Theoretical analysis of the performance of a conical solar concentrator

This paper describes a study of the conical solar energy concentrator with tubular axial absorber. The concentrated power is evaluated, in a dimensionless form, as a function of the mirror surface quality and the absorber-to-aperture diameter ratio. The irradiated length of the absorber is determined and the axial concentration distribution along its surface is expressed mathematically. An integrated, or average, concentration ratio is used to measure the concentrating power of the reflector-absorber assembly. In addition to the mirror reflectivity, the performance is shown to be influenced by three parameters—the apex angle, the diameter ratio and the truncation ratio. The effects of these parameters on the concentrated power, the concentration profile and the reflector-surface area are investigated.     

Performance analysis of the stationary-reflector/tracking-absorber solar collector

This is an analytical study of the performance of the stationary-reflector/tracking-absorber (SRTA) solar collector with tubular absorber. The mathematical treatment and the derived formulae are generalized for any rim angle and any absorber-to-reflector diameter ratio. The effects of these two parameters on the average concentration ratio are investigated.Different multi-reflection zones of the mirror are identified. Their contributions to the total concentrated power and the local concentration ratio, at different absorber points, are assessed.The concentration profile along the absorber is determined under different conditions. The influence of mirror reflectance on the flux density at different points is evaluated.The circumferentially-distorted concentration profile at times of oblique incidence is displayed. The absorber surface is divided into bright, faint and dim regions. A mathematical procedure is presented to contour these regions. Their occurrence and area growth are shown to be dependent on the rim angle and diameter ratio.     

Effect of multiple reflections on the performance of plane booster mirrors

This paper presents an analytical study of a stationary V-trough concentrator. It consists of an array of east-west oriented trapezoidal channels with two side reflecting walls and a tubular absorber as a receiver at the base. The formulae for concentration factor and reflector surfaces have been derived. It is explicitly shown that the concentration ratio and reflector surface area depend upon the number of reflections the solar rays undergo before reaching the absorber, the cone apex angle, the coefficient of reflection and the acceptance angle. Results are presented graphically in such a way that one can choose the optimum configuration and the minimum material required to achieve a given concentration factor. The concentration ratio ranges from 1·2 to 3·6. The variations of the collector's efficiency with temperature difference for different numbers of reflections, acceptance angles, convective heat transfer coefficients and coefficients of reflectivity have been predicted.     

Mirror enclosures for double-exposure solar collectors

A conventional flat-plate collector panel can be employed in a double-exposure configuration when the panel is glazed on both sides and when mirrors are provided to reflect solar radiation onto the back side of the panel. In this paper, several flat-mirror configurations are evaluated and optimal configurations are determined for different solar energy applications at lat. 35, 40 and 45°. The various mirror configurations are evaluated theoretically by calculating direct-beam and diffuse solar radiation enhancement factors. The enhancement factors are defined as the ratio of the solar flux absorbed by both sides of a double-exposure panel to that absorbed by an identical single-exposure panel tilted at the latitude angle from the horizontal. The enhancement factors are calculated using the method of images and take account of the variation of glazing transmittance with incident angle. Optimal mirror configurations were determined for direct-beam solar radiation for both fixed-mirror configurations and adjustable-mirror configurations with semi-annual mirror rotations. Optimal fixed-mirror configurations were obtained for both winter space-heating and year-round applications. An adjustable-mirror configuration, however, was determined to be optimal for year-round solar collection and overall to be most adaptable to a variety of solar energy applications. The same adjustable-mirror configuration was determined to be optimal at all three latitudes and therefore a single design can be employed at diverse locations.     

Performance of a concentrating photovoltaic/thermal solar collector

The performance of a parabolic trough photovoltaic/thermal collector with a geometric concentration ratio of 37× is described. Measured results under typical operating conditions show thermal efficiency around 58% and electrical efficiency around 11%, therefore a combined efficiency of 69%. The impact of non-uniform illumination on the solar cells is investigated using purpose built equipment that moves a calibrated solar cell along the line of the receiver and measures short circuit current. The measured illumination flux profile along the length shows significant variation, despite the mirror shape error being less than 1 mm for most of the mirror area. The impact of the illumination non-uniformities due to the shape error, receiver support post shading and gaps between the mirrors is shown to have a significant effect on the overall electrical performance. The flux profile transverse to the receiver length is also investigated. Peak flux intensities are shown to be around 100 suns. The impact on efficiency due to open circuit voltage reduction is discussed.     

