Theoretical analysis of error transfer from surface slope to refractive ray and their application to the solar concentrated collector

This paper discusses the error transfer from the slope of optical surface to the focus ray. It presents a general equation to calculate the standard deviation of the refractive ray error from that of slope error of the optical surface through geometric optics analysis, applying the equation to calculate the standard deviation of the focus ray error in 6 kinds of solar concentrator, and providing typical results. The results indicate that the slope errors in two directions are transferred to any one direction of the focus ray when the incidence angle is more than 0; for a point focus Fresnel lens, a point focus parabolic glass mirror, and a line focus parabolic glass mirror, the error transferring coefficient from the optical surface to the focus ray will increase when the rim angle or distance of reflection or refraction point to the axis increases; for a TIR-R concentrator, it will decrease; for a glass heliostat, it relates to the incidence angle and azimuth of the reflecting point. The results show that the slope error of the optical surface may be enlarged more than ten folds to the focus ray to decrease the optical efficiency of the solar concentrator greatly.     

Ray tracing and simulation for the beam-down solar concentrator

The ray tracing equations for the beam-down solar concentrator have been derived in this paper. Based on the equations, a new module for the simulation of the beam-down solar concentrating system has been developed and incorporated into the code HFLD. To validate the ray tracing equations, a simple beam-down solar concentrating system consisting of 3 heliostats and a hyperboloid reflector is simulated. The concentrated spots at the lower focal point of the hyperboloid reflector for the beam-down system are calculated by the modified code HFLD and then compared with that calculated by the commercial software Zemax. It is found that the calculated results coincide with each other basically. Furthermore, a beam-down solar concentrator consisting of 31 heliostats, a tower reflector and a CPC is designed and simulated by using the modified code HFLD. The concentrated spots of the beam-down solar concentrator are calculated.     

On the performance of cylindrical parabolic solar concentrators with flat absorbers

An integral relationship is developed for evaluating the intensity distribution on flat absorbers used with cylindrical parabolic solar concentrators. Calculations are presented for perfect cross-section concentrators using various models, rim angles, off-axis angles and defocusing amounts. Peak concentration ratios are shown to vary as the sine of the rim angle. Off-axis and defocused operations are shown to result in considerable reduced intensities. The effect of surface slope errors is also investigated. Normally distributed surface slop errors with a standard deviation of 0.25 degree are shown to reduce peak intensities by more than a factor of 3.     

Assessing the impact of non-ideal optical factors on optimized solar dish collector system with mirror rearrangement

An optimized solar dish collector (OPSDC) system was proposed in our previous work, which can achieve excellent the optical efficiency and flux uniformity under ideal optics. On this basis, the impacts of the non-ideal optical factors on the optical performance of OPSDC system with a cylindrical and conical receiver are studied in detail and compared with the conventional solar dish collector (COSDC) system in this paper. Where the non-ideal optical factors considered are relatively comprehensive, including the mirror slope error, tracking error, installation error of the mirror and receiver, and receiver's absorptivity degeneration. An optical model with the non-ideal optical factors is built in detail by the ray tracing method, and the corresponding ray tracing codes are developed and verified by literatures and optical software OptisWorks 2012. The results show that the OPSDC system not only has a significantly smaller peak local concentration ratio (LCR) and non-uniformity factor than the COSDC system under the same non-ideal optical factor, but also has excellent optical performance. This means that OPSDC system can effectively avoid the heat absorber generating high-temperature hot spots, thus significantly improving its working reliability and service lifetime. In addition, the tracking error, installation error of the receiver and mirror all lead to the increase of the peak LCR and non-uniform factor, while the mirror slope error and absorber's absorptivity degeneration are conducive to reducing the peak LCR and non-uniform factor. This work can provide a reference for error control of COSDC system and OPSDC system in manufacturing, installation and operation.     

