Stochastic prediction of hourly global solar radiation for Patra,Greece

This paper describes the stochastic prediction of the hourly profile of the intensity of the global solar radiation, I(h; n_j) for any day n_j at a site. The prediction model requires one, two, or three morning measurements of the global solar radiation in a day n_j, makes use of a rich data bank of past years recorded data, and provides I(h; n_j) values for the rest hours of the day. The model is validated by comparing the I(h; n_j) profiles generated for Patra, Greece, with the solar radiation measurements recorded for Winter, Autumn and Spring days, when solar radiation fluctuations often appear to be strong, while also comparing with the predicted by the METEONORM package I(h; n_j) profile. Conclusions are deducted for the predictive power of the model. The proposed model, which is developed in MATLAB for the purpose of this research, provides I(h; n_j) profile predictions very close to the measured values and offers itself as a promising tool for a predictive on-line daily load management.     

Correlation between hourly diffuse and global radiation for New Delhi

Estimation of hourly insolation on tilted surfaces is required in simulation of solar energy systems. This necessitates splitting of hourly global horizontal insolation into diffuse and direct components. Many models have been developed for this purpose, and the aim of this study is to develop a correlation between hourly diffuse ratio and clearness index for New Delhi. The correlation is developed on the basis of measured data for two years. The performance of this correlation was checked by calculating the difference between computed and measured diffuse radiation. The correlation proved to perform quite well. A comparison of the present correlation with those for other locations showed that such correlations are location dependent.     

A model to predict expected mean and stochastic hourly global solar radiation I(h;nj) values

This paper describes an improved approach for (a) the estimation of the mean expected hourly global solar radiation I(h;n_j), for any hour h of a day n_j of the year, at any site, and (b) the estimation of stochastically fluctuating I(h;n_j) values, based on only one morning measurement of a day. Predicted mean expected values are compared, on one hand with recorded data for the period of 1995–2000 and, on the other, with results obtained by the METEONORM package, for the region of Patra, Greece. The stochastically predicted values for the 17th January and 17th July are compared with the recorded data and the corresponding values predicted by the METEONORM package. The proposed model provides I(h;n_j) predictions very close to the measurements and offers itself as a promising tool both for the on-line daily management of solar power sources and loads, and for a cost effective PV sizing approach.     

A model for calculating hourly global solar radiation from satellite data in the tropics

A model for calculating global solar radiation from geostationary satellite data is presented. The model is designed to calculate the monthly average hourly global radiation in the tropics with high aerosol load. This model represents a physical relation between the earth-atmospheric albedo derived from GMS5 satellite data and the absorption and scattering coefficients of various atmospheric constituents. The absorption of solar radiation by water vapour which is important for the tropics, was calculated from ambient temperature and relative humidity. The relationship between the visibility and solar radiation depletion due to aerosols was developed for a high aerosol load environment. This relationship was used to calculate solar radiation depletion by aerosols in the model. The total column ozone from TOMS/EP satellite was employed for the determination of solar radiation absorbed by ozone. Solar radiation from four pyranometer stations was used to formulate the relationship between the satellite band earth-atmospheric albedo and broadband earth-atmospheric albedo required by the model. To test its performance, the model was used to compute the monthly average hourly global radiation at 25 solar radiation monitoring stations in tropical areas in Thailand. It was found that the values of monthly average of hourly global radiations calculated from the model were in good agreement with those obtained from the measurements, with the root mean square difference of 10%. After the validation the model was employed to generate hourly solar radiation maps of Thailand. These maps reveal the diurnal and season variation of solar radiation over the country.     

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.     

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.     

