Re-examination of ASHRAE insolation models with reference to Indian locations

Recently, the Indian Meteorological Department has made available measured horizontal global and diffuse radiation data for cloudless days for many Indian locations. A study is undertaken to re-examine the normal incident and diffuse radiation models suggested by ASHRAE using data for seven locations. Both models were found to be valid, but the diffuse radiation model needs refinement. The computed values of A, B and C were found to be different from those of ASHRAE. Comparison of computed insolation using these values of A, B and C with measured data shows good agreement. Calculation performed with ASHRAE values shows disagreement with measured data by some amount for global and by significant amounts for diffuse radiation.     

Evaluation and comparison of hourly solar radiation models

In this paper, an attempt has been made to develop a new model to evaluate the hourly solar radiation for composite climate of New Delhi. The comparison of new model for hourly solar radiation has been carried out by using various model proposed by others. The root mean square error (RMSE) and mean bias error (MBE) have been used to compare the accuracy of new and others model. The results show that the ASHRAE and new proposed model estimate hourly solar radiation better for composite climate of New Delhi in comparison to other models. Hourly solar radiation estimated by constants obtained by new model (modified ASHRAE model) for composite climate of India is fairly comparable with measured data. The percentage mean bias error with new constants for New Delhi was found as low as 0.15 and 0% for hourly beam and diffuse radiation, respectively. There is a 1.9–8.5% RMSE between observed and predicted values of beam radiation using new constants for clear days. The statistical analysis has been used for the present study. Copyright © 2008 John Wiley & Sons, Ltd.     

Monthly average clear-sky broadband irradiance database for worldwide solar heat gain and building cooling load calculations

This paper establishes the formulation of a new clear-sky solar radiation model appropriate for algorithms calculating cooling loads in buildings. The aim is to replace the ASHRAE clear-sky model of 1967, whose limitations are well known and are reviewed. The new model is derived in two steps. The first step consists of obtaining a reference irradiance dataset from the REST2 model, which uses a high-performance, validated, two-band clear-sky algorithm. REST2 requires detailed inputs about atmospheric conditions such as aerosols, water vapor, ozone, and ground albedo. The development of global atmospheric datasets used as inputs to REST2 is reviewed. For the most part, these datasets are derived from space observations to guarantee universality and accuracy. In the case of aerosols, point-source terrestrial measurements were also used as ground truthing of the satellite data. The second step of the model consists of fits derived from a REST2-based reference irradiance dataset. These fits enable the derivation of compact, but relatively accurate expressions, for beam and diffuse clear-sky irradiance. The fitted expressions require the tabulation of only two pseudo-optical depths for each month of the year. The resulting model, and its tabulated data, are expected to be incorporated in the 2009 edition of the ASHRAE Handbook of Fundamentals.     

Solar radiation models—A review

Solar radiation models for predicting the average daily and hourly global radiation, beam radiation and diffuse radiation on horizontal surface are reviewed in this article. Estimations of monthly average hourly global radiation from daily summations are discussed. It was observed that Collares‐Pereira and Rabl model as modified by Gueymard (CPRG) yielded the best performance for estimating mean hourly global radiation incident on a horizontal surface for Indian regions. Estimations of monthly average hourly beam and diffuse radiation are discussed. It was observed that Singh‐Tiwari and Jamil‐Tiwari both models generally give better results for climatic conditions of Indian regions. Therefore, their use is recommended for composite climate of Indian regions. Empirical correlations developed to establish a relationship between the hourly diffuse fraction and the hourly clearness index using hourly global and diffuse irradiation measurements on a horizontal surface are discussed. Fifty models using the Angstrom–Prescott equation to predict the average daily global radiation with hours of sunshine are considered. It was reported that Ertekin and Yaldiz model showed the best performance against measured data of Konya, Turkey. Copyright © 2010 John Wiley & Sons, Ltd.     

