Energy distribution in the focal region of an offsetfeed paraboloidal solar stove

A specific class of paraboloidal reflectors namely the offsetfeed paraboloidal reflectors which find application in space communications is utilized for concentration of solar energy at a fixed point (focus) maintained throughout the day in shade. The energy distributions on spherical receiver centered around the focus and on a flat sectorial receiver held in a plane perpendicular to the focal line have been studied for the case of perfect tracking in hour angle and declination axes. The spill-over of energy due to non-tracking in hour-angle or declination axis for specific periods in the case of a flat sectorial receiver has been studied and plotted. A summary of the results and suggested applications of this configuration are presented. A comparison of performance is made between wedge-type and circular aperture type offsetfeed reflectors.     

Two-stage concentrator permitting concentration factors up to 300x with one-axis tracking

Economic operation of high-efficiency concentrator solar cells requires solar concentration ratios which up to now can only be achieved with two-axis tracking. In this paper we present a two-stage concentrator approaching concentration ratios up to 300X while being tracked around only one polar axis. Its principle is as follows: a parabolic trough focuses the direct solar radiation onto a line parallel to the polar tracking axis. The half rim angle of this first concentrating stage is chosen to be equal to the sun's maximum declination of 23.5°. The second stage consists of a row of dielectric, nonimaging 3-D-concentrators, which couple the concentrated light directly into square solar cells. In contrast to linear secondaries the 3-D-secondaries make use of the limited divergence of ± 23.5° in the NS-direction to achieve additional concentration. The performance of the system depends sensitively on how well the angular acceptance characteristic of the second stage matches with the square-shaped angular irradiance distribution in the focal line of the parabolic trough. A new concentrator profile has been found that exhibits an almost ideal square acceptance characteristic with a very sharp cut-off. A prototype two-stage concentrator has been constructed with a total geometrical concentration of 214X. In outdoor measurements a total optical efficiency of 77.5% was obtained.     

Properties of a general azimuth–elevation tracking angle formula for a heliostat with a mirror-pivot offset and other angular errors

The solar field of a central receiver system (CRS) is an array of dual-axis tracking heliostats on the ground beside or around a central tower, with each heliostat tracking the sun to continuously reflect the solar beam onto the fixed tower-top receiver. Azimuth–elevation tracking (also called altitude–azimuth tracking) is the most common and popular tracking methods used for heliostats. A general azimuth–elevation tracking angle formula was developed previously for a heliostat with a mirror-pivot offset and other typical geometric errors. The angular error parameters in this tracking angle formula are the tilt angle, ψ_t, and the tilt azimuth angle, ψ_a, for the azimuth axis from the vertical direction, the dual-axis non-orthogonal angle, τ₁ (bias angle of the elevation axis from the orthogonal to the azimuth axis), and the non-parallel degree, μ, between the mirror surface plane and the elevation axis (canting angle of the mirror surface plane relative to the elevation axis). This tracking angle formula is re-rewritten here as a series of easily solved expressions. A more numerically stable expression for the mirror-center normal is then presented that is more useful than the original mirror–normal expression in the tracking angle formula. This paper discusses some important angular parametric properties of this tracking angle formula. This paper also gives an approach to evaluate the tracking accuracy around each helistat rotational axis from experimental tracking data using this general tracking angle formula. This approach can also be used to determine the heliostat zero angle positioning errors of the two rotational axes. These supplementary notes make the general azimuth–elevation tracking angle formula more useful and effective in solar field tracking designs.     