Prediction of global daily solar radiation using higher order statistics

The main concern of the present paper is to present and to analyse two procedures for modelling daily global solar radiation. The first one uses the clearness index techniques and the second one uses a totally different type of approach for taking in consideration important properties of such data, including non-Gaussian shape and non-stationarity. This procedure uses the difference between the extraterrestrial and the observed daily global radiation denoted “lost solar component”. Both procedures are based on higher order statistics for generating the global solar radiation using mainly a random process. The prediction results show that the sequences of values generated have the same statistical characteristics as those of sequences observed. The comparison between the two methods used indicates that the developed model based on the “lost solar component” is better than the model obtained using the conventional procedure based on the clearness index.     

Parameterization of a simple model to estimate monthly global solar radiation based on meteorological variables, and evaluation of existing solar radiation models for Tabouk, Saudi Arabia

Using 9 years of solar radiation data, we established a simple model to calculate the monthly mean global solar radiation on a horizontal surface in Tabouk (28.38° N, 36.6° E, Saudi Arabia). The model correlates the global solar radiation with five meteorological parameters. These parameters are the perceptible water vapor, air temperature, relative humidity, atmospheric pressure, and the mean monthly daily fraction of possible sunshine hours. The estimated global radiation from the model was compared with the measured values using the mean bias error (MBE), coefficient of correlation (R), root mean square error (RMSE), and mean percentage error (MPE). The t statistics were also applied as another indication of suitability. The model has a high coefficient of correlation (R = 0.99), MBE = −14 × 10⁻⁴ kW h/m², RMSE = 0.10 kW h/m², and MPE = −0.03%. It is believed that the model developed in this work is applicable for estimating, with great accuracy. The monthly mean daily global radiation at any site having similar conditions to those found in Tabouk.Furthermore, 29 regression models available in the literature were used to estimate the global solar radiation data for Tabouk. The selected models were different in terms of the variables they use and in the number of the variables they contained. The models were compared on the basis of the statistical errors considered above. Apart from Abdall’s model, which showed a reasonable estimate (MPE = −2.04%, MBE = −0.22 kW h/m², and RMSE = 0.59 kW h/m²), all the models under or overestimate the measured solar radiation values. Comparisons between these models and the produced model, from this study, were also considered. According to the statistical results, the model of Abdall showed the prediction closest to those estimated using the developed model.     

Evaluation of a cloud cover based model for estimation of hourly global solar radiation in Western Canada

Cloud cover based solar radiation models are relatively simple and convenient as the models require the input of cloud cover data which are mostly available from the meteorological stations. In this study, the performance of a cloud cover based solar radiation model (Kasten–Czeplak model) with original or locally fitted coefficients was evaluated for estimating the hourly global solar radiation for four different locations in Western Canada. The average value of R², mean bias error, and root mean square error are 0.69, ?61.6, and 157.9?W?m^?2, respectively, for the model with original coefficients, whereas 0.82, 4.4, 107.1?W?m^?2 with locally fitted coefficients. Results show that the Kasten–Czeplak model with locally fitted coefficients satisfactorily estimated the hourly solar radiation of four different locations in Western Canada. Also, the results indicate that the model with original coefficients has very limited accuracy under intermediate cloud cover conditions.     

On a universal model for the prediction of the daily global solar radiation

A model to predict the mean expected daily global solar radiation, H(n) on a day n, at a site with latitude φ is proposed. The model is based on two cosine functions. A regression analysis taking into account the mean measured values H_m.meas(n) obtained from SoDa database for 42 sites in the Northern Hemisphere resulted in a set of mathematical expressions of split form to predict H(n). The parameters of the two cosine model for 0°<φ < 23° are obtained by regression analysis using a sum of 3–8 Gaussian functions, while for 23°<φ < 71° the two cosine model parameters are expressed by a sum of exponential functions or the product of an exponential and a cosine function. The main equation of the model and the set of parametric expressions provide H(n) for any φ on Earth. Validation results of this model are provided along with the statistical estimators NMBE, NRMSE and t-statistic in comparison to the corresponding values from three databases of NASA, SoDa and the measured values from ground stations provided in Meteonorm.     

