Climatic influences on solar modelling in China

Correlation between clearness index and sunshine duration is useful to the estimation of the solar radiation for areas where measured solar radiation data are not available. Regression techniques were used to investigate the correlations between daily global solar radiation and sunshine duration for different climates in China. Measurements made during the 30-year period (1971–2000) from 40 measuring stations covering major thermal and solar climatic zones across China have been gathered and analysed. The correlations were developed for each individual station as well as for each of the major climates. It was found that the Angstrom–Prescott equation tended to give a good estimation of global solar radiation based on the corresponding measured sunshine hours. A simple two-parameter linear regression equation was proposed for each of the major thermal and solar climatic zones.     

Statistical analysis of solar measurements in Algeria using beta distributions

A method of smoothing solar data by beta probability distributions is implemented in this paper. In the first step, this method has been used to process daily sunshine duration data recorded at thirty-three meteorological stations in Algeria for eleven year periods or more. In the second step, it has been applied to hourly global solar irradiation flux measured in Algiers during the 1987/89 period. For each location and each month of the year, beta probability density functions fitting the monthly frequency distributions of the daily sunshine duration measurements are obtained. Both the parameters characterising the resulting beta distributions are then mapped, enabling us to build the frequency distributions of sunshine duration for every site in Algeria. In the case of solar radiation for Algiers, the recorded data have been processed following two different ways. The first one consists in sorting the hourly global solar irradiation data into eight typical classes of the daily clearness index. The second one is based on the repartition of these data per month. The results of the first classification show that for each class of daily clearness index, the hourly data under consideration are modelled by only one beta distribution. When using the second classification, linear combinations of two beta distributions are found to fit the monthly frequency distributions of the hourly solar radiation data.     

CLEAR SKY SOLAR INSOLATION DATA FOR ISLAMABAD

Monthly mean values of both integrated and instantaneous clear sky solar radiation components for Islamabad territory are presented and discussed. The components include global normal, direct normal, global horizontal, direct and diffuse horizontal radiations, sunshine duration, number of clear days and ambient temperature for solar energy applications. Direct normal irradiance values are used to get clear sky sunshine duration by ab-initio. The need for replacing the conventional sunshine recorder is discussed.     

Techniques for the precise estimation of hourly values of global, diffuse and direct solar radiation

The method usually used to compute solar radiation, when no measured data are available, is the well-known regression technique relating mean daily totals of global and diffuse solar radiation with the mean duration of sunshine. Using this method and taking into account the first order multiple reflections between the ground and the atmosphere, regression parameters were obtained from the monthly mean values of daily totals of global solar radiation and sunshine at a network of 16 stations in India. Daily values of global and diffuse solar radiation were then computed for 121 stations, where sunshine data are available for periods of 6–28 yr, using interpolated values of the regression parameters. Where no sunshine data were available, global and diffuse solar radiation were computed from cloud observations, using the inverse relationship between sunshine and cloudiness. Further, using the empirical relationship between daily totals and the corresponding hourly values of global and diffuse solar radiation, two sets of curves were prepared valid for the whole country, using which mean hourly values of global and diffuse radiation could be deduced from the corresponding daily totals, with a high degree of accuracy. The paper discusses the validity of the techniques used for computing daily and hourly values of global and diffuse solar radiation from sunshine and cloud amounts at an extended network of 145 stations in India and stresses the fact that such techniques are successful, only if accurate data on both radiation and sunshine are available at a widely distributed network of stations for a minimum period from at least 5 to 6 yr, using carefully calibrated and well-maintained instruments of the required quality. Theoretical models have also been used to compute clear sky noon values of global, diffuse and direct solar radiation from the solar constant, allowing for attenuation by atmospheric constituents such as ozone, water vapour, dust and aerosols. Using a simple model, calculations of global and diffuse solar radiation on clear days were made for 145 stations from values of the solar constant and measured values of ozone, water vapour and atmospheric turbidity. A method of extending the technique to overcast skies and partly clouded skies is discussed. The values of the mean annual transmission factor for global solar radiation under cloud-free conditions using the two methods show excellent agreement and establishes the soundness of the regression technique on one hand and the reliability of the theoretical model used for computing clear sky radiation, on the other.     

