Modelling of diffuse solar fraction with multiple predictors

For some locations both global and diffuse solar radiation are measured. However, for many locations, only global radiation 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 direct on some other plane using trigonometry, we need to have diffuse radiation on the horizontal plane available. There are regression relationships for estimating the diffuse on a tilted surface from diffuse on the horizontal. Models for estimating the diffuse on the horizontal from horizontal global that have been developed in Europe or North America have proved to be inadequate for Australia [13]. Boland et al. [2] developed a validated model for Australian conditions. Boland et al. [3] detailed our recent advances in developing the theoretical framework for the use of the logistic function instead of piecewise linear or simple nonlinear functions and was the first step in identifying the means for developing a generic model for estimating diffuse from global and other predictors. We have developed a multiple predictor model, which is much simpler than previous models, and uses hourly clearness index, daily clearness index, solar altitude, apparent solar time and a measure of persistence of global radiation level as predictors. This model performs marginally better than currently used models for locations in the Northern Hemisphere and substantially better for Southern Hemisphere locations. We suggest it can be used as a universal model.     

An hourly diffuse fraction model with correction for variability and surface albedo

The paper presents an improved version of a previously published model for the diffuse fraction of hourly global irradiance. In addition to hourly solar elevation and clearness index, an hour-to-hour variability index and regional surface albedo are included among the input parameters. Moreover, to prevent excessively high normal incidence beam irradiances at very low solar elevations, the model does not allow a solar elevation dependent maximum beam transmittance to be exceeded. This new model is tuned to 32 years of data from Bergen, Norway. Moreover, a test against independent data from four European stations showed that the model performs better than the models of Erbs et al. (1982), Maxwell (1987) and Perez et al. (1992).     

Prediction of hourly and daily diffuse fraction using neural network,as compared to linear regression models

For most of the locations all over Egypt the records of diffuse radiation in whatever scale are non-existent. In case that it exists, the quality of these records is not as good as it should be for most purposes and so an estimate of its values is desirable. To achieve such a task, an artificial neural network (ANN) model has been proposed to predict diffuse fraction (K_D) in hourly and daily scale. A comparison between the performances of the ANN model with that of two linear regression models has been reported. An attempt was also done to describe the ANN outputs in terms of first order polynomials relating K_D with clearness index (K_T) and sunshine fraction (S/S₀). If care is taken in considering the corresponding regional climatic differences, these correlations can be generalized and transferred to other sites. The results hint that the ANN model is more suitable to predict diffuse fraction in hourly and daily scales than the regression models in the plain areas of Egypt.     

Model for computation of solar fraction in a single-slope solar still

A new model that calculates the distribution of solar radiation inside a single-slope solar still has been proposed. In this model, the solar fraction on a vertical surface is divided into beam and diffuse parts and the optical view factors of surfaces inside the still are taken into account. To validate the model, outdoor tests of a conventional solar still were conducted under different weather conditions at the University of Strathclyde. The proposed model is compared with the previous one. It is found that the beam solar fraction is affected by both the geometry of the solar still and position of the sun in the sky. In contrast, the diffuse solar fraction is only dependent on the geometry of the solar distiller. The present model exhibited a lower root mean square error than that of the previous model. It appears that splitting the solar fraction into beam and diffuse parts improves the accuracy of modelling the performance of a single-slope solar still.     

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.     

A comparative study to estimate daily diffuse solar radiation over India

A detailed study of monthly average daily diffuse solar radiation for selected Indian locations have been performed using five years (2001–2005) measured data. The data of four prominent locations (Jodhpur, Calcutta, Bombay and Pune), representing varying weather conditions of the entire country, have been taken for the present study. The correlations between the diffuse fraction (H_d/H) and the sunshine fraction (S/S₀) have been developed using regression analysis method for each selected location as well as for all Indian locations, we call it All India Correlation (AIC). The results obtained from present AIC are well compared with the measured data along with the estimates of Liu and Jordan, Gopinathan and Iqbal for different locations. The comparisons between various data conclude that AIC can be used to estimate diffuse fraction for any location in India. For further validation and to show the accuracy of present correlations, statistical tests of root mean square error (RMSE), mean bias error (MBE) and mean percentage error (MPE) are also performed.     

