to assess the proper surface profiles and optical transmissions of the different elements analyzed, so they will allow for the expected module performance. This thesis is closed by Chapter 4, in which Köhler integration is presented as a good approach to obtain uniform distributions in Solid State Lighting applications (i.e. illumination with LEDs), being particularly effective when dealing with color mixing requirements. This chapter shows it through the particular example of a DFK concentrator, which has been used for CPV applications in the previous chapters. An alternative known method for color mixing purposes (anomalous deflections) has also been used to design a thin aplanatic TIR lens. This lens fulfills conservation of étendue, thus ensuring no light blocking and no light dilution at the same time. Both approaches present clear advantages over the classical techniques employed in lighting to obtain uniform illumination distributions: diffusers and kaleidoscopic lightpipe mixing.

Low-cost irradiance sensors for irradiation assessments inside tree canopies.

The solar irradiation that a crop receives is directly related to the physical and biological processes that affect the crop. However, the assessment of solar irradiation poses certain problems when it must be measured through fruit inside the canopy of a tree. In such cases, it is necessary to check many test points, which usually requires an expensive data acquisition system. The use of conventional irradiance sensors increases the cost of the experiment, making them unsuitable. Nevertheless, it is still possible to perform a precise irradiance test with a reduced price by using low-cost sensors based on the photovoltaic effect. The aim of this work is to develop a low-cost sensor that permits the measurement of the irradiance inside the tree canopy. Two different technologies of solar cells were analyzed for their use in the measurement of solar irradiation levels inside tree canopies. Two data acquisition system setups were also tested and compared. Experiments were performed in Ademuz (Valencia, Spain) in September 2011 and September 2012 to check the validity of low-cost sensors based on solar cells and their associated data acquisition systems. The observed difference between solar irradiation at high and low positions was of 18.5% ± 2.58% at a 95% confidence interval. Large differences were observed between the operations of the two tested sensors. In the case of a-Si cells based mini-modules, an effect of partial shadowing was detected due to the larger size of the devices, the use of individual c-Si cells is recommended over a-Si cells based mini-modules.

Free-form optical systems for nonimaging applications : Sistemas ópticos anamórficos para aplicaciones anidólicas

