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.     

Experimental testing of models for the estimation of hourly solar radiation on vertical surfaces at Arcavacata di Rende

More than 55,000 data of hourly solar radiation on a horizontal surface and on vertical surfaces exposed to the south, west, north and east, measured at Arcavacata di Rende (CS), were compared with hourly radiation data calculated by various calculation models.Erbs, Reindl et al. and Skartveit et al. correlations for the split of hourly global radiation in the diffuse and beam components were used together with the isotropic sky model and three anisotropic sky models.The agreement between experimental and calculated data is generally good.     

A computer simulation of solar radiation

Various algebraic formulas for representing solar radiation data are discussed and the results obtained are compared.     

Analysis of terrestrial solar radiation exergy

Based on Candau’s definition of radiative exergy, the exergy of the extraterrestrial and the terrestrial solar radiation are computed and compared by using the solar spectral radiation databank developed by Gueymard. The results show that within the spectrum region from 0.28 to 4.0 μm, the total energy quality factor (i.e., the exergy-to-energy ratio) of extraterrestrial solar radiation is about 0.9292, and that of the global terrestrial solar radiation is about 0.9171 under US standard atmosphere condition and zero solar zenith angle. The terrestrial solar spectral radiation exergy flux is large in the near ultraviolet and the visible light region. The reference radiation exergy spectra are obtained under atmospheric conditions consistent with ASTM standard G173-03. The effect of tilt angle on the terrestrial solar radiative exergy for inclined surface, and the effect of air mass on total energy quality factor of the terrestrial solar radiation for horizontal surface are analyzed. With the increase of tilt angle, the terrestrial solar spectral radiation exergy flux initially increases and then decreases, the total energy quality factor of the diffuse part decreases monotonically, while that of the direct part is invariant. The total energy quality factor of the direct, the diffuse and the global terrestrial solar radiation all decrease with the increase of air mass.     

Development of a method for generating operational solar radiation maps from satellite data for a tropical environment

Despite a considerable number of publications which use satellite data to map solar radiation, relatively few studies have been undertaken in a tropical environment. In this study, we have developed a method to produce operational solar radiation maps from satellite data for this environment. The method is based on a physical model which relates the satellite-derived earth–atmospheric reflectivity from visible channel of GMS-4 and GMS-5 to the transmissivity of the atmosphere. Cloud reflectivity was determined from satellite data, while radiation absorbed by water vapour, ozone and aerosols and radiation scattered by aerosols were determined from ground-based meteorological data. Techniques for determining the radiation depleted by these atmospheric constituents over a whole country were also presented. Satellite data of a six-year period (1993–1998) with approximately ten thousand satellite images were used to construct the maps. When tested against an independent data set, monthly average of daily global irradiation calculated from this method agree with that obtained from the measurements with the relative root mean square difference of 6.8% with respect to the mean values. Solar radiation is presented as twelve maps showing the monthly average of global irradiation and one map showing the yearly average of global irradiation. Radiation patterns from the maps show a strong influence of the tropical monsoons.     

Estimation of horizontal diffuse solar radiation with measured daily data in China

Three most widely used diffuse radiation models are calibrated using the daily data between January 1 1994 and December 31 1998 from 16 stations all over China. The second-degree polynomial relationship between R_D/R_G and n/N (Iqbal model) is suitable for diffuse radiation estimation in China. The averaged correlation coefficient R² is 0.84 and the maximum value is 0.93 at the 16 stations, and the Iqbal model works better in the eastern part of China than in the west. The A.A. El-Sebaii model could not be used to estimate diffused radiation accurately in China, with an averaged R²=0.47. The Liu and Jordan model could also be used for diffuse radiation estimation in China, and the averaged value of R² and parameter X₀ is 0.81 and 0.233, respectively. There is an evident linear relationship among the parameters X₀, a and b of the Liu and Jordan model.     

Global,direct and diffuse solar radiation on horizontal and tilted surfaces in Jeddah,Saudi Arabia

The measured data of global and diffuse solar radiation on a horizontal surface, the number of bright sunshine hours, mean daily ambient temperature, maximum and minimum ambient temperatures, relative humidity and amount of cloud cover for Jeddah (lat. 21°42′37′′N, long. 39°11′12′′E), Saudi Arabia, during the period (1996–2007) are analyzed. The monthly averages of daily values for these meteorological variables have been calculated. The data are then divided into two sets. The sub-data set I (1996–2004) are employed to develop empirical correlations between the monthly average of daily global solar radiation fraction (H/H₀) and the various weather parameters. The sub-data set II (2005–2007) are then used to evaluate the derived correlations. Furthermore, the total solar radiation on horizontal surfaces is separated into the beam and diffuses components. Empirical correlations for estimating the diffuse solar radiation incident on horizontal surfaces have been proposed. The total solar radiation incident on a tilted surface facing south H_t with different tilt angles is then calculated using both Liu and Jordan isotropic model and Klucher’s anisotropic model. It is inferred that the isotropic model is able to estimate H_t more accurate than the anisotropic one. At the optimum tilt angle, the maximum value of H_t is obtained as ∼36 (MJ/m² day) during January. Comparisons with 22 years average data of NASA SSE Model showed that the proposed correlations are able to predict the total annual energy on horizontal and tilted surfaces in Jeddah with a reasonable accuracy. It is also found that at Jeddah, the solar energy devices have to be tilted to face south with a tilt angle equals the latitude of the place in order to achieve the best performance all year round.     

