Storage requirements for PV power ramp-rate control

Short-term variability in the power generated by large grid-connected photovoltaic (PV) plants can negatively affect power quality and the network reliability. New grid-codes require combining the PV generator with some form of energy storage technology in order to reduce short-term PV power fluctuation. This paper proposes an effective method in order to calculate, for any PV plant size and maximum allowable ramp-rate, the maximum power and the minimum energy storage requirements alike. The general validity of this method is corroborated with extensive simulation exercises performed with real 5-s one year data of 500 kW inverters at the 38.5 MW Amaraleja (Portugal) PV plant and two other PV plants located in Navarra (Spain), at a distance of more than 660 km from Amaraleja.

Equipment and procedures for ON-SITE testing of PV plants and BIPV

Actual system performance of a PV system can differ from its expected behaviour.. This is the main reason why the performance of PV systems should be monitored, analyzed and, if needed, improved on. Some of the current testing procedures relating to the electrical behaviour of PV systems are appropriated for detecting electrical performance losses, but they are not well-suited to reveal hidden defects in the modules of PV plants and BIPV, which can lead to future losses. This paper reports on the tests and procedures used to evaluate the performance of PV systems, and especially on a novel procedure for quick on-site measurements and defect recognition caused by overheating in PV modules located in operating PV installations.

Automatic fault detection on BIPV systems without solar irradiation data

BIPV systems are small PV generation units spread out over the territory, and whose characteristics are very diverse. This makes difficult a cost-effective procedure for monitoring, fault detection, performance analyses, operation and maintenance. As a result, many problems affecting BIPV systems go undetected. In order to carry out effective automatic fault detection procedures, we need a performance indicator that is reliable and that can be applied on many PV systems at a very low cost. The existing approaches for analyzing the performance of PV systems are often based on the Performance Ratio (PR), whose accuracy depends on good solar irradiation data, which in turn can be very difficult to obtain or cost-prohibitive for the BIPV owner. We present an alternative fault detection procedure based on a performance indicator that can be constructed on the sole basis of the energy production data measured at the BIPV systems. This procedure does not require the input of operating conditions data, such as solar irradiation, air temperature, or wind speed. The performance indicator, called Performance to Peers (P2P), is constructed from spatial and temporal correlations between the energy output of neighboring and similar PV systems. This method was developed from the analysis of the energy production data of approximately 10,000 BIPV systems located in Europe. The results of our procedure are illustrated on the hourly, daily and monthly data monitored during one year at one BIPV system located in the South of Belgium. Our results confirm that it is possible to carry out automatic fault detection procedures without solar irradiation data. P2P proves to be more stable than PR most of the time, and thus constitutes a more reliable performance indicator for fault detection procedures. We also discuss the main limitations of this novel methodology, and we suggest several future lines of research that seem promising to improve on these procedures.

3D simulation of complex shading affecting PV systems taking benefit from the power of graphics cards developed for the video game industry

Shading reduces the power output of a photovoltaic (PV) system. The design engineering of PV systems requires modeling and evaluating shading losses. Some PV systems are affected by complex shading scenes whose resulting PV energy losses are very difficult to evaluate with current modeling tools. Several specialized PV design and simulation software include the possibility to evaluate shading losses. They generally possess a Graphical User Interface (GUI) through which the user can draw a 3D shading scene, and then evaluate its corresponding PV energy losses. The complexity of the objects that these tools can handle is relatively limited. We have created a software solution, 3DPV, which allows evaluating the energy losses induced by complex 3D scenes on PV generators. The 3D objects can be imported from specialized 3D modeling software or from a 3D object library. The shadows cast by this 3D scene on the PV generator are then directly evaluated from the Graphics Processing Unit (GPU). Thanks to the recent development of GPUs for the video game industry, the shadows can be evaluated with a very high spatial resolution that reaches well beyond the PV cell level, in very short calculation times. A PV simulation model then translates the geometrical shading into PV energy output losses. 3DPV has been implemented using WebGL, which allows it to run directly from a Web browser, without requiring any local installation from the user. This also allows taken full benefits from the information already available from Internet, such as the 3D object libraries. This contribution describes, step by step, the method that allows 3DPV to evaluate the PV energy losses caused by complex shading. We then illustrate the results of this methodology to several application cases that are encountered in the world of PV systems design. Keywords: 3D, modeling, simulation, GPU, shading, losses, shadow mapping, solar, photovoltaic, PV, WebGL