Comparison of the optics of non-tracking and novel types of tracking solar thermal collectors for process heat applications up to 300 °C

Evacuated CPC (compound parabolic concentrator) collectors with non-tracking reflectors are compared with two novel tracking collectors: a parabolic trough and an evacuated tube collector with integrated tracking reflector. Non-tracking low concentrating CPC collectors are mostly mounted in east–west direction with a latitude dependent slope angle. They are suitable at most for working temperatures up to 200–250 °C. We present a tracking evacuated tube-collector with a trough-like concentrating mirror. Single-axis tracking of the mirror is realized with a magnetic mechanism. The mirror is mounted inside the evacuated tube and hence protected from environmental influences. One axis tracking in combination with a small acceptance angle allows for higher concentration as compared to non-tracking concentrating collectors. Ray-tracing analysis shows a half acceptance angle of about 5.7° at geometrical concentration ratio of 3.2. Losses of well constructed evacuated tube collectors (heat conductivity through the manifolds inside the thermally insulated terminating housing are low) are dominated by radiation losses of the absorber. Hence, reducing the absorber size can lead to higher efficiencies at high operating temperature levels. With the presented collector we aim for operating temperatures up to 350 °C. At temperatures of 300 °C we expect with anti-reflective coating of the glass tube and a selective absorber coating efficiencies of 0.65. This allows for application in industrial process heat generation, high efficient solar cooling and power generation. A first prototype, equipped with a standard glass tube and a black paint absorber coating, was tested at ZAE Bayern. The optical efficiency was measured to be 0.71. This tube-collector is compared by ray-tracing with non-tracking market available tube-collectors with geometrical concentration ratios up to 1.1 and with a low cost parabolic trough collector of Industrial Solar Technology (IST) with an acceptance half angle about 1.5°, a geometrical concentration ratio of 14.4 and a measured optical efficiency of 0.69.     

Effect of manual tilt adjustments on incident irradiance on fixed and tracking solar panels

Hourly typical meteorological year (TMY3) data was utilized with the Perez radiation model to simulate solar radiation on fixed, azimuth tracking and two axis tracking surfaces at 217 geographically diverse temperate latitude sites across the contiguous United States of America. The optimum tilt angle for maximizing annual irradiation on a fixed south-facing panel varied from being equal to the latitude at low-latitude, high clearness sites, to up to 14° less than the latitude at a north-western coastal site with very low clearness index. Across the United States, the optimum tilt angle for an azimuth tracking panel was found to be on average 19° closer to vertical than the optimum tilt angle for a fixed, south-facing panel at the same site. Azimuth tracking increased annual solar irradiation incident on a surface by an average of 29% relative to a fixed south-facing surface at optimum tilt angle. Two axis tracking resulted in an average irradiation increase of 34% relative to the fixed surface. Introduction of manual surface tilt changes during the year produced a greater impact for non-tracking surfaces than it did for azimuth tracking surfaces. Even monthly tilt changes only resulted in an average annual irradiation increase of 5% for fixed panels and 1% for azimuth tracked surfaces, relative to using a single optimized tilt angle in each case. In practice, the decision whether to manually tilt panels requires balancing the added cost in labor and the panel support versus the extra energy generation and the cost value of that energy. A Supplementary spreadsheet file is available that gives individual results for each of the 217 simulated sites.     

High temperature solar collector with optimal concentration: Non-focusing fresnel lens with secondary concentrator

A non-evacuated collector consisting of a linear Fresnel lens and a second stage concentrator of the CPC type is described and tested in detail. Use of a Fresnel lens accomplishes two different objectives simultaneously: it allows for the design of a nearly ideal light collector (of the CPC type) of high concentration and height-to-aperture ratio close to 1 and plays the role of a cover, making the collector less sensitive to the environment than one with exposed reflector surface. The geometric concentration is 15.56 and the acceptance half angle is 3°. The optical efficiency measured with an Active Cavity Radiometer (ACR) is 65.6 per cent and the efficiency at of 0.235 is 48 per cent (ΔT = T_avfluid − T_amb = 200°C, I_ACR = 850 W/m²). Heat loss measurements for double glazed configurations are reported and the resulting efficiency at of 0.3 is predicted to be 48 per cent. These numbers are expected to be raised by 3 percentage points for a next generation of lenses. The collector is mounted with its tracking axis oriented oriented NS since EW tracking axis orientation is impractical for a linear Fresnel lens, but its wide acceptance angle permits tracking by a simple clock mechanism at constant speed. Two different strategies are considered (i) polar mount, (ii) two adjustments of the tracking axis a year (summer and winter); the predicted yearly performance is calculated for four locations and four working fluid temperatures.The projected cost is estimated to be $70.00/m² (1976 dollars), possible because the construction of the collector lends itself to the use of inexpensive materials such as plastic and glass.     

