Estimation of global solar radiation under clear sky radiation in Turkey

In this study, the usability of clear sky radiation for predicting the average global solar radiation was investigated. For this aim, the various regression analyses were applied by using and parameters. Also, equations which represent the two periods of the year, winter and summer, were developed by using these parameters.The equations developed by using and have approximately the same results.Having the better values of the equations developed by using the change of summer and winter is another result.In addition, the use of the RMSE and MBE in isolation is not an adequate indicator of model performance. Using the t-statistic method and the harmony of results obtained with each method will prove that the results are reliable     

Evaluation of the WRF model solar irradiance forecasts in Andalusia (southern Spain)

In this work, we evaluate the reliability of three-days-ahead global horizontal irradiance (GHI) and direct normal irradiance (DNI) forecasts provided by the WRF mesoscale atmospheric model for Andalusia (southern Spain). GHI forecasts were produced directly by the model, while DNI forecasts were obtained based on a physical post-processing procedure using the WRF outputs and satellite retrievals. Hourly time resolution and 3 km spatial resolution estimates were tested against ground measurements collected at four radiometric stations along the years 2007 and 2008. The evaluation was carried out independently for different forecast horizons (1, 2 and 3 days ahead), the different seasons of the year and three different sky conditions: clear, cloudy and overcast. Results showed that the WRF model presents considerable skill in forecasting both GHI and DNI, overall, better than a trivial persistence model. Nevertheless, both MBE and RMSE values presented a marked dependence on the sky conditions and season of the year. Particularly, for 24 h lead time, the MBE of the forecasted GHI was 2% for clear-skies and 18% for cloudy conditions. However, the MBE of the forecasted DNI increased up to about 10% and 75% for clear and cloudy conditions, respectively. Regarding RMSE values, in the case of forecasted GHI, results ranged from below 10% under clear-skies to 50% for cloudy conditions. In the case of forecasted DNI, RMSE ranged from 20% to 100% for clear and cloudy skies, respectively. This proved the higher sensitivity of DNI to the sky conditions. In general, an increment of the MBE and RMSE values with the cloudiness was observed. This reflects a still limited ability of the WRF model to properly forecast cloudy conditions compared to clear skies. Nevertheless, the model was able to accurately forecast steep changes in the sky (cloudiness) conditions. Finally, WRF performed considerable better than the persistence model for clear skies both for GHI and DNI, with relative RMSE values about a half. However, for cloudy conditions, performance was similar.     

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.     

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.     

Evaluation of numerical weather prediction for intra-day solar forecasting in the continental United States

Numerical weather prediction (NWP) is generally the most accurate tool for forecasting solar irradiation several hours in advance. This study validates the North American Model (NAM), Global Forecast System (GFS), and European Centre for Medium-Range Weather Forecasts (ECMWF) global horizontal irradiance (GHI) forecasts for the continental United States (CONUS) using SURFRAD ground measurement data. Persistence and clear sky forecasts are also evaluated. For measured clear conditions all NWP models are biased by less than 50 W m⁻². For measured cloudy conditions these biases can exceed 200 W m⁻² near solar noon. In general, the NWP models (especially GFS and NAM) are biased towards forecasting clear conditions resulting in large, positive biases.Mean bias errors (MBE) are obtained for each NWP model as a function of solar zenith angle and forecast clear sky index, kt^∗, to derive a bias correction function through model output statistics (MOS). For forecast clear sky conditions, the NAM and GFS are found to be positively biased by up to 150 W m⁻², while ECMWF MBE is small. The GFS and NAM forecasts were found to exceed clear sky irradiances by up to 40%, indicating an inaccurate clear sky model. For forecast cloudy conditions (kt^∗ < 0.4) the NAM and GFS models have a negative bias of up to −150 W m⁻². ECMWF forecasts are most biased for moderate cloudy conditions (0.4 < kt^∗ < 0.9) with an average over-prediction of 100 W m⁻².MOS-corrected NWP forecasts based on solar zenith angle and kt^∗ provide an important baseline accuracy to evaluate other forecasting techniques. MOS minimizes MBE for all NWP models. Root mean square errors for hourly-averaged daytime irradiances are also reduced by 50 W m⁻², especially for intermediate clear sky indices. The MOS-corrected GFS provides the best solar forecasts for the CONUS with an RMSE of about 85 W m⁻², followed by ECMWF and NAM. ECMWF is the most accurate forecast in cloudy conditions, while GFS has the best clear sky accuracy.     

