Prediction of monthly mean daily diffuse solar radiation using artificial neural networks and comparison with other empirical models

An artificial neural network (ANN) model for estimating monthly mean daily diffuse solar radiation is presented in this paper. Solar radiation data from 9 stations having different climatic conditions all over China during 1995–2004 are used for training and testing the ANN. Solar radiation data from eight typical cities are used for training the neural networks and data from the remaining one location are used for testing the estimated values. Estimated values are compared with measured values in terms of mean percentage error (MPE), mean bias error (MBE) and root mean square error (RMSE). The results of the ANN model have been compared with other empirical regression models. The solar radiation estimations by ANN are in good agreement with the actual values and are superior to those of other available models. In addition, ANN model is tested to predict the same components for Zhengzhou station over the same period. Results indicate that ANN model predicts the actual values for Zhengzhou with a good accuracy of 94.81%. Data for Zhengzhou are not included as a part of ANN training set. Hence, these results demonstrate the generalization capability of this approach and its ability to produce accurate estimates in China.     

Data bank Comparison of monthly mean hourly sunshine fraction estimation techniques from calculated diffuse radiation values

Mean monthly hourly values of global I and diffuse radiation I_d, along with mean monthly daily values of the sunshine fraction σ_d available for four locations in the United Kingdom, are used to develop six models relating I_d/I with the monthly mean hourly clearness index K_t, the estimated monthly mean hourly sunshine fraction σ_h and the monthly mean solar elevation at mid hour α. Two available methods are used to predict the values of σ_h from σ_d and the calculated I_d data are compared. Statistical tests performed for a total of six locations, including those used to develop the models, show that the best results are obtained when σ_h predicted with the method developed by Page is employed in the estimation correlation.     

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.     

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:     

Global solar radiation estimation from measurements of visibility and air temperature extremes

Solar radiation is the main source of energy for the survival of life and its associated activities. It is important to know accurate solar radiation value in areas such as agricultural activities, solar energy systems, heating, and meteorology. In this study, we present a model for the estimation of solar radiation value with other meteorological parameters in cases where solar radiation cannot be measured or not available. This model is based on the relationship between solar radiation and measured air temperature and visibility extremes. As is known, the incident global solar radiation is attenuated by clouds, aerosols, ozone layer, water vapor, etc.. In the model, the attenuation of the solar radiation is expressed by dew point temperature, visibility, and the maximum and minimum air temperatures. Dew-point temperature refers to the effect of water vapor on solar radiation, air temperature extremes are used to signify cloudiness. Visibility also gives the effect on the attenuation of solar radiation by air pollutants and aerosols in the model. The model was applied to the data taken from meteorological stations in Turkey. Error analysis was performed and compared with the models in the literature and satisfactory results were obtained.

Abbreviations H: Daily total global solar radiation, units of MJ ? m^?2 ? day^?1; H₀: Extraterrestrial solar radiation, units of MJ ? m^?2 ? day^?1; H_m: Measured daily total global solar radiation, units of MJ ? m^?2 ? day^?1; H_c: Calculated daily total global solar radiation, units of MJ ? m^?2 ? day^?1; T_min: Daily minimum temperature, units of °C; T_max: Daily maximum temperature, units of °C; RH: T_dew: Relative humidity, units of %rh; Dew-point temperature, units of °C     

Estimation and prediction of global solar radiation over Greece

A regression analysis of the relative monthly values of global solar radiation ( ) the corresponding values of sunshine (n/N), for the period 1961-75, was performed to determine the constants a and b of the Ångström formula, for Athens. The constants a and b were also determined by a graphical relationship between the average annual relative sunshine (n/N) and these constants, for the same station. The latter method was then used to determine the constants a and b for 33 other stations widely distributed throughout Greece, after making a relative correction to these constants. In this way, monthly and annual values of global solar radiation were estimated for 34 stations over Greece from sunshine measurements. The geographical distribution of the annual totals of global solar radiation over Greece was mapped and some types and sub-types were identified.Further, a stepwise multiple regression analysis of the annual total amounts of global solar radiation and the three factors (latitude, longitude and altitude) was carried out; the validity of the assumption of the linear relationship between the annual totals of global solar radiation and the three factors was examined.     

ESTIMATION OF SOLAR RADIATION ENERGY OF ETHIOPIA FROM SUNSHINE DATA

Measurements of global solar radiation on a horizontal surface, for nine meteorological stations in Ethiopia, are compared with their corresponding values computed based on Ångström relations, Regression coefficients are obtained and correlation equations are determined to predict the global solar radiation. The result shows that Ångström relations are valid for Ethiopian locations, and the correlation equations can be used to predict the monthly mean daily global solar radiation in the locations considered in this study.

