Reliability analysis of solar photovoltaic system using hourly mean solar radiation data

This paper presents the hourly mean solar radiation and standard deviation as inputs to simulate the solar radiation over a year. Monte Carlo simulation (MCS) technique is applied and MATLAB program is developed for reliability analysis of small isolated power system using solar photovoltaic (SPV). This paper is distributed in two parts. Firstly various solar radiation prediction methods along with hourly mean solar radiation (HMSR) method are compared. The comparison is carried on the basis of predicted electrical power generation with actual power generated by SPV system. Estimation of solar photovoltaic power using HMSR method is close to the actual power generated by SPV system. The deviation in monsoon months is due to the cloud cover. In later part of the paper various reliability indices are obtained by HMSR method using MCS technique. Load model used is IEEE-RTS. Reliability indices, additional load hours (ALH) and additional power (AP) reduces exponentially with increase in load indicates that a SPV source will offset maximum fuel when all of its generated energy is utilized. Fuel saving calculation is also investigated. Case studies are presented for Sagardeep Island in West Bengal state of India.     

Estimation of hourly solar radiation for India

The ASHRAE constants predict high values of the hourly beam radiation and very low values of the hourly diffuse radiation when used to predict radiation at Indian locations. Hence a procedure has been developed for the estimation of direct, diffuse and global hourly solar radiation on a horizontal surface for any location in India. To calculate hourly solar radiation, an exponential curve, similar to the one used by ASHRAE, was fitted to the measured solar radiation data of six cities from different regions of India. The statistical analysis was carried out for the data computed using ASHRAE constants and the set of constants obtained for India using the measured data of four different Indian cities selected randomly. Three statistical indicators were used to compare the accuracy of the developed procedure. The results show that ASHRAE constants are not suitable to estimate hourly solar radiation in India. Hourly solar radiation estimated by constants obtained for India are fairly comparable with measured data. The mean percentage error with Indian constants for these four Indian cities was found as low as 2.27, −6.29 and −6.09% for hourly beam, diffuse and global radiation, respectively.     

Direct beam and hemispherical terrestrial solar spectral distributions derived from broadband hourly solar radiation data

Multiple junction and thin film photovoltaic (PV) technologies respond differently to varying terrestrial spectral distributions of solar energy. PV device and system designers are concerned with the impact of spectral variation on PV specific technologies. Spectral distribution data are generally very rare, expensive, and difficult to obtain. We modified an existing empirical spectral conversion model to convert hourly broadband global (total hemispherical) horizontal and direct normal solar radiation to representative spectral distributions. Hourly average total hemispherical and direct normal beam solar radiation, such as provided in Typical Meteorological Year (TMY) data, are spectral model input data. Default or prescribed atmospheric aerosols and water vapor are possible inputs. Individual hourly and monthly and annual average spectral distributions are computed for a specified tilted surface. The spectral range is from 300 nm to 1800 nm. The model is a modified version of the Nann and Riordan SEDES2 model. Measured hemispherical spectral distributions for a wide variety of conditions at the Solar Radiation Research Laboratory at the National Renewable Energy Laboratory, Golden, Co. and Florida Solar Energy Center (Cocoa, FL) show that reasonable spectral accuracy of about ±10% is obtainable with exceptions for weather events such as snow. Differing cloud climatology and variable albedo and aerosol optical depth atmospheric conditions can lead to spectral model differences of 30–40%.     

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.     

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.     

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.     

Stochastic simulation model of hourly total solar radiation

A stochastic simulation model of hourly global solar radiation is presented in this paper. It is developed by introducing the concept of “time dependent frequency distribution” (TDFD) of hourly insolation values. In this model the two most critical aspects of time series simulation, i.e., the reproduced time series values which have the appropriate time dependent frequency distribution for the parameter being simulated and the correlation between successive values, are taken into account. The elimination of the TDFD of the data and the transformation of the data distribution to a Gaussian distribution (required for the stationary time series analysis) were carried out using a mapping technique. The autocorrelation function of the transformed data showed that the produced time series is stationary. Then, an antimapping coefficient matrix is developed, which provides a simple yet an effective simulation device. The described model has been applied in Athens (Greece) where hourly insolation data covering a period of two years are used. The theoretical results obtained using this simulation model, regarding both the TDFD and the correlation, are in agreement with the measured data.     