General models for optimum tilt angles of solar panels: Turkey case study

This paper deals with finding the optimum tilt angle of solar panels for solar energy applications. The optimization of tilt angles was performed using solar radiation data measured for eight big provinces in Turkey. The optimum angle for tilted surfaces varying from 0° to 90° in steps of 1° was calculated by searching for the values of which the daily total solar radiation was at a maximum for a specific period. It was found that the optimum tilt angle changed between 0° and 65° throughout the year in Turkey. It was seen that the optimum tilt angle reached a minimum of 0° in June and July and, the monthly average daily total radiation at this angle was generally at a maximum. In addition, the optimum tilt angle increased during the winter months and reached a maximum in December in all provinces. Likewise, general correlations were developed to estimate the optimum tilt angle of solar collectors used in Turkey and their accuracies were compared on the basis of statistical error tests of Mean Bias Error (MBE), Root Mean Square Error (RMSE), t-statistic (t-stat) and correlation coefficient (r).     

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

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

Nocturnal infrared clear sky temperatures correlated with screen temperatures and GPS-derived PWV in southern Australia

Infrared (IR) clear sky temperatures (Tsky), screen level temperature (T) and Precipitable Water Vapour (PWV) were collected for a period of 2 years from a coastal region of southern Australia. IR sky temperatures were derived from simple infrared detectors, which have been developed by the authors for inexpensive monitoring of cloud cover, while data for PWV were obtained from Global Positioning Satellite (GPS) transmissions. Meteorological data were obtained from the Australian Bureau of Meteorology. Based on these data, statistical regression analyses between nocturnal Tsky and the T and PWV (one variable fit) were conducted. Direct proportional relationships between Tsky and T and between Tsky and PWV were found. The one variable fit was further optimized by applying the multiple regression fit between Tsky and both T and PWV. The resulting multilinear model was essentially unbiased, with a correlation coefficient (R²) of 0.97, mean bias error (MBE) of ?2.7 × 10^?5 °C, and root mean square error (RMSE) of about 1.6 °C. The performance of the multilinear model was tested against a 1-year independent data set. In this case, the predictability of the model was superior, with MBE and RMSE being 0.13 °C and 2.23 °C respectively. After correcting the daytime observations for the biases caused by solar heating of the detection system, the performance of this model in calculating the daytime measurements was tested and showed MBE and RMSE values of 1.3 °C and 2.5 °C, respectively. Additionally, twenty schemes from the literature were tested and assessed for predicting the measured sky temperature. The performances of these models were all different. Whereas most of them underestimated the measured sky temperatures, three of these models showed a reasonable prediction ability. Finally, the multilinear model was compared with the simulated sky temperatures obtained using MODTRAN software. Perfect agreements were found between the two temperatures.     

Comparison of two PV array models for the simulation of PV systems using five different algorithms for the parameters identification

Simulation is of primal importance in the prediction of the produced power and automatic fault detection in PV grid-connected systems (PVGCS). The accuracy of simulation results depends on the models used for main components of the PV system, especially for the PV module. The present paper compares two PV array models, the five-parameter model (5PM) and the Sandia Array Performance Model (SAPM). Five different algorithms are used for estimating the unknown parameters of both PV models in order to see how they affect the accuracy of simulations in reproducing the outdoor behavior of three PVGCS. The arrays of the PVGCS are of three different PV module technologies: Crystalline silicon (c-Si), amorphous silicon (a-Si:H) and micromorph silicon (a-Si:H/μc-Si:H).The accuracy of PV module models based on the five algorithms is evaluated by means of the Route Mean Square Error (RMSE) and the Normalized Mean Absolute Error (NMAE), calculated for different weather conditions (clear sky, semi-cloudy and cloudy days). For both models considered in this study, the best accuracy is obtained from simulations using the estimated values of unknown parameters delivered by the ABC algorithm. Where, the maximum error values of RMSE and NMAE stay below 6.61% and 2.66% respectively.     

POTSOL: Model to predict extraterrestrial and clear sky solar radiation

A model was developed to predict potential and clear sky solar radiation for any latitude. The model (POTSOL) uses the fundamental geometric relationships between the earth and sun to predict the theoretical solar radiation outside the earth's atmosphere, clear sky solar radiation received at the earth's surface after accounting for atmospheric interference, and clear sky solar radiation on a panel with any tilt angle between 0° and 90° from the horizontal. The only model input parameters are latitude (PHI), clearness number (CN), and panel tilt angle (PT). The model was verified using weather data obtained from the National Climatic Center, Asheville, North Carolina for Ely, Nevada.     