Developing regional calibration coefficients for estimation of hourly global solar radiation in Ireland

This study proposed regional coefficients for estimating hourly global solar radiation through the adaptation of some empirical models that relate radiation to climatological and geographical variables. A total of 10 models were adapted over 7 stations in Ireland. The performance of the models was evaluated using some selected error indicators including the global performance index which combines all other error indices. The results indicated that the sunshine based regional calibration coefficients generated through a polynomial approach was most superior over other models with the lowest RMSE (0.2–0.3?MJm^?2?hr^?1), MAE (0.1–0.2?MJm^?2?hr^?1) and Pbias (0–7.0%) and highest R² and KGE (>0.85). The study found no local effect such as instrumental siting, observational uncertainty and climate on the variations of these coefficients. This outcome will therefore facilitate the design of various local and/or regional solar energy applications at microscale in a temperate region.     

Investigating different diffuse solar radiation models to analyse solar radiation on inclined surfaces in Oman

In this paper, a detailed analysis of the solar radiation on horizontal and tilted surfaces for six locations in Oman is presented. The locations are (from North to South): Majis/Sohar, Sur, Fahud, Masira, Marmul, and Salalah. These locations spread over Oman and cover different types of landscape. The method is validated through the use of measured data. The effect of tilt angle and orientation on the incident solar radiation is presented along with optimum surface tilt angles and directions for maximum solar radiation collection in these six locations. The solar radiation models used in this paper show good agreement with measured data. The results presented in this paper are extremely useful for quick estimation of solar radiation for calculations of buildings’ cooling load and solar collector system performance. This can be easily extended for other locations with similar landscapes and geographical conditions.     

Estimation of global solar radiation using artificial neural networks

This paper introduces a neural network technique for the estimation of global solar radiation. There are 41 radiation data collection stations spread all over the kingdom of Saudi Arabia where the radiation data and sunshine duration information are being collected since 1971. The available data from 31 locations is used for training the neural networks and the data from the other 10 locations is used for testing. The testing data was not used in the modeling to give an indication of the performance of the system in unknown locations. Results indicate the viability of this approach for spatial modeling of solar radiation.     

Novel approach in developing hourly global solar radiation model based on peak sunshine hours

The present study explores a novel approach to derive the hourly global solar radiation (HGSR) for any given latitude based on the peak sunshine hours (PSHs). The proposed analytical model describes a relationship between the HGSR and the day length and the PSHs. The applicability of this model is evaluated by comparing the actual and derived values of HGSR for two cities Chennai (13°04′N, 80°17′E) and New Delhi (29°06′N, 77°22′E). To judge the goodness of the proposed model a set of error metrics has been developed by evaluating the variation of actual HGSR from the simulated value for a given day over 12 months. The overall average mean bias error for one year is 1.015% and 1.08% for Chennai and New Delhi, respectively. The agreement between the actual and the simulated values is generally good, with an appreciable correlation of 95%. In particular, unlike the other models this approach requires only two inputs which are easily available for any location. The proposed technique is useful for any solar application designer for deriving the hourly solar radiation values for a given day of any location with less available climate data.     

A simple and efficient algorithm to estimate daily global solar radiation from geostationary satellite data

Surface global solar radiation (GSR) is the primary renewable energy in nature. Geostationary satellite data are used to map GSR in many inversion algorithms in which ground GSR measurements merely serve to validate the satellite retrievals. In this study, a simple algorithm with artificial neural network (ANN) modeling is proposed to explore the non-linear physical relationship between ground daily GSR measurements and Multi-functional Transport Satellite (MTSAT) all-channel observations in an effort to fully exploit information contained in both data sets. Singular value decomposition is implemented to extract the principal signals from satellite data and a novel method is applied to enhance ANN performance at high altitude. A three-layer feed-forward ANN model is trained with one year of daily GSR measurements at ten ground sites. This trained ANN is then used to map continuous daily GSR for two years, and its performance is validated at all 83 ground sites in China. The evaluation result demonstrates that this algorithm can quickly and efficiently build the ANN model that estimates daily GSR from geostationary satellite data with good accuracy in both space and time.     