Empirical correlations as a means for estimating monthly average daily global radiation: A critical overview

In regions where solar energy is abundant, solar energy can play a vital role in attaining energy sustainability. Sizing solar energy systems requires the availability of solar radiation data on horizontal surface which can then be used to calculate solar radiation intensity on any tilted surface using appropriate conversion factors or formula. In many parts of the world, especially in developing countries, such data is not readily available. Many researchers have found that monthly average daily value of global solar radiation on horizontal surface can be estimated when meteorological parameters such as duration of sunshine, number of rainy days, relative humidity, etc. are available. Many empirical correlations have been developed based on this approach. The development of such a correlation has been made possible through the availability of solar and other meteorological data required for their validation. This paper presents a review on the existing empirical correlations and critically looks at the practicality of such correlations. This raises the question on the appropriateness of the past and present approaches adopted by researchers in this field. The paper also discusses various related aspects and proposes new directions for future research.     

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.     

Generation of a typical meteorological year using sunshine duration data

In this paper, we discuss the possibility of using the daily sunshine duration or the daily sunshine duration over day-length data instead of daily global solar radiation in order to develop a Typical Meteorological Year, TMY2, for localities with abundant data of daily sunshine duration. The analysis is done using the latest methodology proposed in the literature. The number of coinciding months is about 40% when daily sunshine duration or the daily sunshine duration over day-length data is used instead of daily global solar radiation as one of the parameters in obtaining TMY2. Such a relatively low figure is probably due to the unreliable solar radiation data recorded by Robitzch-type actinographs used in the present work.     

Evaluation and establishment of diffuse solar radiation models for Bursa,Turkey

The main objective of the present study is to evaluate the applicability of the diffuse solar radiation models from previous studies and establish new models for Bursa. Therefore, 35 regression models from previous studies in the literature are used and categorized as follows: (1) cloudness index is the function of clearness index; (2) cloudness index is the function of relative sunshine duration; (3) the diffuse coefficient is the function of the clearness index; and (4) the diffuse coefficient is the function of the relative sunshine duration. Also, new four diffuse solar radiation models were developed using 1968–2015 long-term global solar radiation and sunshine duration data. The new models are then compared with 35 empirical equations available in previous studies in terms of different statistical tests. Consequently, Models 6 and 8 are found as the most accurate and high-performance empirical models for estimation of the monthly mean diffuse solar radiation on a horizontal surface for Bursa, Turkey.     

The Sun’s apparent position and the optimal tilt angle of a solar collector in the northern hemisphere

In this paper, the Julian dating system is adopted to calculate the Sun’s apparent position. Both the sunshine duration and the optimal installation angle of a fixed solar collector are obtained for different time periods and latitudes in the northern hemisphere. To simulate different operating environments, both kinds of radiation flux are considered, i.e. extraterrestrial radiation and the global radiation calculated using an empirical model. The results show that Julian dating system is precise enough to predict the Sun’s locus according to analyses of the solar declination and the azimuth and elevation angles. The orientation that a solar collector must be installed at can be roughly estimated by determining the sunshine duration. The majority of the Sun’s path lies in the southern sky over a year, and hence the sunshine duration in the southern sky is longer, except for locations with latitudes below 1.5°. The yearly optimal angles are positive (approximately 0.91 and 0.76 multiplied by the latitude for extraterrestrial and global radiation, respectively), for latitudes below 65^o. Above this, the curves are flatter, and the differences between the two types of radiation flux become greater. The ratio of the yearly irradiation captured by a collector installed at its yearly optimal angle to that captured by the ground surface increases with latitude, and reaches a maximum of 1.71 and 1.35 near latitudes of 65° for extraterrestrial and global radiation, respectively. The efficiency of a solar collector decreases when operating in a cloudy environment. The amount of global radiation incident on the ground surface is about 0.51-0.66 times that of extraterrestrial radiation throughout the hemisphere.     