This study also proves that the results made by ENEC et al, using the generalised Frere's coefficients, is unsatisfactory for the prediction of monthly mean daily global solar radiation. On the other hand, the work of Dogniaux and Lemoine, using the regression coefficients a and b as a function of latitude and atmospheric turbidity and grouping large range latitudes to extend the application, can give better estimation. However, for more accurate estimation, several additional meteorological stations have to be evaluated and their regression coefficients have to be determined before grouping in to one relationship to express the variations of a and b under any conditions of equipment and location.     

Uses of sunshine duration to estimate the global solar radiation over eight meteorological stations in Egypt

The climatological Ångstrom regression coefficients have been determined by three methods and used to predict the global solar radiation over eight meteorological stations. Each of the three methods depends on the correlation between two ratios. The first ratio is between the long period of monthly average sunshine duration and the corresponding maximum of daily sunshine duration (day length) N, and the second ratio is between the measured monthly average daily global solar radiation and the corresponding monthly mean daily extraterrestrial solar radiation on the horizontal surface ₀. A comparison between the measured data and the estimated values has been done. The t-statistics is used as a statistical indicator to choose the coefficients of the best method that gives a percentage of error less than 10%.     

Comprehensive study of solar conditions in Mozambique: the effect of trade winds on solar components

A new algorithm to simulate all solar components and optimum slopes, β_opt, based on new models for direct normal beam and diffuse radiation and an analytical model to predict β_opt, developed at the University of Botswana is applied for complete study of solar conditions in Mozambique. The components of solar radiation depend to a large extent on the number of h of sunshine. However, it is obvious that cloud-cover is determined mainly by the prevailing trade winds, which carry moisture and rain clouds. This is of especial concern in coastal areas. In the current work, hourly, I, daily, H and monthly mean, components of solar radiation and the optimum slopes of a north–south aligned collector are simulated and analyzed for 21 synoptic stations in Mozambique. Monthly mean daily direct normal, solar radiation maps are plotted for December and June and discussed. It is found that, to a great extent, isoinsolation curves are determined by the prevailing trade winds, mountain chains and coastal conditions. Plotted maps of annual mean daily direct normal and global solar radiation also show tremendous dependence on the prevailing winds. Several special locations in Mozambique with quite high or very low solar radiation components are pointed out and the reasons explained.     

Compilation and evaluation of solar and wind energy resources in Sudan

A number of years worth of data concerning the solar radiation on a horizontal surface, sunshine duration and wind speed in Sudan have been compiled, evaluated and presented in this article.Measurements of global solar radiation on a horizontal surface at 16 stations for several years are compared with predictions made by several independent methods. In the first method the Angstrom formula was used to correlate relative global solar irradiance to the corresponding relative duration of bright sunshine.Regression coefficients are obtained and used for prediction of global solar irradiance. The predicted values were consistent with measured values (± 8.01% variation).In the second method, by Barbaro et al. [Solar Energy, 1978, 20, 431] sunshine duration and minimum air mass were used to drive an empirical correlation for the global radiation. The predicted values compared well with measured values (± 12% variation).The diffuse solar irradiance is estimated. The results of two formulas have close agreement. A radiation map of Sudan was prepared from the estimated radiation values. The annual daily mean global radiation ranges from 3.05 to 7.62 kW h m⁻² per day.Routine wind data from 70 stations were analyzed. Monthly averaged wind speed and average powers were determined for each station. The derived annual average speeds range from 1.53 to 5.07 m s⁻¹. Maximum extractable average wind powers were found to vary between 1.35 and 49.5 W m⁻². A wind map of Sudan was also prepared.Sudan possessed a relatively high abundance of sunshine and moderate wind speed. It is concluded that Sudan is blessed with abundant solar and wind energy.     

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.     

Some comments on time variation in solar radiation over Baghdad, Iraq

In the present work an attempt was made to study and examine some aspects of radiation climatology which are important in solar energy utilization. The yearly cumulative global radiation for Baghdad is 216 MJ/m² per year, while the annual total of daily diffuse radiation at Baghdad is about 70.82 MJ/m². The mean monthly values of clearness index K_T present a maximum of 65.9% in August and a minimum value of 48.4% in January. The annual mean of daily global radiation and its spectral OG1, RG2 and RG8 at Baghdad is about, 18.03, 13.53, 10.86 and 9.36 MJ/m², respectively. Over the year, the highest UV radiation were received during June and July (243 Wh/m²) and the lowest in December (79 Wh/m²). Furthermore, UV radiation constituted on average 3.25% of global radiation.     

