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.     

Evaluation of models to predict insolation on tilted surfaces

An empirical study was performed to evaluate the validity of various insolation models which employ either an isotropic or an anisotropic distribution approximation for sky light when predicting insolation on tilted surfaces. Data sets of measured hourly insolation values were obtained over a 6-month period using pyranometers which received diffuse and total solar radiation on a horizontal plane and total radiation on surfaces tilted toward the equator at 37° and 60° angles above the horizon. Data on the horizontal surfaces were used in the insolation models to predict insolation on the tilted surface; comparisons of measured vs calculated insolation on the tilted surface were examined to test the validity of the sky light approximations. It was found that the Liu-Jordan isotropic distribution model provides a good fit to empirical data under overcast skies but underestimates the amount of solar radiation incident on tilted surfaces under clear and partly cloudy conditions. The anisotropic-clear-sky distribution model by Temps and Coulson provides a good prediction for clear skies but overstimates the solar radiation when used for cloudy days. An anisotropic-all-sky model was formulated in this effort which provided excellent agreement between measured and predicted insolation throughout the 6-month period.     

A note on diffuse solar radiation on a tilted surface

We are presenting a note on comparative study of diffuse component of solar radiation on tilted surface with different angle of inclination. The monthly mean daily diffuse radiation have been calculated on inclined surfaces from the data of horizontal surface using the Circumsolar and Isotropic model and the anisotropic model of Klucher and Hay at Lucknow (Latitude 26.75°, Longitude 80.85°), Uttar Pradesh, India. These calculated results are compared with our measured value. The comparison shows that Klucher model who considered the effect of cloudy sky conditions gives comparatively good estimations particularly at low inclination angles.     

Evaluation of models for predicting insolation on slopes within the Colorado alpine tundra

This empirical study evaluates insolation predictions for the Colorado tundra from models based upon isotropic and anisotropic distribution approximations for diffuse sky and reflected solar radiation. The data set of hourly insolation values was obtained from 40 locations on an alpine ridge by simultaneous measurement of direct beam irradiance and total insolation to the horizontal ridge crest and two nearby sloping surfaces. Six models are used to predict insolation, two based on the isotropic distribution of diffuse solar radiation and four on anisotropic diffuse distribution fields. Three models (one isotropic and two anisotropic) employ measurements of normal direct beam irradiance while the other 3 models incorporate the correlation between the “clearness index” and the ratio of diffuse sky to total insolation. The precision of insolation estimates from models using the correlation method is only slightly less than from other models. Accounting for the increase of diffuse radiation in the circumsolar sky improves insolation predictions. However, inclusion of additional regions of diffuse radiation anisotropy decreases model accuracy. Errors of insolation estimates for the alpine tundra from all models vary in a systematic manner as a function of relative azimuth and ground slope angles.     

Computational derivation of irradiance on building surfaces: An empirically-based model comparison

Performance simulation applications require reliable information regarding the intensity of solar irradiance on arbitrarily oriented building surfaces in order to properly predict buildings' energy use or to configure building-integrated solar energy systems. Since measured irradiance databases typically include only horizontal irradiance values, solar radiation intensity on inclined surfaces must be computationally derived. In this context, the present paper compares six options to derive, from horizontal irradiance data, solar radiation intensity levels on inclined surfaces. To evaluate these options, simulated downward vertical irradiance on four orientations were compared with measurements obtained in Austria. Two options that use both global and diffuse horizontal irradiance values for sky radiance generation delivered slightly better results than the others, which require only global horizontal irradiance. However, the range of errors was rather high for all options. Even for the best-ranked option, no more than 64% of the results had a relative error of less than ±20%.     

Spectral and temperature correction of silicon photovoltaic solar radiation detectors

Silicon photovoltaic sensors are an inexpensive alternative to standard thermopile sensors for the measurement of solar radiation. However, their temperature and spectral response render them less accurate for global horizontal irradiance and unsuitable for direct beam and diffuse horizontal irradiance unless they can be reliably corrected. A correction procedure for the rotating shadowband radiometer, which measures all three components, based on a three-way parameterization of the solar position and sky conditions is proposed. After correction, root-mean-square errors for the global and diffuse horizontal irradiance and the direct normal irradiance are about 10, 12, and 13 W/m² in comparison with coincident, 5-minute thermopile measurements. While the numerical results are specific to the rotating shadowband instrument, the correction algorithm should apply universally.     