An internal cusp reflector for an evacuated tubular heat pipe solar thermal collector

This study involves the optical analysis of a slightly concentrating, symmetric cusp reflector inside a tubular glass envelope with a cylindrical heat pipe as the solar absorber. The basic design features of this non-tracking, evacuated, modular collector and the principles of heat removal are shown in Figs. 1 and 2. Differential equations of the cusp reflector optics, given the geometrical restrictions in Figs. 1 and 2, are derived, and solutions for the largest possible aperture inside a given diameter envelope and acceptance angle are presented.As an extension of the same study, the optical efficiency of a single collector tube has been simulated by means of a Monte Carlo Ray-Tracing Program. For a concentration ratio of 1.15, the flux distribution around the heat pipe is computed as a function of incidence angle. In addition, the impact of mirror defects and absorber misalignment on the optical performance are analyzed.     

太阳能利用中的跟踪控制方式的研究

对太阳能利用中的开环、闭环和混合控制跟踪控制方式的特点进行了分析。通过计算几种单轴跟踪方式的跟踪角，根据跟踪角和太阳的时角间的关系，对单轴跟踪时的控制方式的选择进行了研究。特别是使用了MATLAB程序处理数据，得到南北水平轴跟踪时跟踪角和太阳时角间的关系图像，着重分析了此时采取混合跟踪的可行性和适用性。对几种跟踪控制方式的优缺点进行了分析和总结，分析了他们的特点和适用性。     

Correlation analysis and MLP/CMLP for optimum variables to predict orientation and tilt angles in intelligent solar tracking systems

Different solar tracking variables have been employed to build intelligent solar tracking systems without considering the dominant and optimum ones. Thus, several low performance intelligent solar tracking systems have been designed and implemented due to the inappropriate combination of solar tracking variables and intelligent predictors to drive the solar trackers. This research aims to investigate and evaluate the most effective and dominant variables on dual‐ and single‐axis solar trackers and to find the appropriate combination of solar variables and intelligent predictors. The optimum variables will be found by using correlation results between different variables and both orientation and tilt angles. Then, to use the selected variables to develop different intelligent solar trackers. The results revealed that month, day, and time are the most effective variables for horizontal single‐axis and dual‐axis solar tracking systems. Using these variables in cascade multilayer perceptron (CMLP) and multilayer perceptron (MLP) produced high performance. These predictors could predict both orientation and tilt angles efficiently. It is found that day variable is very effective to increase the performance of solar trackers although day variable is neither correlated nor significant with both orientation and tilt angles. Linear regression predicted less than 70% of the given data in most cases, whereas nonlinear models could predict the optimum orientation and tilt angles. In single‐axis tracker, month, day, and time variables achieved prediction rates of 96.85% and 96.83% for three hidden layers of MLP and CMLP, respectively, whereas the MSE are 0.0025 and 0.0008, respectively. In dual‐axis solar tracker, MLP and CMLP predicted 96.68% and 97.98 % respectively, with MSE of 0.0007 for both.     

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...     

Simple procedure for predicting long term average performance of nonconcentrating and of concentrating solar collectors