Empirical model development and comparison with existing correlations

This study utilized monthly mean daily values of global solar-radiation and sunshine duration at 41 locations in Saudi Arabia and developed an empirical correlation for the estimation of global solar radiation at locations where it is not measured. The paper also presents the comparison between the present correlation and other models developed under different geographical and varied meteorological conditions. The comparisons are made using standard statistical tests, namely mean bias error (MBE), root mean square error (RMSE), mean percentage error (MPE), and mean absolute bias error (MABE) tests. The errors are calculated using monthly mean daily measured and estimated values of global solar radiation at all 41 locations. The study found that the present correlation produced the best estimates of global solar radiation.     

A comparative study of solar irradiation models on various inclined surfaces for India

This paper presents a statistical approach for the estimation of the diffuse/global irradiation on various inclined surfaces from the measured data of horizontal surface. In fact diffuse solar radiation on an inclined plane consists of two components: sky diffuse radiation and reflected radiation from the ground. For analyzing estimation of the daily tilted sky diffuse component from the daily horizontal diffuse irradiance, we have considered six models Badescu, Circumsolar, Skartveit and Olseth, Hay, Klucher and Liu and Jordan (Isotropic). All these models except Badescu adopted the same methodology for estimating the ground-reflected radiation component, therefore, only sky diffuse component was analyzed at Lucknow (latitude 26.75°, longitude 80.50°), India location. Statistical analysis showed that the Skartveit and Olseth model gives good prediction for the low inclination angle however; Klucher model gave better performance for highly inclined south-facing surfaces. The Root Mean Square Errors (% RMSE) value varies from 3.45% to 24.15% except for Badescu and Circumsolar model which predict worse results. In general, Klucher’s model provides close agreement with the measurements.     

Solar resources estimation combining digital terrain models and satellite images techniques

One of the most important steps to make use of any renewable energy is to perform an accurate estimation of the resource that has to be exploited. In the designing process of both active and passive solar energy systems, radiation data is required for the site, with proper spatial resolution. Generally, a radiometric stations network is used in this evaluation, but when they are too dispersed or not available for the study area, satellite images can be utilized as indirect solar radiation measurements. Although satellite images cover wide areas with a good acquisition frequency they usually have a poor spatial resolution limited by the size of the image pixel, and irradiation must be interpolated to evaluate solar irradiation at a sub-pixel scale. When pixels are located in flat and homogeneous areas, correlation of solar irradiation is relatively high, and classic interpolation can provide a good estimation. However, in complex topography zones, data interpolation is not adequate and the use of Digital Terrain Model (DTM) information can be helpful. In this work, daily solar irradiation is estimated for a wide mountainous area using a combination of Meteosat satellite images and a DTM, with the advantage of avoiding the necessity of ground measurements. This methodology utilizes a modified Heliosat-2 model, and applies for all sky conditions; it also introduces a horizon calculation of the DTM points and accounts for the effect of snow covers. Model performance has been evaluated against data measured in 12 radiometric stations, with results in terms of the Root Mean Square Error (RMSE) of 10%, and a Mean Bias Error (MBE) of +2%, both expressed as a percentage of the mean value measured.     

Computation of beam solar radiation at normal incidence using artificial neural network

In this paper, an artificial neural network (ANN) model is developed for estimating beam solar radiation. Introducing a newly defined parameter, known as reference clearness index (RCI), computation of monthly mean daily beam solar radiation at normal incidence has been carried out. This RCI is defined as the ratio of measured beam solar radiation at normal incidence to the beam solar radiation as computed by Hottel's clear day model. Solar radiation data from 11 stations having different climatic conditions all over India have been used for training and testing the ANN. The feedforward back-propagation algorithm is used in this analysis. The results of ANN model have been compared with measured data on the basis of root mean square error (RMSE) and mean bias error (MBE). It is found that RMSE in the ANN model varies 1.65–2.79% for Indian region.     

Atmospheric aerosol influence on the Brazilian solar energy assessment: Experiments with different horizontal visibility bases in radiative transfer model

The radiative transfer model BRASIL-SR is used by Brazilian Institute for Space Research for the assessment of the solar irradiation in Brazil. The model parameterizes the influence of aerosols in the solar radiation transmittance using climate averages of horizontal visibility, which does not represent the actual atmospheric condition in Brazil, especially during dry season. In clear sky conditions, aerosols are a major source of bias in solar radiation models. Their concentration have large spatial and temporal variability particularly in the Brazilian Midwestern region from April until October, due to forest fires, and in Southeastern region due to pollution from megacities. In this study, meteorological data from METAR comprising the years of 2006, 2007 and 2008 were analyzed to evaluate the seasonal variability of the horizontal visibility in Brazil to better represent the influence of aerosols on the model estimations of surface solar irradiation. New horizontal visibility values was generated to each month simulated, to provide input data to the BRASIL-SR model and site specific ground data were used to validate the model estimates. The global, direct beam and diffuse solar irradiation estimates obtained by making use of the new horizontal visibility data presented an overall lower BIAS and RMSE deviations.     