A comparative study of solar irradiation models on various inclined surfaces for India

This paper presents a statistical approach for the estimation of the diffuse/global irradiation on various inclined surfaces from the measured data of horizontal surface. In fact diffuse solar radiation on an inclined plane consists of two components: sky diffuse radiation and reflected radiation from the ground. For analyzing estimation of the daily tilted sky diffuse component from the daily horizontal diffuse irradiance, we have considered six models Badescu, Circumsolar, Skartveit and Olseth, Hay, Klucher and Liu and Jordan (Isotropic). All these models except Badescu adopted the same methodology for estimating the ground-reflected radiation component, therefore, only sky diffuse component was analyzed at Lucknow (latitude 26.75°, longitude 80.50°), India location. Statistical analysis showed that the Skartveit and Olseth model gives good prediction for the low inclination angle however; Klucher model gave better performance for highly inclined south-facing surfaces. The Root Mean Square Errors (% RMSE) value varies from 3.45% to 24.15% except for Badescu and Circumsolar model which predict worse results. In general, Klucher’s model provides close agreement with the measurements.     

The estimation of daily, clear sky, solar radiation intercepted by a tilted surface

The amount of solar energy that is intercepted by surfaces of any orientation is estimated from a new model of the clear sky, spatial distribution of solar radiation. The model was developed from measurements made during clear sky conditions and uses direct, isotropic reflected, and anisotropic diffuse radiation. The effects of azimuth, tilt, season, latitude, atmospheric turbidity, and reflectivity of the surroundings were computed using hourly measurements of normal beam and horizontal total radiation at four stations in the United States. A transformation of the co-ordinates of orientation produced a general relationship between orientation and intercepted energy. The general relationship was tested against measurements from six locations in the Northern Hemisphere and was found to be valid. The model is also a better estimator of energy intercepted by a tilted surface than are the more commonly used 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.     

Comments on “Calculations of monthly average insolation on tilted surfaces” by S. A. Klein

The amount of solar energy that is intercepted by surfaces of any orientation is estimated from a new model of the clear sky, spatial distribution of solar radiation. The model was developed from measurements made during clear sky conditions and uses direct, isotropic reflected, and anisotropic diffuse radiation. The effects of azimuth, tilt, season, latitude, atmospheric turbidity, and reflectivity of the surroundings were computed using hourly measurements of normal beam and horizontal total radiation at four stations in the United States. A transformation of the co-ordinates of orientation produced a general relationship between orientation and intercepted energy. The general relationship was tested against measurements from six locations in the Northern Hemisphere and was found to be valid. The model is also a better estimator of energy intercepted by a tilted surface than are the more commonly used models.     

Solar radiation on tilted south oriented surfaces: validation of transfer-models

Three transfer-models in use for estimating solar radiation on tilted surfaces are tested. A 12 year series of hourly global, diffuse, and reflected solar irradiation measured with horizontal pyranometers as well as hourly global solar irradiation measured with tilted south oriented pyranometers is available. One model uses daily irradiation, the other two use hourly irradiation. The models converting hourly solar irradiation on a horizontal surface to a tilted surface yield better results than that using daily irradiation. The best results are gained if pairs of hourly global and diffuse solar irradiation are available. The root mean square errors exceed 10% only if the sky is covered by more than 85% with clouds or if the solar elevation angle is less than 10°.     

A simple clear skies model for the luminous efficacy of diffuse solar radiation on inclined surfaces

In the present work we study the luminous efficacy of diffuse solar radiation incident on vertical surfaces for a clear sky and mean hourly values of diffuse irradiance and diffuse illuminance. We develop a model easy to use, similar to a model previously obtained for horizontal surfaces. To develop the present model for vertical surfaces we assume that the slope of the surface influences diffuse illuminance and diffuse irradiance in the same way. As a consequence of this hypothesis, the luminous efficacy of diffuse solar radiation is assumed to be the same for both horizontal and inclined surfaces.     

Improved photovoltaic energy output for cloudy conditions with a solar tracking system

This work describes measurements of the solar irradiance made during cloudy periods in order to improve the amount of solar energy captured during such periods. It is well-known that 2-axis tracking, in which solar modules are pointed at the sun, improves the overall capture of solar energy by a given area of modules by 30-50% versus modules with a fixed tilt. On sunny days the direct sunshine accounts for up to 90% of the total solar energy, with the other 10% from diffuse (scattered) solar energy. However, during overcast conditions nearly all of the solar irradiance is diffuse radiation that is isotropically-distributed over the whole sky. An analysis of our data shows that during overcast conditions, tilting a solar module or sensor away from the zenith reduces the irradiance relative to a horizontal configuration, in which the sensor or module is pointed toward the zenith (horizontal module tilt), and thus receives the highest amount of this isotropically-distributed sky radiation. This observation led to an improved tracking algorithm in which a solar array would track the sun during cloud-free periods using 2-axis tracking, when the solar disk is visible, but go to a horizontal configuration when the sky becomes overcast. During cloudy periods we show that a horizontal module orientation increases the solar energy capture by nearly 50% compared to 2-axis solar tracking during the same period. Improving the harvesting of solar energy on cloudy days is important to using solar energy on a daily basis for fueling fuel-cell electric vehicles or charging extended-range electric vehicles because it improves the energy capture on the days with the lowest hydrogen generation, which in turn reduces the system size and cost.     

