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.     

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.     

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.     

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.     

Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation

Accurately computing solar irradiance on external facades is a prerequisite for reliably predicting thermal behavior and cooling loads of buildings. Validation of radiation models and algorithms implemented in building energy simulation codes is an essential endeavor for evaluating solar gain models. Seven solar radiation models implemented in four building energy simulation codes were investigated: (1) isotropic sky, (2) Klucher, (3) Hay–Davies, (4) Reindl, (5) Muneer, (6) 1987 Perez, and (7) 1990 Perez models. The building energy simulation codes included: EnergyPlus, DOE-2.1E, TRNSYS-TUD, and ESP-r. Solar radiation data from two 25 days periods in October and March/April, which included diverse atmospheric conditions and solar altitudes, measured on the EMPA campus in a suburban area in Duebendorf, Switzerland, were used for validation purposes. Two of the three measured components of solar irradiances – global horizontal, diffuse horizontal and direct-normal – were used as inputs for calculating global irradiance on a south-west façade. Numerous statistical parameters were employed to analyze hourly measured and predicted global vertical irradiances. Mean absolute differences for both periods were found to be: (1) 13.7% and 14.9% for the isotropic sky model, (2) 9.1% for the Hay–Davies model, (3) 9.4% for the Reindl model, (4) 7.6% for the Muneer model, (5) 13.2% for the Klucher model, (6) 9.0%, 7.7%, 6.6%, and 7.1% for the 1990 Perez models, and (7) 7.9% for the 1987 Perez model. Detailed sensitivity analyses using Monte Carlo and fitted effects for N-way factorial analyses were applied to assess how uncertainties in input parameters propagated through one of the building energy simulation codes and impacted the output parameter. The implications of deviations in computed solar irradiances on predicted thermal behavior and cooling load of buildings are discussed.     

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.     

Calculation of solar radiation intercepted by nubian vault and dome shaped buildings

This paper is concerned with the geometrical analysis of a Nubian vault and a hemispherical dome shaped building. From a rigorous analysis, exact expressions have been established for the angle of incidence of solar radiation at these surfaces. These expressions are then used to calculate the total incident solar radiation at different times and at various latitudes. Finally a comparison is made between the solar radiation intercepted by a unit area of each of these building geometries and a flat geometry. For a reference block of 17·4 m² carpet area, it is found that for latitudes up to 40°N, a Nubian vault form building envelope with East–West orientation receives minimum solar radiation. © 1997 by John Wiley & Sons, Ltd.     

倾斜面太阳辐射量计算方法研究

倾斜面辐射数据是保证准确设计太阳能利用系统的基础数据,一般由水平面数据计算得出。针对现有计算模型误差较大的现状考虑,试验测试了水平面及不同倾角斜面上的太阳辐射数据,提出了针对直接辐射转换系数的修正方法;通过倾斜面散射辐射数据的计算和分析,在散射辐射模型的基础上,建立耦合计算模型。试验与模型计算结果表明,散射辐射的各向同性受天气工况的影响,耦合模型具有较高的准确性,计算值与实测值的偏差可控制在5.3%以内。     