Mathematical modelling of a thin layer drying of apricots in a solar energized rotary dryer

In this paper we present a mathematical modelling of a thin layer forced solar drying of apricots. An indirect forced convection solar dryer consisting of a solar heater and a rotary column cylindrical drying (RCCD) cabinet was used in the experiments. Air heated by the solar air heater was forced through the apricots by an electrical fan. Moreover, the natural sun drying experiments were conducted for the comparison at the same time. Fourteen different thin layer mathematical drying models were compared according to their coefficients of determination (r,χ², RMSE) to estimate solar drying curves. The effects of the drying air temperature, velocity and the rotation speed of column on the drying model constants and coefficients were predicted by multiple regressions using a linear type model. Copyright © 2004 John Wiley & Sons, Ltd.     

Estimation of height-dependent solar irradiation and application to the solar climate of Iran

An explicitly height-dependent model has been used to estimate the solar irradiation over Iran which has a vast range of altitudes. The parameters of the model have been chosen on general grounds and not by parameters best fitting to any of the available measured irradiation data in Iran. The estimated global solar irradiation on the horizontal surface shows a very good agreement (4.1% deviation) with the 17-year long pyranometric measurements in Tehran, and also, is in good agreement with other, shorter available measured data. The entire data base of the Iranian meteorological stations have been used to establish a simple relation between the sunshine duration records and the cloud cover reports which can be utilized in solar energy estimations for sites with no sunshine duration recorders.Clear sky maps of Iran for direct solar irradiation on tracking, horizontal, and south-facing vertical planes are presented. The global solar irradiation map for horizontal surface with cloudiness is zoned into four irradiation zones. In about four-fifths of the land in Iran, the annual-mean daily global solar irradiation on horizontal surface ranges from 4.5 to 5.4 kWh/m².     

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:     

Recent improvements of the Meteorological Radiation Model for solar irradiance estimates under all-sky conditions

This study presents the recent improvements of the Meteorological Radiation Model (MRM v6) against previous model versions for more accurate estimates of the solar radiation components, i.e. global, diffuse and direct. The MRM v6 follows a different approach for the simulation of the atmospheric conditions by selecting the most appropriate aerosol model (desert, urban, maritime or continental), and usage of look-up tables for the spectral variation of the aerosol optical depth (AOD) and single scattering albedo (SSA). Furthermore, the MRM v6 uses hourly data of sunshine duration in order to achieve better simulations under cloudy skies. The results show that the MRM v6 improves the estimates of the measured global, diffuse and direct solar irradiances at Athens, Greece since the Root Mean Square Error (RMSE) becomes 13.7%, 40.8% and 24.2%, respectively, against 18.0%, 44.5% and 34.1% for the MRM v5. A decrease is also found in Mean Bias Error (MBE), especially for the diffuse (from 26.2% to 19.5%) and direct (from −9.0% to −2.4%) irradiances, indicating that the inclusion of the aerosol properties in MRM v6 significantly improves the estimations. The MRM simulations are very satisfactory on monthly basis indicating that the model is suitable for solar energy applications.     

Luminous efficacy of direct solar radiation for all sky types

Three models for the luminous efficacy of direct solar radiation on a horizontal surface, valid for all sky conditions, have been developed in the present work, and two of them are proposed. In all the models a function for the direct luminous efficacy for all sky conditions relative to the direct luminous efficacy for clear skies is obtained, using the function for the direct luminous efficacy for clear skies given in a previous work, and the brightness index as a new independent variable. One of the two models is obtained by fitting the values of the relative luminous efficacy as a function of the brightness index. The other proposed model is developed by obtaining in the first place models for direct illuminance and direct irradiance, both relative to the corresponding clear sky models, and then finding the ratio between the relative direct illuminance and irradiance models. Statistical assessment of the direct illuminance values estimated with the proposed models gives similar values for the MBE and the RMSE. However, the model obtained from illuminance and irradiance models is mathematically coherent.