REST2: High-performance solar radiation model for cloudless-sky irradiance, illuminance, and photosynthetically active radiation – Validation with a benchmark dataset

REST2, a high-performance model to predict cloudless-sky broadband irradiance, illuminance and photosynthetically active radiation (PAR) from atmospheric data, is presented. Its derivation uses the same two-band scheme as in the previous CPCR2 model, but with numerous improvements. Great attention is devoted to precisely account for the effect of aerosols, in particular.Detailed research-class measurements from Billings, OK are used to assess the performance of the model for the prediction of direct, diffuse and global broadband irradiance. These measurements were made in May 2003 during a sophisticated radiative closure experiment, which involved the best radiometric instrumentation currently available and many ancillary instruments. As a whole, these exceptional measurements constitute the only known modern benchmark dataset made specifically to test the intrinsic performance of radiation models. Using this dataset as reference, it is shown that REST2 performs better than CPCR2 for irradiance, illuminance or PAR predictions. The availability of the turbidity data required by REST2 or other similar models is also discussed, as well as the effect that turbidity has on each component of broadband irradiance, PAR irradiance and illuminance, and on the diffuse/global PAR ratio.     

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.     

Assessment of diffuse solar energy under general sky condition using artificial neural network

In this paper, artificial neural network (ANN) models are developed for estimating monthly mean hourly and daily diffuse solar radiation. Solar radiation data from 10 Indian stations, having different climatic conditions, all over India have been used for training and testing the ANN model. The coefficient of determination (R²) for all the stations are higher than 0.85, indicating strong correlation between diffuse solar radiation and selected input parameters. The feedforward back-propagation algorithm is used in this analysis. Results of ANN models have been compared with the measured data on the basis of percentage root-mean-square error (RMSE) and mean bias error (MBE). It is found that maximum value of RMSE in ANN model is 8.8% (Vishakhapatnam, September) in the prediction of hourly diffuse solar radiation. However, for other stations same error is less than 5.1%. The computation of monthly mean daily diffuse solar radiation is also carried out and the results so obtained have been compared with those of other empirical models. The ANN model shows the maximum RMSE of 4.5% for daily diffuse radiation, while for other empirical models the same error is 37.4%. This shows that ANN model is more accurate and versatile as compared to other models to predict hourly and daily diffuse solar radiation.     

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.     

Prediction of direct and global solar irradiance using broadband models: Validation of REST model

In the present paper, three parametric models Yang, CPCR2 and REST (without considering transmittance due to nitrogen dioxide) have been analyzed for four Indian stations, namely New Delhi, Mumbai, Pune and Jaipur over the period of 1995–2002, under cloudless conditions. These stations have different climatic conditions. The beam radiation at normal incidence as well as global solar radiation at horizontal surface was computed for these locations during all seasons except monsoon (June to September). The computed values of beam and global irradiance was compared with reference values in case of beam and measured values in case of global solar radiation on the basis of percentage root mean square error (RMSE) and mean bias error (MBE). The maximum RMSE is 6.5% in REST model, as compare to 15% in Yang and 11% in CPCR2 model for predicting direct normal irradiance. The predicted global radiation at horizontal is showing maximum RMSE 7% in REST model, 13.4% in Yang and 25.9% in CPCR2 model. This shows that REST model has good agreement with measured data for these Indian stations as compare to other two models.     

Diffuse solar irradiation model evaluation in the North Mediterranean Belt area

The performance of daily and hourly diffuse horizontal solar irradiation models and correlations is examined using an assembled data set of multivariate meteorological time series from countries in the North Mediterranean Belt area. The correlations reviewed use only daily global, hourly global or daily diffuse irradiation as input, for the daily or hourly time scale. The best overall performance was presented by the Frutos correlation for the estimation of the daily diffuse radiation by an adapted version of the Liu and Jordan correlation for the mean daily diffuse radiation profile, and by the Hollands and Crha model for estimation of hourly diffuse values from the corresponding global values. The results show that the best correlation for each site varies. Two empirical piecewise correlations were also developed by the authors with the help of the data bank available, yielding models that showed even better fits to the data. The results show some seasonal and location dependence.     

