Models For Global Solar Radiation Research Articles

Statistical Approach for Modeling of Daily Global Solar Radiation on Horizontal Surfaces Over Hebron City, Palestine

Understanding solar radiation data is essential for modeling solar energy systems because it is non-polluting, non-depletable, reliable, and pollution free. Four-years measured average daily global solar radiation data on horizontal surfaces at Hebron city in Palestine were used for the model assessment. Statistical results showed that all four suggested models can accurately predict the solar irradiance of a 31° 57' N (latitude angle of Hebron) on a horizontal oriented surface, indicating the good predictive ability for modeling a horizontal surface. The obtained models have a high value of regression coefficient and give best fit through the measured values. This work illustrates also the use of mathematical formula to develop a predictive model for the duration of sunshine using measured solar radiation data for Hebron city. The present work showed that the predicted results were in good agreement with the observed data, and the expected solar radiation behavior.

Estimation of global solar radiation on horizontal surface in Erzincan, Turkey

In the applications of solar energy, the solar radiation data and their components in a region must be known for the design of a system. In the locations where no solar radiation data is available, this parameter can be determined by performing a reasonable correlation. In the study, the models of global solar radiation on the horizontal surface in the literature are investigated, and new empirical models based on the sunshine hour data for Erzincan, Turkey are developed. In order to indicate the performance of the models, the statistical test methods of mean bias error (MBE), root mean square error (RMSE) and mean relative error (MRE) are used. The results obtained indicate that the correlations developed in the study predict the global solar radiation reasonably well for the future projections. Key words: Solar energy, global solar radiation, sunshine hours, correlation, empirical models.

Generation of typical solar radiation data for different climates of China

In this study, typical solar radiation data are generated from both measured data and synthetic generation for 35 stations in six different climatic zones of China. (1) By applying the measured weather data during at least 10 years from 1994 to 2009, typical meteorological years (TMYs) for 35 cities are generated using the Finkelstein–Schafer statistical method. The cumulative distribution function (CDF) of daily global solar radiation (DGSR) for each year is compared with the CDF of DGSR for the long-term years in six different climatic stations (Sanya, Shanghai, Zhengzhou, Harbin, Mohe and Lhasa). The daily global solar radiation as typical data obtained from the TMYs are presented in the Table. (2) Based on the recorded global radiation data from at least 10 years, a new daily global solar radiation model is developed with a sine and cosine wave (SCW) equation. The results of the proposed model and other empirical regression models are compared with measured data using different statistical indicators. It is found that solar radiation data, calculated by the new model, are superior to these from other empirical models at six typical climatic zones. In addition, the novel SCW model is tested and applied for 35 stations in China.

Daily total global solar radiation modeling from several meteorological data

This paper investigates the modeling of the daily total global solar radiation in Adana city of Turkey using multi-linear regression (MLR), multi-nonlinear regression (MNLR) and feed-forward artificial neural network (ANN) methods. Several daily meteorological data, i.e., measured sunshine duration, air temperature and wind speed and date of the year, i.e., monthly and daily, were used as independent variables to the MLR, MNLR and ANN models. In order to determine the relationship between the total global solar radiation and other meteorological data, and also to obtain the best independent variables, the MLR and MNLR analyses were performed with the “Stepwise” method in the Statistical Packages for the Social Sciences (SPSS) program. Thus, various models consisting of the combination of the independent variables were constructed and the best input structure was investigated. The performances of all models in the training and testing data sets were compared with the measured daily global solar radiation values. The obtained results indicated that the ANN method was better than the other methods in modeling daily total global solar radiation. For the ANN model, mean absolute error (MAE), mean absolute percentage error (MAPE), correlation coefficient (R) and coefficient of determination (R 2) for the training/testing data set were found to be 0.89/1.00 MJ/m2 day, 7.88/9.23%, 0.9824/0.9751, and 0.9651/0.9508, respectively.

