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.     

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

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

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.     

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.     

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.     

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.     

An analysis of thermal and solar zone radiation models using an Angstrom–Prescott equation and artificial neural networks

The correlation between the clearness index and sunshine duration is useful in the estimation of the solar radiation for areas where measured solar radiation data are unavailable. Regression techniques and artificial neural networks were used to investigate the correlations between daily global solar radiation (GSR) and sunshine duration for different climates in China. Measurements made during the 30-year period (1971–2000) from 41 measuring stations covering 9 thermal and 7 solar climate zones and sub-zones across China were gathered and analysed. The performance of the regression and the ANN models in the thermal and solar zones was analysed and compared. The coefficient of determination (R²), Nash–Sutcliffe efficiency coefficient (NSEC), mean bias error (MBE) and root-mean-square error (RMSE) were determined. It was found that the regression models in both the thermal and the solar climate zones showed a strong correlation between the clearness index and sunshine duration (R²=0.79–88). There appeared to be an increasing trend of larger MBE and RMSE from colder climates in the north to warmer climates in the south. In terms of the thermal and solar climate zone models, there was very little to choose between the two models.     

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.     

Solar radiation over Saudi Arabia and comparisons with empirical models

We present a comparison between models developed by the present authors and 16 other models for different geographical and varied meteorological conditions. The comparisons are made using the mean bias error (MBE), root mean square error (RMSE), mean percentage error (MPE), and mean absolute bias error (MABE). These errors are calculated using monthly-mean, measured daily and estimated values of total solar radiation for 41 locations in Saudi Arabia. We find that our latitude, longitude, altitude, and sunshine-duration-dependent model given in Eq. (1)produced the best estimates for global solar radiation. The second- and third-best estimates were obtained from our linear model and other models given in Eq. (2)and Eq. (11), respectively.     

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.     

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:     

Correlations for estimation of daily global solar radiation with hours of bright sunshine in Turkey

In this study, seven different empirical equations are employed to estimate the monthly average daily global solar radiation on a horizontal surface for provinces in the different regions of Turkey, using only the relative duration of sunshine. Daily global solar radiation and sunshine measurement data collected for the provinces of Turkey are obtained from the Turkish State Meteorological Service. The regression constants of the new models developed in this study are found for the provinces of Turkey, as well as that of some models given in the literature. In order to indicate the performance of the models, the statistical test methods of the mean bias error (MBE), mean absolute bias error (MABE), mean relative error (MRE), root mean square error (RMSE) and correlation coefficient (r) are used.     

Study of models for predicting the diffuse irradiance on inclined surfaces

Solar irradiance data on various inclined surfaces at different orientations are important information for active solar-system analyses and passive energy-efficient building designs. In many parts of the world, however, the basic solar irradiance data for the surfaces of interest are not always readily available. Traditionally, different mathematical models have been developed to predict the solar irradiance on various inclined surfaces using “horizontal” data. Alternatively, the diffuse irradiance of a sloping plane can be calculated by integrating the radiance distribution generated with a sky radiance model. This paper presents the evaluation of two slope irradiance models, namely, the Perez point-source model (PEREZSIM) and the Muneer model (MUNEERSIM), and two sky-distribution models, namely, the Perez all-weather model (PEREZSDM) and the Kittler standard-sky model (KITTLERSDM). Three-year (1999–2001) measured average hourly sky radiance and horizontal sky diffuse irradiance data were used for the model assessment. Statistical results showed that all four models can accurately predict the solar irradiance of a 22.3° (latitude angle of Hong Kong) inclined south-oriented surface, indicating the good predictive ability for modelling an inclined surface with a small tilted angle. In general, the KITTLERSDM and PEREZSIM show the best predictions for vertical solar irradiance at this location, followed by the PEREZSDM, then the MUNEERSIM.     

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.     

