Stochastic simulation of hourly global radiation sequences

Stochastic simulation of hourly global radiation carried out with Auto-Regressive Moving Average and Factor Analysis techniques is found unable to describe the statistical features of time sequences. A Markov transition-matrix approach operating on atmospheric transmittance provides a simple yet effective simulation device. Two novel sophisticated models, the transmittance transition tensor and the Gaussian mapping technique are not justified in this context.     

Monthly mean hourly global solar radiation estimation

In this paper, selected empirical models were used to estimate the monthly mean hourly global solar radiation from the daily global radiation at three sites in the east coast of Malaysia. The purpose is to determine the most accurate model to be used for estimating the monthly mean hourly global solar radiation in these sites. The hourly global solar radiation data used for the validation of selected models were obtained from the Malaysian Meteorology Department and University Malaysia Terengganu Renewable Energy Station. In order to indicate the performance of the models, the statistical test methods of the normalized mean bias error, normalized root mean square error, correlation coefficient and t-statistical test were used. The monthly mean hourly global solar radiation values were calculated by using six models and the results were compared with corresponding measured data. All the models fit the data adequately and can be used to estimate the monthly mean hourly global solar radiation. This study finds that the Collares-Pereira and Rabl model performed better than the other models. Therefore the Collares-Pereira and Rabl model is recommended to estimate the monthly mean hourly global radiations for the east coast of Malaysia with humid tropical climate and in elsewhere with similar climatic conditions.     

Prediction of hourly diffuse solar radiation from measured hourly global radiation on a horizontal surface

A statistical procedure has been employed to develop correlations between the hourly global horizontal radiation and its diffuse component. Several years', hourly radiation data from three Canadian stations and two French stations have been employed for this purpose. The relationships have been developed in dimensionless form which predict for particular solar altitudes when is given.Under heavily cloudy conditions or when the sky is completely covered ( ), diffuse radiation increases linearly with the global radiation. In this region, solar altitude has no bearing on the fraction of diffuse radiation.As goes beyond 0.35, the effect of solar altitude begins to appear and the region immediately following this may be considered as partly-cloudy-skies conditions. In the beginning of this region, the diffuse component increases briefly with the increase in global radiation and then begins to decrease as the partly cloudy skies become clearer. At particular solar altitudes, a minimum value of the diffuse radiation is reached. The value of where reaches its minimum value varies with solar altitude.The region beyond which a minimum value of is reached may be considered as mainly-clear-sky conditions. In this region, increases again with , lower solar altitudes giving a higher percentage of diffuse radiation.Under partly cloudy skies and under clear skies, solar altitudes lower than 30° had a marked effect on the fraction of diffuse radiation. However, solar altitudes greater than 30° had minimal influence on the fraction of diffuse radiation.     

Time series analysis of hourly global horizontal solar radiation

Accurate design and optimization of short response time solar energy systems with storage are sensitive to the stationary and sequential characteristics of hourly solar radiation. We perform monthly time series analyses of hourly global horizontal solar radiation for a wide range of climatic stations that span temperate and tropical conditions. The stationary statistics for individual hours are found to be very similar to the corresponding results for daily total global horizontal radiation, in keeping with a related fundamental observation of Liu & Jordan. Investigation of sequential properties shows that autocorrelation coefficients are, to a good approximation, independent of time of day and that persistence times are nearly as long as the entire daylight period, mainly due to the effect of very strong correlations at one-hour lag times. The isolated effect of two-hour and longer lag times, via the partial autocorrelation coefficients, is found to be negligible in most, but by no means all, instances. Finally, we find no universal correlation between hourly autocorrelation coefficients and monthly average radiation figures.     

Characterization and simulation of hourly exposure series of global radiation

A statistical model which captures the main features of hourly exposure series of global radiation is proposed. This model is used to obtain a procedure to generate radiation series without imposing, a priori, any restriction on the form of the probability distribution function of the series. The statistical model was taken from the stationary stochastic processes theory. Data were obtained from ten different Spanish locations. As monthly hourly exposure series of global radiation are not stationary, they are modified in order to remove the observed trends. A multiplicative autoregressive moving average model with regular and seasonal components was used. It is statistically accepted that this is the true model which generates most of the analyzed sequences. However, the underlying parameters of the model vary from one location to another and from one month to another. Therefore, it is necessary to examine further the relationship between the parameters of the model and the available data from most locations.     

A model for the diffuse fraction of hourly global radiation

Hourly values of diffuse and beam irradiance are often required in cases where, at best, only global irradiance is available. For use in the evaluation of the climatological potential for solar energy utilization in Norway, an analytical model is proposed expressing the hourly diffuse fraction of global irradiance in terms of hourly solar elevation and clearness index. This model, developed for average snow-free close to sea level conditions in Norway, fairly well fits the average picture of an extensive independent data base.     

