Stochastic approach for daily solar radiation modeling

Mathematical modeling of solar radiation continues to be an important issue in renewable energy applications. In general, existing models are mostly empirical and data dependent. In this paper, a novel approach for solar radiation modeling is proposed and illustrated. The proposed application consists of hidden Markov processes, which are widely used in various signal processing topics including speech modeling with successful results. In the experimental work, mean of hourly measured ambient temperature values are considered as observations of the model, whereas mean of hourly solar radiation values are considered as the hidden events, which constitute the outcomes of the proposed mathematical model. Both solar radiations and temperatures are converted to quantized number of states. Finally, after a training stage that forms the transition probability values of the described states, the hidden Markov model parameters are obtained and tested. The tests are repeated for various numbers of states and observations are presented. Plausible modeling results with distinct properties in terms of accuracy are achieved.     

Development of a method for generating operational solar radiation maps from satellite data for a tropical environment

Despite a considerable number of publications which use satellite data to map solar radiation, relatively few studies have been undertaken in a tropical environment. In this study, we have developed a method to produce operational solar radiation maps from satellite data for this environment. The method is based on a physical model which relates the satellite-derived earth–atmospheric reflectivity from visible channel of GMS-4 and GMS-5 to the transmissivity of the atmosphere. Cloud reflectivity was determined from satellite data, while radiation absorbed by water vapour, ozone and aerosols and radiation scattered by aerosols were determined from ground-based meteorological data. Techniques for determining the radiation depleted by these atmospheric constituents over a whole country were also presented. Satellite data of a six-year period (1993–1998) with approximately ten thousand satellite images were used to construct the maps. When tested against an independent data set, monthly average of daily global irradiation calculated from this method agree with that obtained from the measurements with the relative root mean square difference of 6.8% with respect to the mean values. Solar radiation is presented as twelve maps showing the monthly average of global irradiation and one map showing the yearly average of global irradiation. Radiation patterns from the maps show a strong influence of the tropical monsoons.     

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.     

A computer simulation of solar radiation

Various algebraic formulas for representing solar radiation data are discussed and the results obtained are compared.     

Correlation between daily diffuse and global radiation for India

Solar radiation characteristics have been studied in various countries and many correlations developed. In the absence of such studies, the same correlations are applied in other countries. Since radiation records are now available in most developing countries, it is possible to perform similar studies for these regions. The purpose of this study is to use daily global and diffuse radiation data for 13 stations in India to establish a correlation between the daily diffuse ratio and the clearness index. Plotting individual values of the daily diffuse ratio against the clearness index for all Indian Stations showed the existence of a definite relationship between them, confirming the validity of Liu and Jordan approach. It was found that a cubic equation provides a fairly accurate fit for this relationship. Comparison with other studies showed that no single correlation is applicable to all regions, and that each region possesses its own characteristics. Although the stations considered had diverse latitude, climate and geographical variations, the study showed that none had any effect on the correlation.     

On the effects of solar radiation variations on solar heating system performances

The effect of solar radiation availability on the performance of different solar heating systems has been studied. The systems include a solar water heater, passive solar houses and district solar heating systems with seasonal heat storage. Also, different collector orientations and collector types have been investigated. The hourly radiation data were generated by a simple computational simulation procedure. It was found that district solar heating systems with concentrating collectors and passive solar houses showed the largest variations for the given conditions.     

A model for calculating hourly global solar radiation from satellite data in the tropics

A model for calculating global solar radiation from geostationary satellite data is presented. The model is designed to calculate the monthly average hourly global radiation in the tropics with high aerosol load. This model represents a physical relation between the earth-atmospheric albedo derived from GMS5 satellite data and the absorption and scattering coefficients of various atmospheric constituents. The absorption of solar radiation by water vapour which is important for the tropics, was calculated from ambient temperature and relative humidity. The relationship between the visibility and solar radiation depletion due to aerosols was developed for a high aerosol load environment. This relationship was used to calculate solar radiation depletion by aerosols in the model. The total column ozone from TOMS/EP satellite was employed for the determination of solar radiation absorbed by ozone. Solar radiation from four pyranometer stations was used to formulate the relationship between the satellite band earth-atmospheric albedo and broadband earth-atmospheric albedo required by the model. To test its performance, the model was used to compute the monthly average hourly global radiation at 25 solar radiation monitoring stations in tropical areas in Thailand. It was found that the values of monthly average of hourly global radiations calculated from the model were in good agreement with those obtained from the measurements, with the root mean square difference of 10%. After the validation the model was employed to generate hourly solar radiation maps of Thailand. These maps reveal the diurnal and season variation of solar radiation over the country.     

Analysis of short-term solar radiation data

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

A brief review of models for computing solar radiation on inclined surfaces

Modelling of solar energy systems requires estimation of the hourly radiation incident on surfaces of different tilts and orientations. Most meteorological stations report radiation values on a daily rather than hourly basis. Again, the value of the diffuse component may or may not be reported. Hence, different strategies may be encountered, for each location, with the common goal of computing hourly radiation on inclined surfaces.

