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 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.     

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.     

Estimating Solar Irradiance on Inclined Surfaces: A Review and Assessment of Methodologies

A variety of numerical models for calculating the solar irradiance for an inclined surface are described and evaluated using data for Vancouver, B.C., Canada. While all the hourly models have a common approach for calculating the direct component of the solar irradiance there is a variety of methods for calculating the diffuse irradiance based on the portion of the sky hemisphere within the field of view of the surface. A less significant distinction between the models is in the methods used to calculate the amount of radiation received as a result of reflection from adjacent surfaces.

The paper demonstrates that the principal features of the anisotropic distribution of sky radiance must be included in the numerical computations since the use of the unrealistic isotropic model leads to significant short and long term errors. Inclusion of directional reflectance in the slope irradiance calculations will lead to increased accuracy for the estimated values, with greatest improvement being achieved in the winter months due to a zenith angle dependency on the significance of the directional reflectance.

Errors in estimating the slope irradiance with an anisotropic model are shown to compare favourably with the errors associated with a direct measurement of the solar irradiance.     

An assessment of a revised Olmo et al. model to predict solar global radiation on a tilted surface at Beer Sheva,Israel

A model to convert horizontal solar global radiation to that on a tilted surface is presented. It is based upon a relatively simple model proposed by [Olmo FJ, Vida J, Foyo I, Castro-Diez Y, Alados-Arboledas L. Prediction of global irradiance on inclined surfaces from horizontal global irradiance. Energy 24 (1999) 689–704]., which requires only measurements of horizontal solar radiation but was found to produce significant errors when tested with data from another site. The present model assumes the availability of databases for at least two of the three solar radiation types, viz., global, beam and diffuse. The horizontal global radiation is converted to that on a tilted surface by applying the Olmo model to the diffuse component, whereas the beam component is converted by using the geometrical relationship between the two surfaces. The original Olmo anisotropic radiation correction factor is now assumed to be a function of sky conditions. The solar radiation databases were converted to subsets corresponding to clear, partially cloudy and cloudy sky based upon clearness index values. The three anisotropic correction factors were determined by fitting to a 12-months database. The present model was then tested by applying it to a second database consisting of 24-months not involved in the model development. It was found to give better results than three highly regarded more complex models.     

An anisotropic shadow ring correction method for the horizontal diffuse irradiance measurements

Diffuse irradiance is usually measured with a shadow ring which prevents beam radiation from entering the measuring instrument. The shadow ring also obscures part of the sky, and therefore, it is necessary to correct the measured diffuse irradiance. This correction is often assumed to be constant at a certain time of the year and at a certain latitude. However, the radiance distribution of the sky is not isotropic, and the anisotropy must be taken into account in the correction. In this paper, a new numerical method for calculating the shadow ring correction is presented. The correction factor is calculated directly from the radiance distribution of the sky. For Helsinki latitude (60°N), the yearly average isotropic correction factor is 1.10 and the additional anisotropic correction factor is about 1.05. Realistic sky models, e.g. Perez all-weather model, were used in the calculation.     

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.     

MEO shadowring method for measuring diffuse solar irradiance: Corrections based on sky cover

The present paper deals with atmospheric corrections factors proposed as a function of the atmospheric transmissivity in order to correct the diffuse solar irradiance measured with the Melo-Escobedo-Oliveira Shadowring Measuring Method (MEO shadowring Method). Global irradiance was measured by an Eppley-PSP pyranometer; direct normal irradiance by an Eppley-NIP pyrheliometer fitted to a ST-3 sun tracking device and diffuse irradiance by an Eppley-PSP pyranometer fitted to a MEO shadowring. The Solar Radiometric Laboratory at Sao Paulo State University provided the measurements during the years 1996–2005. Two correction models for diffuse solar irradiance were proposed: All Sky Correction Model (ASC Model) and Sky Cover Correction Model (SCC Model). The MBE and RMSE statistical indicators performed the validations. The correction models showed results in the same order of magnitude: ASC Model showed 0.81% deviation, while SCC Model showed 0.66% deviation. Therefore, the correction models proposed as a function of the sky covering (atmospheric transmissivity) were efficient to correct the isotropic diffuse irradiance, approaching the measured and reference diffuse irradiance less than 1%. Corrections show dependence on sky coverage and seasonality. The results presented that the sky cover corrections improve the MEO shadowring method, allowing the generation of a reliable global, direct and diffuse radiation database without high financial investments.     

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.     