The Liu and Jordan method of calculating long term average energy collection of flat plate collectors is simplified (by about a factor of 4), improved, and generalized to all collectors, concentrating and nonconcentrating. The only meteorological input needed are the long term average daily total hemispherical isolation on a horizontal surface and, for thermal collectors the average ambient temperature. The collector is characterized by optical efficiency, heat loss (or U-value), heat extraction efficiency, concentration ratio and tracking mode. An average operating temperature is assumed. If the operating temperature is not known explicitly, the model will give adequate results when combined with the , f-chart of Klein and Beckman.A conversion factor is presented which multiplies the daily total horizontal insolation to yield the long term average useful energy delivered by the collector. This factor depends on a large number of variables such as collector temperature, optical efficiency, tracking mode, concentration, latitude, clearness index, diffuse insolation etc., but it can be broken up into several component factors each of which depends only on two or three variables and can be presented in convenient graphical on analytical form. In general, the seasonal variability of the weather will necessitate a separate calculation for each month of the year; however, one calculation for the central day of each month will be adequate. The method is simple enough for hand calculation.Formulas and examples are presented for five collector types: flat plate, compound parabolic concentrator, concentrator with east-west tracking axis, concentrator with polar tracking axis, and concentrator with 2-axis tracking. The examples show that even for relatively low temperature applications and cloudy climates (50°C in New York in February), concentrating collectors can outperform the flat plate.The method has been validated against hourly weather data (with measurements of hemispherical and beam insolation), and has been found to have an average accuracy better than 3 per cent for the long term average radiation available to solar collectors. For the heat delivery of thermal collectors the average error has been 5 per cent. The excellent suitability of this method for comparison studies is illustrated by comparing in a location independent manner the radiation availability for several collector types or operating conditions: 2-axis tracking versus one axis tracking; polar tracking axis versus east-west tracking axis; fixed versus tracking flat plate; effect of ground reflectance; and acceptance for diffuse radiation as function of concentration ratio.     

Determination of the angular parameters in the general altitude–azimuth tracking angle formulas for a heliostat with a mirror-pivot offset based on experimental tracking data

A set of general altitude–azimuth tracking angle formulas for a heliostat with a mirror-pivot offset and other geometrical errors were developed previously. The angular parameters with respect to the geometrical errors are the tilt angle, ψ_t, and the tilt azimuth angle, ψ_a, of the azimuth axis, the bias angle, τ₁, of the altitude axis from the orthogonal to the azimuth axis, and the canting angle, μ, of the mirror surface plane relative to the altitude axis. In view of the importance the zero angle position errors of the two rotational axes (α₀ is for the zero angle position error of the altitude axis and γ₀ for the zero angle position error of the azimuth axis), the original general tracking angle formulae have been slightly modified by replacing the tracking angles in the original tracking formulas with the difference between the nominal tracking angles and the zero angle position errors. The six angular parameters (ψ_a, ψ_t, γ₀, τ₁, α₀, μ) for a specific altitude–azimuth tracking heliostat could be determined from experimental tracking data using a least squares fit and the classical Hartley-Meyer solution algorithm. The least squares model is used on data for a specially designed heliostat model with two sets of laser beam tracking test data to show the effectiveness of the least squares model and the Hartley-Meyer algorithm.     

小型菲涅尔定焦线聚光系统关键参数影响特性研究

基于线性菲涅尔透镜聚光特性和极轴式跟踪原理,提出一种采用圆弧腔体吸收器的小型菲涅尔定焦线聚光系统。采用蒙特卡洛光线追迹方法与数理统计原理,详细研究太阳赤纬角、太阳时角和腔体内表面吸收率等关键参数对聚光系统光学性能的影响。结果表明,腔体内表面吸收率对光学效率因子的影响最显著,其次为太阳赤纬角、太阳时角。腔体内表面吸收率分别为1.00、0.85、0.75时,系统平均光学效率因子分别为0.950、0.865、0.799。太阳赤纬角对能流均匀性影响最显著,其次为太阳时角、腔体内表面吸收率。在太阳赤纬角分别为0°、8°、16°、23.45°时的平均均匀因子分别为0.507、0.519、0.561、0.612。该系统可减少余弦损失、降低焦线偏移对端部损失的影响。     

Yearly distributed insolation model and optimum design of a two dimensional compound parabolic concentrator

Optimum acceptance angle of a compound parabolic concentrator (CPC) is studied by the use of an insolation model proposed in this paper. The insolation consists of two components; diffuse and direct. The direct radiation is supposed to be distributed in the field within ±23.5° of declination on the celestial hemisphere and the diffuse radiation is assumed to have uniform irradiance. This yearly insolation model suggests that the optimum half-acceptance angle at the two-dimensional CPC becomes 26° irrespective of the change of the diffuse radiation fraction. This result leads us to the conclusion that, almost all over the world, a common CPC could be used as an optimum concentration for many solar radiation collecting systems.     