La óptica anidólica es una rama de la óptica cuyo desarrollo comenzó a mediados de la década de 1960. Este relativamente nuevo campo de la óptica se centra en la transferencia eficiente de la luz, algo necesario en muchas aplicaciones, entre las que destacamos los concentradores solares y los sistemas de iluminación. Las soluciones de la óptica clásica a los problemas de la transferencia de energía de la luz sólo son adecuadas cuando los rayos de luz son paraxiales. La condición paraxial no se cumple en la mayoría de las aplicaciones para concentración e iluminación. Esta tesis contiene varios diseños free-form (aquellos que no presentan ninguna simetría, ni de rotación ni lineal) cuyas aplicaciones van destinadas a estos dos campos. El término nonimaging viene del hecho de que estos sistemas ópticos no necesitan formar una imagen del objeto, aunque no formar la imagen no es una condición necesaria. Otra palabra que se utiliza a veces en lugar de nonimaging es la palabra anidólico, viene del griego "an+eidolon" y tiene el mismo significado. La mayoría de los sistemas ópticos diseñados para aplicaciones anidólicas no presentan ninguna simetría, es decir, son free-form (anamórficos). Los sistemas ópticos free-form están siendo especialmente relevantes durante los últimos años gracias al desarrollo de las herramientas para su fabricación como máquinas de moldeo por inyección y el mecanizado multieje. Sin embargo, solo recientemente se han desarrollado técnicas de diseño anidólicas capaces de cumplir con estos grados de libertad. En aplicaciones de iluminación el método SMS3D permite diseñar dos superficies free-form para controlar las fuentes de luz extensas. En los casos en que se requiere una elevada asimetría de la fuente, el objeto o las restricciones volumétricos, las superficies free-form permiten obtener soluciones de mayor eficiencia, o disponer de menos elementos en comparación con las soluciones de simetría de rotación, dado que las superficies free-form tienen más grados de libertad y pueden realizar múltiples funciones debido a su naturaleza anamórfica. Los concentradores anidólicos son muy adecuados para la captación de energía solar, ya que el objetivo no es la reproducción de una imagen exacta del sol, sino sencillamente la captura de su energía. En este momento, el campo de la concentración fotovoltaica (CPV) tiende hacia sistemas de alta concentración con el fin de compensar el gasto de las células solares multi-unión (MJ) utilizadas como receptores, reduciendo su área. El interés en el uso de células MJ radica en su alta eficiencia de conversión. Para obtener sistemas competitivos en aplicaciones terrestres se recurre a sistemas fotovoltaicos de alta concentración (HCPV), con factores de concentración geométrica por encima de 500x. Estos sistemas se componen de dos (o más) elementos ópticos (espejos y/o lentes). En los sistemas presentados a lo largo de este trabajo se presentan ejemplos de concentradores HCPV con elementos reflexivos como etapa primaria, así como concentradores con elementos refractivos (lente de Fresnel). Con la necesidad de aumentar la eficiencia de los sistemas HCPV reales y con el fin de proporcionar la división más eficiente del espectro solar, células conteniendo cuatro o más uniones (con un potencial de alcanzar eficiencias de más del 45% a una concentración de cientos de soles) se exploran hoy en día. En esta tesis se presenta una de las posibles arquitecturas de división del espectro (spectrum-splitting en la literatura anglosajona) que utilizan células de concentración comercial. Otro campo de aplicación de la óptica nonimaging es la iluminación, donde es necesario proporcionar un patrón de distribución de la iluminación específico. La iluminación de estado sólido (SSL), basada en la electroluminiscencia de materiales semiconductores, está proporcionando fuentes de luz para aplicaciones de iluminación general. En la última década, los diodos emisores de luz (LED) de alto brillo han comenzado a reemplazar a las fuentes de luz convencionales debido a la superioridad en la calidad de la luz emitida, elevado tiempo de vida, compacidad y ahorro de energía. Los colimadores utilizados con LEDs deben cumplir con requisitos tales como tener una alta eficiencia, un alto control del haz de luz, una mezcla de color espacial y una gran compacidad. Presentamos un colimador de luz free-form con microestructuras capaz de conseguir buena colimación y buena mezcla de colores con una fuente de LED RGGB. Una buena mezcla de luz es importante no sólo para simplificar el diseño óptico de la luminaria sino también para evitar hacer binning de los chips. La mezcla de luz óptica puede reducir los costes al evitar la modulación por ancho de pulso y otras soluciones electrónicas patentadas para regulación y ajuste de color. Esta tesis consta de cuatro capítulos. Los capítulos que contienen la obra original de esta tesis son precedidos por un capítulo introductorio donde se presentan los conceptos y definiciones básicas de la óptica geométrica y en el cual se engloba la óptica nonimaging. Contiene principios de la óptica no formadora de imagen junto con la descripción de sus problemas y métodos de diseño. Asimismo se describe el método de Superficies Múltiples Simultáneas (SMS), que destaca por su versatilidad y capacidad de controlar varios haces de rayos. Adicionalmente también se describe la integración Köhler y sus aplicaciones en el campo de la energía fotovoltaica. La concentración fotovoltaica y la iluminación de estado sólido son introducidas junto con la revisión de su estado actual. El Segundo y Tercer Capítulo contienen diseños ópticos avanzados con aplicación en la concentración solar principalmente, mientras que el Cuarto Capítulo describe el colimador free-form con surcos que presenta buena mezcla de colores para aplicaciones de iluminación. El Segundo Capítulo describe dos concentradores ópticos HCPV diseñados con el método SMS en tres dimensiones (SMS3D) que llevan a cabo integración Köhler en dos direcciones con el fin de proporcionar una distribución de irradiancia uniforme libre de aberraciones cromáticas sobre la célula solar. Uno de los diseños es el concentrador XXR free-form diseñado con el método SMS3D, donde el espejo primario (X) y la lente secundaria (R) se dividen en cuatro sectores simétricos y llevan a cabo la integración Köhler (proporcionando cuatro unidades del array Köhler), mientras que el espejo intermedio (X) presenta simetría rotacional. Otro concentrador HCPV presentado es el Fresnel-RXI (FRXI) con una lente de Fresnel funcionando como elemento primario (POE) y una lente RXI como elemento óptico secundario (SOE), que presenta configuración 4-fold con el fin de realizar la integración Köhler. Las lentes RXI son dispositivos nonimaging conocidos, pero su aplicación como elemento secundario es novedosa. Los concentradores XXR y FRXI Köhler son ejemplos académicos de muy alta concentración (más de 2,000x, mientras que los sistemas