The potential of different artificial neural network (ANN) techniques in daily global solar radiation modeling based on meteorological data

The main objective of present study is to predict daily global solar radiation (GSR) on a horizontal surface, based on meteorological variables, using different artificial neural network (ANN) techniques. Daily mean air temperature, relative humidity, sunshine hours, evaporation, and wind speed values between 2002 and 2006 for Dezful city in Iran (32°16′N, 48°25′E), are used in this study. In order to consider the effect of each meteorological variable on daily GSR prediction, six following combinations of input variables are considered: (I) Day of the year, daily mean air temperature and relative humidity as inputs and daily GSR as output. (II) Day of the year, daily mean air temperature and sunshine hours as inputs and daily GSR as output. (III) Day of the year, daily mean air temperature, relative humidity and sunshine hours as inputs and daily GSR as output. (IV) Day of the year, daily mean air temperature, relative humidity, sunshine hours and evaporation as inputs and daily GSR as output. (V) Day of the year, daily mean air temperature, relative humidity, sunshine hours and wind speed as inputs and daily GSR as output. (VI) Day of the year, daily mean air temperature, relative humidity, sunshine hours, evaporation and wind speed as inputs and daily GSR as output. Multi-layer perceptron (MLP) and radial basis function (RBF) neural networks are applied for daily GSR modeling based on six proposed combinations. The measured data between 2002 and 2005 are used to train the neural networks while the data for 214 days from 2006 are used as testing data. The comparison of obtained results from ANNs and different conventional GSR prediction (CGSRP) models shows very good improvements (i.e. the predicted values of best ANN model (MLP-V) has a mean absolute percentage error (MAPE) about 5.21% versus 10.02% for best CGSRP model (CGSRP 5)).

Estimating global solar radiation using artificial neural network and air temperature data in a semi-arid environment

Global solar radiation (GSR) data are desirable for many areas of research and applications in various engineering fields. However, GSR is not as readily available as air temperature data. Artificial neural networks (ANNs) are effective tools to model nonlinear systems and require fewer inputs. The objective of this study was to test an artificial neural network (ANN) for estimating the global solar radiation (GSR) as a function of air temperature data in a semi-arid environment. The ANNs (multilayer perceptron type) were trained to estimate GSR as a function of the maximum and minimum air temperature and extraterrestrial radiation. The data used in the network training were obtained from a historical series (1994–2001) of daily climatic data collected in weather station of Ahwaz located in Khuzestan plain in the southwest of Iran. The empirical Hargreaves and Samani equation (HS) is also considered for the comparison. The HS equation calibrated by applying the same data used for neural network training. Two historical series (2002–2003) were utilized to test the network and for comparison between the ANN and calibrated HS method. The study demonstrated that modelling of daily GSR through the use of the ANN technique gave better estimates than the HS equation. RMSE and R 2 for the comparison between observed and estimated GSR for the tested data using the proposed ANN model are 2.534 MJ m −2 day −1 and 0.889 respectively.

Numerical methods applied to global solar radiation modeling – comparison with measured data

PurposeThe purpose of this paper is to predict the global solar radiation intensity in areas where meteorological stations do not exist and information on solar radiation cannot be obtained experimentally.Design/methodology/approachThe approach to achieve the objective of the paper is developing multiple regression relations between the global solar radiation intensity (the dependent variable) and geographical, geometrical, astronomical and meteorological parameters (the independent variables). The independent variables used for this purpose were selected based on their ease of measurability outside the meteorological station and without expensive equipment. The number of independent variables is arbitrarily chosen and directly affects the accuracy of predictions.FindingsLinear regression relations using one, two, three, four, five, six, and seven independent variables were developed to predict the global solar radiation intensity on horizontal surfaces. An advanced computer program based on least square analysis was used to obtain the regression coefficients. The relations having the highest correlation coefficients were selected. The study shows even when only one independent variable (declination angle) is used, the one variable regression relation predicts the global solar radiation with an accuracy that is satisfactory in most engineering applications.Originality/valueThe diversity of regression relations introduced in this paper gives the engineer such a broad freedom of choice, that knowing only an astronomical parameter of the site makes him capable of estimating the global solar radiation intensity within acceptable margins. The predicted values of global solar radiation intensity by this approach can be used for the design and performance estimation in solar applications. The statistical model developed in this research was validated when compared with the measured data in Yazd airport. The measured data used to analyze the model equations were collected in a 13‐year period. No investigation of this type exists having such degree of accuracy in geographical, geometrical, astronomical and meteorological parameters in Iran.