Evaluation of 12 models to estimate hourly diffuse irradiation on inclined surfaces

This study evaluates the performance of 12 models to estimate hourly diffuse solar irradiation on inclined surfaces from those measured on horizontal surfaces. Total solar irradiation incident on a tilted surface consists of three components including: beam, diffuse and reflected from the ground. On a semi-hourly basis, the beam component can be calculated by the ratio of the incidence angle to the solar zenith angle. The reflected component has a small effect on calculations and may be calculated with an isotropic model. In contrast, models for estimating the diffuse component show major differences, which justify the validation study that this paper discusses. Twelve models were tested against recorded south- and west-facing slope irradiances at Karaj (35°55^′N; 50°56^′E), Iran. The following models were included: Badescu [Ba], Tian et al. [Ti], Perez et al. [P9], Reindl et al. [Re], Koronakis [Kr], Perez et al. [P8], Skartveit and Olseth [SO], Steven and Unsworth [SU], Hay [Ha], Klucher [Kl], Temps and Coulson [TC], and Liu and Jordan [LJ].The relative root mean square error (RMSE), for the south-facing surface ranges from 10.16% to 54.89% for the SO and TC models, respectively. For the west-facing surface, RMSE ranges from 30.71% for the P9 model to 63.53% for the TC model. Statistical indices show that all models produce large errors for the west-facing surface. Statistical indices for the south-facing surface show reasonably good agreement with measured data.     

Computing global and diffuse solar hourly irradiation on clear sky. Review and testing of 54 models

Fifty-four broad band models for computation of global and diffuse irradiance on horizontal surface are shortly presented and tested. The input data for these models consist of surface meteorological data, atmospheric column integrated data and data derived from satellite measurements. The testing procedure is performed for two meteorological stations in Romania (South-Eastern Europe). The testing procedure consists of forty-two stages intended to provide information about the sensitivity of the models to various sets of input data. There is no model to be ranked “the best” for all sets of input data. Very simple models as well as more complex models may belong to the category of “good models”. The best models for solar global radiation computation are, on equal-footing, ESRA3, Ineichen, METSTAT and REST2 (version 81). The second best models are, on equal-footing, Bird, CEM and Paulescu & Schlett. The best models for solar diffuse radiation computation are, on equal-footing, ASHRAE2005 and King. The second best model is MAC model. The best models for computation of both global and diffuse radiation are, on equal-footing, ASHRAE 1972, Biga, Ineichen and REST2 (version 81). The second best is Paulescu & Schlett model.     

Numerical simulation of the effect of hydrogen addition fraction on catalytic micro-combustion characteristics of methane-air

Understanding of micro-scale combustion mechanism is very essential to the development of micro-power devices, so hydrogen assisted catalytic combustion of methane on platinum was studied in this paper. The combustion of preheated mixtures of methane-hydrogen-air in a micro-combustor was modeled by a two-dimensional model including an elementary-step surface reaction mechanism. It was demonstrated that the model could predict the effects of changes of hydrogen fraction. It was shown that the mole fraction of H, OH and C(s) increase and ignition time decreases with hydrogen addition. It was also shown that the improving effect of hydrogen on the ignition temperature of the fuel and O(s) coverage is particularly evident at relatively low hydrogen fraction. The promotion of the combustion stability is due to the decrease of coefficient of variation with hydrogen addition. The methane combustion will move toward the more stabilized reaction and there is a great potential to reduce the pressure fluctuation.     