A numerical approach to the flux density integral for reflected sunlight

A computer model of the central receiver system must evaluate the flux density on the receiver due to sunlight reflected by the heliostats in the collector field. Several approaches are available but each has its limitations. The Monte-Carlo approach represents all of the heliostat behavior but is relatively slow in terms of CPU time and is not suitable for optimization purposes. FLASH is an analytically exact approach for flat polygonal heliostats but is slow and not applicable to dished heliostats or aureole effects. Cone optics programs evaluate the flux density by a direct numerical integration of the double integral, but this method is very slow if accuracy is required. HCOEF is a two dimensional Hermite polynomial method which is relatively fast and can be extended to include canting, focusing, solar limb, and guidance error effects. However, the polynomial approximation breaks down for near heliostats, small guidance errors, and aureole effects. The new image generators based on KGEN overcome this limitation, but running times compare to FLASH and are 3 or 4 slower than HCOEF.The new approach proposed in this study assumes isotropic gaussian guidance errors. Hence, the flux density integral reduces to several iterated single integrals which can be precalculated and stored in a table for interpolation as needed. The LBL solar telescope data are fed into a convolution integral which represents the guidance errors. Aureole effects can be switched on or off at this point. A vector of convoluted solar data is input to another integration which gives the table of normalized flux contributions. The tabular values depend on the position of the flux point with respect to an edge of the heliostat as seen in the image plane. The image map of the heliostat is linear unless ripples or irregularities occur; hence, effects due to canting and dishing can be included by a ray trace of the heliostat vertices.The use of tabular interpolation is not as fast as expected because of the time required to calculate the distance between the flux point and the image of the vertices. The accuracy of this method is limited by interpolation errors, and better results can be obtained with the same CPU time if more core is used for a larger table. It is possible to eliminate the table by introducing a Romberg type of integrator which bisects the interval until sufficient accuracy is achieved; however, this approach is inefficient unless the images are relatively small compared to the receiver.The convolution process in KGEN is fast and can be used to calculate moments for HCOEF and coefficients for FLASH which utilize the LBL data.     

Graphical analysis of sun concentrating collectors

A computer-aided graphical method is employed to find the optimum sizes and positions of the receivers of solar power collecting devices. Cylindrical collectors with parabolic and circular cross sections are considered. The usual ray tracing procedure is modified by drawing two extra rays deviating ±δ degrees from the normal reflection angle. Depending on the magnitude of δ, these extra rays can be used to represent the finite size of the sun, the acceptance angle of the device, the ray's deviation due to errors in the contour of the mirror's surface, or errors in the solar tracking system. The focal zone, defined as the envelope formed by these extra rays, defines the position, size and shape of the receiver needed to absorb the concentrated radiation. For a given size of aperture, there is an optimum reflector focal length corresponding to a receiver of the minimum possible size. The errors in the mirror's surface contour can be estimated from the fabrication procedure and these values may be used to find the size of the receiver.     

Prediction and optimization of the performance of parabolic solar dish concentrator with sphere receiver using analytical function

Parabolic solar dish concentrator with sphere receiver is less studied. We present an analytic function to calculate the intercept factor of the system with real sun brightness distribution and Gaussian distribution, the results indicate that the intercept factor is related to the rim angle of reflector and the ratio of receiver angle to the optical error when the optical error is larger than or equal to 5 mrad, but is related to the rim angle, receiver angle and optical error in less than 5 mrad optical error. Furthermore we propose a quick process to optimize the system to provide the maximum solar energy to net heat efficiency for different optical error under typical condition. The results indicate that the parabolic solar dish concentrator with sphere receiver has rather high solar energy to net heat efficiency which is 20% more than solar trough and tower system including higher cosine factor and lower heat loss of the receiver.     

新型太阳能聚焦器焦面能流分布仿真

考虑太阳光不平行度,应用蒙特卡洛光线跟踪法及光线的镜面反射定律,并采用数值模拟的方法分析了焦面位置误差、指向误差等对一种新型展开式太阳能聚焦器焦面光斑形状及能流分布的影响。结果表明:焦面位置误差绝对值越大,焦面光斑半径越大,焦面能流峰值越小;焦面误差绝对值相同时,焦面光斑形状及能流分布几乎一样;指向误差越大,光斑越偏离焦面中心,并且光斑由圆形逐渐演变成椭圆形,光斑长短径之比越大。结论可以为该新型空间太阳能聚焦吸热系统的设计提供参考依据。     

Exact solutions for multilayer optical structures.: Application to PV modules

The analysis of multilayer optical devices is important in solar technology as they can be found in a large variety of equipment, particularly in photovoltaic modules. Absorbed and transmitted light by a set of thick layers are usually obtained by ray tracing procedures. When the optical structure is formed by more than one layer, the calculation of both the absorbed and transmitted light is rather complex due to multiple interactions between the several interfaces of the optical device. This paper describes a general analytic procedure, valid for any number of layers, to calculate the absorbed and transmitted light, e.g. solar radiation, through a set of thick optical layers. Consideration of incoming and outgoing light fluxes at each interface, and the assumption that the last interface acts as a light sink, leads to a closed system of equations that can be solved sequentially. Results are applied to analyze the optical behavior of an encapsulated solar cell and a photovoltaic module.     