Evaluation of temperature-based global solar radiation models in China

Estimation of global solar radiation ( R s ) from the daily range of air temperature (Δ T) offers an important alternative in the absence of measured R s or sunshine duration because of the wide availability of air temperature data. In this paper, we assessed 16 R s models including modified versions of the Bristow and Campbell (B–C) and the Hargreaves (Harg) models across a wide range of agro-ecological conditions in China. Using long-term data from 15 sites in Northeast, North China Plain and Northwest China, we explored the main factors affecting model parameters and the predictive accuracy and proposed empirical equations to estimate these parameters. Two schemes in calculating Δ T were employed: Δ T 1 (based on single day T min) used in the Harg and Δ T 2 (based on 2-day average of T min) used in the B–C model. Results showed that the original B–C model performed similarly to the best performing modified Harg model, but significantly outperformed the original Harg model with a 4–7% higher accuracy. The common practice of fixing some parameters in the B–C model caused the most significant effect and resulted in a 3–9% lower accuracy than that of the original model. In contrast, modifications had the smallest effect and yielded little improvement and are thus unnecessary. The Δ T scheme had a moderate effect, with Δ T 1 generally resulting in a higher accuracy especially in high altitude areas. This indicates that the effect of cold or warm air advection is negligible in the B–C model even in a temperate climate. The accuracy of the temperature-based models was affected mainly by the magnitude of Δ T, with larger Δ T resulting in higher accuracy. Parameters of the B–C model correlated significantly with many commonly used geographical and meteorological factors, meaning that they are more easily obtainable without the need for calibration and consequently R s measurement. The parameter of the original Harg model correlated insignificantly with all the examined factors, meaning that it has to be calibrated. Main findings in this study are valuable in clarifying the relative impact of different approaches in applications on model accuracy, in demonstrating the advection effect, in identifying the dominant factors of model parameters and thus in increasing their availability.

ANN-based modelling and estimation of daily global solar radiation data: A case study

In this paper, an artificial neural network (ANN) models for estimating and modelling of daily global solar radiation have been developed. The data used in this work are the global irradiation H G , diffuse irradiation H D , air temperature T and relative humidity H u . These data are available from 1998 to 2002 at the National Renewable Energy Laboratory (NREL) website. We have developed six ANN-models by using different combination as inputs: the air temperature, relative humidity, sunshine duration and the day of year. For each model, the output is the daily global solar radiation. Firstly, a set of 4 × 365 points (4 years) has been used for training each networks, while a set of 365 points (1 year) has been used for testing and validating the ANN-models. It was found that the model using sunshine duration and air temperature as inputs, gives good accurate results since the correlation coefficient is 97.65%. A comparative study between developed ANN-models and conventional regression models is presented in this study.

Distributed Modeling of Global Solar Radiation over Rugged Terrain of the Yellow River Basin

In rugged terrain,the global solar radiation(GSR) reaching on the surface is composed of three parts,i.e.direct solar radiation,diffuse solar radiation and terrain reflected solar radiation.The theories of these three kinds of solar radiation are different.Respective models are established which necessarily take integrated consideration of astronomical and geographic factors,local topographic factors(i.e.slope,aspect and terrain inter-shielding effect) and atmospheric physics factors are needed.Based on DEM(Digital Elevation Model) data and remote sensing data,a distributed model for calculating GSR over rugged terrain is developed,with routine meteorological observations as input.This model takes all consideration of factors influencing GSR.Using the established model,normals of annual GSR quantity with resolution of 1 km×1 km for the Yellow river basin was generated.Results suggest that influenced by local topographic factors,i.e.azimuth,slope and terrain inter-shielding effect,annual GSR quantity over mountainous areas is smaller than that over plains generally.The influences of local topographic factors on GSR are changing with seasons and are more obvious in seasons that have a lower solar elevation angle.

A Global Solar Radiation Model for the Design of Solar Energy Systems

A Global Solar Radiation Model for the Design of Solar Energy Systems

Mapping a topographic global solar radiation model implemented in a GIS and refined with ground data

AbstractThis study proposes a methodology to compute solar radiation values on the Earth surface on a monthly and annual basis and taking into account the relief, which is not an usual approach although it has enormous importance for environmental studies. It consists of two steps: a computational, physically‐based model (potential solar radiation) and a refining through meteorological data (interpolated solar radiation). The potential solar radiation model allows computing the incident energy assuming uniform atmospheric standard optical density. The only information required is a Digital Elevation Model (DEM, 180 m resolution in our case) and a number of meteorological stations providing global solar radiation data (74 in our case). This model, implemented into the MiraMon Geographic Information System (GIS), takes into account astronomical, atmospheric and geographical factors. Atmospheric effects are considered through correctors obtained by comparing the potential values with the observed at the meteorological stations. The resulting monthly correctors have been spatially interpolated to build up anomaly maps, which allow to obtain a refined solar radiation cartography. The potential model has proven to be very precise as it gives results close to the interpolated radiation values, allowing a conversion to interpolated solar radiation maps with errors of 7.3% (March), 6.1% (June), 6.4% (September) and 13.1% (December) computed from a leave‐one‐out cross‐validation. These results are always better than those obtained by classical interpolators, and still better if the process is run on the rugged terrain areas. A sensitivity analysis estimates the influence of the DEM quality on the model, concluding that an RMS error of 8 m in the DEM heights represents an RMS error of 133 kJ·m−2·day−1 (mean monthly) on the results. Finally, we have applied the model to obtain the 12‐monthly (based on daily average) global solar radiation maps of Catalonia (NE of Iberian Peninsula) as well as the annual one. Copyright © 2008 Royal Meteorological Society