Solar radiation modelling in the urban context

This paper describes alternative methods for predicting surface irradiance in the urban context. In this the focus is on means of accounting for the effects of nearby obstructions on reducing direct sky radiation and on contributing reflected radiation. The first two methods involve abstracting the urban skyline into an effective canyon using isotropic and anisotropic tilted surface irradiance models. The third predicts the irradiance contribution from two hemispheres which are discretised into patches––given the radiance of the sky and dominant obstructions (if these exist) and associated view factors––so that we have a new simplified radiosity algorithm (SRA). Results from the three methods (isotropic canyon (IC), anisotropic canyon (AC) and simplified radiosity algorithm (SRA)) are compared with a ‘truth model' under the following circumstances: (i) unobstructed sky, (ii) sky obstructed by black surfaces, (iii) sky obstructed by grey diffusely reflecting surfaces. Results show conclusively that the SRA offers superior accuracy at comparable speed to the canyon models. The SRA also compares well with a ray tracing program, it can handle urban scenes of arbitrary geometric complexity and is readily amenable for inclusion into standard computer programs that require surface irradiance as an input.     

Solar radiation modeling and measurements for renewable energy applications: data and model quality

Measurement and modeling of broadband and spectral terrestrial solar radiation is important for the evaluation and deployment of solar renewable energy systems. We discuss recent developments in the calibration of broadband solar radiometric instrumentation and improving broadband solar radiation measurement accuracy. An improved diffuse sky reference and radiometer calibration and characterization software for outdoor pyranometer calibrations are outlined. Several broadband solar radiation model approaches, including some developed at the National Renewable Energy Laboratory, for estimating direct beam, total hemispherical and diffuse sky radiation are briefly reviewed. The latter include the Bird clear sky model for global, direct beam, and diffuse terrestrial solar radiation; the Direct Insolation Simulation Code (DISC) for estimating direct beam radiation from global measurements; and the METSTAT (Meteorological and Statistical) and Climatological Solar Radiation (CSR) models that estimate solar radiation from meteorological data. We conclude that currently the best model uncertainties are representative of the uncertainty in measured data.     

On shadowband correction methods for diffuse irradiance measurements

Diffuse irradiance, G_d, is an important variable in solar resource assessment. The diffuse irradiance can be worked out from global, G, and direct, G_b, irradiance measurements, but this method involves the use of relatively expensive tracking mechanisms. Alternatively, a widely accepted technique uses a pyranometer with a shadowband. Because the shadowband screens the sensor from part of the diffuse radiation coming in from the sky, a correction must be made to the measurements. However, because of the anisotropy of diffuse radiation it is difficult to compute an exact theoretical correction. In this study we use two data sets registered in two locations in Spain. The first one consists in coincident hourly values of global, direct, and diffuse irradiance; the latter by means of shadowband. The other data set includes the same variables but as 5-minute values. Our goal is to study the necessary correction factor for diffuse irradiance measurements obtained by means of shadowband. After testing several well-known correction methods, we have developed two different correction models, using two-thirds of the hourly data set, while the remaining one-third and the whole 5-minute data set have been used for validation purposes. The last validation test suggests that our anisotropic models provide reliable corrections for conditions different than the ones where they have been developed. The results obtained by the developed models show a negligible mean bias deviation. Approximately 55% of cases present deviations lower than 5% over the mean value of diffuse irradiance.     

A method for monitoring insolation in remote regions

A method is proposed for measuring the beam and diffuse components of solar radiation via the use of a set of fixed pyranometers tilted in various orientations. A detailed error analysis is performed for the two cases of three and four pyranometers, and it is shown how orientations may be found such that the resultant errors on the derived beam and diffuse components may be expected to be of a magnitude comparable to the errors associated with the pyranometers themselves. Attention is drawn to the fact that certain anisotropic models for the diffuse component may be recast—via the definition of “effective” beam and diffuse components—in such a manner that they take on the mathematical simplicity of an isotropic model.     

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.     

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.     

Yearly distributed insolation model and optimum design of a two dimensional compound parabolic concentrator

Optimum acceptance angle of a compound parabolic concentrator (CPC) is studied by the use of an insolation model proposed in this paper. The insolation consists of two components; diffuse and direct. The direct radiation is supposed to be distributed in the field within ±23.5° of declination on the celestial hemisphere and the diffuse radiation is assumed to have uniform irradiance. This yearly insolation model suggests that the optimum half-acceptance angle at the two-dimensional CPC becomes 26° irrespective of the change of the diffuse radiation fraction. This result leads us to the conclusion that, almost all over the world, a common CPC could be used as an optimum concentration for many solar radiation collecting systems.     

Comparative assessment of plane-of-array irradiance models

A comparative assessment of four mathematical models, used for predicting plane-of-array irradiance, is performed. These models are due to Liu-Jordan, Duffie-Beckman, Klucher, and Perez. Out of these four, the Liu-Jordan and the Duffie-Beckman models represent isotropic sky conditions and the other two model the anisotropic sky. The plane-of-array irradiance predicted by these models are compared against observed field data in Florida, North Caroline, and California. The time periods of interest are hourly, daily, and monthly. It is observed that the isotropic sky model can accurately predict only the monthly average of daily plane-of-array irradiance during the summer. Prediction on the daily or hourly time frame are either not possible or are predicted inaccurately by the isotropic sky model. Between the two anisotropic sky models, the Perez model performed the best, while the Klucher model constantly overestimated for the California location. Results found are consistent with those reported in previous studies.