Isotropic distribution approximation in solar energy estimations

The isotropic distribution approximation commonly used for the estimation of the diffuse solar energy received by a tilted surface, is examined by studying the ratio of the energy computed using this approximation and that computed with an exact procedure. This examination is carried out for a tilted flat surface located at the bottom of five different models of the cloudfree, midlatitude, summer atmosphere. These models are assumed to rest on a ground absorbing all incident energy. The outward normal to the flat surface is confined to the sun's meridian plane. The first model is free of aerosols and absorbing gases. Absorption by average amounts of carbon dioxide, oxygen, ozone, and water vapor is included in the remaining four models. The second model is also free of aerosols, but the last three models contain aerosols in the form of a spherical polydispersion made from a substance with a spectrally independent refractive index of 1.5-0.0li. Models 3 and 4 are expected to represent, respectively, the average and strongly turbid conditions encountered over large continental areas. Models 3 and 5 contain aerosols with different size distribution characteristics, but have the same amount of aerosol mass loading per unit horizontal area.Values of the direct solar radiation and of the diffuse sky radiation incident upon the tilted surface were calculated at 77 unequally spaced wavelengths in the spectral region 0.305-2.5 μm. This spectral resolution provides acceptable values of various wavelength integrals in the presence of absorption by the aforementioned gases. Furthermore, the field of the diffuse radiation was evaluated at a sufficient number of points in the zenith, and azimuth angles for obtaining reliable integrations over the respective parameters under various conditions. The diffuse radiation was calculated after taking into account all orders of scattering.It has been shown that the use of the isotropic distribution approximation results in a significant under- or over-estimation of the diffuse energy depending upon the tilt angle of the surface, position of the sun, and atmospheric conditions.     

Evaluating the solar resource: a review of problems resulting from temporal, spatial and angular variations

Accurate assessment of the availability of solar energy at the Earth's surface is hampered by difficulties associated with the variability of solar radiation in space and time and with the angular position in the sky hemisphere. This paper assesses each of these problem areas by highlighting the difficulties and the attempts to offset them. Major emphasis is placed on extrapolation and interpolation procedures, the sensitivity of inclined surfaces to variations in the solar input, numerical models for calculating the irradiance of inclined surfaces and the time scales for which these computations are valid.Finally, the reader is urged to consider the significance of these difficulties in light of both radiation measurement errors and the sensitivity of the application to imprecise determinations of the radiation environment.     

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.     

Some aspects of modelling the energy balance of a room in regard to the impact of solar energy

The architecture of a building is crucial in determining its thermal energy balance and indoor comfort conditions. Knowledge of solar radiation availability and its transmission through a building envelope to the interior of the building helps an architect to design the building in an energy efficient way. Nowadays, in highly populated urban areas, attics are used as living spaces and the building envelope includes inclined external walls and windows in roofs. This paper presents some aspects of modelling the energy balance of rooms with different orientations and with vertical or inclined surfaces of building envelope, with stress on the impact of solar energy. The dynamics of energy flow through windows is analysed in more detail. One dimensional energy flow through the centre of glass area (based on a thermal resistance model), two-dimensional energy flow through the edge of glass area and two-dimensional heat flow through the opaque frame are analysed. The third dimension is also considered in a simplified way by taking into account the specific perimeter of the edge or frame. Stress is put on modelling the solar energy input. Solar radiation is modelled as short wave radiation that is transmitted directly to the room through glazing and as energy absorbed by the building envelope (glass panes, frame and opaque external walls) that becomes internal heat sources and is transferred indirectly to the room. The model developed has been used for numerical simulation using MATLAB as the programming language. This model predicts (amongst other things) the solar energy impact on the energy balance of a room in a building. It allows many cases of rooms and their envelopes to be run and evaluated and as a result both general and detailed conclusions can be drawn. Some results are presented in both graphical and tabular form.     

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.     

Calculation of Escaped Solar Energy in Glazing Façade Buildings

ABSTRACT

In building's cooling load calculation, solar heat gain through transparent envelope is calculated by using solar heat gain coefficient which is a thermal performance parameter of window. In traditional buildings, window-wall ratio is small so it's is assumed that the incoming solar radiation can't escape through the window again. But this hypothesis isn't suitable for glazing façade buildings. To calculate the escaped solar energy ratio, a solar radiation model is established on the basis of radiosity-irradiation method and calculated by using the commercial software of Matlab. The impact of time, room geometric dimensioning and absorptance of interior surfaces are evaluated. The numerical calculation results show that the escaped solar radiation ratio varies according to solar radiation incident angle in different times and its maximum value is 8.85% in summer solstice; compare to the width, the depth and height of the room affect the ratio significantly; the reflectance of the floor has greater impact on the escaped solar energy ratio than of other internal surfaces. Finally a fitting formula of escaped solar energy ratio is provided as a function of the ratio between the window area and the internal surface area and of the internal surfaces' absorptance.     