Estimation of monthly mean daily diffuse radiation in China

In this study, several equations are employed to estimate monthly mean daily diffuse solar radiation for eight typical meteorological stations in China. Estimated values are compared with measured values in terms of statistical error tests such as mean percentage error (MPE), mean bias error (MBE), root mean square error (RMSE). All the models fit the data adequately and can be used to estimate monthly mean daily diffuse solar radiation from global solar radiation and sunshine hours. This study finds that the quadratic model performed better than the other models:     

Estimation of global solar radiation in arid and semi-arid climates of East and West Iran

In Iran, most of the models used so far, have provided solar estimation for a few specific locations based on the short-term solar observations. Using different radiation models, (e.g. Sabbagh, Paltridge–Proctor, Daneshyar) and various input parameters (e.g. cloud cover, sunshine duration, relative humidity, temperature, and altitude) we developed a general height-depended formula for the prediction of the direct and diffuse monthly average daily solar radiation for 64 mountainous arid and semi-arid locations in West and East Iran. The models mentioned are modified and new coefficients are defined for the diffuse component based on the long-term observed diffuse data. Model results are validated against up to 13-year daily solar observations at 10 solar radiation sites. In comparison with the previous studies, the newly developed method performs more accurate estimation (less than 3% MPE error) in the arid and semi-arid regions. Comparison of the model results indicates that calibration of the coefficients made to the diffuse formula against the longer period experimental data can improve the estimations of global solar radiation.     

中国不同气候区日总太阳辐射计算模型适用性分析及通用计算模型优化

利用中国5个气候区96个气象台站的1981—2010年的日值气象数据,对比分析12个基于日照百分率和12个基于温度的日总太阳辐射计算模型在不同气候区的适用性。采用判定系数（R²）、均方根误差（RMSE）、平均绝对误差（MABE）、平均误差（MBE）和全局性能系数（GPI）5个评价指标,确定各气候区最适宜的模型形式。以该模型为基准,建立适用于中国不同气候区的基于日照百分率和基于温度的日总太阳辐射通用计算模型。结果表明,三次方形式的基于日照百分率和基于日较差-平均温度的模型在各气候区计算精度均最高;以该模型为基础,建立适用于中国不同气候区的基于日照百分率和基于温度的日总太阳辐射通用计算模型,其平均R²分别为0.91和0.68。     

Direct and indirect uncertainties in the prediction of tilted irradiance for solar engineering applications

Global radiation measured on fixed-tilt, south-facing planes (40° and vertical) and a 2-axis tracker at NREL’s Solar Radiation Research Lab. in Golden, CO is compared to predictions from ten transposition models, in combination with either optimal or suboptimal input data of horizontal irradiance. Suboptimal inputs are typically used in everyday engineering calculations, for which the necessary data are usually unavailable for the site under scrutiny, and must be estimated in some way. The performance of the transposition models is first evaluated for ideal conditions when optimal data are used. In this specific case, it is found that the Gueymard and Perez models provide the best estimates of global tilted irradiance under clear skies in particular.The performance of four direct/diffuse separation models is also evaluated. Their predictions of direct and diffuse radiation appear biased in most cases, with a model-dependent magnitude. Finally, the performance of the resulting combinations of separation and transposition models is analyzed in a variety of situations. When only global irradiance is known, the accuracy of the tilted irradiance predictions degrades significantly, and is mainly conditioned by the local performance of the direct/diffuse separation method. For the south-facing vertical surface, inaccuracies in the ground reflection calculations becomes another key factor and significantly increase the prediction error. The Reindl transposition algorithm appears to perform best in this case. When using suboptimal input data for the prediction of plane-of-array irradiance on a moderately tilted plane (40°S) or a 2-axis tracking plane, the Hay, Reindl and Skartveit models are less penalized than others and tend to perform better. It is concluded that further research should be conducted to improve the overall process of predicting irradiance on tilted planes in realistic situations where no local high-quality irradiance or albedo measurements are available.     