Solar radiation modelling using ANNs for different climates in China

Artificial neural networks (ANNs) were used to develop prediction models for daily global solar radiation using measured sunshine duration for 40 cities covering nine major thermal climatic zones and sub-zones in China. Coefficients of determination ( R 2) for all the 40 cities and nine climatic zones/sub-zones are 0.82 or higher, indicating reasonably strong correlation between daily solar radiation and the corresponding sunshine hours. Mean bias error (MBE) varies from −3.3 MJ/m 2 in Ruoqiang (cold climates) to 2.19 MJ/m 2 in Anyang (cold climates). Root mean square error (RMSE) ranges from 1.4 MJ/m 2 in Altay (severe cold climates) to 4.01 MJ/m 2 in Ruoqiang. The three principal statistics (i.e., R 2, MBE and RMSE) of the climatic zone/sub-zone ANN models are very close to the corresponding zone/sub-zone averages of the individual city ANN models, suggesting that climatic zone ANN models could be used to estimate global solar radiation for locations within the respective zones/sub-zones where only measured sunshine duration data are available.

Evaluation of global solar radiation models for Konya, Turkey

Abstract Solar radiation data are required by solar engineers, architects, agriculturists and hydrologists for many applications such as solar heating, cooking, drying and interior illumination of buildings. In order to achieve this, several empirical models have been developed to predicted the solar radiation all over the world. The main objective of this study is to review the global solar radiation models available in the literature. In order to evaluate the applicability of 50 models for computing the monthly average daily global radiation on a horizontal surface, the geographical and meteorological data of Konya, Turkey (37°52′N latitude, 32°29′E longitude) was used. The models were compared on the basis of statistical error tests such as the percentage error (e), mean percentage error (MPE), root mean square error (RMSE), mean bias error (MBE), regression coefficient (R) and Nash–Sutcliffe equation (NSE). According to the results, the Ertekin and Yaldiz model showed the best estimation of the global solar radiation on a horizontal surface for Konya, Turkey, by means of the MPE (0.004266%), RMSE (0.022576 MJ/m2), MBE (0.000000 MJ/m2), R (0.999993) and NSE (0.999985) statistical tests: H = 20.296019 - 0.096134 H 0 + 0.317593 δ - 0.146422 RH + 10.705159 S S 0 - 0.288332 T + 0.021331 TS + 0.359791 C + 0.207588 P - 0.076444 E

05/02611 Simulation of global solar radiation based on cloud observations

A stochastic model for simulating global solar radiation on a horizontal surface has been developed for use in power systems reliability calculations. The importance of an appropriate model for global solar radiation has increased with the increased use of photovoltaic power generation. The global solar radiation shows not only regular yearly and daily variations but also a random behavior. The yearly and daily variations can be described in a deterministic way while the random behavior has a high correlation with the state of the atmosphere. The astronomic effects can easily be described mathematical with only some minor simplifications but the atmospheric effects are more complicated to describe. The transmittivity of solar radiation in the atmosphere depends on various factors, e.g. humidity, air pressure and cloud type. By using cloud observations as input for the simulations, the local meteorological conditions can be accounted for. The model is usable for any geographical location if cloud observations are available. This is especially useful for development countries where long-term solar radiation measurement can be hard to obtain. Cloud observations can be performed without any expensive equipment and have been a standard parameter for many years throughout the world. Standard observations are done according to the Oktas-scale. It is the interval between observations that sets the resolution of the simulation: the observations are normally only every hour or every third hour. The model can easily be combined with cloud coverage simulations for a more general model. For some calculations higher resolution could be needed. This can be obtained by including a stochastic model for the short-term variations. Simulations have been verified by using measured data.

Reliability of a small power system using solar power and hydro

This paper studies the availability of the electricity supply when the sources consist of a combination of solar energy and a small hydro installation. Instead of flow-of-river, a small reservoir is used. By not using the hydro energy during sunny periods, the natural flow-of-river fills up the reservoir for later use. A model for global solar radiation is proposed with an astronomical part (deterministic) and a meteorological part (stochastic). The meteorological part is based on a Markov model of the cloud coverage. The solar model does not require solar radiation measurements, just cloud observations. A case study has been performed for Timbuktu (16.75°N, 0.07°W) in which generation availability is simulated for four different cases: solar power only; solar power with storage; solar and hydro power and solar and hydro power with storage. To be able to use exclusively renewable energy sources, a combination of sources is needed to secure the reliability of the supply. Using solar cells in combination with a small reservoir is favorable. Even with a weak flow the affect of the flow on the day time reliability is minor, but great benefits can be found for reliability during low load hours (night time).