Hybrid methodology for hourly global radiation forecasting in Mediterranean area

The renewable energies prediction and particularly global radiation forecasting is a challenge studied by a growing number of research teams. This paper proposes an original technique to model the insolation time series based on combining Artificial Neural Network (ANN) and Auto-Regressive and Moving Average (ARMA) model. While ANN by its non-linear nature is effective to predict cloudy days, ARMA techniques are more dedicated to sunny days without cloud occurrences. Thus, three hybrids models are suggested: the first proposes simply to use ARMA for 6 months in spring and summer and to use an optimized ANN for the other part of the year; the second model is equivalent to the first but with a seasonal learning; the last model depends on the error occurred the previous hour. These models were used to forecast the hourly global radiation for five places in Mediterranean area. The forecasting performance was compared among several models: the 3 above mentioned models, the best ANN and ARMA for each location. In the best configuration, the coupling of ANN and ARMA allows an improvement of more than 1%, with a maximum in autumn (3.4%) and a minimum in winter (0.9%) where ANN alone is the best.     

A multivariate qualitative model for the prediction of daily global radiation from three hourly global radiation values

A new model for the prediction of daily global radiation using three hourly radiation values is proposed. This model is obtained by multivariate regression analysis. The hourly clearness index and various qualitative variables are used as independent variables. The hourly values are obtained from net ground measures of hourly global radiation corresponding to the hours in which Meteosat secondary images are available over Europe. The qualitative variables allow us to include additional non-numerical information, specifically, the season of the year. The proposed model is the same for all the locations analysed. This model can be used for the prediction of daily global radiation based on hourly global radiation data obtained from satellite images.     

Correlation between hourly diffuse and global radiation for New Delhi

Estimation of hourly insolation on tilted surfaces is required in simulation of solar energy systems. This necessitates splitting of hourly global horizontal insolation into diffuse and direct components. Many models have been developed for this purpose, and the aim of this study is to develop a correlation between hourly diffuse ratio and clearness index for New Delhi. The correlation is developed on the basis of measured data for two years. The performance of this correlation was checked by calculating the difference between computed and measured diffuse radiation. The correlation proved to perform quite well. A comparison of the present correlation with those for other locations showed that such correlations are location dependent.     

Using probabilistic finite automata to simulate hourly series of global radiation

A model to generate synthetic series of hourly exposure of global radiation is proposed. This model has been constructed using a machine learning approach. It is based on the use of a subclass of probabilistic finite automata which can be used for variable-order Markov processes. This model allows us to represent the different relationships and the representative information observed in the hourly series of global radiation; the variable-order Markov process can be used as a natural way to represent different types of days, and to take into account the “variable memory” of cloudiness. A method to generate new series of hourly global radiation, which incorporates the randomness observed in recorded series, is also proposed. As input data this method only uses the mean monthly value of the daily solar global radiation. We examine if the recorded and simulated series are similar. It can be concluded that both series have the same statistical properties.     

A comparison of methods for estimating hourly diffuse solar radiation from global solar radiation

Four methods of estimating hourly diffuse irradiation from hourly global irradiation are compared, using global and diffuse irradiation data from the Australian Bureau of Meteorology for five widely separated Australian locations. A development of one of these methods with constants derived from the data for each place is found to perform best when judged on a criterion of absolute error, and this performance in maintained when constants averaged over the five locations are used. The derived constants are also given for all other Australian locations for which both global and diffuse data are available, and a method is suggested for deriving suitable values of the constants for places situated between 20° and 45° S for which only global radiation data are available. A previously reported dependence of the proportion of diffuse radiation on latitude is demonstrated.     

Stochastic prediction of hourly global solar radiation for Patra,Greece

This paper describes the stochastic prediction of the hourly profile of the intensity of the global solar radiation, I(h; n_j) for any day n_j at a site. The prediction model requires one, two, or three morning measurements of the global solar radiation in a day n_j, makes use of a rich data bank of past years recorded data, and provides I(h; n_j) values for the rest hours of the day. The model is validated by comparing the I(h; n_j) profiles generated for Patra, Greece, with the solar radiation measurements recorded for Winter, Autumn and Spring days, when solar radiation fluctuations often appear to be strong, while also comparing with the predicted by the METEONORM package I(h; n_j) profile. Conclusions are deducted for the predictive power of the model. The proposed model, which is developed in MATLAB for the purpose of this research, provides I(h; n_j) profile predictions very close to the measured values and offers itself as a promising tool for a predictive on-line daily load management.     

Estimation of the diffuse radiation fraction for hourly,daily and monthly-average global radiation

Hourly pyrheliometer and pyranometer data from four U.S. locations are used to establish a relationship between the hourly diffuse fraction and the hourly clearness index k_T. This relationship is compared to the relationship established by Orgill and Hollands and to a set of data from Highett, Australia, and agreement is within a few percent in both cases. The transient simulation program TRNSYS is used to calculate the annual performance of solar energy systems using several correlations. For the systems investigated, the effect of simulating the random distribution of the hourly diffuse fraction is negligible. A seasonally dependent daily diffuse correlation is developed from the data, and this daily relationship is used to derive a correlation for the monthly-average diffuse fraction.     