Characterisation of the operation & maintenance phase in PV rural electrification programmes

Con 1.300 millones de personas en el mundo sin acceso a la electricidad (la mayoría en entornos rurales de países empobrecidos), la energía solar fotovoltaica constituye una solución viable técnica y económicamente para electrificar las zonas más remotas del planeta donde las redes eléctricas convencionales no llegan. Casi todos los países en el mundo han desarrollado algún tipo de programa de electrificación fotovoltaica rural durante los últimos 40 años, principalmente los países más pobres, donde a través de diferentes modelos de financiación, se han instalado millones de sistemas solares domiciliarios (pequeños sistemas fotovoltaicos para uso doméstico). Durante este largo período, se han ido superando muchas barreras, como la mejora de la calidad de los sistemas fotovoltaicos, la reducción de costes, la optimización del diseño y del dimensionado de los sistemas, la disponibilidad financiera para implantar programas de electrificación rural, etc. Gracias a esto, la electrificación rural descentralizada ha experimentado recientemente un salto de escala caracterizada por la implantación de grandes programas con miles de sistemas solares domiciliarios e integrando largos períodos de mantenimiento. Muchos de estos grandes programas se están llevando a cabo con limitado éxito, ya que generalmente parten de supuestos e hipótesis poco contrastadas con la realidad, comprometiendo así un retorno económico que permita el desarrollo de esta actividad a largo plazo. En este escenario surge un nuevo reto: el de cómo garantizar la sostenibilidad de los grandes programas de electrificación rural fotovoltaica. Se argumenta que la principal causa de esta falta de rentabilidad es el imprevisto alto coste de la fase de operación y mantenimiento. Cuestiones clave tales como la estructura de costes de operación y mantenimiento o la fiabilidad de los componentes del sistema fotovoltaico no están bien caracterizados hoy en día. Esta situación limita la capacidad de diseñar estructuras de mantenimiento capaces de asegurar la sostenibilidad y la rentabilidad del servicio de operación y mantenimiento en estos programas. Esta tesis doctoral tiene como objetivo responder a estas cuestiones. Se ha realizado varios estudios sobre la base de un gran programa de electrificación rural fotovoltaica real llevado a cabo en Marruecos con más de 13.000 sistemas solares domiciliarios instalados. Sobre la base de este programa se ha hecho una evaluación en profundidad de la fiabilidad de los sistemas solares a partir de los datos de mantenimiento recogidos durante 5 años con más de 80.000 inputs. Los resultados han permitido establecer las funciones de fiabilidad de los equipos tal y como se comportan en condiciones reales de operación, las tasas de fallos y los tiempos medios hasta el fallo para los principales componentes del sistema, siendo este el primer caso de divulgación de resultados de este tipo en el campo de la electrificación rural fotovoltaica. Los dos principales componentes del sistema solar domiciliario, la batería y el módulo fotovoltaico, han sido analizados en campo a través de una muestra de 41 sistemas trabajando en condiciones reales pertenecientes al programa solar marroquí. Por un lado se ha estudiado la degradación de la capacidad de las baterías y por otro la degradación de potencia de los módulos fotovoltaicos. En el caso de las baterías, los resultados nos han permitido caracterizar la curva de degradación en capacidad llegando a obtener una propuesta de nueva definición del umbral de vida útil de las baterías en electrificación rural. También sobre la base del programa solar de Marruecos se ha llevado a cabo un estudio de caracterización de los costes reales de operación y mantenimiento a partir de la base de datos de contabilidad del programa registrados durante 5 años. Los resultados del estudio han permitido definir cuáles son costes que más incidencia tienen en el coste global. Se han obtenido los costes unitarios por sistema instalado y se han calculado los montantes de las cuotas de mantenimiento de los usuarios para garantizar la rentabilidad de la operación y mantenimiento. Finalmente, se propone un modelo de optimización matemática para diseñar estructuras de mantenimiento basado en los resultados de los estudios anteriores. La herramienta, elaborada mediante programación lineal entera mixta, se ha aplicado al programa marroquí con el fin de validar el modelo propuesto. ABSTRACT With 1,300 million people worldwide deprived of access to electricity (mostly in rural environments), photovoltaic solar energy has proven to be a cost‐effective solution and the only hope for electrifying the most remote inhabitants of the planet, where conventional electric grids do not reach because they are unaffordable. Almost all countries in the world have had some kind of rural photovoltaic electrification programme during the past 40 years, mainly the poorer countries, where through different organizational models, millions of solar home systems (small photovoltaic systems for domestic use) have been installed. During this long period, many barriers have been overcome, such as quality enhancement, cost reduction, the optimization of designing and sizing, financial availability, etc. Thanks to this, decentralized rural electrification has recently experienced a change of scale characterized by new programmes with thousands of solar home systems and long maintenance periods. Many of these large programmes are being developed with limited success, as they have generally been based on assumptions that do not correspond to reality, compromising the economic return that allows long term activity. In this scenario a new challenge emerges, which approaches the sustainability of large programmes. It is argued that the main cause of unprofitability is the unexpected high cost of the operation and maintenance of the solar systems. In fact, the lack of a paradigm in decentralized rural services has led to many private companies to carry out decentralized electrification programmes blindly. Issues such as the operation and maintenance cost structure or the reliability of the solar home system components have still not been characterized. This situation does not allow optimized maintenance structure to be designed to assure the sustainability and profitability of the operation and maintenance service. This PhD thesis aims to respond to these needs. Several studies have been carried out based on a real and large photovoltaic rural electrification programme carried out in Morocco with more than 13,000 solar home systems. An in‐depth reliability assessment has been made from a 5‐year maintenance database with more than 80,000 maintenance inputs. The results have allowed us to establish the real reliability functions, the failure rate and the main time to failure of the main components of the system, reporting these findings for the first time in the field of rural electrification. Both in‐field experiments on the capacity degradation of batteries and power degradation of photovoltaic modules have been carried out. During the experiments both samples of batteries and modules were operating under real conditions integrated into the solar home systems of the Moroccan programme. In the case of the batteries, the results have enabled us to obtain a proposal of definition of death of batteries in rural electrification. A cost assessment of the Moroccan experience based on a 5‐year accounting database has been carried out to characterize the cost structure of the programme. The results have allowed the major costs of the photovoltaic electrification to be defined. The overall cost ratio per installed system has been calculated together with the necessary fees that users would have to pay to make the operation and maintenance affordable. Finally, a mathematical optimization model has been proposed to design maintenance structures based on the previous study results. The tool has been applied to the Moroccan programme with the aim of validating the model.