convencionales hoy en día no suelen llegar a 1,000x) preparados para las células solares N-unión (con N>3), que probablemente requerirán una mayor concentración y alta uniformidad espectral de irradiancia con el fin de obtener sistemas CPV terrestres eficientes y rentables. Ambos concentradores están diseñados maximizando funciones de mérito como la eficiencia óptica, el producto concentración-aceptancia (CAP) y la uniformidad de irradiancia sobre la célula libre de la aberración cromática (integración Köhler). El Tercer Capítulo presenta una arquitectura para la división del espectro solar basada en un módulo HCPV con alta concentración (500x) y ángulo de aceptancia alto (>1º) que tiene por objeto reducir ambas fuentes de pérdidas de las células triple unión (3J) comerciales: el uso eficiente del espectro solar y la luz reflejada de los contactos metálicos y de la superficie de semiconductor. El módulo para la división del espectro utiliza el espectro solar más eficiente debido a la combinación de una alta eficiencia de una célula de concentración 3J (GaInP/GaInAs/Ge) y una de contacto posterior (BPC) de concentración de silicio (Si), así como la técnica de confinamiento externo para la recuperación de la luz reflejada por la célula 3J con el fin de ser reabsorbida por la célula. En la arquitectura propuesta, la célula 3J opera con su ganancia de corriente optimizada (concentración geométrica de 500x), mientras que la célula de silicio trabaja cerca de su óptimo también (135x). El módulo de spectrum-splitting consta de una lente de Fresnel plana como POE y un concentrador RXI free-form como SOE con un filtro paso-banda integrado en él. Tanto POE como SOE realizan la integración Köhler para producir homogeneización de luz sobre la célula. El filtro paso banda envía los fotones IR en la banda 900-1,150nm a la célula de silicio. Hay varios aspectos prácticos de la arquitectura del módulo presentado que ayudan a reducir la complejidad de los sistemas spectrum-splitting (el filtro y el secundario forman una sola pieza sólida, ambas células son coplanarias simplificándose el cableado y la disipación de calor, etc.). Prototipos prueba-de-concepto han sido ensamblados y probados a fin de demostrar la fabricabilidad del filtro y su rendimiento cuando se combina con la técnica de reciclaje de luz externa. Los resultados obtenidos se ajustan bastante bien a los modelos y a las simulaciones e invitan al desarrollo de una versión más compleja de este prototipo en el futuro. Dos colimadores sólidos con surcos free-form se presentan en el Cuarto Capítulo. Ambos diseños ópticos están diseñados originalmente usando el método SMS3D. La segunda superficie ópticamente activa está diseñada a posteriori como una superficie con surcos. El diseño inicial de dos espejos (XX) está diseñado como prueba de concepto. En segundo lugar, el diseño RXI free-form es comparable con los colimadores RXI existentes. Se trata de un diseño muy compacto y eficiente que proporciona una muy buena mezcla de colores cuando funciona con LEDs RGB fuera del eje óptico como en los RGB LEDs convencionales. Estos dos diseños son dispositivos free-form diseñados con la intención de mejorar las propiedades de mezcla de colores de los dispositivos no aplanáticos RXI con simetría de revolución y la eficiencia de los aplanáticos, logrando una buena colimación y una buena mezcla de colores. La capacidad de mezcla de colores del dispositivo no-aplanático mejora añadiendo características de un aplanático a su homólogo simétrico sin pérdida de eficiencia. En el caso del diseño basado en RXI, su gran ventaja consiste en su menor coste de fabricación ya que el proceso de metalización puede evitarse. Aunque algunos de los componentes presentan formas muy complejas, los costes de fabricación son relativamente insensibles a la complejidad del molde, especialmente en el caso de la producción en masa (tales como inyección de plástico), ya que el coste del molde se reparte entre todas las piezas fabricadas. Por último, las últimas dos secciones son las conclusiones y futuras líneas de investigación. ABSTRACT Nonimaging optics is a branch of optics whose development began in the mid-1960s. This rather new field of optics focuses on the efficient light transfer necessary in many applications, among which we highlight solar concentrators and illumination systems. The classical optics solutions to the problems of light energy transfer are only appropriate when the light rays are paraxial. The paraxial condition is not met in most applications for the concentration and illumination. This thesis explores several free-form designs (with neither rotational nor linear symmetry) whose applications are intended to cover the above mentioned areas and more. The term nonimaging comes from the fact that these optical systems do not need to form an image of the object, although it is not a necessary condition not to form an image. Another word sometimes used instead of nonimaging is anidolic, and it comes from the Greek “an+eidolon” and has the same meaning. Most of the optical systems designed for nonimaging applications are without any symmetry, i.e. free-form. Free-form optical systems become especially relevant lately with the evolution of free-form tooling (injection molding machines, multi-axis machining techniques, etc.). Nevertheless, only recently there are nonimaging design techniques that are able to meet these degrees of freedom. In illumination applications, the SMS3D method allows designing two free-form surfaces to control very well extended sources. In cases when source, target or volumetric constrains have very asymmetric requirements free-form surfaces are offering solutions with higher efficiency or with fewer elements in comparison with rotationally symmetric solutions, as free-forms have more degrees of freedom and they can perform multiple functions due to their free-form nature. Anidolic concentrators are well suited for the collection of solar energy, because the goal is not the reproduction of an exact image of the sun, but instead the collection of its energy. At this time, Concentration Photovoltaics (CPV) field is turning to high concentration systems in order to compensate the expense of multi-junction (MJ) solar cells used as receivers by reducing its area. Interest in the use of MJ cells lies in their very high conversion efficiency. High Concentration Photovoltaic systems (HCPV) with geometric concentration of more than 500x are required in order to have competitive systems in terrestrial applications. These systems comprise two (or more) optical elements, mirrors and/or lenses. Systems presented in this thesis encompass both main types of HCPV architectures: concentrators with primary reflective element and concentrators with primary refractive element (Fresnel lens). Demand for the efficiency increase of the actual HCPV systems as well as feasible more efficient partitioning of the solar spectrum, leads to exploration of four or