A method for estimating monthly global solar radiation

In this paper a method is followed for estimating monthly totals of global solar radiation from a combination of calculations of monthly cloudless global solar radiation, surface meteorological observations, and empirical formulae relating sunshine duration to global solar radiation. The percent deviation of calculated from observed values is not negligible, but is much less than errors obtained by using extraterrestrial solar radiation totals. In case of values of monthly global solar radiation which are estimated for other regions, the resulted possible errors should be determined again. Some techniques leading to adaptation of the regression equations for other areas are argued.     

Efficiency assessment for a small heliostat solar concentration plant

In this paper, a small non‐imaging focusing heliostat is presented, and an analytical model for assessing its performance is described. The main novelty of the system lies in the tracking mechanism and the mirror mount, which are based on off‐the‐shelf components and allow a good trade‐off between accuracy and costs. The concentrator mirrors are moved by this two‐axis tracking machinery to reflect the sun's rays onto a fixed target, the dimensions of which can be varied to suit the user's needs. A prototype plant to be located in central Italy was designed and simulated with a ray‐tracing algorithm, and it comprises 90 heliostats for a total reflective area of 7.5 m². The reflected solar rays are tracked taking the mechanical positioning errors of the tracking system into account. The total flux of radiation energy hitting the target was determined, and intensity distribution maps were drawn. Simulations showed that the system's optical efficiency can exceed 90% in summer, despite the tracking errors, mainly because of the smaller distance between the heliostats and the receiver. The solar concentration ratio over a receiver of 250 mm in diameter reached 80 suns with a very good uniformity. Over a 400‐mm receiver, the concentrated radiation was less uniform, and the solar concentration ratio reached 50 suns, with a higher optical efficiency and collected solar radiation. The present concentration ratio is still suitable for many applications ranging from the electric power production, industrial process heat, and solar cooling. Copyright © 2014 John Wiley & Sons, Ltd.     

EVALUATION OF DISCRETIZATION ERRORS IN FINITE-VOLUME RADIANT HEAT TRANSFER PREDICTIONS

The application of the finite-volume method to problems of gray, participating-medium radiation heat transfer requires that space be discretized into volumes and direction into solid angles. The radiation transfer equation is replaced by a set of algebraic equations, one for each combination of volume and solid angle. The solution of these equations, which provides the radiation heat transfer, is subject to error as a result of both the spatial and directional discretization. The errors that arise from spatial discretization are well documented, but those that arise from the directional discretization have received little attention and are poorly understood. The present study shows that errors arising from directional discretization cause the radiant heat flux transport within a solid angle to be concentrated along the direction of its centerline. Spatial discretization often results in an artificial spreading of the radiation, so errors due to directional and spatial discretization tend to cancel. There is an additional source of directional discretization error when control-volume boundaries bisect solid angles. This study evaluates the size of this error, and proposes methods of reducing it.     

太阳位置算法的计算误差对辐射预测的影响

以往太阳辐射预测计算的研究多采用柯伯方程等误差较大的公式,往往忽略了太阳方位参数计算误差对辐射预测计算模型的影响。忽略其他因素影响,仅计算不同太阳方位参数误差所对应的太阳辐照度,计算结果与天文年历标准值的计算结果进行对比,发现太阳方位参数的误差不仅对太阳辐照度计算造成7%以上的误差（时角大于70°时）,而且在日出和日落之间临界点时也会产生极大的数值计算误差。针对以上问题,本文提出了引入儒略日为时间变量和采用大数据量最小二乘法拟合改进的数值模拟法,在保持计算公式简易的同时,显著降低了临界点的计算误差,而且辐射计算结果的相对误差小于0.2%。     

CPV系统中太阳能转换效率分析方法的探讨

太阳能转换效率是评价太阳能系统优劣的重要指标。在聚光光伏系统中,太阳能转换效率受太阳跟踪误差的影响较大。文章分析了太阳跟踪误差与太阳能转换效率之间的关系,提出了基于跟踪误差的太阳能转换效率误差分析法,填补了光伏产业中缺少太阳能转换效率评定标准的空白。文章以北京地区某日全天太阳光照辐射量数据为例,采用了两种经典的太阳位置算法,对文章所提出的误差分析法进行了验证说明。理论分析和验证表明,误差分析法可以作为评价太阳能系统能量转换效率的评定依据。     

Numerical investigation of the solar concentrating characteristics of 3D CPC and CPC-DC

A Monte Carlo Ray Tracing (MCRT) method was expanded with a bisection module to solve high-order nonlinear equations. Applying this modified MCRT method, the solar concentrating characteristics of a 3D Compound Parabolic Concentrator (3D CPC) were investigated. Moreover, a two-stage solar concentrator formed by a dish concentrator in tandem with a single 3D CPC (CPC-DC) was presented in this paper. Considering the influence of the tracking errors and slope errors, the solar concentrating performances of the CPC-DC was performed using the modified MCRT method. For DC having a rim angle of 45°, the numerical results show that the interception efficiency of the DC is about 4.0% higher than that of CPC-DC, but the concentrator ratio of the CPC-DC is twice as large as that of DC.     