Monthly average daily global solar radiation in P.D.R. Yemen

In this paper a study has been made to estimate average global radiation using hours of bright sunshine and measured solar radiation data available for six locations in P.D.R. Yemen. For Aden, data were obtained from Aden Airport. For other locations in P.D.R. Yemen data were obtained from Agricultural Research Center's meteorological sections. Linear regression analysis of the monthly average global radiation and the sunshine duration data of six locations has been performed using the least squares technique. All the above mentioned data have been used in Ångström's correlation to find the monthly average daily global solar radiation. Results obtained are useful for any solar energy system application in P.D.R. Yemen.     

Multilayer Perceptron approach for estimating 5-min and hourly horizontal global irradiation from exogenous meteorological data in locations without solar measurements

Only one thousand stations around the world measures solar radiation sometimes with a poor quality. The objective of this paper is to show if solar irradiations at short time scale, hourly and 5-min, (very under-studied time-step) can be estimated from more available and cheaper data using Artificial Neural Networks. 7 meteorological and 3 calculated parameters are used as inputs; 1023 inputs combinations are possible for each time-step; the best inputs combinations are pursued. A variable selection method based on Pearson's coefficient is firstly used between inputs and between output and inputs; some inputs are redundant (particularly calculated ones) and/or with a weak link with solar radiation (as wind speed and direction), sunshine duration is strongly correlated with solar irradiation. The models have a good adequacy mainly with sunshine duration in the input set. For hourly data, the performances of the 6 and 10 inputs model are nRMSE = 13.90% (nMAE = 13.28%, R² = 0.979) and nRMSE = 13.33% (nMAE = 12.72%, R² = 0.9812); without sunshine duration, the model nRMSE (with 5 inputs) falls to 28.27%. For 5-min data, the 6 and 10 inputs models have a nRMSE equal to 19.35% and 18.65% which is very good for such a time-step. A comparison with literature highlighted the quality of these models.     

Radial Basis Function Network-based prediction of global solar radiation data: Application for sizing of a stand-alone photovoltaic system at Al-Madinah,Saudi Arabia

In this paper, Radial Basis Function network (RBF) is used for modelling and predicting the daily global solar radiation data using other meteorological data such as air temperature, sunshine duration, and relative humidity. These data were recorded in the period 1998–2002 at Al-Madinah (Saudi Arabia) by the National Renewable Energy Laboratory. Four RBF-models have been developed for predicting the daily global solar radiation. It was found that the RBF-model which uses the sunshine duration and air temperature as input parameters, gives accurate results as the correlation coefficient in this case is 98.80%. A comparative study between developed RBF, Multilayer perceptron and conventional regression models are presented and discussed in this paper, In addition, an application for estimating the sizing of a stand-alone PV system at Al-Maidinah is presented in order to show the effectiveness of the developed RBF-model.     

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.     

Estimation of global solar radiation using artificial neural networks

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

Computation of solar radiation from observations of cloud cover

Techniques of computation of global and diffuse solar radiation from the daily duration of bright sunshine and cloud cover are well-known. However, since radiation computations from cloud cover data provide rather imprecise results, this method is resorted to only when sunshine data are not available. To obtain a better idea of the inverse relationship between the long-term averages of sunshine duration and total cloud cover, an analysis of the monthly mean values of the fraction of the sky C, covered by clouds of all types and the duration of bright sunshine, n, was carried out. The relationship between C and (1−n/N′), where N′ is the maximum possible hours of sunshine, was found to be non-linear. The shape of the regression line connecting the two parameters also shows that ground observations of cloud cover always tend to be overestimates. The differences between such estimates and cloud cover values derived from sunshine duration tend to become zero when skies are either clear or overcast and are a maximum for cloud cover values in the range 0.4–0.7. A cubic regression equation was derived relating C and (1−n/N′) and using this relationship, it has been possible to compute sunshine duration from cloud cover data to an accuracy of about 4–7 per cent and from the cloud derived sunshine data, to compute monthly mean values of global solar radiation to an accuracy of about 6–10 per cent and diffuse solar radiation within an accuracy of about 10–15 per cent.     