more junction solar cells or submodules. They have a potential of reaching over 45% efficiency at concentration of hundreds of suns. One possible architectures of spectrum splitting module using commercial concentration cells is presented in this thesis. Another field of application of nonimaging optics is illumination, where a specific illuminance distribution pattern is required. The Solid State Lighting (SSL) based on semiconductor electroluminescence provides light sources for general illumination applications. In the last decade high-brightness Light Emitting Diodes (LEDs) started replacing conventional light sources due to their superior output light quality, unsurpassed lifetime, compactness and energy savings. Collimators used with LEDs have to meet requirements like high efficiency, high beam control, color and position mixing, as well as a high compactness. We present a free-form collimator with microstructures that performs good collimation and good color mixing with RGGB LED source. Good light mixing is important not only for simplifying luminaire optical design but also for avoiding die binning. Optical light mixing may reduce costs by avoiding pulse-width modulation and other patented electronic solutions for dimming and color tuning. This thesis comprises four chapters. Chapters containing the original work of this thesis are preceded by the introductory chapter that addresses basic concepts and definitions of geometrical optics on which nonimaging is developed. It contains fundamentals of nonimaging optics together with the description of its design problems, principles and methods, and with the Simultaneous Multiple Surface (SMS) method standing out for its versatility and ability to control several bundles of rays. Köhler integration and its applications in the field of photovoltaics are described as well. CPV and SSL fields are introduced together with the review on their background and their current status. Chapter 2 and Chapter 3 contain advanced optical designs with primarily application in solar concentration; meanwhile Chapter 4 portrays the free-form V-groove collimator with good color mixing property for illumination application. Chapter 2 describes two HCPV optical concentrators designed with the SMS method in three dimensions (SMS3D). Both concentrators represent Köhler integrator arrays that provide uniform irradiance distribution free from chromatic aberrations on the solar cell. One of the systems is the XXR free-form concentrator designed with the SMS3D method. The primary mirror (X) of this concentrator and secondary lens (R) are divided in four symmetric sectors (folds) that perform Köhler integration; meanwhile the intermediate mirror (X) is rotationally symmetric. Second HCPV concentrator is the Fresnel-RXI (FRXI) with flat Fresnel lens as the Primary Optical Element (POE) and an RXI lens as the Secondary Optical Element (SOE). This architecture manifests 4-fold configuration for performing Köhler integration (4 array units), as well. The RXI lenses are well-known nonimaging devices, but their application as SOE is novel. Both XXR and FRXI Köhler HCPV concentrators are academic examples of very high concentration (more than 2,000x meanwhile conventional systems nowadays have up to 1,000x) prepared for the near future N-junction (N>3) solar cells. In order to have efficient and cost-effective terrestrial CPV systems, those cells will probably require higher concentrations and high spectral irradiance uniformity. Both concentrators are designed by maximizing merit functions: the optical efficiency, concentration-acceptance angle (CAP) and cell-irradiance uniformity free from chromatic aberrations (Köhler integration). Chapter 3 presents the spectrum splitting architecture based on a HCPV module with high concentration (500x) and high acceptance angle (>1º). This module aims to reduce both sources of losses of the actual commercial triple-junction (3J) solar cells with more efficient use of the solar spectrum and with recovering the light reflected from the 3J cells’ grid lines and semiconductor surface. The solar spectrum is used more efficiently due to the combination of a high efficiency 3J concentration cell (GaInP/GaInAs/Ge) and external Back-Point-Contact (BPC) concentration silicon (Si) cell. By employing external confinement techniques, the 3J cell’s reflections are recovered in order to be re-absorbed by the cell. In the proposed concentrator architecture, the 3J cell operates at its optimized current gain (at geometrical concentration of 500x), while the Si cell works near its optimum, as well (135x). The spectrum splitting module consists of a flat Fresnel lens (as the POE), and a free-form RXI-type concentrator with a band-pass filter embedded in it (as the SOE), both POE and SOE performing Köhler integration to produce light homogenization. The band-pass filter sends the IR photons in the 900-1,150nm band to the Si cell. There are several practical aspects of presented module architecture that help reducing the added complexity of the beam splitting systems: the filter and secondary are forming a single solid piece, both cells are coplanar so the heat management and wiring is simplified, etc. Two proof-of-concept prototypes are assembled and tested in order to prove filter manufacturability and performance, as well as the potential of external light recycling technique. Obtained measurement results agree quite well with models and simulations, and show an opened path to manufacturing of the Fresnel RXI-type secondary concentrator with spectrum splitting strategy. Two free-form solid V-groove collimators are presented in Chapter 4. Both free-form collimators are originally designed with the SMS3D method. The second mirrored optically active surface is converted in a grooved surface a posteriori. Initial two mirror (XX) design is presented as a proof-of-concept. Second, RXI free-form design is comparable with existing RXI collimators as it is a highly compact and a highly efficient design. It performs very good color mixing of the RGGB LED sources placed off-axis like in conventional RGB LEDs. Collimators described here improve color mixing property of the prior art rotationally symmetric no-aplanatic RXI devices, and the efficiency of the aplanatic ones, accomplishing both good collimation and good color mixing. Free-form V-groove collimators enhance the no-aplanatic device's blending capabilities by adding aplanatic features to its symmetric counterpart with no loss in efficiency. Big advantage of the RXI design is its potentially lower manufacturing cost, since the process of metallization may be avoided. Although some components are very complicated for shaping, the manufacturing costs are relatively insensitive to the complexity of the mold especially in the case of mass production (such as plastic injection), as the cost of the mold is spread in many parts. Finally, last two sections are conclusions and future lines of investigation.