Determination of the optimal tilt angle and orientation for solar photovoltaic arrays

This paper deals with the determination of optimum tilt angle and orientation for solar photovoltaic arrays in order to maximize incident solar irradiance exposed on the array, for a specific period of time. The method is extended, by introducing a second objective, i.e. minimization of variance of the produced power, in terms of hourly power generation throughout the given period of time. The proposed method uses both well-established models and data collected from the particular area where the photovoltaic panels will be installed and is built upon four steps. In the first step, the recorded data are used in order to select the most accurate, among several isotropic and anisotropic models that can be found in the literature, for predicting diffuse solar irradiance on inclined surfaces. In the second step, the recorded data and the selected model are used to construct a database that contains the averages and the variances of the hourly global solar irradiance on tilted surfaces over specific periods of time, for various tilt angles and orientations. In the third step, the database of the previous step is utilized to produce meta-models that correlate tilt angle and orientation with mean global irradiance and its variance on tilted surfaces. Finally, an optimization problem is formulated, aiming to determining the optimum values of tilt angle and orientation, taking into account the constraints and limitations of the system.     

Measurement and comparison of diffuse solar irradiance models on inclined surfaces in Valladolid (Spain)

This paper presents the performance of 10 arithmetic models used to estimate diffuse solar irradiance on inclined surfaces in a comparative study with actual data readings made available on an hourly and a daily basis. The data readings have been taken from a south facing surface inclined at 42° in an area at some distance from the provincial capital in the Spanish province of Valladolid. In order to confirm the results, three statistical parameters have been used in the study; root mean square error (RMSE), mean bias error (MBE) and Stone’s t-statistic. The results obtained favour the Muneer model, followed by the Reindl model, for hourly as well as for daily values. The Temps–Coulson model gives rise to great discrepancies with respect to the values measured. The results for the Perez model are not good due to the use of parameters that are not specifically calculated for the area in this study, which underlines the need to take an area’s features into account so that predictions for diffuse irradiance measured on inclined surfaces may be as accurate as possible.     

Comparison of calculated and measured values of total radiation on tilted surfaces in Dhahran, Saudi Arabia

The total radiation data measured at Dhahran (lat. 26°18′N, long. 50°08′E), Saudi Arabia, on a surface inclined at 26° from the horizontal for the period March 1984 to April 1985 was used to test three models for calculation of total radiation on inclined surfaces. These models are one isotropic model and two anisotropic models. The total and diffuse radiation measured on a horizontal surface were used when calculating with these models. The above models were compared on the basis of the statistical error tests using the root mean square error (RMSE) and the mean bias error (MBE). The RMSE varied between 0.399% and 5.578%. Our results were compared with similar calculation for Woodbridge, Ontario, Canada (lat. 43.8°N). The comparison showed that the choice of one or another model is location, inclination of the surface and time dependent. For Woodbridge the anisotropic models Klucher and Hay were found to be more accurate than the isotropic model. The present study shows that, for hot-arid areas, the isotropic model is more accurate for tilt angle values around the latitude of the location.     

Statistical validation of daylength definitions for estimation of global solar radiation in Toledo,Spain

The different daylength calculation procedures that can be employed to estimate solar radiation using an Angström–Prescott regression have not been sufficiently evaluated. In this study, daily global solar radiation data measured in Toledo (Spain) during the period 1986–1995 were used to test five daylength estimation models using different definitions of sunrise/sunset and twilight. Models were compared using the root mean square error (RMSE), the mean bias error (MBE) and the t-statistic. In the first two cases, the differences found between the results from the different models were small. Analysis using the t-statistic, on the other hand, showed that the use of civil twilight to calculate daylength produced the best estimates of global solar radiation for Toledo.     

Forecasting of global and direct solar irradiance using stochastic learning methods, ground experiments and the NWS database

We develop and validate a medium-term solar irradiance forecasting model by adopting predicted meteorological variables from the US National Weather Service’s (NWS) forecasting database as inputs to an Artificial Neural Network (ANN) model. Since the inputs involved are the same as the ones available from a recently validated forecasting model, we include mean bias error (MBE), root mean square error (RMSE), and correlation coefficient (R²) comparisons between the more established forecasting model and the proposed ones. An important component of our study is the development of a set of criteria for selecting relevant inputs. The input variables are selected using a version of the Gamma test combined with a genetic algorithm. The solar geotemporal variables are found to be critically important, while the most relevant meteorological variables include sky cover, probability of precipitation, and maximum and minimum temperatures. Using the relevant input sets identified by the Gamma test, the developed forecasting models improve RMSEs for GHI by 10-15% over the reference model. Prediction intervals based on regression of the squared residuals on the input variables are also derived.     

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.