In this study, five different schemes are presented to achieve this goal. In each scheme, certain correlations are required which are discussed in detail. The study is divided into five sections, each dealing with a specific type of correlation. These sections are: (i) correlations between daily diffuse and global radiation; (ii) correlations between hourly/daily global radiation; (iii) correlations between hourly/daily diffuse radiation; (iv) correlations between hourly diffuse and global radiation; and (v) models for computing diffuse sky radiation on inclined surfaces. The last section deals extensively with the anisotropic nature of sky diffuse radiation.

The important aspects of all correlation studies are highlighted, and the relative merits and demerits of their results are brought to light.

Mathematical expressions, where available, for models/correlations are provided so that the reader will have access to a comprehensive study. This information should be useful for modelling purposes in which computation of radiation on surfaces of different orientations and tilts is required.     

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.     

Models of solar radiation with hours of bright sunshine: A review

In the design and study of solar energy, information on solar radiation and its components at a given location is very essential. 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. For this purpose, in the past, several empirical correlations have been developed in order to estimate the solar radiation around the world. The main objective of this study is to review the global solar radiation models available in the literature. There are several formulate which relate global radiation to other climatic parameters such as sunshine hours, relative humidity and maximum temperature. The most commonly used parameter for estimating global solar radiation is sunshine duration. Sunshine duration can be easily and reliably measured and data are widely available.     

Generation of synthetic daily global solar radiation data based on ERA-Interim reanalysis and artificial neural networks

Four variables (total cloud cover, skin temperature, total column water vapour and total column ozone) from meteorological reanalysis were used to generate synthetic daily global solar radiation via artificial neural network (ANN) techniques. The goal of our study was to predict solar radiation values in locations without ground measurements, by using the reanalysis data as an alternative to the use of satellite imagery. The model was validated in Andalusia (Spain), using measured data for nine years from 83 ground stations spread over the region. The geographical location (latitude, longitude), the day of the year, the daily clear sky global radiation, and the four meteorological variables were used as input data, while the daily global solar radiation was the only output of the ANN. Sixty five ground stations were used as training dataset and eighteen stations as independent dataset. The optimum network architecture yielded a root mean square error of 16.4% and a correlation coefficient of 94% for the testing stations. Furthermore, we have successfully tested the forecasting capability of the model with measured radiation values at a later time. These results demonstrate the generalization capability of this approach over unseen data and its ability to produce accurate estimates and forecasts.     

A statistical approach for sub-hourly solar radiation reconstruction

This paper proposes a computational-statistics based approach for solar radiation reconstruction at sub-hourly intervals. A dimensionless form of stochastic variable, V, which is defined as the difference between the theoretical global solar radiation in clear-sky conditions and the actual solar radiation, normalized by the clear-sky global solar radiation, is introduced and adopted in this work. The probability density function of V is calculated from historical data using a Gaussian kernel density estimator. With the developed model, the only input information required for the reconstruction procedure is the cloud condition of the sky (i.e., fair, partly cloudy, overcast, and rain/snow etc.). A case study in simulating solar radiation in Singapore is conducted to validate the accuracy of the model. The calculated results agree well with the measured data. The normalized root mean square error (NRMSE) is on average 23.4% and 7.2% for the one-minute temporal resolution and hourly integral values, respectively.     

Investigation of cloudless solar radiation with PV module employing Matlab-Simulink

This paper focuses on a novel approach to the prediction of Voltage-Current (V-I) characteristics of a Photovoltaic panel under varying weather conditions and also the modelling of hourly cloudless solar radiation to provide the insolation on a PV module of any orientation, located at any site. The empirical model developed in this study uses standard specifications together with the actual solar radiation and cell temperature. This proposed work develops a Matlab-Simulink model to generate solar radiation at any location and for any time of the year. A new model for V-I characteristics and maximum power operation of a Photovoltaic (PV) module is also presented, which aims to model the effect on V-I and P-V curves of varying climatic conditions. Moreover, this model has been implemented using the Matlab-Simulink and is used to investigate the effect of meteorological conditions on the performance of a PV module generator. Thus the combined model of cloudless solar radiation and the photovoltaic module provides a tool that may be loaded in the library for analysis purpose. It is found that the predicted solar radiation strongly agrees with the experimental data.     

Modeling the variability of solar radiation data among weather stations by means of principal components analysis

Measurements of global terrestrial solar radiation (R_s) are commonly recorded in meteorological stations. Daily variability of R_s has to be taken into account for the design of photovoltaic systems and energy efficient buildings. Principal components analysis (PCA) was applied to R_s data recorded at 30 stations in the Mediterranean coast of Spain. Due to equipment failures and site operation problems, time series of R_s often present data gaps or discontinuities. The PCA approach copes with this problem and allows estimation of present and past values by taking advantage of R_s records from nearby stations. The gap infilling performance of this methodology is compared with neural networks and alternative conventional approaches. Four principal components explain 66% of the data variability with respect to the average trajectory (97% if non-centered values are considered). A new method based on principal components regression was also developed for R_s estimation if previous measurements are not available. By means of multiple linear regression, it was found that the latent variables associated to the four relevant principal components can be fitted according to the latitude, longitude and altitude of the station where data were recorded from. Additional geographical or climatic variables did not increase the predictive goodness-of-fit. The resulting models allow the estimation of daily R_s values at any location in the area under study and present higher accuracy than artificial neural networks and some conventional approaches considered. The proposed methodology for estimating R_s based on geographical parameters would be of interest to design solar energy systems and to select their best location.     