Wide-angle, high-concentration photovoltaics to compete with flat plate systems

A novel photovoltaic concentrator enables highly uniform irradiance on a small number of efficient solar cells. The maximum electrical power of a photovoltaic (PV) energy installation depends on three factors: the available irradiance, the size of the systems collecting sunlight, and the rate at which the device transforms light into electricity (the conversion efficiency). Developers can maximize the irradiance by carefully selecting the site and orientation of the solar facility. But they can only expand their sunlight collection systems for standard flat plate PV devices by increasing the number of solar cells, at greater cost. Here, we consider the advantages of an alternative PV system that produces more energy without increasing the number of cells used (actually, reducing it), by improving the conversion rates.We also present a new device that may enhance the commercial viability of such technologies.

Development and characterization of an FK photovoltaic concentrator for maximum conversion efficiency

The outdoor measurements of a single-cell concentrator PV module reaching a regressed 35.6% efficiency and a maximum peak efficiency of 36.0% (both corrected @Tcell=25ºC) are presented. This is the result of the joint effort by LPI and Solar Junction to demonstrate the potential of combining their respective state-of-the-art concentrator optics and solar cells. The LPI concentrator used is an FK, which is an advanced nonimaging concentrator using 4-channel Köhler homogenization, with a primary Fresnel lens and a refractive secondary made of glass. Solar Junction’s cell is a triplejunction solar cell with the A-SLAMTM architecture using dilute-nitrides.

About the origin of low wafer performance and crystal defect generation on seed-cast growth of industrial mono-like silicon ingots

The era of the seed-cast grown monocrystalline-based silicon ingots is coming. Mono-like, pseudomono or quasimono wafers are product labels that can be nowadays found in the market, as a critical innovation for the photovoltaic industry. They integrate some of the most favorable features of the conventional silicon substrates for solar cells, so far, such as the high solar cell efficiency offered by the monocrystalline Czochralski-Si (Cz-Si) wafers and the lower cost, high productivity and full square-shape that characterize the well-known multicrystalline casting growth method. Nevertheless, this innovative crystal growth approach still faces a number of mass scale problems that need to be resolved, in order to gain a deep, 100% reliable and worldwide market: (i) extended defects formation during the growth process; (ii) optimization of the seed recycling; and (iii) parts of the ingots giving low solar cells performance, which directly affect the production costs and yield of this approach. Therefore, this paper presents a series of casting crystal growth experiments and characterization studies from ingots, wafers and cells manufactured in an industrial approach, showing the main sources of crystal defect formation, impurity enrichment and potential consequences at solar cell level. The previously mentioned technological drawbacks are directly addressed, proposing industrial actions to pave the way of this new wafer technology to high efficiency solar cells.