An atmospheric model applied to some actinometric stations of Sicily

In this paper the application of an atmospheric model proposed by S. Barbaro et al. in a previous work for computing the direct and diffuse solar radiation is extended to some actinometric stations in Sicily, namely Gela, Messina, Pantelleria, Trapani and Ustica. The comparison of the monthly average values of the global radiation computed by this method with the experimental data shows a good agreement, that confirms the encouraging results obtained for Palermo in the previous work. This further test of the validity of the proposed model allows this one may be used with good reliability to predict the radiation on locations lacking in actinometric instruments. Finally, the influence of the diffuse component on the global radiation is computed and the results are plotted with the relative regression curves.     

Techniques for obtaining the monthly mean hourly diffuse radiation from daily values

The classical equation of Liu and Jordan for estimating the monthly mean hourly to daily diffuse ratio (r_d) was tested for applicability to locations in Spain. While the model predicts the r_d ratios and the monthly mean, hourly diffuse (I_d) values accurately at low hour angles close to solar noon, errors involved in the estimation increase rapidly as one approaches high angles away from solar noon. A technique is suggested to overcome this discrepancy. The proposed method, which employs the monthly mean daylength S_o as the only input parameter, may be used to evaluate the r_d ratios accurately for locations in Spain when measured data are not available. A set of second-order polynomial equations relating r_d and S_o, obtained from the analysis of longterm, measured hourly diffuse radiation data for several stations in Spain, is recommended for estimation purposes.     

Estimation of solar radiation over Jordan—predicted tables

As measured solar radiation data for all parts of Jordan are not available, they have to be estimated using correlation relations and models. This paper presents, for the first time, values of solar radiation over Jordan as estimated from these relations. Measurements of global solar irradiance on a horizontal surface and sunshine duration at nine meteorological stations in Jordan are correlated and used for prediction of the regression coefficients of an Angstrom type correlation relation at these stations and others which only have records of sunshine duration. Regional regression coefficients are obtained and used for prediction of global solar irradiance. The agreement with measurements is better than 5% and 1% on monthly and yearly basis respectively. Estimation of diffuse solar irradiance by Page's and also Liu and Jordan's correlations, as well as the direct beam component are also performed and the results are examined and presented. The abundance of solar energy in Jordan is evident from the daily average global solar irradiance which ranges between 5 and 7 kWh/m². A correlation of Angstrom type of the form: H/Ho = 0.448+0.203 S/So is found suitable for Jordan with correlation coefficient r = 0.93.     

Computation of monthly mean daily global solar radiation in China using artificial neural networks and comparison with other empirical models

In this paper, an artificial neural network (ANN) model is developed for estimating monthly mean daily global solar radiation of 8 typical cities in China. The feed-forward back-propagation algorithm is applied in this analysis. The results of the ANN model and other empirical regression models have been compared with measured data on the basis of mean percentage error (MPE), mean bias error (MBE) and root mean square error (RMSE). It is found that the solar radiation estimations by ANN are in good agreement with the measured values and are superior to those of other available empirical models. In addition, ANN model is tested to predict the same components for Kashi, Geermu, Shenyang, Chengdu and Zhengzhou stations over the same period. Data for Kashi, Geermu, Shenyang, Chengdu and Zhengzhou are not used in the training of the networks. Results obtained indicate that the ANN model can successfully be used for the estimation of monthly mean daily global solar radiation for Kashi, Geermu, Shenyang, Chengdu and Zhengzhou. These results testify the generalization capability of the ANN model and its ability to produce accurate estimates in China.     

Optimization of tilt angle for solar panel: Case study for Madinah,Saudi Arabia

This article analyzes the optimal choice of the tilt angle for the solar panel in order to collect the maximum solar irradiation. In this paper, the collector surface is assumed to be facing toward equator. The study is based upon the measured values of daily global and diffuse solar radiation on a horizontal surface. It is shown that the optimal angle of tilt (β_opt) for each month, allows us to collected the maximum solar energy for Madinah site. Annual optimum tilt angle is found to be approximately equal to latitude of the location. It is found that the loss in the amount of collected energy when using the yearly average fixed angle is around 8% compared with the monthly optimum tilt β_opt.     

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.     

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.     

Analysis of short-term solar radiation data

Solar radiation data are available for many locations on an hourly basis. Simulation studies of solar energy systems have generally used these hourly values to estimate long-term annual performance, although solar radiation can exhibit wide variations during an hour. Variations in solar radiation during an hour, such as on a minute basis, could result in inaccurate performance estimates for systems that respond quickly and non-linearly to solar radiation. In addition, diffuse fraction regressions and cumulative frequency distribution curves have been developed using hourly data and the accuracy of these regressions when applied to short-term radiation has not been established. The purpose of this research is to investigate the inaccuracies caused by using hourly rather than short-term (i.e., minute and 3 min) radiation data on the estimated performance of solar energy systems. The inaccuracies are determined by examination of the frequency distribution and diffuse fraction relationships for short-term solar radiation data as compared to existing regressions and by comparing calculated radiation on tilted surfaces and utilizability based on hourly and short-term radiation data.