Empirical correlation of estimating global solar radiation using meteorological parameters

An empirical model for the estimation of solar energy on the basis of Angstrom's model is proposed in this work. Seven regression equations are developed by using different meteorological parameters such as mean sunshine duration per hour, temperature, relative humidity, wind speed, and rainfall. The performance of the model is determined on the basis of statistical indicators like correlation coefficient(r), coefficient of determination (R²), root mean square error (RMSE), mean percentage error (MPE), and mean bias error (MBE). The results show that the equation with the highest value of r, R² and the least value of RMSE, MPE, and MBE provides better results.     

Generation of synthetic daily global solar radiation data based on ERA-Interim reanalysis and artificial neural networks

Four variables (total cloud cover, skin temperature, total column water vapour and total column ozone) from meteorological reanalysis were used to generate synthetic daily global solar radiation via artificial neural network (ANN) techniques. The goal of our study was to predict solar radiation values in locations without ground measurements, by using the reanalysis data as an alternative to the use of satellite imagery. The model was validated in Andalusia (Spain), using measured data for nine years from 83 ground stations spread over the region. The geographical location (latitude, longitude), the day of the year, the daily clear sky global radiation, and the four meteorological variables were used as input data, while the daily global solar radiation was the only output of the ANN. Sixty five ground stations were used as training dataset and eighteen stations as independent dataset. The optimum network architecture yielded a root mean square error of 16.4% and a correlation coefficient of 94% for the testing stations. Furthermore, we have successfully tested the forecasting capability of the model with measured radiation values at a later time. These results demonstrate the generalization capability of this approach over unseen data and its ability to produce accurate estimates and forecasts.     

New sunshine-based models for predicting global solar radiation using PSO (particle swarm optimization) technique

PSO (particle swarm optimization) technique is applied to estimate monthly average daily GSR (global solar radiation) on horizontal surface for different regions of Iran. To achieve this, five new models were developed as well as six models were chosen from the literature. First, for each city, the empirical coefficients for all models were separately determined using PSO technique. The results indicate that new models which are presented in this study have better performance than existing models in the literature for 10 cities from 17 considered cities in this study. It is also shown that the empirical coefficients found for a given latitude can be generalized to estimate solar radiation in cities at similar latitude. Some case studies are presented to demonstrate this generalization with the result showing good agreement with the measurements. More importantly, these case studies further validate the models developed, and demonstrate the general applicability of the models developed. Finally, the obtained results of PSO technique were compared with the obtained results of SRTs (statistical regression techniques) on Angstrom model for all 17 cities. The results showed that obtained empirical coefficients for Angstrom model based on PSO have more accuracy than SRTs for all 17 cities.     

Monthly ratios of PAR to global solar radiation measured at northern Tibetan Plateau, China

Using narrowband and broadband solar radiation measurements collected at Wudaoliang (WDL) site in northern Tibetan Plateau (NTP) from September 1993 to December 1998, the relationship between monthly photosynthetically active radiation (Q_P) and global solar radiation (R_S) values is analyzed. Temporal variability of the ratio (Q_P/R_S) and its further dependence on several meteorological variables are presented. The narrowband ratio exhibited diurnal and seasonal variability with high values during morning and afternoon hours and low values around noon in winter time, whereas during summer period the ratio was decreased from morning to afternoon. The ratio (Q_P/R_S) was correlated positively with several atmospheric parameters such as water vapor pressure and low-level cloud amount; in contrast, the ratio was negatively correlated with clearness index, relative sunshine duration and atmospheric turbidity. It was also found that both the relative sunshine duration and water vapor pressure are the most influential parameters on the estimations of the spectral PAR ratio. Finally, an empirically derived model is proposed for estimating monthly average PAR values over the northern Tibetan Plateau. Verification results further ensured that the proposed model predicts monthly global PAR values accurately.