Improved multiple linear regression based models for solar collectors

Mathematical modelling is the theoretically established tool to investigate and develop solar thermal collectors as environmentally friendly technological heat producers. In the present paper, the recent and accurate multiple linear regression (MLR) based collector model in Ref. [1] is empirically improved to minimize the modelling error. Two new, improved models called IMLR model and MPR model (where MPR is the abbreviation of multiple polynomial regression) are validated and compared with the former model (MLR model) based on measured data of a real collector field. The IMLR and the MPR models are significantly more precise while retaining simple usability and low computational demand. Many attempts to decrease the modelling error further show that the gained precision of the IMLR model cannot be significantly improved any more if the regression functions are linear in terms of the input variables. In the MPR model, some of the regression functions are nonlinear (polynomial) in terms of the input variables.     

Global,diffuse and direct solar radiation at the surface in the city of Rio de Janeiro: Observational characterization and empirical modeling

The city of Rio de Janeiro and others 18 cities compose the Metropolitan Area of Rio de Janeiro. The main objective of this work is to characterize observationally the diurnal and seasonal evolution of the solar radiation components in the city of Rio de Janeiro. The measurements of global and diffuse solar radiation and standard meteorological variables at the surface have been carried out regularly at the Geoscience Institute of Federal University of Rio de Janeiro since October of 2011. The microclimatic conditions show that the period 2011–2014 was warmer during most of the year and drier in summer and spring in comparison with climate normal. All solar radiation components present a well defined diurnal cycle with maximum at noon. The estimates of global and direct solar radiation indicate a great potential available for solar energy at the surface, particularly in summer. The behavior of the clearness index and diffuse solar radiation fraction is similar in summer and winter. The Angstrom formula represents properly the estimate of the monthly average daily value of global solar radiation. The sigmoid logistic function is statistically more significant in comparison with others correlation models to represent the diffuse fraction as a function clearness index.     

Modeling and numerical simulation of solar chimney power plants

The solar chimney power plant is a simple solar thermal power plant that is capable of converting solar energy into thermal energy in the solar collector. In the second stage, the generated thermal energy is converted into kinetic energy in the chimney and ultimately into electric energy using a combination of a wind turbine and a generator. The purpose of this study is to conduct a more detailed numerical analysis of a solar chimney power plant. A mathematical model based on the Navier-Stokes, continuity and energy equations was developed to describe the solar chimney power plant mechanism in detail. Two different numerical simulations were performed for the geometry of the prototype in Manzanares, Spain. First, the governing equations were solved numerically using an iterative technique. Then, the numerical simulation was performed using the CFD software FLUENT that can simulate a two-dimensional axisymmetric model of a solar chimney power plant with the standard k-epsilon turbulence model. Both the predictions were compared with the available experimental data to assess the validity of the model. The temperature, velocity and pressure distributions in the solar collector are illustrated for three different solar radiations. Reasonably good quantitative agreement was obtained between the experimental data of the Manzanares prototype and both the numerical results.     

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.     

An investigation of the performance of 14 models for estimating hourly diffuse irradiation on inclined surfaces at tropical sites

The performance of 14 models for estimating hourly diffuse irradiation on inclined surfaces was investigated. In order to obtain solar radiation data for this investigation, equipment for measuring solar radiation on inclined surfaces facing to the north, south, east and the west at different tilted angles to the horizontal surface (30°, 60° and 90°) were constructed and installed at two tropical sites in Thailand, namely Nakhon Pathom (13.82 °N, 100.04 °E) and Ubon Ratchathani (15.25 °N, 104.87 °E). Radiation data encompassing different periods of 1–4 years were used in this work. Diffuse irradiance measurements at different tilted angles were compared with various model algorithms. Results show that the Muneer and Gueymard models have comparable performance in terms of root mean square difference (RMSD) and these models give the lowest RMSD, as compared to that of the other models.     

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.     

