Analysis of experimental data on diffuse solar radiation in Athens,Greece, for building applications

Proper design and performance prediction of solar energy systems requires accurate information on the availability of solar radiation. The diffuse-to-total radiation correlation, originally developed by Liu and Jordan, has been extensively used as the technique and provided excellent results, although it was latitude dependent and not universally applicable. Thus, diffuse fraction correlations of this type have been developed by few other authors and for different location. This paper presents an analysis of hourly diffuse radiation on a horizontal surface. Hourly pyranometer data from Athens, Greece, are used to establish relationships between the diffuse fraction and the clearness index k _T for hourly and daily values. The results of the proposed equations are then compared with earlier equations. For the urban conditions of Athens the developed correlation fit to the empirical data.     

Analysis of solar radiation measurements at Al-Arish area, North Sinai, Egypt

This paper presents basic data for a five year period from 1986 to 1990 for global and diffuse solar radiation data at Al-Arish (31°04′N, 33°49′E). These data have been processed, analysed, presented, arranged in tables and graphs and discussed. Mean annual monthly and daily total, the diurnal variation and the frequency of daily totals of global solar radiation are computed and discussed. A correlation between the hourly values of the clearness and diffuse index were obtained and the recommended correlation equations were also given. The isopleths of hourly global radiation were also designed and discussed. The frequency distribution and the frequency of extended periods of low radiation income have been studied which are of particular interest in the field performance of solar energy systems.     

Comparative study of various correlations in estimating hourly diffuse fraction of global solar radiation

Proper design and performance predictions of solar energy systems require accurate information on the availability of solar radiation. The diffuse-to-global solar radiation correlation, originally developed by Liu and Jordan, has been extensively used as the technique providing accurate results, although it is latitude dependent. Thus, in the present study, empirical correlations of this type were developed to establish a relationship between the hourly diffuse fraction (k_d) and the hourly clearness index (k_t) using hourly global and diffuse irradiation measurements on a horizontal surface performed at Athalassa, Cyprus. The proposed correlations were compared against 10 models available in the literature in terms of the widely used statistical indicators, rmse, mbe and t test. From this analysis, it can be concluded that the proposed yearly correlation predicts diffuse values accurately, whereas all candidate models examined appear to be location-independent for diffuse irradiation predictions.     

Evaluation of conventional and high-performance routine solar radiation measurements for improved solar resource, climatological trends, and radiative modeling

The solar renewable energy community depends on radiometric measurements and instrumentation for data to design and monitor solar energy systems, and develop and validate solar radiation models. This contribution evaluates the impact of instrument uncertainties contributing to data inaccuracies and their effect on short-term and long-term measurement series, and on radiation model validation studies. For the latter part, transposition (horizontal-to-tilt) models are used as an example. Confirming previous studies, it is found that a widely used pyranometer strongly underestimates diffuse and global radiation, particularly in winter, unless appropriate corrective measures are taken. Other types of measurement problems are also discussed, such as those involved in the indirect determination of direct or diffuse irradiance, and in shadowband correction methods. The sensitivity of the predictions from transposition models to inaccuracies in input radiation data is demonstrated. Caution is therefore issued to the whole community regarding drawing detailed conclusions about solar radiation data without due attention to the data quality issues only recently identified.     

Estimation of the diffuse radiation fraction for hourly,daily and monthly-average global radiation

Hourly pyrheliometer and pyranometer data from four U.S. locations are used to establish a relationship between the hourly diffuse fraction and the hourly clearness index k_T. This relationship is compared to the relationship established by Orgill and Hollands and to a set of data from Highett, Australia, and agreement is within a few percent in both cases. The transient simulation program TRNSYS is used to calculate the annual performance of solar energy systems using several correlations. For the systems investigated, the effect of simulating the random distribution of the hourly diffuse fraction is negligible. A seasonally dependent daily diffuse correlation is developed from the data, and this daily relationship is used to derive a correlation for the monthly-average diffuse fraction.     

Correlation between hourly diffuse and global radiation for New Delhi

Estimation of hourly insolation on tilted surfaces is required in simulation of solar energy systems. This necessitates splitting of hourly global horizontal insolation into diffuse and direct components. Many models have been developed for this purpose, and the aim of this study is to develop a correlation between hourly diffuse ratio and clearness index for New Delhi. The correlation is developed on the basis of measured data for two years. The performance of this correlation was checked by calculating the difference between computed and measured diffuse radiation. The correlation proved to perform quite well. A comparison of the present correlation with those for other locations showed that such correlations are location dependent.     