Study of models for predicting the diffuse irradiance on inclined surfaces

Solar irradiance data on various inclined surfaces at different orientations are important information for active solar-system analyses and passive energy-efficient building designs. In many parts of the world, however, the basic solar irradiance data for the surfaces of interest are not always readily available. Traditionally, different mathematical models have been developed to predict the solar irradiance on various inclined surfaces using “horizontal” data. Alternatively, the diffuse irradiance of a sloping plane can be calculated by integrating the radiance distribution generated with a sky radiance model. This paper presents the evaluation of two slope irradiance models, namely, the Perez point-source model (PEREZSIM) and the Muneer model (MUNEERSIM), and two sky-distribution models, namely, the Perez all-weather model (PEREZSDM) and the Kittler standard-sky model (KITTLERSDM). Three-year (1999–2001) measured average hourly sky radiance and horizontal sky diffuse irradiance data were used for the model assessment. Statistical results showed that all four models can accurately predict the solar irradiance of a 22.3° (latitude angle of Hong Kong) inclined south-oriented surface, indicating the good predictive ability for modelling an inclined surface with a small tilted angle. In general, the KITTLERSDM and PEREZSIM show the best predictions for vertical solar irradiance at this location, followed by the PEREZSDM, then the MUNEERSIM.     

Measurements and predictions of solar radiation incident on horizontal surfaces at Santa Fe, Argentina (31° 39′S, 60° 43′W)

Measurements and predictions of solar radiation during a period of 10 years on horizontal surfaces at Santa Fe (31° 39′ S, 60° 43′ W), Argentina, reported as average daily global radiation for each month, are presented. Data are compared to those obtained with a previously published and verified model for computing solar radiation on horizontal planes at the earth's surface for cloudless sky days. Measurements show an important reduction of global radiation with respect to the cloudless sky model predictions for all months of the year. Conversely, averaged daily diffuse solar radiation calculated with Page's formula shows a small increment with respect to the predicted diffuse solar radiation for cloudless sky conditions. When direct solar radiation data, calculated from global and diffuse solar radiation values, are compared to theoretical prediction, a significant decrease is observed. This trend is similar to that obtained for global solar radiation.     

A new neural network model for evaluating the performance of various hourly slope irradiation models: Implementation for the region of Athens

The present study is divided into two parts. The first part deals with the comparison of various hourly slope irradiation models, found in the literature, and the selection of the most accurate for the region of Athens. In the second part the prediction of global solar irradiance on inclined surfaces is performed, based on neural network techniques.The models tested are classified as isotropic (Liu and Jordan, Koronakis, Jimenez and Castro, Badescu, Tian) and anisotropic (Bugler, Temps and Coulson, Klucher, Ma and Iqbal, Reindl) based on the treatment of diffuse irradiance. For the aforementioned models, a qualitative comparison, based on diagrams, was carried out, and several statistical indices were calculated (coefficient of determination R², mean bias error MBE, relative mean bias error MBE/A(%), root mean square error RMSE, relative root mean square error RMSE/A(%),statistical index t-stat), in order to select the optimal.The isotropic models of “Tian” and “Badescu” show the best accordance to the recorded values. The anisotropic model of “Ma&Iqbal” and the pseudo-isotropic model of “Jimenez&Castro”, show poor performance compared to other models. Finally, a neural network model is developed, which predicts the global solar irradiance on a tilted surface, using as input data the total solar irradiance on a horizontal surface, the extraterrestrial radiation, the solar zenith angle and the solar incidence angle on a tilted plane. The comparison with the aforementioned models has shown that the neural network model, predicts more realistically the total solar irradiance on a tilted surface, as it performs better in regions where the other models show underestimation or overestimation in their calculations.     

Solar irradiance on non-horizontal surfaces at the East-Mediterranean coastal plain of Israel

A large volume of global, diffuse and direct solar radiation observed at the National Radiation Center in Bet-Dagan (the East-Mediterranean coastal plain of Israel) has been analysed to evaluate the solar irradiance climatology on non-horizontal surfaces of various slope aspects and tilt angles. The isotropic approximation was used with respect to the diffuse sky radiation, as well as with regard to the reflected radiation from the ground. The feasibility of applying this approximation for the assessment of the insolation climate on non-horizontal surfaces is discussed. The monthly curves of daily total insolation on inclined surfaces were drawn, and their characteristic patterns for the various slope aspects and seasons are examined.     

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.