Investigation of solar declination

A new expression for solar declination angle calculation has been developed using data for four years of periodical changes. The accuracy of the proposed formula related to astronomical ephemerides is obtained using the method of the minimum sum of square errors. The calculated values vary between 1.285 and 2.776° for the selected whole year while the value for four years is 6.686°. The mean bias error differs between −0.009 and −0.050°. The standard deviation is 0.128 and 0.181, respectively. The equation proposed in this study can easily be used for solar declination computation for each day of a selected year.     

关于不同单轴跟踪方式的对比分析

针对4种太阳能单轴跟踪方式,即传统的东西轴向方式、南北轴向方式以及偏离角轴向方式和倾斜角轴向方式,提出了通过计算新参数(瞬时利用系数和日利用系数)来分析对比各种单轴跟踪方式的方法,该方法以太阳光的入射余角为参变量,并考虑了端部损失面积的影响。以南京地区一项关于槽式集热系统的设计为例,根据所建模型进行了相应计算,分析了该系统采用各种单轴跟踪方式时所呈现出的特点。该文所建模型可用来指导实际设计中,在各种地区条件下按需求选择最为合适的单轴跟踪方式。     

Accurate altitude-azimuth tracking angle formulas for a heliostat with mirror-pivot offset and other fixed geometrical errors

High precision tracking formulas were developed for a receiver-oriented toroidal heliostat with the standard spinning-elevation tracking geometry in a previous paper. The spinning-elevation tracking geometry included some mirror-pivot offset, orthogonal intersecting rotational axes and the elevation axis being parallel to the mirror surface plane. This paper analyzes the tracking accuracy of these standard spinning elevation tracking formulas to show that they are accurate with negligible tracking error. Hence, the mirror-surface-center normal obtained from these formulas is accurate for any dual-axis tracking heliostat. Then, the accurate mirror-surface-center normal information is used to determine general altitude-azimuth tracking angles for a heliostat with a mirror-pivot offset and other geometrical errors. The main geometrical errors in a typical altitude-azimuth tracking geometry are the azimuth axis tilt from the vertical, the non-orthogonality between the two heliostat rotational axes, the non-parallel degree between the mirror surface plane and the altitude axis, and the encoder reference errors. An actual heliostat in a solar field is used as an example to demonstrate use of the general altitude-azimuth tracking formulas, with the tracking angles for this heliostat on typical days graphically illustrated. The altitude-azimuth tracking angle formulas are further verified by an indoor laser-beam tracking test on a specially designed heliostat model.     

Compensation of Axis Errors of Azimuth and Zenith Moving Concentrators in Programmable Solar-Tracking Systems

The solar-energy industry is currently concerned with improving software systems of sun-tracking concentrators. It is a feature of programmable tracking that there is no feedback from the tracked object, unlike in the case of optical tracking. In this regard, the accuracy of programmable tracking is affected by a large number of factors—in particular, axis-alignment errors. An error-checking algorithm is considered for the azimuth and zenith concentrator axes in programmable sun tracking. Effects of these errors on the accuracy of programmable tracking are assessed. It is shown that zenith axis errors have the same amount of influence as the vertical deviation of the azimuth axis, primarily affecting the azimuth angle, while its influence on the solar elevation can be neglected. The cumulative effect of axial errors is most noticeable when they have the same signs and lie in the same plane.     

Computation of the solar irradiance incident on concentrating collectors based in Turkey

This study aims to provide thorough information on the solar radiation received by the five main design types of concentrating collectors for the conditions of Turkey. These are namely, compound parabolic concentrator with north-south axis and east-west axis alignment, parabolic trough with north-south axis and east-west axis tracking, and concentrator with two-axis tracking. Either daily or hourly means of solar radiation are calculated for different slope, orientation and area concentration ratio (or half-acceptance angle). In this study, a computer program, based on previously developed correlations, is used. Through the graphical display, the results are presented for the six climatologically different stations which are representative of the country's conditions. With some modifications, the results will be valid for almost all known designs of concentrating collectors.