Silicon PV module customization using laser technology for new BIPV applications

It is well known that lasers have helped to increase efficiency and to reduce production costs in the photovoltaic (PV) sector in the last two decades, appearing in most cases as the ideal tool to solve some of the critical bottlenecks of production both in thin film (TF) and crystalline silicon (c-Si) technologies. The accumulated experience in these fields has brought as a consequence the possibility of using laser technology to produce new Building Integrated Photovoltaics (BIPV) products with a high degree of customization. However, to produce efficiently these personalized products it is necessary the development of optimized laser processes able to transform standard products in customized items oriented to the BIPV market. In particular, the production of semitransparencies and/or freeform geometries in TF a-Si modules and standard c-Si modules is an application of great interest in this market. In this work we present results of customization of both TF a-Si modules and standard monocrystalline (m-Si) and policrystalline silicon (pc-Si) modules using laser ablation and laser cutting processes. A discussion about the laser processes parameterization to guarantee the functionality of the device is included. Finally some examples of final devices are presented with a full discussion of the process approach used in their fabrication.

A multi-level analysis of innovation diffusion: The case of solar photovoltaic systems in Germany and the disillusion of grid parity

¿Suministrarán las fuentes de energía renovables toda la energía que el mundo necesita algún día? Algunos argumentan que sí, mientras que otros dicen que no. Sin embargo, en algunas regiones del mundo, la producción de electricidad a través de fuentes de energía renovables ya está en una etapa prometedora de desarrollo en la que su costo de generación de electricidad compite con fuentes de electricidad convencionales, como por ejemplo la paridad de red. Este logro ha sido respaldado por el aumento de la eficiencia de la tecnología, la reducción de los costos de producción y, sobre todo, los años de intervenciones políticas de apoyo financiero. La difusión de los sistemas solares fotovoltaicos (PV) en Alemania es un ejemplo relevante. Alemania no sólo es el país líder en términos de capacidad instalada de sistemas fotovoltaicos (PV) en todo el mundo, sino también uno de los países pioneros donde la paridad de red se ha logrado recientemente. No obstante, podría haber una nube en el horizonte. La tasa de difusión ha comenzado a declinar en muchas regiones. Además, las empresas solares locales – que se sabe son importantes impulsores de la difusión – han comenzado a enfrentar dificultades para manejar sus negocios. Estos acontecimientos plantean algunas preguntas importantes: ¿Es ésta una disminución temporal en la difusión? ¿Los adoptantes continuarán instalando sistemas fotovoltaicos? ¿Qué pasa con los modelos de negocio de las empresas solares locales? Con base en el caso de los sistemas fotovoltaicos en Alemania a través de un análisis multinivel y dos revisiones literarias complementarias, esta tesis doctoral extiende el debate proporcionando riqueza múltiple de datos empíricos en un conocimiento de contexto limitado. El primer análisis se basa en la perspectiva del adoptante, que explora el nivel "micro" y el proceso social que subyace a la adopción de los sistemas fotovoltaicos. El segundo análisis es una perspectiva a nivel de empresa, que explora los modelos de negocio de las empresas y sus roles impulsores en la difusión de los sistemas fotovoltaicos. El tercero análisis es una perspectiva regional, la cual explora el nivel "meso", el proceso social que subyace a la adopción de sistemas fotovoltaicos y sus técnicas de modelado. Los resultados incluyen implicaciones tanto para académicos como políticos, no sólo sobre las innovaciones en energía renovable relativas a la paridad de red, sino también, de manera inductiva, sobre las innovaciones ambientales impulsadas por las políticas que logren la competitividad de costes. ABSTRACT Will renewable energy sources supply all of the world energy needs one day? Some argue yes, while others say no. However, in some regions of the world, the electricity production through renewable energy sources is already at a promising stage of development at which their electricity generation costs compete with conventional electricity sources’, i.e., grid parity. This achievement has been underpinned by the increase of technology efficiency, reduction of production costs and, above all, years of policy interventions of providing financial support. The diffusion of solar photovoltaic (PV) systems in Germany is an important frontrunner case in point. Germany is not only the top country in terms of installed PV systems’ capacity worldwide but also one of the pioneer countries where the grid parity has recently been achieved. However, there might be a cloud on the horizon. The diffusion rate has started to decline in many regions. In addition, local solar firms – which are known to be important drivers of diffusion – have started to face difficulties to run their businesses. These developments raise some important questions: Is this a temporary decline on diffusion? Will adopters continue to install PV systems? What about the business models of the local solar firms? Based on the case of PV systems in Germany through a multi-level analysis and two complementary literature reviews, this PhD Dissertation extends the debate by providing multiple wealth of empirical details in a context-limited knowledge. The first analysis is based on the adopter perspective, which explores the “micro” level and the social process underlying the adoption of PV systems. The second one is a firm-level perspective, which explores the business models of firms and their driving roles in diffusion of PV systems. The third one is a regional perspective, which explores the “meso” level, i.e., the social process underlying the adoption of PV systems and its modeling techniques. The results include implications for both scholars and policymakers, not only about renewable energy innovations at grid parity, but also in an inductive manner, about policy-driven environmental innovations that achieve the cost competiveness.

Understanding and improving the chemical vapor deposition process for solar grade silicon production