Precipitated iron: a limit on gettering efficacy in multicrystalline silicon

A phosphorus diffusion gettering model is used to examine the efficacy of a standard gettering process on interstitial and precipitated iron in multicrystalline silicon. The model predicts a large concentration of precipitated iron remaining after standard gettering for most as-grown iron distributions. Although changes in the precipitated iron distribution are predicted to be small, the simulated post-processing interstitial iron concentration is predicted to depend strongly on the as-grown distribution of precipitates, indicating that precipitates must be considered as internal sources of contamination during processing. To inform and validate the model, the iron distributions before and after a standard phosphorus diffusion step are studied in samples from the bottom, middle, and top of an intentionally Fe-contaminated laboratory ingot. A census of iron-silicide precipitates taken by synchrotron-based X-ray fluorescence microscopy confirms the presence of a high density of iron-silicide precipitates both before and after phosphorus diffusion. A comparable precipitated iron distribution was measured in a sister wafer after hydrogenation during a firing step. The similar distributions of precipitated iron seen after each step in the solar cell process confirm that the effect of standard gettering on precipitated iron is strongly limited as predicted by simulation. Good agreement between the experimental and simulated data supports the hypothesis that gettering kinetics is governed by not only the total iron concentration but also by the distribution of precipitated iron. Finally, future directions based on the modeling are suggested for the improvement of effective minority carrier lifetime in multicrystalline silicon solar cells.

VentanaTM power train features and performance

Most CPV systems are based on Fresnel lenses. Among these, LPI-patented Fresnel-Köhler (FK) concentrator outstands owing to performance and practical reasons. The VentanaTM power train is the first off-the-shelf commercial product based on the FK and comprises both the primary (POE) lenses (a 36-units 1×1 m2 acrylic panel manufactured by EVONIK and 10×) and glass (or Savosil) secondary optics (SOE). This high concentration optical train (Cg=1,024×, ~250mm optical depth) fits with 5×5 mm2 (at least) solar cells. The optical train is the fruit of a 1-year development that has included design, modeling, prototyping and characterization, and through the process LPI had the opportunity to find out how well the actual performance correlates with models, but also learned practical aspects of a CPV system of this kind, some of which have very positive impact on system performance and reliability.

Performance of UV-enhanced PMMA fresnel lenses and impact on LCOE

Tiny increases in the transmittance of optical materials within a CPV module can have an important impact on the economy of a plant. This is certainly true in systems comprising multi-junction solar cells, whose high performance, based on a balanced photocurrent generation among the series-connected junctions, is very sensitive to spectrum variations. Every efficiency point gained causes not only an increase in the kilowatts hour produced, but a higher benefit on it, since the difference between electricity tariff and Levelized Cost of Electricity (LCOE) rises. This work studies the impact on the LCOE of a plant based on modules comprising PMMA lenses of two different types, standard UV blocking grade which is normally used for outdoor applications at high DNI climate and a specialty stabilized UV-enhanced transmittance acrylic (see Figure 1). Energy production will be compared for these two systems throughout the year at different sites to analyze when (season, time of the day) and where the usage of the enhanced PMMA is justified.

Experimental confirmation of FK concentrator insensitivity to chromatic aberrations

The FK concentrator has demonstrated during the last years that compares very well with other Fresnel-based concentrator optics for CPV. There are several features that provide the FK high performance: (1) high optical efficiency; (2) large tolerance to tracking misalignment and manufacturing errors, thanks to a high CAP (Concentration-Acceptance Product); (3) good irradiance uniformity and low chromatic dispersion on the cell surface. Non-uniformities in terms of absolute irradiance and spectral content produced by conventional CPV systems can originate electrical losses in multi-junction (MJ) solar cells. The aim of this work is to analyze the influence of these non-uniformities in the FK concentrator performance and how FK concentrator provides high electrical efficiencies thanks to its insensitivity to chromatic aberrations, especially when components move away from the module nominal position due to manufacturing misalignments. This analysis has been done here by means of both, experimental on-sun measurements and simulations based on 3D fully distributed circuit model for MJ cells.

