Design of reflectors which will distribute sunlight in a specified manner

A differential equation is obtained for the shape of a reflecting surface which will distribute axially symmetric light intensity into a specified irradiance over a receiver surface which is symmetric about the direction of the incident light. Results are applied to the design of rotationally symmetric solar reflectors and also to a 2-dimensional geometry, that is one in which the reflector is a cylinder with its axis perpendicular to the incident beam. The procedure is used to numerically calculate the shape of reflectors which will uniformly concentrate collimated light and also light from a point source over a flat receiver surface. Results are also applied to determine the shape of a reflector which will distribute collimated light uniformly over the surface of a cylinder and also over a sphere.     

Diffuse and global solar spectral irradiance under cloudless skies

A simple empirical model to calculate solar spectral diffuse and global irradiance under cloudless skies is presented here. This formulation takes into account absorption of radiation by molecules such as O₃, H₂O and the uniformly-mixed gases. Attenuation by Rayleigh scattering and aerosol extinction are included. Aerosol attenuation is calculated through Ångström's turbidity parameters α and β. The diffuse radiation is assumed to be composed of three parts: (1) Rayleigh-scattered diffuse irradiance; (2) aerosol-scattered diffuse irradiance; and (3) irradiance arising out of multiple reflections between the atmosphere and the ground. The global irradiance is the sum of these three components of diffuse irradiance plus the direct irradiance. The input parameters include an extraterrestrial spectrum, zenith angle, turbidity coefficient β, wavelength exponent α, ground albedo _g, water vapor content and ozone content. The model is shown to yield very good results up to air mass two when compared to accurate theoretical calculations. No comparisons with measured spectra are presented because of a lack of accurate specifications of input parameters. Results are presented to show the effect of variation of certain of the input parameters.     

Comparison of the Olmo model with global irradiance measurements on vertical surfaces at Madrid

The recently published Olmo model estimates global irradiance on inclined planes. It only requires the horizontal global irradiance and the sun’s azimuth and elevation as input parameters. As a consequence, it does not contain empirical coefficients that need determination for each location. Olmo and co-authors found a good agreement between predicted and experimental values obtained at their measuring site when a factor accounting for ground-reflected radiation was introduced in the model. In the present paper, the Olmo model is assessed in Madrid for vertical planes facing north, south, east and west. The model gives a root mean square error of ≅27%, when all data are used. With the data for the north-facing plane it becomes worse, i.e. ≅52%.In general, the model performs badly when the surface receives only diffuse radiation. This is the case when the vertical plane does not “see” the sun’s disk, or when for intermediate or overcast skies no direct radiation is incident on both, vertical and horizontal surfaces.A distinctive feature, observed when the model is used with the data for the south, east or west-facing planes, is that many points in the plot of the calculated versus measured global irradiance clearly follow an undulating pattern.     

Prediction of global solar irradiance based on time series analysis: Application to solar thermal power plants energy production planning

Due to strong increase of solar power generation, the predictions of incoming solar energy are acquiring more importance. Photovoltaic and solar thermal are the main sources of electricity generation from solar energy. In the case of solar thermal energy plants with storage energy system, its management and operation need reliable predictions of solar irradiance with the same temporal resolution as the temporal capacity of the back-up system. These plants can work like a conventional power plant and compete in the energy stock market avoiding intermittence in electricity production.This work presents a comparisons of statistical models based on time series applied to predict half daily values of global solar irradiance with a temporal horizon of 3 days. Half daily values consist of accumulated hourly global solar irradiance from solar raise to solar noon and from noon until dawn for each day. The dataset of ground solar radiation used belongs to stations of Spanish National Weather Service (AEMet). The models tested are autoregressive, neural networks and fuzzy logic models. Due to the fact that half daily solar irradiance time series is non-stationary, it has been necessary to transform it to two new stationary variables (clearness index and lost component) which are used as input of the predictive models. Improvement in terms of RMSD of the models essayed is compared against the model based on persistence. The validation process shows that all models essayed improve persistence. The best approach to forecast half daily values of solar irradiance is neural network models with lost component as input, except Lerida station where models based on clearness index have less uncertainty because this magnitude has a linear behaviour and it is easier to simulate by models.     