Thermal modeling of passive and active solar stills for different depths of water by using the concept of solar fraction

This communication presents the thermal analysis of passive and active solar distillation system by using the concept of solar fraction inside the solar still with the help of AUTOCAD 2000 for given solar azimuth and altitude angle and latitude, longitude of the place. Experiments have been conducted for 24 h (9 am to 8 am) for New Delhi climatic conditions (latitude 28°35′N, longitude 77°12′E) during the months of November and December for different water depths in the basin (0.05, 0.1 and 0.15 m) for passive as well as active solar distillation system. Analytical expressions for water and glass cover temperatures and yield have been derived in terms of design and climatic parameters. It is observed that

(i) the solar fraction plays a very important role at lower values of solar altitude angle;

(ii) the internal convective heat transfer coefficient decreases with the increase of water depth in the basin due to decrease in water temperature;

(iii) there is a fair agreement between the experimental observation and theoretical prediction during daytime as compared to that during the night.

Comparison of artificial intelligence and empirical models for estimation of daily diffuse solar radiation in North China Plain

Accurate diffuse solar radiation (H_d) data is highly crucial for the development and utilization of solar energy technologies. However, due to expensive cost and technology requirements, measurements of H_d are not available in many regions of North China Plain (NCP), where the diffuse and direct solar radiation are affected by severe particulate pollution. Thus, development of models for precisely estimating H_d is indeed essential in NCP. On this account, the present studies proposed four artificial intelligence models, including the extreme learning machine (ELM), backpropagation neural networks optimized by genetic algorithm (GANN), random forests (RF), and generalized regression neural networks (GRNN), for estimating daily H_d at two meteorological stations of NCP. Daily global solar radiation and sunshine duration along with the estimated extraterrestrial radiation and maximum possible sunshine duration were selected as model inputs to train the models. Meanwhile, the proposed AI models were compared with the empirical Iqbal model to test their performance using measured H_d data. The results indicated that the ELM, GANN, RF, and GRNN models all performed much better than the empirical Iqbal model for estimating daily H_d. All the models underestimated H_d for both stations, with average relative error ranging from ?5.8% to ?5.4% for AI models and 19.1% for Iqbal model in Beijing, ?5.9% to ?4.3% and ?26.9% in Zhengzhou, respectively. Generally, GANN model had the best accuracy, and ELM ranked next, followed by RF and GRNN models. The ELM model had a slightly poorer performance but the highest computation speed, and both the GANN and ELM models could be highly recommended to estimate daily H_d in NCP of China.     

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.     

Use of neural networks for the creation of hourly global and diffuse solar irradiance data at representative locations in Greece

In this work, a new approach is tested by applying neural networks treatment to meteorological time-series data sets, recorded during 1991–2000 at certain Greek locations, in order to create fully appropriate solar data information. Neural networks, in this case, are used for creating missing mean, maximum and minimum global and diffuse solar irradiance hourly data, when educated with other known meteorological time-series hourly values. For this purpose, hourly data of air temperature, relative humidity, sunshine duration, clouds’ octals, as well as local latitude are used with regard to these sites. Neural networks’ education process outputs are checked against known hourly values of solar irradiance, based upon the mentioned meteorological hourly raw data necessary for this action recorded at the National Observatory of Athens, the actinometric station at the Technological Education Institute (TEI) of Piraeus, and six other locations. Selection of these sites is representative of the climatic conditions in Greece, from north to south and east to west. Following the same scheme, the produced hourly global and diffuse mean hourly solar irradiance values are in a very good agreement (p<0.01) with actual measurements.     

Modeling thermal asymmetries in double slope solar stills

Solar distillation literature reports a generalized use of stills with single and double slope condensing covers, where modeling equations describe a solution approach that considers the condenser as a single element. The solution for a double slope still analysis is generally forced to the case of one with a single flat condensing cover. This paper proposes a new lumped parameters mathematical model to study the asymmetries that arise in the temperature and distillate yield in double slope solar stills. The condenser is studied as a two-element system and non-simplified equations for heat transfer and optical transmission characteristics are used. The model is tested for the case with the strongest thermal differences and validated with experimental data. Overall results show a good correlation between predictions and experimentation.