基于三角腔体吸收器的透射式菲涅尔定焦线系统聚光特性分析

为解决线性菲涅尔太阳能集热系统单轴跟踪过程中出现的聚光焦线偏移以及降低系统跟踪能耗等问题,提出一种透射式菲涅尔定焦线太阳能聚光器.该聚光器采用极轴跟踪方式与线性菲涅尔透镜定期滑移调节方式相结合,可实现固定焦线聚光.将该聚光器与三角腔体吸收器所组成的太阳能集热系统,利用基于蒙特卡罗光线追迹法的TracePro光学软件分析...     

A design method for parallel solar-heat pump systems

In this paper, a method is developed for predicting the performance of parallel solar-heat pump systems. This procedure requires as inputs the fraction of the space and water heating load met by solar energy, and the fraction of the load that would have been met by the same heat pump operating without a solar system (a stand-alone system). The procedure then combines these results in a way which accounts for the interaction of the solar system and the heat pump and yields the performance of the combined system. The purchased energy fractions determined from this procedure are compared to those from detailed simulations. The standard deviation of the prediction errors are within 1.3 per cent of the load, and within the accuracy with which system parameters are known.     

A novel approach to improve the performance of solar-driven Stirling engine using solar-driven ejector cooling cycle

In this paper, a novel system to enhance the performance of a solar-driven finite speed alpha-type Stirling engine is proposed and evaluated. Part of the concentrated solar energy is used to drive an ejector refrigeration system. The cooling produced in the ejector cooling cycle is used to cool the Stirling engine to enhance its efficiency. Model equations to describe the systems are proposed and solved numerically. The results indicate that the new system produces averagely 3.3 times electrical power more than the conventional one. Moreover, the proposed system improves the Stirling engine efficiency by up to 46% in comparison with 19.15% for the conventional Stirling engine under solar radiation intensity of (1 kW/m²). Also, the results showed that the solar radiation intensity and wind speed are the most influential parameters that affect the proposed system efficiency. The new system is recommended to use in desert climates where high average daily solar radiation intensity, low wind speeds, and water shortage exist. Economic analysis is carried out to determine the feasibility of the proposed system under different economic parameters. It is found that, for instance, the simple payback period is 4.64 years for the new system when the selling price of electricity is 0.35 $/kWh.     

Experimental and numerical investigation on solar concentrating characteristics of a sixteen-dish concentrator

The concentrated solar flux distributions of a sixteen-dish concentrator (SDC) were measured applying a thermal infrared imager in combination with water-cooled Lambert target, and predicted using a Monte Carlo ray tracing method (MCRT). A slope error of 2.2 mrad is detected by comparing the experimental and numerical results. Then, a two-stage concentrator system, formed by the SDC in tandem with a three-dimensional compound parabolic concentrator (3D CPC–SDC), is constructed based on the geometrical optics approach. The interception performances and the energy concentration ratio images (ECR) are presented for both the SDC and the 3D CPC–SDC. The results show that the ECR profiles of the SDC depend on the receiver sizes, whereas that of the 3D CPC–SDC is rather steady because most sunlight enters the receiver via several reflections with the 3D CPC mirror. The 3D CPC–SDC is capable of increasing the geometric concentration ratio (GCR) at the expense of a little interception efficiency.     

附着液滴的玻璃层太阳辐射传递模型

针对液滴和玻璃层的太阳辐射传递特点,提出附着液滴玻璃层的太阳辐射传递模型。将入射的太阳辐射进行直散分离,基于蒙特卡洛射线追踪法对直射辐射光学性能进行计算,同时将入射角进行离散,分别在各角度范围内采用蒙特卡洛射线追踪法的直射辐射原理计算散射辐射光学性能。为了对模型进行验证,通过实验测试液滴覆盖率和太阳入射角对附着液滴玻璃层光学性能的影响,并与模型计算结果进行比较。结果表明：实验结果与计算结果差别较小,总透过率最大误差仅约为0.05,模型的准确性较高。附着液滴的玻璃层能有效降低太阳辐射透过率,且太阳辐射透过率随液滴覆盖率的增大而减小,随入射角的增大而减小。