Statistical properties of hourly global radiation

A model is described which generates synthetic daily sequences of hourly radiation values, on the horizontal plane, for any location, with the daily clearness index K_t as input. The model assumes that for each K_t and solar hour the probability density of the hourly clearness index k_t is (simply) a truncated Gaussian function. A first-order autoregressive model is fitted for the k_t variable, normalised using parametrisations for the time-dependent average and standard deviation values. Values generated by this ARMA (1,0) model can then be transformed backwards to generate synthetic sequances of k_t values. Using a diffuse fraction correlation and a tilted radiation model, the horizontal global data can be transformed to any desired plane, thus providing solar system designers with the necessary hourly data for the accurate sizing of every type of solar system, including stand-alone, high solar fraction and passive ones.     

Solar-energy availability in the north-eastern Arabian peninsula

The solar energy potential of north-east Saudi Arabia is investigated based on measurements of a complete year's data at a coastal location near Dhahran. High resolution, real time solar radiation data were collected and processed. Hourly, daily and monthly statistics of solar radiation were made from the 1 min averaged recorded values. Clearness index is discussed on the basis of hourly, daily and monthly averages. The variation of the diffuse fraction of total radiation is also determined and the results discussed.     

Evaluation of hourly tilted surface radiation models

This study investigates the performance of the isotropic and four anisotropic hourly tilted surface radiation models by using monthly average hourly utilizable energy as a standard of measure. Utilizable energy is the radiation above a specified threshold level. Differences between the utilizable energy measured and the utilizable energy predicted are observed for various surface slope/azimuth orientations and critical radiation levels. Normalized root mean square difference and normalized mean bias difference statistics are formed to quantify the ability of each model to estimate the utilizable energy on a tilted surface. The influence of horizontal diffuse radiation on tilted surface model performance is examined by comparing the predicted utilizable energy on a tilted surface using both measured horizontal diffuse and estimated horizontal diffuse found from diffuse fraction correlations. On an overall basis, the isotropic sky model showed the poorest performance and is not recommended for estimating the hourly radiation on a tilted surface. The anisotropic models have comparable performance to each other. There was no significant degradation of tilted surface model performance when the diffuse radiation is estimated from a diffuse fraction correlation rather than obtained from measurements.     

Estimation of symmetric and asymmetric hourly global and diffuse radiation from daily values

The validity of the correlations[1–3] to estimate the hourly global and diffuse solar radiation components for an independent dataset of fourteen locations is examined in this article. The correlations for the diffuse component[2,3] are found to be in rather poor agreement with the data. An improved correlation for the diffuse component that includes a daily diffuse fraction as a parameter is developed. The influence of this improved correlation on estimating the beam radiation component is examined. A convenient form of describing asymmetry for these three components of solar radiation distribution is proposed and validated.     

Experimental and theoretical investigation of global and diffuse solar radiation in the United Arab Emirates

In the present study, the global, direct and diffuse components of solar radiation as well as temperature, relative humidity and wind speed have been continuously monitored and analysed on an hourly, daily and monthly basis. The monthly average daily total solar radiation varies from 2700 W h/m² in December to 8000 W h/m² in June with an average clearness index of 0.65. Experimental data are compared to the predictions of different theoretical models as functions of declination and hour angles. Correlations are obtained describing the variation of hourly, daily and monthly averages of total and diffuse solar radiation using polynomial expressions. Empirical correlations describing the dependence of the daily average diffuse to total radiation ratio on the clearness index are also obtained. Data for the daily diffuse to total radiation ratio are compared to correlations obtained by other investigators. The comparison shows a reasonable agreement with some scatter due to the seasonal dependence of the correlation. Comparison of calculations with experimental measurements under clear sky conditions show excellent agreement with a maximum error of 8%.     

Estimation of daily diffuse solar radiation in China

Applying the measured global and diffuse solar radiation data from 78 meteorological stations in China, a countrywide general correlation model for calculating the daily diffuse radiation was derived on the basis of Liu and Jordan method. Two widely used statistics: root mean square error and mean bias error were used to assess the performance of the correlation. And the correlation shows good behavior when applied to most of the stations. Subsequently, with the measured data from the 78 stations, an analysis of geographical distribution of solar energy resource in China was also presented in the form of clearness index (the ratio of global solar radiation to extraterrestrial radiation) percentage frequency, and results show that the solar energy resource in western and northern China is relatively abundant.     