Evaluation and comparison of hourly solar radiation models

In this paper, an attempt has been made to develop a new model to evaluate the hourly solar radiation for composite climate of New Delhi. The comparison of new model for hourly solar radiation has been carried out by using various model proposed by others. The root mean square error (RMSE) and mean bias error (MBE) have been used to compare the accuracy of new and others model. The results show that the ASHRAE and new proposed model estimate hourly solar radiation better for composite climate of New Delhi in comparison to other models. Hourly solar radiation estimated by constants obtained by new model (modified ASHRAE model) for composite climate of India is fairly comparable with measured data. The percentage mean bias error with new constants for New Delhi was found as low as 0.15 and 0% for hourly beam and diffuse radiation, respectively. There is a 1.9–8.5% RMSE between observed and predicted values of beam radiation using new constants for clear days. The statistical analysis has been used for the present study. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Estimation of half-hour solar radiation values from hourly values

A statistical Markovian insolation model for predicting the time-sequence of half-hour solar radiation values on a horizontal surface which uses the hourly insolation values is developed. The hourly transition density function, governing the diurnal evolution of the hourly solar radiation values, is used for obtaining the half-hour transition density function. A transition density function is a measure of the probability of the event at the next immediate hour of interest when the event at the present hour is given. The estimation of half-hour transition density function is done through the fundamental decomposition theorem for the density function. This assumes a set of well defined intermediate states. As a first approximation, the half-hour transition density function is assumed to be temporally stationary. Furthermore, it is assumed that the cumulative probability distribution functions of the normalised initial hour solar radiation value and the normalised initial half-hour solar radiation values are not significantly different; the hourly, or half-hourly solar flux values are normalised by the corresponding extraterrestrial solar flux values. The validity of these assumptions is established through the successful time-sequence predictions of the half-hour insolation values. The time-sequence aspect of solar radiation values is proved by comparing the predicted joint cumulative distribution functions for several successive normalised half-hour values, with the corresponding distribution function for the recorded values. In order to prove that the predicted and actual distribution functions are from the same set, the non-parametric statistical test proposed by Kolmogorov and Smirnov has been used.     

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.     

A method to generate synthetic hourly solar radiation globally

This paper develops a stochastic procedure for generating synthetic sets of hourly solar irradiation values, suitable for use in solar simulation design work. The daily atmospheric transmittance K_t for the day in question is broken down into hourly irradiation events by a stochastic disaggregation procedure. The necessary disaggregation models were constructed using the quasi-universal hourly atmospheric transmittance k_t, instead of the irradiation itself, as the random variable. Analyses of meteorological records revealed that both the marginal probability and stochastic features of sets of hourly events k_t within an individual day can be closely predicted using the K_t for the day. Results indicated that the parameters defining the disaggregation procedure were independent of geographical location. The values of k_t are found to be closely modeled by a Beta distribution, and a mean correlation coefficient between successive hourly values of k_t was found to be 0.54±0.14. An algorithm is described from which unlimited hourly solar irradiation data may, therefore, be generated using only the 12 monthly means of daily events, .     

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.     

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.     

The diffuse fraction of hourly solar radiation for Amman/Jordan

This paper presents various correlations of the hourly clearness index K_t with the hourly diffuse fraction K_d on a horizontal surface for Amman/Jordan. The first correlation is based on Orgill and Hollands method, but using weighted averages. The second correlation is based on hourly integrated values of K_t's and K_d's without any grouping. A refinement of the latter correlation is attempted by including a random shock.     

A simple hourly all-sky solar radiation model based on meteorological parameters

An hourly solar radiation model for cloudy skies, based on meteorological data, was developed andtested. As a means of comparison, the SOLMET regression and Watt models were also tested. The present model was examined for individual cloud types using measured solar radiation to judge the effectiveness of the model in the presence of particular clouds.     

A simple hourly clear-sky solar radiation model based on meteorological parameters

An hourly solar radiation model, based on observed meteorological data, was developed and tested. As a means of comparison, the Watt and Bird models and the Solmet regression models were also tested. Several conclusions were drawn about the parameterization of solar radiation-depleting parameters. It was determined that a reasonable estimate of lower layer aerosol extinction can be determined using humidity, visibility, and mixing height. The parameterization of water vapor absorption obtained by atmospheric rather than laboratory observations was found to give better model results.     

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.     

Univariate and multivariate forecasting of hourly solar radiation with artificial intelligence techniques

This paper introduces a new approach for the forecasting of mean hourly global solar radiation received by a horizontal surface. In addition to the traditional linear methods, several artificial-intelligence-based techniques are studied. These include linear, feed-forward, recurrent Elman and Radial Basis neural networks alongside the adaptive neuro-fuzzy inference scheme. The problem is examined initially for the univariate case, and is extended to include additional meteorological parameters in the process of estimating the optimum model. The results indicate that the developed artificial intelligence models predict the solar radiation time series more effectively compared to the conventional procedures based on the clearness index. The forecasting ability of some models can be further enhanced with the use of additional meteorological parameters.     

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.