Outline of Europe-Japan collaborative research on concentrator photovoltaics

The Europe-Japan Collaborative Research Project on Concentrator Photovoltaics (CPV) has been initiated under support by the EC (European Commission) and NEDO (New Energy and Industrial Technology Development Organization) since June 2011. This is project (NGCPV Project; a New Generation of Concentrator PhotoVoltaic cells, modules and systems) is aiming to accelerate the move to very high efficiency and lower cost CPV technologies and to enhance widespread deployment of CPV systems. 7 organizations such as UPM, FhG-ISE Imperial College, BSQ, CEA-INES, ENEA, and PSE in Europe and 9 organizations such as TTI, Univ. Tokyo, AIST, Sharp Co. Daido Steel Co., Kobe Univ., Miyazaki Univ., Asahi Kasei Co., and Takano Co. participate in this project. The targets of this project are 1) to develop world-record efficiency CPV cells of more than 45%, 2) to develop world-record efficiency CPV modules of 35%, 3) to establish standard measurements of CPV cells and modules, 4) to install 50kW CPV system in Spain, to carry out field test of CPV system and to manage power generation of CPV systems, and 5) to develop high-efficiency and low-cost new materials and structure cells such as III-V-N, III-V-on-Si tandem, quantum dots and wells. This paper presents outline of this project and most recent results such as world record efficiency (37.9% under 1-sun) cell and high-efficiency (43.5% under 240-306 suns) concentrator cell with inverted epitaxial grown InGaP/GaAs/InGaAs 3-junction solar cells.

Estudio de las propiedades mecánicas de obleas de silicio

En esta tesis se propone un procedimiento para evaluar la resistencia mecánica de obleas de silicio cristalino y se aplica en diferentes casos válidos para la industria. En el sector de la industria fotovoltaica predomina la tecnología basada en paneles de silicio cristalino. Estos paneles están compuestos por células solares conectadas en serie y estas células se forman a partir de obleas de silicio. Con el objetivo de disminuir el coste del panel, en los últimos años se ha observado una clara tendencia a la reducción del espesor de las obleas. Esta reducción del espesor modifica la rigidez de las obleas por lo que ha sido necesario modificar la manera tradicional de manipularlas con el objetivo de mantener un bajo ratio de rotura. Para ello, es necesario conocer la resistencia mecánica de las obleas. En la primera parte del trabajo se describen las obleas de silicio, desde su proceso de formación hasta sus propiedades mecánicas. Se muestra la influencia de la estructura cristalográfica en la resistencia y en el comportamiento ya que el cristal de silicio es anisótropo. Se propone también el método de caracterización de la resistencia. Se utiliza un criterio probabilista basado en los métodos de dimensionamiento de materiales frágiles en el que la resistencia queda determinada por los parámetros de la ley de Weibull triparamétrica. Se propone el procedimiento para obtener estos parámetros a partir de campañas de ensayos, modelización numérica por elementos finitos y un algoritmo iterativo de ajuste de los resultados. En la segunda parte de la tesis se describen los diferentes tipos de ensayos que se suelen llevar a cabo con este material. Se muestra además, para cada uno de los ensayos descritos, un estudio comparativo de diferentes modelos de elementos finitos simulando los ensayos. Se comparan tanto los resultados aportados por cada modelo como los tiempos de cálculo. Por último, se presentan tres aplicaciones diferentes donde se ha aplicado este procedimiento de estudio. La primera aplicación consiste en la comparación de la resistencia mecánica de obleas de silicio en función del método de crecimiento del lingote. La resistencia de las tradicionales obleas monocristalinas obtenidas por el método Czochralski y obleas multicristalinas es comparada con las novedosas obleas quasi-monocristalinas obtenidas por métodos de fundición. En la segunda aplicación se evalúa la profundidad de las grietas generadas en el proceso de corte del lingote en obleas. Este estudio se realiza de manera indirecta: caracterizando la resistencia de grupos de obleas sometidas a baños químicos de diferente duración. El baño químico reduce el espesor de las obleas eliminando las capas más dañadas. La resistencia de cada grupo es analizada y la comparación permite obtener la profundidad de las grietas generadas en el proceso de corte. Por último, se aplica este procedimiento a un grupo de obleas con características muy especiales: obleas preparadas para formar células de contacto posterior EWT. Estas obleas presentan miles de agujeros que las debilitan considerablemente. Se aplica el procedimiento de estudio propuesto con un grupo de estas obleas y se compara la resistencia obtenida con un grupo de referencia. Además, se propone un método simplificado de estudio basado en la aplicación de una superficie de intensificación de tensiones. ABSTRACT In this thesis, a procedure to evaluate the mechanical strength of crystalline silicon wafers is proposed and applied in different studies. The photovoltaic industry is mainly based on crystalline silicon modules. These modules are composed of solar cells which are based on silicon wafers. Regarding the cost reduction of solar modules, a clear tendency to use thinner wafers has been observed during last years. Since the stiffness varies with thickness, the manipulation techniques need to be modified in order to guarantee a low breakage rate. To this end, the mechanical strength has to be characterized correctly. In the first part of the thesis, silicon wafers are described including the different ways to produce them and the mechanical properties of interest. The influence of the crystallographic structure in the strength and the behaviour (the anisotropy of the silicon crystal) is shown. In addition, a method to characterize the mechanical strength is proposed. This probabilistic procedure is based on methods to characterize brittle materials. The strength is characterized by the values of the three parameters of the Weibull cumulative distribution function (cdf). The proposed method requires carrying out several tests, to simulate them through Finite Element models and an iterative algorithm in order to estimate the parameters of the Weibull cdf. In the second part of the thesis, the different types of test that are usually employed with these samples are described. Moreover, different Finite Element models for the simulation of each test are compared regarding the information supplied by each model and the calculation times. Finally, the method of characterization is applied to three examples of practical applications. The first application consists in the comparison of the mechanical strength of silicon wafers depending on the ingot growth method. The conventional monocrystalline wafers based on the Czochralski method and the multicrystalline ones are compared with the new quasi-monocrystalline substrates. The second application is related to the estimation of the crack length caused by the drilling process. An indirect way is used to this end: several sets of silicon wafers are subjected to chemical etchings of different duration. The etching procedure reduces the thickness of the wafers removing the most damaged layers. The strength of each set is obtained by means of the proposed method and the comparison permits to estimate the crack length. At last, the procedure is applied to determine the strength of wafers used for the design of back-contact cells of type ETW. These samples are drilled in a first step resulting in silicon wafers with thousands of tiny holes. The strength of the drilled wafers is obtained and compared with the one of a standard set without holes. Moreover, a simplified approach based on a stress intensification surface is proposed.