Estimation of hourly solar radiation for India

The ASHRAE constants predict high values of the hourly beam radiation and very low values of the hourly diffuse radiation when used to predict radiation at Indian locations. Hence a procedure has been developed for the estimation of direct, diffuse and global hourly solar radiation on a horizontal surface for any location in India. To calculate hourly solar radiation, an exponential curve, similar to the one used by ASHRAE, was fitted to the measured solar radiation data of six cities from different regions of India. The statistical analysis was carried out for the data computed using ASHRAE constants and the set of constants obtained for India using the measured data of four different Indian cities selected randomly. Three statistical indicators were used to compare the accuracy of the developed procedure. The results show that ASHRAE constants are not suitable to estimate hourly solar radiation in India. Hourly solar radiation estimated by constants obtained for India are fairly comparable with measured data. The mean percentage error with Indian constants for these four Indian cities was found as low as 2.27, −6.29 and −6.09% for hourly beam, diffuse and global radiation, respectively.     

Entropy generation through combined non-grey gas radiation and forced convection between two parallel plates

The current study presents a numerical computation of combined gas radiation and forced convection through two parallel plates. A laminar flow of a temperature-dependent and non-grey gas in the entrance region of the channel was investigated. Over-heated water vapor was chosen as a gas because of its large absorption bands. Some special attention was given to entropy generation and its dependence on geometrical and thermodynamic parameters. The radiative part of the study was solved using the “Ray Tracing” method through S₄ directions, associated with the “statistical narrow band correlated-k” (SNBCK) model. The temperature fields were used to calculate the distributions of local and global entropy generation.     

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.     

A simplified model for generating sequences of global solar radiation data for isolated sites: Using artificial neural network and a library of Markov transition matrices approach

The purpose of this work is to develop a hybrid model which will be used to predict the daily global solar radiation data by combining between an artificial neural network (ANN) and a library of Markov transition matrices (MTM) approach. Developed model can generate a sequence of global solar radiation data using a minimum of input data (latitude, longitude and altitude), especially in isolated sites. A data base of daily global solar radiation data has been collected from 60 meteorological stations in Algeria during 1991–2000. Also a typical meteorological year (TMY) has been built from this database. Firstly, a neural network block has been trained based on 60 known monthly solar radiation data from the TMY. In this way, the network was trained to accept and even handle a number of unusual cases. The neural network can generate the monthly solar radiation data. Secondly, these data have been divided by corresponding extraterrestrial value in order to obtain the monthly clearness index values. Based on these monthly clearness indexes and using a library of MTM block we can generate the sequences of daily clearness indexes. Known data were subsequently used to investigate the accuracy of the prediction. Furthermore, the unknown validation data set produced very accurate prediction; with an RMSE error not exceeding 8% between the measured and predicted data. A correlation coefficient ranging from 90% and 92% have been obtained; also this model has been compared to the traditional models AR, ARMA, Markov chain, MTM and measured data. Results obtained indicate that the proposed model can successfully be used for the estimation of the daily solar radiation data for any locations in Algeria by using as input the altitude, the longitude, and the latitude. Also, the model can be generalized for any location in the world. An application of sizing PV systems in isolated sites has been applied in order to confirm the validity of this model.     

Effects of air pollution for estimating global solar radiation in India

Solar energy is the primary resource for all biological, chemical and physical processes. The amount of global solar radiation is an important parameter for solar energy applications. It is common to estimate a monthly average of daily global solar radiation using different regression models. These models in turn exploit the correlation between solar radiation and various atmospheric factors. These factors are commonly derived from meteorological, geographical and climatological data that are readily available for majority of weather stations across the world. In this paper, a novel regression model that can predict location-independent daily global solar radiation is presented. The proposed exponential quadratic model captures the correlation between measured global solar radiation values, sunshine hour and Air Pollution Index for Indian cities. In addition to this, an extended study of several other regression models (e.g. linear, quadratic, exp.-linear and exp.-quadratic) is also presented. This analysis with real data from Indian cities suggests that air pollution is a more significant factor than location when predicting solar radiation. Finally, the model parameters (regression coefficients) for each model are listed out. Additionally, the generalised model equation for the best performing model is also presented.