Esta Tesis Doctoral se centra en la investigación del proceso de producción de polisilicio para aplicaciones fotovoltaicas (FV) por la vía química; mediante procesos de depósito en fase vapor (CVD). El polisilicio para la industria FV recibe el nombre de silicio de grado solar (SoG Si). Por un lado, el proceso que domina hoy en día la producción de SoG Si está basado en la síntesis, destilación y descomposición de triclorosilano (TCS) en un reactor CVD -denominado reactor Siemens-. El material obtenido mediante este proceso es de muy alta pureza, pero a costa de un elevado consumo energético. Así, para alcanzar los dos principales objetivos de la industria FV basada en silicio, bajos costes de producción y bajo tiempo de retorno de la energía invertida en su fabricación, es esencial disminuir el consumo energético de los reactores Siemens. Por otro lado, una alternativa al proceso Siemens considera la descomposición de monosilano (MS) en un reactor de lecho fluidizado (FBR). Este proceso alternativo tiene un consumo energético mucho menor que el de un reactor Siemens, si bien la calidad del material resultante es también menor; pero ésta puede ser suficiente para la industria FV. A día de hoy los FBR deben aún abordar una serie de retos para que su menor consumo energético sea una ventaja suficiente comparada con otras desventajas de estos reactores. En resumen, la investigación desarrollada se centra en el proceso de depósito de polysilicio por CVD a partir de TCS -reactor Siemens-; pero también se investiga el proceso de producción de SoG Si en los FBR exponiendo las fortalezas y debilidades de esta alternativa. Para poder profundizar en el conocimiento del proceso CVD para la producción de polisilicio es clave el conocimiento de las reacciones químicas fundamentales y cómo éstas influencian la calidad del producto resultante, al mismo tiempo que comprender los fenómenos responsables del consumo energético. Por medio de un reactor Siemens de laboratorio en el que se llevan a cabo un elevado número de experimentos de depósito de polisilicio de forma satisfactoria se adquiere el conocimiento previamente descrito. Se pone de manifiesto la complejidad de los reactores CVD y de los problemas asociados a la pérdidas de calor de estos procesos. Se identifican las contribuciones a las pérdidas de calor de los reactores CVD, éstas pérdidas de calor son debidas principalmente a los fenómenos de radiación y, conducción y convección vía gases. En el caso de los reactores Siemens el fenómeno que contribuye en mayor medida al alto consumo energético son las pérdidas de calor por radiación, mientras que en los FBRs tanto la radiación como el calor transferido por transporte másico contribuyen de forma importante. Se desarrolla un modelo teórico integral para el cálculo de las pérdidas de calor en reactores Siemens. Este modelo está formado a su vez por un modelo para la evaluación de las pérdidas de calor por radiación y modelos para la evaluación de las pérdidas de calor por conducción y convección vía gases. Se ponen de manifiesto una serie de limitaciones del modelo de pérdidas de calor por radiación, y se desarrollan una serie de modificaciones que mejoran el modelo previo. El modelo integral se valida por medio un reactor Siemens de laboratorio, y una vez validado se presenta su extrapolación a la escala industrial. El proceso de conversión de TCS y MS a polisilicio se investiga mediante modelos de fluidodinámica computacional (CFD). Se desarrollan modelados CFD para un reactor Siemens de laboratorio y para un prototipo FBR. Los resultados obtenidos mediante simulación son comparados, en ambos casos, con resultados experimentales. Los modelos desarrollados se convierten en herramientas para la identificación de aquellos parámetros que tienen mayor influencia en los procesos CVD. En el caso del reactor Siemens, ambos modelos -el modelo integral y el modelado CFD permiten el estudio de los parámetros que afectan en mayor medida al elevado consumo energético, y mediante su análisis se sugieren modificaciones para este tipo de reactores que se traducirían en un menor número de kilovatios-hora consumidos por kilogramo de silicio producido. Para el caso del FBR, el modelado CFD permite analizar el efecto de una serie de parámetros sobre la distribución de temperaturas