Estimation of daily Linke turbidity factor by using global irradiance measurements at solar noon

This work presents a methodology for estimating daily Linke turbidity factor for clear sky days from global horizontal irradiance information at solar noon and monthly mean values of the Linke turbidity factor. The analysis of the method proposed here have been made using the ESRA clear sky model to recalculate the direct normal irradiance using as input the new Linke turbidities. Ground data of three BSRN and six AEMet radiometric meteorological stations have been used for assessing the method. Linke turbidity factor estimated here exhibits higher fluctuations than the monthly means and the comparison of the solar irradiance recalculated with the ground data have shown a noticeable reduction of the root mean square deviation. On the other hand the new Linke turbidity estimations have been compared to those values obtained from normal beam irradiance measures. The discrepancies found point out the high dependence of the reliability of this method with the quality of the ground measurements used.     

基于光伏组件的太阳能资源观测

鉴于太阳能资源的测量和评价是太阳能开发利用的重要基础,按照光伏电池两种主要安装方式(倾斜固定和太阳跟踪),利用单晶、多晶和非晶三种典型的光伏组件设计进行了太阳能光伏资源观测试验,获得了各季节典型晴天条件下各类型光伏组件辐照度的日变化特征和倾斜面光伏组件一年中月均每日可发电量的极大值、极小值及其月份。通过对比各类型光伏组件在太阳跟踪器上和纬度倾斜面上光伏辐照度变化,得出跟踪光伏组件日均光伏曝辐量与倾斜光伏组件日均光伏曝辐量的相比较优势。根据光伏组件的观测结果推算出各类型光伏组件的光伏反演辐照度,与气象辐射观测用总辐射表的总辐射辐照度趋势非常一致,在太阳能光伏主要利用时段相对误差基本在10%以内。     

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.     

Prediction of global irradiance on inclined surfaces from horizontal global irradiance

Knowledge of the radiation components incoming at a surface is required in energy balance studies, technological applications such as renewable energy and in local and large-scale climate studies. Experimental data of global irradiance on inclined planes recorded at Granada (Spain, 37.08°N, 3.57°W) have been used in order to study the pattern of the angular distribution of global irradiance. We have modelled the global irradiance angular distribution, employing horizontal global irradiance as the only radiometric input, and geometric information. We have obtained good results (root mean square deviation about 5%), except for surfaces affected by artificial horizon effects, which are not allowed for in this new model. The Skyscan'834 data set has also been used in order to test the model under completely different conditions from those in Granada, with respect to the amount of cloud, local peculiarities, experimental design and instrumentation. The results prove the validity of our model, even when compared with the Perez et al. model. The model offers a reliable tool for use when solar radiance data are scarce or limited to global horizontal irradiance.     

Instantaneous hourly and daily radiation on tilted surfaces

A simple model to evaluate the irradiance incident on tilted surfaces of various orientations is proposed in this paper. It is based on the knowledge of the monthly daily average values of global and diffuse radiation on horizontal surfaces and their distributions over a period of a day. These distributions are approximated by a modified Gaussian expression with two parameters, which take into account the morning-to-afternoon asymmetries. Integrating the irradiance over a period of an hour or a day, values of monthly hourly average and daily on variously oriented surfaces have been calculated for the locations of Barcelona, Genoa, and Montreal. The calculated values are generally in good agreement with the data derived by the observations.     

晴空条件下光照度和辐射照度的关系

利用国际上知名软件ＬＯＷＴＲＡＮ７,分别计算晴空时总日射和散射条件下辐照度与光照度之间的定量关系,得到不同大气能见度和太阳高度对其影响规律。同时发现,光合有效辐射波段的总日射辐照度和散射辐照度与光照度的关系是线性的,而全波段的总日射辐照度和散射辐照度与光照度的关系是非线的。计算结果与Ｂｒｏｗｎ的测量结果相当接近,证明了计算的可靠性。     

Clear-sky irradiance predictions for solar resource mapping and large-scale applications: Improved validation methodology and detailed performance analysis of 18 broadband radiative models