A revised empirical model to estimate solar radiation using automated surface weather observations

The transition from manual to automated weather observations at US National Weather Service Offices has compromised the ability to use these data as a means for estimating global horizontal and direct solar radiation. The creation of long term model-derived solar radiation climatologies continues to rely on the in situ cloud data that these observations provide, since homogeneous and readily available satellite data does not span the transition. An existing semi-physical solar radiation model is revised to allow for the estimation of hourly solar radiation based on these observations. Model evaluation reveals that errors in solar radiation estimates are comparable to other contemporary solar radiation models that estimate global horizontal solar radiation on both daily (10–15% mean absolute error) and hourly (15–19% mean absolute error) timescales. Hourly mean absolute errors are similar for different sky conditions, while daily percent errors are similar between seasons. Model updates also allow for accurate estimates of solar radiation in various climate regimes; regional patterns in model bias are not evident.     

Estimation of horizontal diffuse solar radiation with measured daily data in China

Three most widely used diffuse radiation models are calibrated using the daily data between January 1 1994 and December 31 1998 from 16 stations all over China. The second-degree polynomial relationship between R_D/R_G and n/N (Iqbal model) is suitable for diffuse radiation estimation in China. The averaged correlation coefficient R² is 0.84 and the maximum value is 0.93 at the 16 stations, and the Iqbal model works better in the eastern part of China than in the west. The A.A. El-Sebaii model could not be used to estimate diffused radiation accurately in China, with an averaged R²=0.47. The Liu and Jordan model could also be used for diffuse radiation estimation in China, and the averaged value of R² and parameter X₀ is 0.81 and 0.233, respectively. There is an evident linear relationship among the parameters X₀, a and b of the Liu and Jordan model.     

A simple and efficient algorithm to estimate daily global solar radiation from geostationary satellite data

Surface global solar radiation (GSR) is the primary renewable energy in nature. Geostationary satellite data are used to map GSR in many inversion algorithms in which ground GSR measurements merely serve to validate the satellite retrievals. In this study, a simple algorithm with artificial neural network (ANN) modeling is proposed to explore the non-linear physical relationship between ground daily GSR measurements and Multi-functional Transport Satellite (MTSAT) all-channel observations in an effort to fully exploit information contained in both data sets. Singular value decomposition is implemented to extract the principal signals from satellite data and a novel method is applied to enhance ANN performance at high altitude. A three-layer feed-forward ANN model is trained with one year of daily GSR measurements at ten ground sites. This trained ANN is then used to map continuous daily GSR for two years, and its performance is validated at all 83 ground sites in China. The evaluation result demonstrates that this algorithm can quickly and efficiently build the ANN model that estimates daily GSR from geostationary satellite data with good accuracy in both space and time.     

The effect of model generated solar radiation data usage in hybrid (wind–PV) sizing studies

Wind speed and solar radiation characteristics belonging to past years of a region are the main input parameters in wind–photovoltaic hybrid system (WPHS) sizing studies. Classically, these data are fed to several scenarios with different solar panel, wind turbine, and storage battery number combinations. The solutions with minimal cost which also satisfy the desired maximum loss of energy probability are selected. Since the utilized data have random fluctuations because of atmospheric phenomenon, past years’ data are unlikely to appear in a similar manner in future years. Hence, using a robust model that characterizes the general behavior of the data instead of directly using past data should yield more accurate sizing solutions. In order to compare the sizing accuracy obtained by directly using the data to the accuracy obtained by indirect modeling from data, an analytical solar radiation model is first explained. Using this model, 3-year solar radiation data of three geographical sites are analyzed. It was observed that the differences between sample-by-sample hourly recordings corresponding to different years are significantly larger than the difference between these recordings and the data model obtained from an arbitrary year. This provides a hint that a sizing approach carried out using the data of a previous year would not be accurate in producing the same Loss of Load Probability (LLP) for a future year. On the contrary, the accuracy would improve if a generic analytical model of the solar radiation is used in the sizing process. This foresight is tested by comparing the LLPs obtained in the two ways mentioned above. Results obtained using available data are in accordance with the aforementioned propositions.     

The impact of solar radiation variability and data discrepancies on the design of PV systems

Different information sources on solar radiation data are usually available for a same site. Significant discrepancies can be observed between these different sources, leading to a certain taste of incertitude. An in-depth analysis of such a problem reveals that this is coherent with the natural and unavoidable variability of the solar radiation phenomenon, and that all the information sources can be considered as equally confident.This article describes in a first place the different available solar radiation information sources for Algeria. Their confidence is analyzed afterwards at the light of the variability observed in the long-term series of crude data of a particular site.Finally, the consequences of solar radiation data discrepancy in terms of energy production and PV sizing uncertainties are also analyzed.