en el lecho fluidizado; y dicha distribución de temperaturas está directamente relacionada con los principales retos de este tipo de reactores. Por último, existen nuevos conceptos de depósito de polisilicio; éstos se aprovechan de la ventaja teórica de un mayor volumen depositado por unidad de tiempo -cuando una mayor superficie de depósito está disponible- con el objetivo de reducir la energía consumida por los reactores Siemens. Estos conceptos se exploran mediante cálculos teóricos y pruebas en el reactor Siemens de laboratorio. ABSTRACT This Doctoral Thesis comprises research on polysilicon production for photovoltaic (PV) applications through the chemical route: chemical vapor deposition (CVD) process. PV polysilicon is named solar grade silicon (SoG Si). On the one hand, the besetting CVD process for SoG Si production is based on the synthesis, distillation, and decomposition of thriclorosilane (TCS) in the so called Siemens reactor; high purity silicon is obtained at the expense of high energy consumption. Thus, lowering the energy consumption of the Siemens process is essential to achieve the two wider objectives for silicon-based PV technology: low production cost and low energy payback time. On the other hand, a valuable variation of this process considers the use of monosilane (MS) in a fluidized bed reactor (FBR); lower output material quality is obtained but it may fulfil the requirements for the PV industry. FBRs demand lower energy consumption than Siemens reactors but further research is necessary to address the actual challenges of these reactors. In short, this work is centered in polysilicon CVD process from TCS -Siemens reactor-; but it also offers insights on the strengths and weaknesses of the FBR for SoG Si production. In order to aid further development in polysilicon CVD is key the understanding of the fundamental reactions and how they influence the product quality, at the same time as to comprehend the phenomena responsible for the energy consumption. Experiments conducted in a laboratory Siemens reactor prove the satisfactory operation of the prototype reactor, and allow to acquire the knowledge that has been described. Complexity of the CVD reactors is stated and the heat loss problem associated with polysilicon CVD is addressed. All contributions to the energy consumption of Siemens reactors and FBRs are put forward; these phenomena are radiation and, conduction and convection via gases heat loss. In a Siemens reactor the major contributor to the energy consumption is radiation heat loss; in case of FBRs radiation and heat transfer due to mass transport are both important contributors. Theoretical models for radiation, conduction and convection heat loss in a Siemens reactor are developed; shaping a comprehensive theoretical model for heat loss in Siemens reactors. Limitations of the radiation heat loss model are put forward, and a novel contribution to the existing model is developed. The comprehensive model for heat loss is validated through a laboratory Siemens reactor, and results are scaled to industrial reactors. The process of conversion of TCS and MS gases to solid polysilicon is investigated by means of computational fluid-dynamics models. CFD models for a laboratory Siemens reactor and a FBR prototype are developed. Simulated results for both CVD prototypes are compared with experimental data. The developed models are used as a tool to investigate the parameters that more strongly influence both processes. For the Siemens reactors, both, the comprehensive theoretical model and the CFD model allow to identify the parameters responsible for the great power consumption, and thus, suggest some modifications that could decrease the ratio kilowatts-hour per kilogram of silicon produced. For the FBR, the CFD model allows to explore the effect of a number of parameters on the thermal distribution of the fluidized bed; that is the main actual challenge of these type of reactors. Finally, there exist new deposition surface concepts that take advantage of higher volume deposited per time unit -when higher deposition area is available- trying to reduce the high energy consumption of the Siemens reactors. These novel concepts are explored by means of theoretical calculations and tests in the laboratory Siemens prototype.