The intrinsic performance of 18 broadband radiative models is assessed, using high-quality datasets from five sites in widely different climates. The selected models can predict direct, diffuse and global irradiances under clear skies from atmospheric data, and have all been (or still are) involved in large-scale applications, for instance to prepare solar resource maps and datasets, or to evaluate solar radiation in GIS software. The input data to the models include accurate aerosol and water vapor measurements by collocated sunphotometers, if needed. Cloud occurrences are meticulously scrutinized through the use of various tools to avoid cloud contamination of the test data. The intrinsic performance of the models is evaluated by comparison between their predictions and measurements at high frequency (1-minute time step at four sites, 3-minute at one site). The total expanded uncertainty of these measurements is estimated at 3% for direct irradiance, and 5% for diffuse and global irradiance.Various statistics are calculated to evaluate the systematic and random differences between the data series, as well as the agreement between the cumulative distribution functions. In the latter case, stringent statistics based on the Komolgorov–Smirnov (KS) test are used. Large differences in performance are apparent between models. Those that require more atmospheric inputs perform usually better than simpler models. Whereas many models can predict the global horizontal irradiance within uncertainty limits similar to those of the radiation measurements, the prediction of direct irradiance is less accurate. Moreover, the prediction of diffuse horizontal irradiance is particularly deficient in most models. The cumulative distribution functions also denote areas of concern.A ranking of all models is proposed, based on four statistical indicators: mean bias difference (MBD), root mean square difference (RMSD), total uncertainty with 95% confidence limits (U₉₅), and the newly introduced Combined Performance Index (CPI), which optimally combines two KS indices with RMSD. For direct irradiance, consistently high rankings are obtained with five models (REST2, Ineichen, Hoyt, Bird, and Iqbal-C, in decreasing order of performance) that require a relatively large number of atmospheric inputs. The inferior performance of models requiring little or no atmospheric inputs suggests that large-scale solar resource products derived from them may be inappropriate for serious solar applications. Additionally, prediction uncertainties under ideal clear-sky conditions can propagate and affect all-sky predictions as well—resulting in potential biases in existing solar resource maps at the continent scale, for instance.     

A case study to prepare for the utilization of aerosol forecasts in solar energy industries

Precise aerosol information is indispensable in providing accurate clear sky irradiance forecasts, which is a very important aspect in solar facility management as well as in solar and conventional power load prediction. In order to demonstrate the need of detailed aerosol information, direct irradiance derived from Aerosol Robotic Network (AERONET) ground based measurements of aerosol optical depth (AOD) was compared in a case study over Europe to irradiance calculated using a standard aerosol scenario. The analysis shows an underestimation of measurement-derived direct irradiance by the scenario-derived direct irradiance for locations in Northern Europe and an overestimation for the Mediterranean region.Forecasted AOD of the European Dispersion and Deposition Model (EURAD) system was validated against ground based AERONET clear sky AOD measurements for the same test period of February 15th to 22nd, 2004. For the time period analyzed, the modelled AOD forecasts of the EURAD system slightly underestimate ground based AERONET measurements. To quantify the effects of varying AOD forecast quality in their impact on the application in solar energy industry, measured and forecasted AOD were used to calculate and compare direct, diffuse, and global irradiance. All other influencing variables (mainly clouds and water vapour) are assumed to be modelled and measured correctly for this analysis which is dedicated to the specific error introduced by aerosol forecasting. The underestimated AOD results in a mean overestimation of direct irradiance of +28 W/m² (+12%), whereas diffuse irradiance is generally underestimated (−19 W/m² or −14%). Mean global irradiance values where direct and diffuse irradiance errors compensate each other are very well represented (on average +9 W/m² or +2%).     

Fuzzy model representation of thermosyphon solar water heating system

The aim of this paper is to focus on improvement in prediction accuracy of model for thermosyphon solar water heating (SWH) system. The work employs grey-box modeling approach based on fuzzy system to predict the outlet water temperature of the said system. The prediction performance results are compared with neural network technique, which has been suggested by various researchers in the last one decade. The outlet water temperature prediction by fuzzy modeling technique is analyzed by using 3 models, one with three inputs (inlet water temperature, ambient temperature, solar irradiance), next with two inputs (inlet water temperature, solar irradiance) and last one with single input (solar irradiance/inlet water temperature). An improved prediction performance is observed with three inputs fuzzy model.     

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.     