Developing regional calibration coefficients for estimation of hourly global solar radiation in Ireland

This study proposed regional coefficients for estimating hourly global solar radiation through the adaptation of some empirical models that relate radiation to climatological and geographical variables. A total of 10 models were adapted over 7 stations in Ireland. The performance of the models was evaluated using some selected error indicators including the global performance index which combines all other error indices. The results indicated that the sunshine based regional calibration coefficients generated through a polynomial approach was most superior over other models with the lowest RMSE (0.2–0.3?MJm^?2?hr^?1), MAE (0.1–0.2?MJm^?2?hr^?1) and Pbias (0–7.0%) and highest R² and KGE (>0.85). The study found no local effect such as instrumental siting, observational uncertainty and climate on the variations of these coefficients. This outcome will therefore facilitate the design of various local and/or regional solar energy applications at microscale in a temperate region.     

Estimation of symmetric and asymmetric hourly global and diffuse radiation from daily values

The validity of the correlations[1–3] to estimate the hourly global and diffuse solar radiation components for an independent dataset of fourteen locations is examined in this article. The correlations for the diffuse component[2,3] are found to be in rather poor agreement with the data. An improved correlation for the diffuse component that includes a daily diffuse fraction as a parameter is developed. The influence of this improved correlation on estimating the beam radiation component is examined. A convenient form of describing asymmetry for these three components of solar radiation distribution is proposed and validated.     

Comparative study of various correlations in estimating hourly diffuse fraction of global solar radiation

Proper design and performance predictions of solar energy systems require accurate information on the availability of solar radiation. The diffuse-to-global solar radiation correlation, originally developed by Liu and Jordan, has been extensively used as the technique providing accurate results, although it is latitude dependent. Thus, in the present study, empirical correlations of this type were developed to establish a relationship between the hourly diffuse fraction (k_d) and the hourly clearness index (k_t) using hourly global and diffuse irradiation measurements on a horizontal surface performed at Athalassa, Cyprus. The proposed correlations were compared against 10 models available in the literature in terms of the widely used statistical indicators, rmse, mbe and t test. From this analysis, it can be concluded that the proposed yearly correlation predicts diffuse values accurately, whereas all candidate models examined appear to be location-independent for diffuse irradiation predictions.     

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.     

Novel approach in developing hourly global solar radiation model based on peak sunshine hours

The present study explores a novel approach to derive the hourly global solar radiation (HGSR) for any given latitude based on the peak sunshine hours (PSHs). The proposed analytical model describes a relationship between the HGSR and the day length and the PSHs. The applicability of this model is evaluated by comparing the actual and derived values of HGSR for two cities Chennai (13°04′N, 80°17′E) and New Delhi (29°06′N, 77°22′E). To judge the goodness of the proposed model a set of error metrics has been developed by evaluating the variation of actual HGSR from the simulated value for a given day over 12 months. The overall average mean bias error for one year is 1.015% and 1.08% for Chennai and New Delhi, respectively. The agreement between the actual and the simulated values is generally good, with an appreciable correlation of 95%. In particular, unlike the other models this approach requires only two inputs which are easily available for any location. The proposed technique is useful for any solar application designer for deriving the hourly solar radiation values for a given day of any location with less available climate data.     

New methodologies to estimate the hourly global solar radiation; Comparisons with existing models

This paper describes two new friendly and reliable approaches to estimate hourly global solar radiation on a horizontal surface even with a pocket calculator.Such fast and reliable predictions for the hourly solar radiation are necessary for the real-time management of both the solar energy sources, like a PV generator output in the one hand and the power loads, on the other.The predicted global solar hourly radiation values are compared with estimates from two existing packages and the recorded solar radiation for the two biggest cities of Greece.The two methodologies presented in this paper can be applied to any other site.     

Comparison of diffuse/global ratios calculated from one-minute, hourly and daily solar radiation data

One-minute values of direct, diffuse and global radiation have been continuously collected at Davis, California (38.5°N, 121.1°W) since 1 January, 1979. These datasets are quality controlled to insure the most accurate and reliable data possible. Analysis of one-minute data has provided an opportunity to evaluate some of the bias that may be inherent in statistical representation of solar radiation data. A simple mean and standard deviation do not adequately describe the variation in the data and we show that a more representative treatment includes the box and whisker analysis. In this the mean, median, first and third quartiles, and the maximum and minimum ranges are presented. It is possible to compute the variability between days more completely with this technique while the means may be very close. This has application to evaluation of solar collectors as a better method of evaluating theire efficiency. This is applied to diffuse/global ratios which show a seasonal dependence although some clear winter days have ratios close to clear summer values; however, the first and third quartile and median distinctly separate these days. Analysis of solar radiation data should be conducted with caution as shown by these results.A simple model is proposed to compute hourly global values from the integrated daily total. Comparisons of calculated with measured hourly values indicated less than a 10 per cent error between 0700 to 1600 with the maximum value being slightly underestimated. This procedure allows one to evaluate solar collectors with only daily values and presents a method for thoroughly evaluating our solar resources.