Evaluation of decomposition models of various complexity to estimate the direct solar irradiance over Belgium

Solar energy production is directly correlated to the amount of radiation received at a given location. Appropriate information on solar resources is therefore very important for designing and sizing solar energy systems. Concentrated solar power projects and photovoltaic tracking systems rely predominantly on direct normal irradiance (DNI). However, the availability of DNI measurements from surface observation stations has proven to be spatially too sparse to quantify solar resources at most potential sites. Satellite data can be used to calculate estimates of direct solar radiation where ground measurements do not exist. Performance of decomposition models of various complexity have been evaluated against one year of in situ observations recorded on the roof of the radiometric tower of the Royal Meteorological Institute of Belgium in Uccle, Brussels. Models were first evaluated on a hourly and sub-hourly basis using measurements of global horizontal irradiance (GHI) as input. Second, the best performing ground-based decomposition models were used to extract the direct component of the global radiation retrieved from Meteosat Second Generation (MSG) images. Results were then compared to direct beam estimations provided by satellite-based diffuse fraction models and evaluated against direct solar radiation data measured at Uccle. Our analysis indicates that valuable DNI estimation can be derived from MSG images over Belgium regardless of the satellite retrieved GHI accuracy. Moreover, the DNI retrieval from MSG data can be implemented on an operational basis.     

The assessment of different models to predict the global solar radiation on a surface tilted to the south

Global and diffuse solar radiation intensities are, in general, measured on horizontal surfaces, whereas stationary solar conversion systems (both flat plate solar collector and PV) are tilted towards the sun in order to maximize the amount of solar radiation incident on the collector surface. Consequently, the solar radiation incident on a tilted surface must be determined by converting the solar radiation intensities measured on a horizontal surface to that incident on the tilted surface of interest. There exist a large number of models designed to perform such a conversion. 11 such models have been tested utilizing data measured in Beer Sheva, Israel. The data consist of hourly global and diffuse solar radiation on a horizontal surface, normal incidence beam and global radiation on a south-oriented surface tilted at 40°. The horizontal diffuse radiation measured using a shadow ring was corrected using four different correction models. This resulted in 44 model permutations. The individual model performance is assessed by an inter-comparison between the calculated and measured solar global radiation on the south-oriented surface tilted at 40° using both graphical and statistical methods. The relative performance of the different models under different sky conditions has been studied. Different grading systems have been applied in an attempt to score the relative performance of the models.     

Prediction of hourly diffuse solar radiation from measured hourly global radiation on a horizontal surface

A statistical procedure has been employed to develop correlations between the hourly global horizontal radiation and its diffuse component. Several years', hourly radiation data from three Canadian stations and two French stations have been employed for this purpose. The relationships have been developed in dimensionless form which predict for particular solar altitudes when is given.Under heavily cloudy conditions or when the sky is completely covered ( ), diffuse radiation increases linearly with the global radiation. In this region, solar altitude has no bearing on the fraction of diffuse radiation.As goes beyond 0.35, the effect of solar altitude begins to appear and the region immediately following this may be considered as partly-cloudy-skies conditions. In the beginning of this region, the diffuse component increases briefly with the increase in global radiation and then begins to decrease as the partly cloudy skies become clearer. At particular solar altitudes, a minimum value of the diffuse radiation is reached. The value of where reaches its minimum value varies with solar altitude.The region beyond which a minimum value of is reached may be considered as mainly-clear-sky conditions. In this region, increases again with , lower solar altitudes giving a higher percentage of diffuse radiation.Under partly cloudy skies and under clear skies, solar altitudes lower than 30° had a marked effect on the fraction of diffuse radiation. However, solar altitudes greater than 30° had minimal influence on the fraction of diffuse radiation.     

Solar radiation models—A review

Solar radiation models for predicting the average daily and hourly global radiation, beam radiation and diffuse radiation on horizontal surface are reviewed in this article. Estimations of monthly average hourly global radiation from daily summations are discussed. It was observed that Collares‐Pereira and Rabl model as modified by Gueymard (CPRG) yielded the best performance for estimating mean hourly global radiation incident on a horizontal surface for Indian regions. Estimations of monthly average hourly beam and diffuse radiation are discussed. It was observed that Singh‐Tiwari and Jamil‐Tiwari both models generally give better results for climatic conditions of Indian regions. Therefore, their use is recommended for composite climate of Indian regions. Empirical correlations developed to establish a relationship between the hourly diffuse fraction and the hourly clearness index using hourly global and diffuse irradiation measurements on a horizontal surface are discussed. Fifty models using the Angstrom–Prescott equation to predict the average daily global radiation with hours of sunshine are considered. It was reported that Ertekin and Yaldiz model showed the best performance against measured data of Konya, Turkey. Copyright © 2010 John Wiley & Sons, Ltd.     