Lifetime improvement after phosphorous diffusion gettering on upgraded metallurgical grade silicon

Wide experimental evidence of the phosphorus diffusion gettering beneficial effect on solar grade silicon is found by measuring electron effective lifetime and interstitial iron concentration in as-grown and post processed samples from two ingots of upgraded metallurgical grade silicon produced by Ferrosolar. Results after two different P-diffusion processes are compared: P emitter diffusion at 850ºC followed by fast cool-down (called “standard process”) or followed by slow cool-down (called “extended process”). It is shown that final lifetimes of this low cost material are in the range of those obtained with conventional material. The extended process can be beneficial for wafers with specific initial distribution and concentration of iron, e.g. materials with high concentration of big Fe precipitates, while for other cases the standard process is enough efficient. An analysis based on the comparison of measured lifetime and dissolved iron concentration with theoretical calculations helps to infer the initial iron distribution and concentration, and according to that, choose the more effective type of gettering.

Experimental and numerical study of cw green laser crystallization of a-Si:H thin films

Crystallization and grain growth technique of thin film silicon are among the most promising methods for improving efficiency and lowering cost of solar cells. A major advantage of laser crystallization and annealing over conventional heating methods is its ability to limit rapid heating and cooling to thin surface layers. Laser energy is used to heat the amorphous silicon thin film, melting it and changing the microstructure to polycrystalline silicon (poly-Si) as it cools. Depending on the laser density, the vaporization temperature can be reached at the center of the irradiated area. In these cases ablation effects are expected and the annealing process becomes ineffective. The heating process in the a-Si thin film is governed by the general heat transfer equation. The two dimensional non-linear heat transfer equation with a moving heat source is solve numerically using the finite element method (FEM), particularly COMSOL Multiphysics. The numerical model help to establish the density and the process speed range needed to assure the melting and crystallization without damage or ablation of the silicon surface. The samples of a-Si obtained by physical vapour deposition were irradiated with a cw-green laser source (Millennia Prime from Newport-Spectra) that delivers up to 15 W of average power. The morphology of the irradiated area was characterized by confocal laser scanning microscopy (Leica DCM3D) and Scanning Electron Microscopy (SEM Hitachi 3000N). The structural properties were studied by micro-Raman spectroscopy (Renishaw, inVia Raman microscope).