Determination of spectral variations by means of component cells useful for CPV rating and design

A methodology is presented to determine both the short-term and the long-term influence of the spectral variations on the performance of Multi-Junction (MJ) solar cells and Concentrating "This is the peer reviewed version of the following article: R. Núñez, C. Domínguez, S. Askins, M. Victoria, R. Herrero, I. Antón, and G. Sala, “Determination of spectral variations by means of component cells useful for CPV rating and design,” Prog. Photovolt: Res. Appl., 2015., which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/pip.2715/full. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving [http://olabout.wiley.com/WileyCDA/Section/id-820227.html#terms]." Photovoltaic (CPV) modules. Component cells with the same optical behavior as MJ solar cells are used to characterize the spectrum. A set of parameters, namely Spectral Matching Ratios (SMRs), is used to characterize spectrally a particular Direct Normal Irradiance (DNI) by comparison to the reference spectrum (AM1.5D-ASTM-G173-03). Furthermore, the spectrally corrected DNI for a given MJ solar cell technology is defined providing a way to estimate the losses associated to the spectral variations. The last section analyzes how the spectrum evolves throughout a year in a given place and the set of SMRs representative for that location are calculated. This information can be used to maximize the energy harvested by the MJ solar cell throughout the year. As an example, three years of data recorded in Madrid shows that losses lower than 5% are expected due to current mismatch for state-of-the-art MJ solar cells.

Atmospheric parameters, spectral indexes and their relation to CPV spectral performance

Air Mass and atmosphere components (basically aerosol (AOD) and precipitable water (PW)) define the absorption of the sunlight that arrive to Earth. Radiative models such as SMARTS or MODTRAN use these parameters to generate an equivalent spectrum. However, complex and expensive instruments (as AERONET network devices) are needed to obtain AOD and PW. On the other hand, the use of isotype cells is a convenient way to characterize spectrally a place for CPV considering that they provide the photocurrent of the different internal subcells individually. Crossing data from AERONET station and a Tri-band Spectroheliometer, a model that correlates Spectral Mismatch Ratios and atmospheric parameters is proposed. Considering the amount of stations of AERONET network, this model may be used to estimate the spectral influence on energy performance of CPV systems close to all the stations worldwide.

Spectral study and classification of worldwide locations considering several multijunction solar cell technologies

Multi-junction solar cells are widely used in high-concentration photovoltaic systems (HCPV) attaining the highest efficiencies in photovoltaic energy generation. This technology is more dependent on the spectral variations of the impinging Direct Normal Irradiance (DNI) than conventional photovoltaics based on silicon solar cells and consequently demands a deeper knowledge of the solar resource characteristics. This article explores the capabilities of spectral indexes, namely, spectral matching ratios (SMR), to spectrally characterize the annual irradiation reaching a particular location on the Earth and to provide the necessary information for the spectral optimization of a MJ solar cell in that location as a starting point for CPV module spectral tuning. Additionally, the relationship between such indexes and the atmosphere parameters, such as the aerosol optical depth (AOD), precipitable water (PW), and air mass (AM), is discussed using radiative transfer models such as SMARTS to generate the spectrally-resolved DNI. The network of ground-based sun and sky-scanning radiometers AERONET (AErosol RObotic NETwork) is exploited to obtain the atmosphere parameters for a selected bunch of 34 sites worldwide. Finally, the SMR indexes are obtained for every location, and a comparative analysis is carried out for four architectures of triple junction solar cells, covering both lattice match and metamorphic technologies. The differences found among cell technologies are much less significant than among locations.

Adaptation Strategies for Discontinuous Galerkin Spectral Element Methods by means of Truncation Error Estimations

In this work a p-adaptation (modification of the polynomial order) strategy based on the minimization of the truncation error is developed for high order discontinuous Galerkin methods. The truncation error is approximated by means of a truncation error estimation procedure and enables the identification of mesh regions that require adaptation. Three truncation error estimation approaches are developed and termed a posteriori, quasi-a priori and quasi-a priori corrected. Fine solutions, which are obtained by enriching the polynomial order, are required to solve the numerical problem with adequate accuracy. For the three truncation error estimation methods the former needs time converged solutions, while the last two rely on non-converged solutions, which lead to faster computations. Based on these truncation error estimation methods, algorithms for mesh adaptation were designed and tested. Firstly, an isotropic adaptation approach is presented, which leads to equally distributed polynomial orders in different coordinate directions. This first implementation is improved by incorporating a method to extrapolate the truncation error. This results in a significant reduction of computational cost. Secondly, the employed high order method permits the spatial decoupling of the estimated errors and enables anisotropic p-adaptation. The incorporation of anisotropic features leads to meshes with different polynomial orders in the different coordinate directions such that flow-features related to the geometry are resolved in a better manner. These adaptations result in a significant reduction of degrees of freedom and computational cost, while the amount of improvement depends on the test-case. Finally, this anisotropic approach is extended by using error extrapolation which leads to an even higher reduction in computational cost. These strategies are verified and compared in terms of accuracy and computational cost for the Euler and the compressible Navier-Stokes equations. The main result is that the two quasi-a priori methods achieve a significant reduction in computational cost when compared to a uniform polynomial enrichment. Namely, for a viscous boundary layer flow, we obtain a speedup of a factor of 6.6 and 7.6 for the quasi-a priori and quasi-a priori corrected approaches, respectively. RESUMEN En este trabajo se ha desarrollado una estrategia de adaptación-p (modificación del orden polinómico) para métodos Galerkin discontinuo de alto orden basada en la minimización del error de truncación. El error de truncación se estima utilizando el método tau-estimation. El estimador permite la identificación de zonas de la malla que requieren adaptación. Se distinguen tres técnicas de estimación: a posteriori, quasi a priori y quasi a priori con correción. Todas las estrategias requieren una solución obtenida en una malla fina, la cual es obtenida aumentando de manera uniforme el orden polinómico. Sin embargo, mientras que el primero requiere que esta solución esté convergida temporalmente, el resto utiliza soluciones no convergidas, lo que se traduce en un menor coste computacional. En este trabajo se han diseñado y probado algoritmos de adaptación de malla basados en métodos tau-estimation. En primer lugar, se presenta un algoritmo de adaptacin isótropo, que conduce a discretizaciones con el mismo orden polinómico en todas las direcciones espaciales. Esta primera implementación se mejora incluyendo un método para extrapolar el error de truncación. Esto resulta en una reducción significativa del coste computacional. En segundo lugar, el método de alto orden permite el desacoplamiento espacial de los errores estimados, permitiendo la adaptación anisotropica. Las mallas obtenidas mediante esta técnica tienen distintos órdenes polinómicos en cada una de las direcciones espaciales. La malla final tiene una distribución óptima de órdenes polinómicos, los cuales guardan relación con las características del flujo que, a su vez, depenen de la geometría. Estas técnicas de adaptación reducen de manera significativa los grados de libertad y el coste computacional. Por último, esta aproximación anisotropica se extiende usando extrapolación del error de truncación, lo que conlleva un coste computational aún menor. Las estrategias se verifican y se comparan en téminors de precisión y coste computacional utilizando las ecuaciones de Euler y Navier Stokes. Los dos métodos quasi a priori consiguen una reducción significativa del coste computacional en comparación con aumento uniforme del orden polinómico. En concreto, para una capa límite viscosa, obtenemos una mejora en tiempo de computación de 6.6 y 7.6 respectivamente, para las aproximaciones quasi-a priori y quasi-a priori con corrección.