Solar radiation utilizability

The nonlinear behaviour of many solar energy systems requires consideration of the fluctuating nature of solar radiation. Utilizability curves constructed for this purpose consider the radiation fluctuation on the basis of hourly or daily insolation values. Solar collectors, however, do not see radiation fluctuations in terms of hourly or daily insolation values, but respond to instantaneous radiation fluctuations caused by clouds. The fluctuation of instantaneous and short-time integrated radiation has been shown to differ significantly from that of daily insolation. This paper presents utilizability curves constructed from the cumulative probability distribution of instantaneous terrestrial insolation values. It is shown that hourly and daily utilizability curves give a conservative estimate of long-term performance. Experimental measurements of the collector performance further suggest the use of instantaneous utilizability curves in place of daily curves. The effect of the collector time constant on utilizability is discussed.     

Solar radiation on Mars

Detailed information on solar radiation characteristics on Mars are necessary for effective design of future planned solar energy systems operating on the surface of Mars. In this paper we present a procedure and solar radiation related data from which the diurnally, hourly and daily variation of the global, direct beam and diffuse insolation on Mars are calculated. The radiation data are based on measured optical depth of the Martian atmosphere derived from images taken of the sun with a special diode on the Viking cameras; and computation based on multiple wavelength and multiple scattering of the solar radiation.     

Monthly average solar radiation in panama—Daily and hourly relations between direct and global insolation

Regressions are developed to estimate daily global and direct radiation and the hourly distribution of direct radiation for Barro Colorado Island, Panama from monthly mean values observed 35 km away at Chiva-Chiva. The ratio model of Liu and Jordan and the logarithmic model of Anderson for estimating direct from global radiation are compared. Both gave satisfactory results after accounting for “seasonal” variation, but the ratio model was preferred in this case for the smaller number of separate regressions required. The ratio model fitted for diffuse radiation at Chiva-Chiva agreed closely with regressions for stations at similar latitude. For a given value of the clearness index, the direct component of solar radiation was relatively (but not absolutely) reduced during the dry season compared with the wet season. A likely explanation for this unexpected result is increased marine and terrestrial aerosol during the dry season when offshore winds are stronger and burning of crop and wasteland occurs. The models of Whillier and of Garnier and Ohmura, which assume constant atmospheric transmittance throughout the day, gave unsatisfactory fits to the hourly distribution of direct radiation. They were also unable to mimic an observed morning/afternoon asymmetry that was strongest in the wet season. Hourly direct radiation was accurately estimated from hourly global radiation by quadratic polynomials fitted separately to the morning and afternoon data. The resulting regressions will enable estimation of radiation in forest understory from measurements of insolation in the open by computerized image analysis of hemispherical canopy photos.     

A brief review of models for computing solar radiation on inclined surfaces

Modelling of solar energy systems requires estimation of the hourly radiation incident on surfaces of different tilts and orientations. Most meteorological stations report radiation values on a daily rather than hourly basis. Again, the value of the diffuse component may or may not be reported. Hence, different strategies may be encountered, for each location, with the common goal of computing hourly radiation on inclined surfaces.

In this study, five different schemes are presented to achieve this goal. In each scheme, certain correlations are required which are discussed in detail. The study is divided into five sections, each dealing with a specific type of correlation. These sections are: (i) correlations between daily diffuse and global radiation; (ii) correlations between hourly/daily global radiation; (iii) correlations between hourly/daily diffuse radiation; (iv) correlations between hourly diffuse and global radiation; and (v) models for computing diffuse sky radiation on inclined surfaces. The last section deals extensively with the anisotropic nature of sky diffuse radiation.

The important aspects of all correlation studies are highlighted, and the relative merits and demerits of their results are brought to light.

Mathematical expressions, where available, for models/correlations are provided so that the reader will have access to a comprehensive study. This information should be useful for modelling purposes in which computation of radiation on surfaces of different orientations and tilts is required.