Evaluation of the PV cell operation temperature in the process of fast switching to open-circuit mode

A procedure for measuring the overheating temperature (ΔT ) of a p-n junction area in the structure of photovoltaic (PV) cells converting laser or solar radiations relative to the ambient temperature has been proposed for the conditions of connecting to an electric load. The basis of the procedure is the measurement of the open-circuit voltage (VO C ) during the initial time period after the fast disconnection of the external resistive load. The simultaneous temperature control on an external heated part of a PV module gives the means for determining the value of VO C at ambient temperature. Comparing it with that measured after switching OFF the load makes the calculation of ΔT possible. Calibration data on the VO C = f(T ) dependences for single-junction AlGaAs/GaAs and triple-junction InGaP/GaAs/Ge PV cells are presented. The temperature dynamics in the PV cells has been determined under flash illumination and during fast commutation of the load. Temperature measurements were taken in two cases: converting continuous laser power by single-junction cells and converting solar power by triple-junction cells operating in the concentrator modules.

The segmental approximation in multijunction solar cells

The segmental approach has been considered to analyze dark and light I-V curves. The photovoltaic (PV) dependence of the open-circuit voltage (Voc), the maximum power point voltage (Vm), the efficiency (?) on the photogenerated current (Jg), or on the sunlight concentration ratio (X), are analyzed, as well as other photovoltaic characteristics of multijunction solar cells. The characteristics being analyzed are split into monoexponential (linear in the semilogarithmic scale) portions, each of which is characterized by a definite value of the ideality factor A and preexponential current J0. The monoexponentiality ensures advantages, since at many steps of the analysis, one can use the analytical dependences instead of numerical methods. In this work, an experimental procedure for obtaining the necessary parameters has been proposed, and an analysis of GaInP/GaInAs/Ge triple-junction solar cell characteristics has been carried out. It has been shown that up to the sunlight concentration ratios, at which the efficiency maximum is achieved, the results of calculation of dark and light I-V curves by the segmental method fit well with the experimental data. An important consequence of this work is the feasibility of acquiring the resistanceless dark and light I-V curves, which can be used for obtaining the I-V curves characterizing the losses in the transport part of a solar cell.