Study of models for predicting the diffuse irradiance on inclined surfaces

Solar irradiance data on various inclined surfaces at different orientations are important information for active solar-system analyses and passive energy-efficient building designs. In many parts of the world, however, the basic solar irradiance data for the surfaces of interest are not always readily available. Traditionally, different mathematical models have been developed to predict the solar irradiance on various inclined surfaces using “horizontal” data. Alternatively, the diffuse irradiance of a sloping plane can be calculated by integrating the radiance distribution generated with a sky radiance model. This paper presents the evaluation of two slope irradiance models, namely, the Perez point-source model (PEREZSIM) and the Muneer model (MUNEERSIM), and two sky-distribution models, namely, the Perez all-weather model (PEREZSDM) and the Kittler standard-sky model (KITTLERSDM). Three-year (1999–2001) measured average hourly sky radiance and horizontal sky diffuse irradiance data were used for the model assessment. Statistical results showed that all four models can accurately predict the solar irradiance of a 22.3° (latitude angle of Hong Kong) inclined south-oriented surface, indicating the good predictive ability for modelling an inclined surface with a small tilted angle. In general, the KITTLERSDM and PEREZSIM show the best predictions for vertical solar irradiance at this location, followed by the PEREZSDM, then the MUNEERSIM.     

Distribution of solar radiation in natural waters under field conditions

Using a submerged fiber optic probe detector, measurements of the radiation field have been made in the surface layers of an aqueous suspension under field conditions. Angular and depth distributions of the radiance were obtained, and in both cases the distributions were strongly influenced by radiation scattering from the collimated beam. For large values of the ratio of the collimated radiation to the total irradiation and for small to moderate values of the angle between the refracted collimated beam and the line of sight of the detector, the depth distribution was characterized by a maximum below the air-water interface. The directional distribution of the radiance, which exhibited a maximum in the direction of the collimated beam, approached isotropic conditions with increasing depth and with decreasing ratio of the collimated radiation to the total irradiation.     

应用盲分离神经网络预测逐日太阳辐射能

提出一种应用盲分离神经网络预测逐日太阳辐射能的方法。首先在卷积混合基础上,应用最大化负熵准则分离原始太阳辐射时间序列,从观测数据中剔除不可靠信息;考虑到太阳负荷的特点,将分离后的样本输入到径向基函数神经网络(RBFN)中,通过调整参数训练网络直到满足约束条件为止,由此恢复盲分离所带来的幅值和排列顺序变化;最后分别比较盲分离神经网络、RBFN和BP网络的预测误差值,结果说明本文建立的模型提高了预测的准确度。     

Voltage fluctuations on distribution level introduced by photovoltaic systems

In moderate climates, short fluctuations in solar irradiance and their impact on the distribution grid will become an important issue with regard to the future large-scale application of embedded photovoltaic systems. Several related studies from the past are recalled. The approach that is presented here applies a localized spectral analysis to the solar irradiance and derived quantities in order to determine the power content of fluctuations, depending on their characteristic persistence. Pseudorandom time series of solar irradiance, based on measured values of the instantaneous clearness index, are applied as input data. Power-flow calculations are carried out in order to assess the impact of fluctuating solar irradiance on the grid voltage. The "fluctuation power index" is defined as a measure for the mean-square value of fluctuations of a specific persistence. A typical scenario is simulated, and the results are interpreted.     

Adaptive neuro-fuzzy inference system-based maximum power point tracking of solar PV modules for fast varying solar radiations

This paper analyses the operation of an adaptive neuro-fuzzy inference system (ANFIS)-based maximum power point tracking (MPPT) for solar photovoltaic (SPV) energy generation system. The MPPT works on the principle of adjusting the voltage of the SPV modules by changing the duty ratio of the boost converter. The duty ratio of the boost converter is calculated for a given solar irradiance and temperature condition by a closed-loop control scheme. The ANFIS is trained to generate maximum power corresponding to the given solar irradiance level and temperature. The response of the ANFIS-based control system is highly precise and offers an extremely fast response. The response time is seen as nearly 1 ms for fast varying cell temperature and 6 ms for fast varying solar irradiance. The simulation is done for fast-changing solar irradiance and temperature conditions. The response of the proposed controller is also presented.     

Time-series analysis of climatic variables

For the climatic variables solar irradiance and ambient temperature, a method has been devised for identifying the important cyclical components. After the contribution of the steady periodic part has been removed, the residual time series are analysed. It is shown that the daily solar irradiance residuals are a first-order autoregressive process while the daily average ambient temperature residuals are a third-order autoregressive process. This is independent of location. These results plus a knowledge of the characteristics of the cyclical components enable one to devise a methodology for generating synthetic series for these variables which are statistically indistinguishable from the original time series. Using this methodology, one can generate input data for models of heat flows in houses or solar hot water systems or other devices.