Change in regime and transfer function models of global solar radiation in Kuwait

The development of the models for global solar radiation in Kuwait is based on removing the annual periodicity and seasonal variation. The first methodology used here is the change in regime technique that relies on dividing the observations into two states, one for clear days and other for non-clear days depending on the duration of the sunshine. Then, for each state, the trend component is expressed as a Fourier series and the stochastic component as an ARMA model. The second methodology used is the transfer function model which depends on two same behavior and highly correlated series such as sunshine duration and daily global radiation. The sunshine duration is considered as an independent input series whereas the global radiation series as the dependent output series. A comparison is made between the two proposed models based on Akaike's Information Criterion (AIC), the Bayesian Information Criterion (BIC), and the coefficient of determination ( R 2).

Simulation of global solar radiation based on cloud observations

A stochastic model for simulating global solar radiation on a horizontal surface has been developed for use in power systems reliability calculations. The importance of an appropriate model for global solar radiation has increased with the increased use of photovoltaic power generation. The global solar radiation shows not only regular yearly and daily variations but also a random behaviour. The yearly and daily variations can be described in a deterministic way while the random behaviour has a high correlation with the state of the atmosphere. The astronomic effects can easily be described mathematical with only some minor simplifications but the atmospheric effects are more complicated to describe. The transmittivity of solar radiation in the atmosphere depends on various factors, e.g. humidity, air pressure and cloud type. By using cloud observations as input for the simulations, the local meteorological conditions can be accounted for. The model is usable for any geographical location if cloud observations are available at the location or at locations with similar climatological conditions. This is especially useful for development countries where long-term solar radiation measurement can be hard to obtain. Cloud observations can be performed without any expensive equipment and have been a standard parameter for many years throughout the world. Standard observations are done according to the Oktas-scale. It is the interval between observations that sets the resolution of the simulation: the observations are normally only every hour or every third hour. The model can easily be combined with cloud coverage simulations, has been proposed, for a more general model. For some calculations higher resolution may be needed. This can be obtained by including a stochastic model for the short-term variations and simple model has been proposed. Errors and limitations of the model are estimated and discussed.

Solar radiation modeling and measurements for renewable energy applications: data and model quality

Measurement and modeling of broadband and spectral terrestrial solar radiation is important for the evaluation and deployment of solar renewable energy systems. We discuss recent developments in the calibration of broadband solar radiometric instrumentation and improving broadband solar radiation measurement accuracy. An improved diffuse sky reference and radiometer calibration and characterization software for outdoor pyranometer calibrations are outlined. Several broadband solar radiation model approaches, including some developed at the National Renewable Energy Laboratory, for estimating direct beam, total hemispherical and diffuse sky radiation are briefly reviewed. The latter include the Bird clear sky model for global, direct beam, and diffuse terrestrial solar radiation; the Direct Insolation Simulation Code (DISC) for estimating direct beam radiation from global measurements; and the METSTAT (Meteorological and Statistical) and Climatological Solar Radiation (CSR) models that estimate solar radiation from meteorological data. We conclude that currently the best model uncertainties are representative of the uncertainty in measured data.

Solar radiation modeling and measurements for renewable energy applications: data and model quality

Measurement and modeling of broadband and spectral terrestrial solar radiation is important for the evaluation and deployment of solar renewable energy systems. We discuss recent developments in the calibration of broadband solar radiometric instrumentation and improving broadband solar radiation measurement accuracy. An improved diffuse sky reference and radiometer calibration and characterization software for outdoor pyranometer calibrations are outlined. Several broadband solar radiation model approaches, including some developed at the National Renewable Energy Laboratory, for estimating direct beam, total hemispherical and diffuse sky radiation are briefly reviewed. The latter include the Bird clear sky model for global, direct beam, and diffuse terrestrial solar radiation; the Direct Insolation Simulation Code (DISC) for estimating direct beam radiation from global measurements; and the METSTAT (Meteorological and Statistical) and Climatological Solar Radiation (CSR) models that estimate solar radiation from meteorological data. We conclude that currently the best model uncertainties are representative of the uncertainty in measured data.