Study of diffuse and global radiation characteristics in India

Recently, the Indian Meteorological Department has made available, for 13 locations in India, pyranometric data for total and diffuse radiation on an hourly and daily basis. The period of observation is from 1957 to 1975. This data is analysed to reexamine the correlations between monthly-average daily values of diffuse and total insolation and between hourly and daily insolation. The relationship between monthly diffuse/total and total/extraterrestrial ratios is found to be linear. The present correlation implies that the diffuse component is significantly larger than that predicted by other correlations. No noticeable effect of location or seasonal variation was found. Comparison of the present data with earlier studies for India indicates a trend of increasing diffuse radiation with the lapse of time. The ratio of hourly to daily insolation agrees with the Liu and Jordan correlation for total insolation but differs significantly for diffuse radiation. The need for refinement of the Liu and Jordan correlation between hourly and daily diffuse radiation is pointed out.     

On the effects of solar radiation variations on solar heating system performances

The effect of solar radiation availability on the performance of different solar heating systems has been studied. The systems include a solar water heater, passive solar houses and district solar heating systems with seasonal heat storage. Also, different collector orientations and collector types have been investigated. The hourly radiation data were generated by a simple computational simulation procedure. It was found that district solar heating systems with concentrating collectors and passive solar houses showed the largest variations for the given conditions.     

Correlation between daily diffuse and global radiation for India

Solar radiation characteristics have been studied in various countries and many correlations developed. In the absence of such studies, the same correlations are applied in other countries. Since radiation records are now available in most developing countries, it is possible to perform similar studies for these regions. The purpose of this study is to use daily global and diffuse radiation data for 13 stations in India to establish a correlation between the daily diffuse ratio and the clearness index. Plotting individual values of the daily diffuse ratio against the clearness index for all Indian Stations showed the existence of a definite relationship between them, confirming the validity of Liu and Jordan approach. It was found that a cubic equation provides a fairly accurate fit for this relationship. Comparison with other studies showed that no single correlation is applicable to all regions, and that each region possesses its own characteristics. Although the stations considered had diverse latitude, climate and geographical variations, the study showed that none had any effect on the correlation.     

Stochastic approach for daily solar radiation modeling

Mathematical modeling of solar radiation continues to be an important issue in renewable energy applications. In general, existing models are mostly empirical and data dependent. In this paper, a novel approach for solar radiation modeling is proposed and illustrated. The proposed application consists of hidden Markov processes, which are widely used in various signal processing topics including speech modeling with successful results. In the experimental work, mean of hourly measured ambient temperature values are considered as observations of the model, whereas mean of hourly solar radiation values are considered as the hidden events, which constitute the outcomes of the proposed mathematical model. Both solar radiations and temperatures are converted to quantized number of states. Finally, after a training stage that forms the transition probability values of the described states, the hidden Markov model parameters are obtained and tested. The tests are repeated for various numbers of states and observations are presented. Plausible modeling results with distinct properties in terms of accuracy are achieved.     

Diffuse solar radiation in Cairo,Egypt

In the present paper, the correlations of Page, Liu and Jordan, and Iqbal were employed to predict the monthly mean daily diffuse solar radiation in Cairo. However, it was found that the coefficients used in these correlations were not applicable in the case of Cairo. New coefficients were obtained and used in the above correlations in order to predict values of the monthly average daily diffuse radiation. The present coefficients were found to be very different from those obtained for conditions in other locations. The estimated diffuse radiations were compared with the measured values. It is concluded that all correlations (i.e. equations which use either the cloudiness index or the relative sunshine) with the present coefficients, may be used to predict the monthly mean daily diffuse radiation in Cairo.     

