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.     

Direct and indirect uncertainties in the prediction of tilted irradiance for solar engineering applications

Global radiation measured on fixed-tilt, south-facing planes (40° and vertical) and a 2-axis tracker at NREL’s Solar Radiation Research Lab. in Golden, CO is compared to predictions from ten transposition models, in combination with either optimal or suboptimal input data of horizontal irradiance. Suboptimal inputs are typically used in everyday engineering calculations, for which the necessary data are usually unavailable for the site under scrutiny, and must be estimated in some way. The performance of the transposition models is first evaluated for ideal conditions when optimal data are used. In this specific case, it is found that the Gueymard and Perez models provide the best estimates of global tilted irradiance under clear skies in particular.The performance of four direct/diffuse separation models is also evaluated. Their predictions of direct and diffuse radiation appear biased in most cases, with a model-dependent magnitude. Finally, the performance of the resulting combinations of separation and transposition models is analyzed in a variety of situations. When only global irradiance is known, the accuracy of the tilted irradiance predictions degrades significantly, and is mainly conditioned by the local performance of the direct/diffuse separation method. For the south-facing vertical surface, inaccuracies in the ground reflection calculations becomes another key factor and significantly increase the prediction error. The Reindl transposition algorithm appears to perform best in this case. When using suboptimal input data for the prediction of plane-of-array irradiance on a moderately tilted plane (40°S) or a 2-axis tracking plane, the Hay, Reindl and Skartveit models are less penalized than others and tend to perform better. It is concluded that further research should be conducted to improve the overall process of predicting irradiance on tilted planes in realistic situations where no local high-quality irradiance or albedo measurements are available.     

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.     

Theoretical variations of the thermal performance of different solar collectors and solar combi systems as function of the varying yearly weather conditions in Denmark

The thermal performances of solar collectors and solar combi systems with different solar fractions are studied under the influence of the Danish design reference year, DRY data file, and measured weather data from a solar radiation measurement station situated at the Technical University of Denmark in Kgs. Lyngby. The data from DRY data file are used for any location in Denmark. The thermal performances of the solar heating systems are calculated by means of validated computer models. The measured yearly solar radiation varies by approximately 23% in the period from 1990 until 2002, and the investigations show that it is not possible to predict the yearly solar radiation on a tilted surface based on the yearly global radiation.The annual thermal performance of solar combi systems cannot with reasonable approximation be fitted to a linear function of the annual total radiation on the solar collector or the annual global radiation. Solar combi systems with high efficient solar collectors are more influenced by weather variations from one year to another than systems with low efficient solar collectors.The annual thermal performance of solar collectors cannot be predicted from the global radiation, but both the annual thermal performance and the annual utilized solar energy can with a reasonable approximation be fitted to a linear function of the yearly solar radiation on the collector for both flat plate and evacuated tubular solar collectors. Also evacuated tubular solar collectors utilize less sunny years with large parts of diffuse radiation relatively better than flat plate collectors.     

Models of diffuse solar radiation

For some locations both global and diffuse solar radiation are measured. However, for many locations, only global is measured, or inferred from satellite data. For modelling solar energy applications, the amount of radiation on a tilted surface is needed. Since only the direct component on a tilted surface can be calculated from trigonometry, we need to have diffuse on the horizontal available. There are regression relationships for estimating the diffuse on a tilted surface from diffuse on the horizontal. Models for estimating the diffuse radiation on the horizontal from horizontal global that have been developed in Europe or North America have proved to be inadequate for Australia [Spencer JW. A comparison of methods for estimating hourly diffuse solar radiation from global solar radiation. Sol Energy 1982; 29(1): 19–32]. Boland et al. [Modelling the diffuse fraction of global solar radiation on a horizontal surface. Environmetrics 2001; 12: 103–16] developed a validated model for Australian conditions. We detail our recent advances in developing the theoretical framework for the approach reported therein, particularly the use of the logistic function instead of piecewise linear or simple nonlinear functions.Additionally, we have also constructed a method, using quadratic programming, for identifying values that are likely to be erroneous. This allows us to eliminate outliers in diffuse radiation values, the data most prone to errors in measurement.     

Assessment of diffuse solar energy under general sky condition using artificial neural network

In this paper, artificial neural network (ANN) models are developed for estimating monthly mean hourly and daily diffuse solar radiation. Solar radiation data from 10 Indian stations, having different climatic conditions, all over India have been used for training and testing the ANN model. The coefficient of determination (R²) for all the stations are higher than 0.85, indicating strong correlation between diffuse solar radiation and selected input parameters. The feedforward back-propagation algorithm is used in this analysis. Results of ANN models have been compared with the measured data on the basis of percentage root-mean-square error (RMSE) and mean bias error (MBE). It is found that maximum value of RMSE in ANN model is 8.8% (Vishakhapatnam, September) in the prediction of hourly diffuse solar radiation. However, for other stations same error is less than 5.1%. The computation of monthly mean daily diffuse solar radiation is also carried out and the results so obtained have been compared with those of other empirical models. The ANN model shows the maximum RMSE of 4.5% for daily diffuse radiation, while for other empirical models the same error is 37.4%. This shows that ANN model is more accurate and versatile as compared to other models to predict hourly and daily diffuse solar radiation.     

Modelling of diffuse solar fraction with multiple predictors

For some locations both global and diffuse solar radiation are measured. However, for many locations, only global radiation is measured, or inferred from satellite data. For modelling solar energy applications, the amount of radiation on a tilted surface is needed. Since only the direct component on a tilted surface can be calculated from direct on some other plane using trigonometry, we need to have diffuse radiation on the horizontal plane available. There are regression relationships for estimating the diffuse on a tilted surface from diffuse on the horizontal. Models for estimating the diffuse on the horizontal from horizontal global that have been developed in Europe or North America have proved to be inadequate for Australia [13]. Boland et al. [2] developed a validated model for Australian conditions. Boland et al. [3] detailed our recent advances in developing the theoretical framework for the use of the logistic function instead of piecewise linear or simple nonlinear functions and was the first step in identifying the means for developing a generic model for estimating diffuse from global and other predictors. We have developed a multiple predictor model, which is much simpler than previous models, and uses hourly clearness index, daily clearness index, solar altitude, apparent solar time and a measure of persistence of global radiation level as predictors. This model performs marginally better than currently used models for locations in the Northern Hemisphere and substantially better for Southern Hemisphere locations. We suggest it can be used as a universal model.     

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.     

倾斜面太阳辐射量计算方法研究

倾斜面辐射数据是保证准确设计太阳能利用系统的基础数据,一般由水平面数据计算得出。针对现有计算模型误差较大的现状考虑,试验测试了水平面及不同倾角斜面上的太阳辐射数据,提出了针对直接辐射转换系数的修正方法;通过倾斜面散射辐射数据的计算和分析,在散射辐射模型的基础上,建立耦合计算模型。试验与模型计算结果表明,散射辐射的各向同性受天气工况的影响,耦合模型具有较高的准确性,计算值与实测值的偏差可控制在5.3%以内。     

Discourses on solar radiation modeling

All solar energy applications require readily available, site-oriented and long-term solar radiation data. A typical database comprises of global, direct and diffuse solar irradiance, duration of sunshine and complementary data like cloud cover, atmospheric turbidity, humidity, temperature, etc. However, most of these stations do not provide complete if any information on solar data, chiefly due to the capital and maintenance costs that measuring instruments incur. For instance, global radiation is the most frequently measured parameter, its two components, i.e. diffuse and direct irradiance are often not measured.Improvements have been made to the meteorological radiation model MRM which, had been developed by Muneer et al. as a simple broadband irradiance estimation model based on synoptic information, by incorporating the sunshine information in the model's regressions. The result of the improvement of the model is a considerable reduction in biases and scatter in the comparison between estimated and measured data. The improved meteorological radiation model, IMRM is more accurate, by up to 70% in some cases, than its predecessor in estimating, global and diffuse horizontal irradiance.When sunshine, atmospheric pressure and temperature are not measured by a nearby station, yet cloud information is recorded, radiation estimation models based on cloud cover, CRM, can be used. Three CRMs have been compared to newly proposed models. It was found that models with locally fitted coefficients gave a more accurate estimation of the solar radiation than CRMs with generalized coefficients. The newly proposed model performed better that the older generation models.The third section of the article deals with estimation of diffuse radiation and possible improvements in its modeling. In this section, apart from clearness index (k_t), influence of the synoptic parameters of sunshine fraction (SF), cloud cover (CC) and air mass (m) on diffuse fraction of global radiation (k) is studied both qualitatively and quantitatively. It is found that, SF shows a strong bearing on the k–k_t relationship followed by CC and then m. As a next step, a series of models are developed for k as a polynomial function of k_t, SF, CC and m. After an extensive evaluation procedure, a regression model is selected such that the diffuse radiation can be estimated with reasonable accuracy without making the model overtly complex. It was found that among all the models, the composite model involving all parameters provides the most accurate estimation of diffuse radiation. The site-specific models are further investigated for any appreciable correlations between different locations and their possible attributions. It was also found that a single model could more than adequately estimate the diffuse radiation for the locations within a given region. Three optimum models are also recommended for each region, in view of the fact that information on all parameters is not necessarily available for all sites. This study reveals a significant improvement from the conventional k–k_t regression models to the presently proposed models, therefore, leading to more accurate estimation of diffuse radiation by approximately 50%.     

Global transmissivity and diffuse fraction of solar radiation for clear and cloudy skies as measured and as predicted by bulk transmissivity models

Measurements of cloudiness and of global, direct, and diffuse radiation taken over a 13 mo period at Davis, CA, are analyzed in terms of global transmission (K_t) and diffuse fraction (K_d) for clear sky conditions and for various cloudiness conditions. A number of global transmission clear sky models are compared with observations for ranges of total water column and turbidity and some are found to give representative values for the global radiation at the ground.The dependence of the diffuse fraction on global transmission is found to be best represented by linear formulae—with different dependencies found for clear and cloudy conditions.Global transmission models are also compared with observations for cloudy conditions and found to give representative values of cloud transmissivities if climatological differences in the cloudiness at the measurement site and those sites used to calibrate the cloud models are considered.These results support the use of routine instantaneous surface meteorological data to calculate the most likely instantaneous global and diffuse radiation on a horizontal surface in the absence of any radiation measurements. These calculated irradiances are best used for solar energy system dynamic modeling in which system responses to typical sequences in meteorological conditions are being examined.     

Combining solar irradiance measurements,satellite-derived data and a numerical weather prediction model to improve intra-day solar forecasting

Isolated power systems need to generate all the electricity demand with their own renewable resources. Among the latter, solar energy may account for a large share. However, solar energy is a fluctuating source and the island power grid could present an unstable behavior with a high solar penetration. Global Horizontal Solar Irradiance (GHI) forecasting is an important issue to increase solar energy production into electric power system. This study is focused in hourly GHI forecasting from 1 to 6 h ahead. Several statistical models have been successfully tested in GHI forecasting, such us autoregressive (AR), autoregressive moving average (ARMA) and Artificial Neural Networks (ANN). In this paper, ANN models are designed to produce intra-day solar forecasts using ground and exogenous data. Ground data were obtained from two measurement stations in Gran Canaria Island. In order to improve the results obtained with ground data, satellite GHI data (from Helioclim-3) as well as solar radiation and Total Cloud Cover forecasts provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) are used as additional inputs of the ANN model. It is shown that combining exogenous data (satellite and ECMWF forecasts) with ground data further improves the accuracy of the intra-day forecasts.     

Estimation of global solar radiation in arid and semi-arid climates of East and West Iran

In Iran, most of the models used so far, have provided solar estimation for a few specific locations based on the short-term solar observations. Using different radiation models, (e.g. Sabbagh, Paltridge–Proctor, Daneshyar) and various input parameters (e.g. cloud cover, sunshine duration, relative humidity, temperature, and altitude) we developed a general height-depended formula for the prediction of the direct and diffuse monthly average daily solar radiation for 64 mountainous arid and semi-arid locations in West and East Iran. The models mentioned are modified and new coefficients are defined for the diffuse component based on the long-term observed diffuse data. Model results are validated against up to 13-year daily solar observations at 10 solar radiation sites. In comparison with the previous studies, the newly developed method performs more accurate estimation (less than 3% MPE error) in the arid and semi-arid regions. Comparison of the model results indicates that calibration of the coefficients made to the diffuse formula against the longer period experimental data can improve the estimations of global solar radiation.     

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.     

Analysis of experimental data on diffuse solar radiation in Athens,Greece, for building applications

Proper design and performance prediction of solar energy systems requires accurate information on the availability of solar radiation. The diffuse-to-total radiation correlation, originally developed by Liu and Jordan, has been extensively used as the technique and provided excellent results, although it was latitude dependent and not universally applicable. Thus, diffuse fraction correlations of this type have been developed by few other authors and for different location. This paper presents an analysis of hourly diffuse radiation on a horizontal surface. Hourly pyranometer data from Athens, Greece, are used to establish relationships between the diffuse fraction and the clearness index k _T for hourly and daily values. The results of the proposed equations are then compared with earlier equations. For the urban conditions of Athens the developed correlation fit to the empirical data.     

Computing diffuse fraction of global horizontal solar radiation: A model comparison

For simulation-based prediction of buildings’ energy use or expected gains from building-integrated solar energy systems, information on both direct and diffuse component of solar radiation is necessary. Available measured data are, however, typically restricted to global horizontal irradiance. There have been thus many efforts in the past to develop algorithms for the derivation of the diffuse fraction of solar irradiance. In this context, the present paper compares eight models for estimating diffuse fraction of irradiance based on a database of measured irradiance from Vienna, Austria. These models generally involve mathematical formulations with multiple coefficients whose values are typically valid for a specific location. Subsequent to a first comparison of these eight models, three better performing models were selected for a more detailed analysis. Thereby, the coefficients of the models were modified to account for Vienna data. The results suggest that some models can provide relatively reliable estimations of the diffuse fractions of the global irradiance. The calibration procedure could only slightly improve the models’ performance.     

Estimation of daily diffuse solar radiation in China

Applying the measured global and diffuse solar radiation data from 78 meteorological stations in China, a countrywide general correlation model for calculating the daily diffuse radiation was derived on the basis of Liu and Jordan method. Two widely used statistics: root mean square error and mean bias error were used to assess the performance of the correlation. And the correlation shows good behavior when applied to most of the stations. Subsequently, with the measured data from the 78 stations, an analysis of geographical distribution of solar energy resource in China was also presented in the form of clearness index (the ratio of global solar radiation to extraterrestrial radiation) percentage frequency, and results show that the solar energy resource in western and northern China is relatively abundant.     

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.