Some recommendations for inclinations and orientations of building elements under solar radiation in Polish conditions

The paper considers solar energy availability on the different surfaces that constitute the building envelope. The main aim of the presented analysis is to give recommendations for architects to help them design standard and low energy buildings in a proper way, including integration of solar active and passive systems into building structure. This requires maximisation of solar energy gains during certain periods of time, and at other times shading.     

Statistical comparison of models for estimating solar radiation on inclined surgaces

The objectives of this study are to compare statistically three models for estimating solar radiation on inclined surfaces and to recommend one that is general and accurate. The isotropic model, and Klucher's and Hay's anisotropic models are chosen for discussion. The hourly and daily formulations of these models are briefly described. Results show that they all produce large errors at steep slopes. The errors are minimum during the summer months. The isotropic model under-estimated consistently throughout the year resulting in the worst performance. Hay's model also under-estimated constantly but by a smaller amount. Klucher's model overestimated in the summer and under-estimated in the winter, but can be considered just as general and accurate as Hay's model for estimating insolation on inclined surfaces.     

Luminous efficacy of daylight under different sky conditions

Dalighting is recognised as an important and useful strategy in terms of energy-efficient building design in hot climates. However, daylighting is always accompanied by unwanted solar heat gain, particularly during the cooling season. To achieve and evaluate daylighting design, solar radiation and outdoor illuminance data are needed. In 1991, a measuring station was installed at the City University of Hong Kong to measure global and diffuse solar radiation and outdoor illuminance. The measured data are analysed, and empirical models to determine luminous efficacy under different sky conditions are developed and presented. Implications for energy efficiency in building designs are discussed.     

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.     

An anisotropic solar irradiance model for tilted surfaces and its comparison with selected engineering algorithms

A physically based hourly radiation model for inclined planes is presented. The sky diffuse component is derived from typical radiance patterns for clear and overcast conditions, taking anisotropic effects into account. New developments are also proposed for the ground reflected component, in order to supplement the usual isotropic assumption. The proposed radiation model, called CDRS, may be used with different input data combinations, the relative advantages of which are discussed. CDRS outputs are in good agreement with four clear sky sophisticated spectral data sets when wideband as well as spectral irradiances are input. When compared to measured data, CDRS also appears to perform well during clear and overcast sky conditions. Good results from only two cloudy days are also obtained, but more systematic tests should be conducted in this case. All the five other selected engineering models exhibit some degree of inaccuracy for certain slope/azimuth/cloudiness combinations. Particularly, the ASHRAE and DOE-2 models give catastrophic results for southward vertical surfaces during overcast conditions. This unexpected result may lead to important bias in building energy consumption simulations. Finally, some experimental and computational problems are pointed out. These could interfere with models accuracy comparison in validation studies.     

Cloud classification in a mediterranean location using radiation data and sky images

Knowledge regarding the solar radiation reaching the earth’s surface and its geographical distribution is very important for the use of solar energy as a resource to produce electricity. Therefore, a proper assessment of available solar resource is particularly important to determine the placement and operation of solar thermal power plants. To perform this analysis correctly, it is necessary to determine the main factors influencing the radiation reaching the earth’s surface, such as the earth’s geometry, terrain, and atmospheric attenuation by gases, particles and clouds. Among these factors, it is important to emphasise the role of clouds as the main attenuating factor of radiation. Information about the amount and type of clouds present in the sky is therefore necessary to analyse both their attenuation levels and the prevalence of different sky conditions. Cloud cover is characterised according to attenuation levels, using the beam transmittance (k_b, ratio of direct radiation incident on the surface to the extraterrestrial solar radiation) and hemispherical sky images. An analysis of the frequency and duration of each type of cloud cover blocking the sun’s disk is also performed. Results show prevailing sky situations that make the studied area very suitable for the use of solar energy systems.