3D isotropic approximation for solar diffuse irradiance on tilted surfaces

A well known 2D approach of Liu and Jordan allows computing isotropic solar diffuse irradiance on a tilted surface. It is a 2D theory as the position of a sky element is characterized by a single (zenith) angle. A more realistic 3D model (that uses both zenith and azimuth angles to describe sky element's position) is developed in this paper for both isotropic diffuse irradiance and ground reflected irradiance incident on an arbitrary oriented surface. The 3D formula predicts a lower diffuse irradiance than the 2D relationship while the ground reflected irradiance is higher in case of the 3D model than in case of the 2D approach. In case of a small tilt angle, the 2D and 3D approximations predict comparable values, higher than the mean of the results obtained with a (reference) non-isotropic model. However, the 3D model is slightly more precise. When a larger tilt angle is considered, the 3D model predicts a few percent larger value than the mean of the values estimated by the reference model while the 2D model gives a significantly higher value.     

The all-sky meteorological radiation model: proposed improvements

The all-sky meteorological radiation model is a broadband solar-radiation estimation model that uses synoptic and sunshine information. The original model due to Muneer–Gul–Kambezidis was improved using regressions based on the sunshine fraction to increase the accuracy of the estimation of diffuse horizontal irradiation, thus achieving an accuracy increase for the estimation of the global horizontal irradiation. The improved model was validated using data from ten worldwide sites and using three statistical indicators:-coefficient of determination between computed and measured global irradiation data and the relevant, mean bias error and the root mean square error of the computed global irradiation. The performance of the new model was improved when compared to that of the original model. The new regression coefficients were found to be more accurate in estimating global horizontal radiation for both fine and coarse datasets.     

Testing of two models for computing global solar radiation on tilted surfaces

Solar radiation data computerly measured at Amman, Jordan was used to verify the performance accuracy of two models for estimation of global radiation on tilted surfaces. The measurements used in this study were the daily totals of global radiation on a horizontal surface, diffuse radiation on a horizontal surface and global radiation on a 45° tilted surface. The measured radiation using microprocessor based weather station was compared with the computerized results obtained from two widely used models for estimating total radiation on tilted surfaces. These are the isotropic model and Hay’s anisotropic model. The study showed that the models are in good agreement with the isotropic model producing slightly better results during the summer months. Hay’s model resulted in better results for the rest of the year.     

Analysis of different comparison parameters applied to solar radiation data from satellite and German radiometric stations

In this paper new comparison parameters are defined for assessing statistical similarity between two data sets. The new parameters are based on the commonly used Kolmogorov-Smirnov test. They allow quantifying differences between the cumulative distribution functions of each data series. These parameters are applied to global horizontal daily irradiation values from pyranometric measurements and satellite data. The test data from 38 stations distributed throughout Germany cover the time from 1995 until 2003. The results affirm that the new parameters contribute valuable information to the comparison of data sets complementing those that are found with the mean bias and root mean squared differences.     

Models of diffuse solar radiation

For some locations both global and diffuse solar radiation are measured. However, for many locations, only global is measured, or inferred from satellite data. For modelling solar energy applications, the amount of radiation on a tilted surface is needed. Since only the direct component on a tilted surface can be calculated from trigonometry, we need to have diffuse on the horizontal available. There are regression relationships for estimating the diffuse on a tilted surface from diffuse on the horizontal. Models for estimating the diffuse radiation on the horizontal from horizontal global that have been developed in Europe or North America have proved to be inadequate for Australia [Spencer JW. A comparison of methods for estimating hourly diffuse solar radiation from global solar radiation. Sol Energy 1982; 29(1): 19–32]. Boland et al. [Modelling the diffuse fraction of global solar radiation on a horizontal surface. Environmetrics 2001; 12: 103–16] developed a validated model for Australian conditions. We detail our recent advances in developing the theoretical framework for the approach reported therein, particularly the use of the logistic function instead of piecewise linear or simple nonlinear functions.Additionally, we have also constructed a method, using quadratic programming, for identifying values that are likely to be erroneous. This allows us to eliminate outliers in diffuse radiation values, the data most prone to errors in measurement.     

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.     

Investigation of cloudless solar radiation with PV module employing Matlab-Simulink

This paper focuses on a novel approach to the prediction of Voltage-Current (V-I) characteristics of a Photovoltaic panel under varying weather conditions and also the modelling of hourly cloudless solar radiation to provide the insolation on a PV module of any orientation, located at any site. The empirical model developed in this study uses standard specifications together with the actual solar radiation and cell temperature. This proposed work develops a Matlab-Simulink model to generate solar radiation at any location and for any time of the year. A new model for V-I characteristics and maximum power operation of a Photovoltaic (PV) module is also presented, which aims to model the effect on V-I and P-V curves of varying climatic conditions. Moreover, this model has been implemented using the Matlab-Simulink and is used to investigate the effect of meteorological conditions on the performance of a PV module generator. Thus the combined model of cloudless solar radiation and the photovoltaic module provides a tool that may be loaded in the library for analysis purpose. It is found that the predicted solar radiation strongly agrees with the experimental data.