Models for obtaining solar radiation from other meteorological data

The application of solar energy requires a knowledge of long-term solar radiation and daylight data. Because of the limited availability of measured data, various formulae have been derived to compute the solar irradiance using other, more commonly available, weather data. In this article two such models are presented, MRM (meteorological radiation model) and CRM (cloud-cover radiation model). MRM requires hourly data for sunshine duration, dry- and wet-bulb temperature; while CRM requires only cloud amount. Both models can generate hour-by-hour data for horizontal global, diffuse, and beam irradiance. A brief comparison of the two models is presented. Results showed that MRM has the advantage over CRM, on account of its consistency with the measured data. Both models are now available via the Internet in the form of electronic spreadsheets.     

Modelling of solar energy potential in Nigeria using an artificial neural network model

In this study, an artificial neural network (ANN) based model for prediction of solar energy potential in Nigeria (lat. 4–14°N, log. 2–15°E) was developed. Standard multilayered, feed-forward, back-propagation neural networks with different architecture were designed using neural toolbox for MATLAB. Geographical and meteorological data of 195 cities in Nigeria for period of 10 years (1983–1993) from the NASA geo-satellite database were used for the training and testing the network. Meteorological and geographical data (latitude, longitude, altitude, month, mean sunshine duration, mean temperature, and relative humidity) were used as inputs to the network, while the solar radiation intensity was used as the output of the network. The results show that the correlation coefficients between the ANN predictions and actual mean monthly global solar radiation intensities for training and testing datasets were higher than 90%, thus suggesting a high reliability of the model for evaluation of solar radiation in locations where solar radiation data are not available. The predicted solar radiation values from the model were given in form of monthly maps. The monthly mean solar radiation potential in northern and southern regions ranged from 7.01–5.62 to 5.43–3.54 kW h/m² day, respectively. A graphical user interface (GUI) was developed for the application of the model. The model can be used easily for estimation of solar radiation for preliminary design of solar applications.     

Comparative study of Ångström’s and artificial neural networks’ methodologies in estimating global solar radiation

The aim of the present research is the comparative development of a variety of models for the estimation of solar radiation on a horizontal surface. By using two different methodologies, models of various complexities have been developed and tested. The first methodology refers to the traditional and long-utilized Ångström’s linear approach which is based on measurements of sunshine duration. The second methodology refers to the relatively new approach based on artificial neural networks (ANN) and it can be based on sunshine duration measurements but also on other climatological parameters. Three Ångström-type models and seven ANN-type models are presented. All of these models are verified against independent data and compared. Lack of sunshine duration measurements renders Ångström’s approach inapplicable; hence the feasibility of applying the ANN models for the calculation of solar radiation in places where there is a lack of sunshine duration measurements is investigated.     

Estimating monthly average daily diffuse solar radiation with multiple predictors: A case study

Solar radiation measurements are not easily available, especially for the diffuse solar radiation. In this study, two models for estimating the diffuse solar radiation are proposed based on multiple predictors including the clearness index, relative sunshine duration, ambient temperature and relative humidity. One of them aims to increase the estimation accuracy, and the other aims to estimate the diffuse solar radiation direct from other meteorological elements in the absence of the global solar radiation. For a case study, the performance of the proposed models is validated by comparing with eight existing models selected from literature against the measured data at Guangzhou station in China. Through the analysis based on statistical error tests, results show that the two models can estimate the monthly average daily diffuse solar radiation with good accuracy.     

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: