The sun’s total and spectral irradiance for solar energy applications and solar radiation models

Using the most recent composite time series of total solar irradiance spaceborne measurements, a solar constant value of 1366.1 W m⁻² is confirmed, and simple quadratic expressions are proposed to predict its daily value from the Zurich sunspot number, the MgII index, or the 10.7 cm radio flux index. Whenever these three indices are available on a daily basis (since 1978), it is possible to predict the sun’s irradiance within 0.1% on average, as accurately as current measurements.Based on this value of the solar constant, an improved approximation of the extraterrestrial solar spectrum from 0 to 1000 μm is proposed. It is obtained by dividing the spectrum into nine bands and selecting representative (and recent) spectra, as well as appropriate scaling coefficients for each band. Comparisons with frequently used spectra are discussed, confirming previous findings of the literature.This synthetic and composite spectrum is proposed at 0.5-nm intervals in the UV (280–400 nm), 1-nm intervals between 0–280 and 400–1705 nm, 5-nm intervals between 1705 and 4000 nm, and progressively larger intervals beyond 4 μm, for a total of 2460 wavelengths.     

Global solar irradiance in Cordoba: Clearness index distributions conditioned to the optical air mass

The biological and photochemical effects of solar radiation and solar energy applications make it really important to characterize the variability of this component. In view of the fact that the clearness index indicates not only the level of availability of solar radiation but also the changes in atmospheric conditions in a given location, since the classic Liu and Jordan study, many papers have dealt with its statistical distribution. Specifically, Tovar et al. [Tovar J, Olmo FJ, Alados-Arboledas L. Solar Energy 1998;62(6):387–393] proposed a model to represent the probability density distributions of the instantaneous clearness index conditioned to the optical air mass from measurements recorded in Granada (Spain). In this work, we have proved the applicability of this model in a different location, Cordoba (Spain), finding that the parameters for fitting the model depend on both the optical air mass and the geographic and climatic conditions.     

Analysing consequence of solar irradiance on amorphous silicon solar cell in variable underwater environments

Harvesting underwater Solar energy using photovoltaic (PV) technology leads to an innovative approach to utilize it in monitoring various underwater sensors, devices, or other autonomous systems using modern-day power electronics. Another huge advantage of placing PV cells underwater comes from the fact that the water itself can provide cooling and cleaning for the cells. Such advantages come with many challenges and constraints due to the underwater spectral change and decrease in Solar radiation with an increase in water depth. In this work, an experimental set-up has been realized to create an underwater environment and further characterized in the indoor environment using the Solar simulator. Moreover, the transfer of Solar radiation through water and the performance of amorphous silicon Solar cell underwater up to 0.2 m has been analysed in changing underwater environments. This investigation shows a better understanding of solar radiation underwater and the amorphous silicon solar cell underwater at shallow depths with considering the water depth up to 0.2 m, salinity 3.5%, total dissolved salts, and other impurities affecting the solar radiation and the performance of amorphous silicon Solar cell in underwater conditions. In addition to that, the maximum power output P_max of amorphous silicon Solar cell is 0.0367 W at 0.2 m in the case of DI water. In contrast, in real seawater and artificial seawater with 3.5% salinity, it shows 0.0337 W and 0.0327 W, respectively.     

New equations for the calculation of the horizon brightness irradiance in the model of Perez

In this technical note authors propose new expressions to calculate the diffuse irradiance coming from the horizon brightness band on a tilted plane. As in the model of Perez, it is assumed that the radiance from this band is a constant. New expressions are more exact than previous ones as they eliminate some of the simplifications considered in the model of Perez. For small slope angles new expressions give irradiance values up to 32.98% higher than with the cited model. Notwithstanding, when slope angle increases obtained differences sharply decrease at the beginning and this decrease becomes practically linear from about 40° on.     

Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation

Accurately computing solar irradiance on external facades is a prerequisite for reliably predicting thermal behavior and cooling loads of buildings. Validation of radiation models and algorithms implemented in building energy simulation codes is an essential endeavor for evaluating solar gain models. Seven solar radiation models implemented in four building energy simulation codes were investigated: (1) isotropic sky, (2) Klucher, (3) Hay–Davies, (4) Reindl, (5) Muneer, (6) 1987 Perez, and (7) 1990 Perez models. The building energy simulation codes included: EnergyPlus, DOE-2.1E, TRNSYS-TUD, and ESP-r. Solar radiation data from two 25 days periods in October and March/April, which included diverse atmospheric conditions and solar altitudes, measured on the EMPA campus in a suburban area in Duebendorf, Switzerland, were used for validation purposes. Two of the three measured components of solar irradiances – global horizontal, diffuse horizontal and direct-normal – were used as inputs for calculating global irradiance on a south-west façade. Numerous statistical parameters were employed to analyze hourly measured and predicted global vertical irradiances. Mean absolute differences for both periods were found to be: (1) 13.7% and 14.9% for the isotropic sky model, (2) 9.1% for the Hay–Davies model, (3) 9.4% for the Reindl model, (4) 7.6% for the Muneer model, (5) 13.2% for the Klucher model, (6) 9.0%, 7.7%, 6.6%, and 7.1% for the 1990 Perez models, and (7) 7.9% for the 1987 Perez model. Detailed sensitivity analyses using Monte Carlo and fitted effects for N-way factorial analyses were applied to assess how uncertainties in input parameters propagated through one of the building energy simulation codes and impacted the output parameter. The implications of deviations in computed solar irradiances on predicted thermal behavior and cooling load of buildings are discussed.     

A simple and efficient procedure for increasing the temporal resolution of global horizontal solar irradiance series

The intermittent nature of instantaneous solar radiation has a considerable impact on the nonlinear behavior of solar energy conversion systems. The time resolution of the Numerical Weather Prediction Models (NWPM) or satellite derived solar irradiance data are typically limited to 1-h (at best 15-min). Unfortunately, this resolution is not sufficient in the design and performance of many solar systems. In this study, a new methodology has been developed to increase the temporal resolution of GHI series from 1-h to 1-min. This methodology uses the clearness index k_t (the ratio of GHI to top-of-atmosphere irradiance on the same plane) to characterize the GHI high-frequency dynamics from a 1-year measurement campaign at a given site. The evaluation of the method with 2 years of measured data in different climatic zones has resulted in KSI(%) (Kolmogorov–Smirnov test Integral parameter) and normalized root mean square deviation values below 8.0% and 1.7% respectively for each month, with negligible bias. Indicators of overall performance show an excellent agreement between measured and modeled 1-min GHI data for each month: average values for Nash-Sutcliffe efficiency, Willmott index of agreement and Legates coefficient of efficiency are found to be 0.94, 0.99 and 1.00, respectively.     

Monthly average clear-sky broadband irradiance database for worldwide solar heat gain and building cooling load calculations

This paper establishes the formulation of a new clear-sky solar radiation model appropriate for algorithms calculating cooling loads in buildings. The aim is to replace the ASHRAE clear-sky model of 1967, whose limitations are well known and are reviewed. The new model is derived in two steps. The first step consists of obtaining a reference irradiance dataset from the REST2 model, which uses a high-performance, validated, two-band clear-sky algorithm. REST2 requires detailed inputs about atmospheric conditions such as aerosols, water vapor, ozone, and ground albedo. The development of global atmospheric datasets used as inputs to REST2 is reviewed. For the most part, these datasets are derived from space observations to guarantee universality and accuracy. In the case of aerosols, point-source terrestrial measurements were also used as ground truthing of the satellite data. The second step of the model consists of fits derived from a REST2-based reference irradiance dataset. These fits enable the derivation of compact, but relatively accurate expressions, for beam and diffuse clear-sky irradiance. The fitted expressions require the tabulation of only two pseudo-optical depths for each month of the year. The resulting model, and its tabulated data, are expected to be incorporated in the 2009 edition of the ASHRAE Handbook of Fundamentals.     

Calculation of the horizon brightness irradiance in the model of Perez using the unit-sphere method

The present technical note describes a computer tool for determining the horizon brightness diffuse irradiance on a tilted plane in the model of Perez. The applied procedure considers the configuration factor concept, which is calculated using the unit-sphere method. The results obtained with this procedure, which is more exact than the one followed by Perez, are compared with the ones obtained with Perez's proposal. It may be observed that for small angles of inclination differences are up to 36%, and that said differences decrease when the angle of inclination increases. For angles higher than 77.15°, differences become lower than 1%. It may be concluded that the described procedure, together with the computer tool for implementing it, is adequate for determining the horizon brightness irradiance on a tilted plane, once the radiance of this area of the sky dome is known.     

Systematic error in the measurement of very high solar irradiance

The measurement of very high solar irradiance is required in an increasingly wide variety of technical applications. There is really only one commercial supplier of heat flux sensors that can be used for this purpose. These gages are calibrated using a black body as the radiant source. A systematic error has been detected when these heat flux sensors are later used to measure the irradiance from concentrated solar radiation; in this case, the calibration constants obtained for these gages in the laboratory must be systematically corrected.     

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.     

Experimental testing of models for the estimation of hourly solar radiation on vertical surfaces at Arcavacata di Rende

More than 55,000 data of hourly solar radiation on a horizontal surface and on vertical surfaces exposed to the south, west, north and east, measured at Arcavacata di Rende (CS), were compared with hourly radiation data calculated by various calculation models.Erbs, Reindl et al. and Skartveit et al. correlations for the split of hourly global radiation in the diffuse and beam components were used together with the isotropic sky model and three anisotropic sky models.The agreement between experimental and calculated data is generally good.     

Evaluation of numerical weather prediction for intra-day solar forecasting in the continental United States

Numerical weather prediction (NWP) is generally the most accurate tool for forecasting solar irradiation several hours in advance. This study validates the North American Model (NAM), Global Forecast System (GFS), and European Centre for Medium-Range Weather Forecasts (ECMWF) global horizontal irradiance (GHI) forecasts for the continental United States (CONUS) using SURFRAD ground measurement data. Persistence and clear sky forecasts are also evaluated. For measured clear conditions all NWP models are biased by less than 50 W m⁻². For measured cloudy conditions these biases can exceed 200 W m⁻² near solar noon. In general, the NWP models (especially GFS and NAM) are biased towards forecasting clear conditions resulting in large, positive biases.Mean bias errors (MBE) are obtained for each NWP model as a function of solar zenith angle and forecast clear sky index, kt^∗, to derive a bias correction function through model output statistics (MOS). For forecast clear sky conditions, the NAM and GFS are found to be positively biased by up to 150 W m⁻², while ECMWF MBE is small. The GFS and NAM forecasts were found to exceed clear sky irradiances by up to 40%, indicating an inaccurate clear sky model. For forecast cloudy conditions (kt^∗ < 0.4) the NAM and GFS models have a negative bias of up to −150 W m⁻². ECMWF forecasts are most biased for moderate cloudy conditions (0.4 < kt^∗ < 0.9) with an average over-prediction of 100 W m⁻².MOS-corrected NWP forecasts based on solar zenith angle and kt^∗ provide an important baseline accuracy to evaluate other forecasting techniques. MOS minimizes MBE for all NWP models. Root mean square errors for hourly-averaged daytime irradiances are also reduced by 50 W m⁻², especially for intermediate clear sky indices. The MOS-corrected GFS provides the best solar forecasts for the CONUS with an RMSE of about 85 W m⁻², followed by ECMWF and NAM. ECMWF is the most accurate forecast in cloudy conditions, while GFS has the best clear sky accuracy.     

A simple approach to the synthetic generation of solar irradiance time series with high temporal resolution

Modeling the performance of some concentrating solar systems for thermal power plants may require high temporal resolution irradiance as input, in order to account for the impact of the cloud transient effects. This work proposes a simple method of generating synthetic irradiance of 10-min intervals from the hourly mean values. Boundary conditions are imposed to preserve the expected behavior under clear sky situations. The procedure consists basically on adding a random fluctuation, which characteristic amplitude depends on the sky conditions, to the hourly interpolated values. The assessment of the method with ground data have shown to main aspects to remark: daily and monthly means from the synthetic data are below 5% of root mean squared deviation compared to the original time series; despite the noticeable uncertainty in the 10-min synthetic irradiance values, the dynamic behavior of the fluctuations is comparable to the original data.     

Forecasting of global and direct solar irradiance using stochastic learning methods, ground experiments and the NWS database

We develop and validate a medium-term solar irradiance forecasting model by adopting predicted meteorological variables from the US National Weather Service’s (NWS) forecasting database as inputs to an Artificial Neural Network (ANN) model. Since the inputs involved are the same as the ones available from a recently validated forecasting model, we include mean bias error (MBE), root mean square error (RMSE), and correlation coefficient (R²) comparisons between the more established forecasting model and the proposed ones. An important component of our study is the development of a set of criteria for selecting relevant inputs. The input variables are selected using a version of the Gamma test combined with a genetic algorithm. The solar geotemporal variables are found to be critically important, while the most relevant meteorological variables include sky cover, probability of precipitation, and maximum and minimum temperatures. Using the relevant input sets identified by the Gamma test, the developed forecasting models improve RMSEs for GHI by 10-15% over the reference model. Prediction intervals based on regression of the squared residuals on the input variables are also derived.     

Evaluation of decomposition models of various complexity to estimate the direct solar irradiance over Belgium

Solar energy production is directly correlated to the amount of radiation received at a given location. Appropriate information on solar resources is therefore very important for designing and sizing solar energy systems. Concentrated solar power projects and photovoltaic tracking systems rely predominantly on direct normal irradiance (DNI). However, the availability of DNI measurements from surface observation stations has proven to be spatially too sparse to quantify solar resources at most potential sites. Satellite data can be used to calculate estimates of direct solar radiation where ground measurements do not exist. Performance of decomposition models of various complexity have been evaluated against one year of in situ observations recorded on the roof of the radiometric tower of the Royal Meteorological Institute of Belgium in Uccle, Brussels. Models were first evaluated on a hourly and sub-hourly basis using measurements of global horizontal irradiance (GHI) as input. Second, the best performing ground-based decomposition models were used to extract the direct component of the global radiation retrieved from Meteosat Second Generation (MSG) images. Results were then compared to direct beam estimations provided by satellite-based diffuse fraction models and evaluated against direct solar radiation data measured at Uccle. Our analysis indicates that valuable DNI estimation can be derived from MSG images over Belgium regardless of the satellite retrieved GHI accuracy. Moreover, the DNI retrieval from MSG data can be implemented on an operational basis.     

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.     

REST2: High-performance solar radiation model for cloudless-sky irradiance, illuminance, and photosynthetically active radiation – Validation with a benchmark dataset

REST2, a high-performance model to predict cloudless-sky broadband irradiance, illuminance and photosynthetically active radiation (PAR) from atmospheric data, is presented. Its derivation uses the same two-band scheme as in the previous CPCR2 model, but with numerous improvements. Great attention is devoted to precisely account for the effect of aerosols, in particular.Detailed research-class measurements from Billings, OK are used to assess the performance of the model for the prediction of direct, diffuse and global broadband irradiance. These measurements were made in May 2003 during a sophisticated radiative closure experiment, which involved the best radiometric instrumentation currently available and many ancillary instruments. As a whole, these exceptional measurements constitute the only known modern benchmark dataset made specifically to test the intrinsic performance of radiation models. Using this dataset as reference, it is shown that REST2 performs better than CPCR2 for irradiance, illuminance or PAR predictions. The availability of the turbidity data required by REST2 or other similar models is also discussed, as well as the effect that turbidity has on each component of broadband irradiance, PAR irradiance and illuminance, and on the diffuse/global PAR ratio.     

Towards downscaling of aerosol gridded dataset for improving solar resource assessment,an application to Spain

Solar radiation estimates with clear sky models require estimations of aerosol data. The low spatial resolution of current aerosol datasets, with their remarkable drift from measured data, poses a problem in solar resource estimation. This paper proposes a new downscaling methodology by combining support vector machines for regression (SVR) and kriging with external drift, with data from the MACC reanalysis datasets and temperature and rainfall measurements from 213 meteorological stations in continental Spain.The SVR technique was proven efficient in aerosol variable modeling. The Linke turbidity factor (TL) and the aerosol optical depth at 550 nm (AOD 550) estimated with SVR generated significantly lower errors in AERONET positions than MACC reanalysis estimates. The TL was estimated with relative mean absolute error (rMAE) of 10.2% (compared with AERONET), against the MACC rMAE of 18.5%. A similar behavior was seen with AOD 550, estimated with rMAE of 8.6% (compared with AERONET), against the MACC rMAE of 65.6%.Kriging using MACC data as an external drift was found useful in generating high resolution maps (0.05° × 0.05°) of both aerosol variables. We created high resolution maps of aerosol variables in continental Spain for the year 2008.The proposed methodology was proven to be a valuable tool to create high resolution maps of aerosol variables (TL and AOD 550). This methodology shows meaningful improvements when compared with estimated available databases and therefore, leads to more accurate solar resource estimations. This methodology could also be applied to the prediction of other atmospheric variables, whose datasets are of low resolution.     

Experimental investigation of a solar energy heating system under the climatic conditions of Edirne

Seasonal storage of solar energy to supply the heat requirement of buildings in Edirne (41°39′54″N) has been examined experimentally. Solar energy has been stored in a cylindrical underground storage unit. Measurement values have been recorded per hour by means of a computerized recorder between July 2005 and May 2006. Monthly average temperature values of the heat storage unit and the surrounding ground have been calculated through the measurement results. The transient heat transfer which takes place between the heat storage unit and the surrounding ground has been calculated by means of the QuickField finite-element analysis program. It has been determined that the most significant deviations between the theoretical and the experimental temperature values turn out to be in question during the heating period. The annual solar fraction of the solar energy heating system has been determined as 53% for space heating and 85% for domestic water heating.