A fixed Fresnel lens with tracking collector

The application of a wide angle concentrating Fresnel lens to a linear solar energy system, in which the optical concentration is stationary while the absorber follows the locus of best foci, is investigated. The two substantial direction possibilities of the linear axis, east-west and polar, are compared to each other. It is shown that such a concentrator may operate about six hours a day throughout the year with an average effective concentration exceeding 10. Specifically, a polar installation, including a fixed lens and a fixed assembly of separate absorbers behind it, may enable sufficient concentration for residential heating and airconditioning without any moving parts.     

Analysis and design of a field of heliostats for a solar power plant

For the design of the mirror field for the CNRS (Centre National de la Recherche Scientifique) project of a several MWe solar energy conversion power plant, an analysis of this concentration system is proposed. Using simulation programs, the problems of the choice of an optimal height of the tower and a convenient slope of the field are solved. By analysing the variation of the thermal power during five test days, it is shown that subject to certain assumptions the maximum output power is about 10 MWe.     

An array of directable mirrors as a photovoltaic solar concentrator

Calculations of the optics of heliostats for use in large thermal power towers have been carried out in considerable detail, chiefly by Vant-Hull et al.[1, 2]. This paper describes a simplified method for calculating the images generated by a special type of concentrator, i.e. an array of independently steered mirrors on a single frame, intended to direct the solar image onto a flat photovoltaic solar cell target. The case of interest is one in which the field of illumination on the target is as uniform as possible, and the emphasis is thus on small “rim angle” geometries (a configuration which also minimizes mirror interference effects). Calculations are presented for constructing the individual mirror target images in terms of three angles: (1) The angle between the photovoltaic target normal and the reflecting mirror (celled here the mirror position angle). (2) The angle between the target center and the sun as measured from the center of the reflecting mirror, and (3) The angle at which the plane defined by the center of the sun, the mirror center and the target center intersects the plane of the target.The overall system efficiency for various mirror configurations, charaterized by such parameters as the maximum mirror angle (i.e. “rim angle”), target-mirror plane separation, and mirror aiming accuracy is discussed in terms of the specifications desirable in an optical concentrator designed specifically to illuminate uniformly a photovoltaic solar cell target.     

Upper bounds for the yearly energy delivery of stationary solar concentrators and the implications for concentrator optical design

Compound parabolic concentrator (CPC) type collectors have been viewed as the optimal design for totally stationary concentrators. However the CPC is ideal only for uniform incident solar flux averaged over the energy collection period. The actual yearly-averaged incident flux map turns out to be highly non-uniform, as a function of projected incidence angle, which implies that concentration can be increased markedly if optical collection efficiency is compromised. The question then becomes: what concentrator angular acceptance function is best matched to nature's radiation flux input, and how much energy can such a concentrator deliver? The recently-invented tailored edge-ray concentrator (TERC) approach could be used to determine optimal reflector contours, given the optimal acceptance angle function. We demonstrate that totally stationary TERCs can have around three times the geometric concentration of corresponding optimized stationary CPCs, with greater energy delivery per absorber area, in particular for applications that are currently being considered for stationary evacuated concentrators with the latest low-emissivity selective coatings, e.g. solar-driven double-stage absorption chillers (at around 170°C) and solar thermal power generation (at around 250°C).     

Comparison of solar concentrators

Even though most variations of solar concentrators have been studied or built at some time or other, an important class of concentrators has been overlooked until very recently. These novel concentrators have been called ideal because of their optical properties, and an example, the compound parabolic concentrator, is being tested at Argonne National Laboratory. Ideal concentrators differ radically from conventional instruments such as focussing parabolas. They act as radiation funnel and do not have a focus. For a given acceptance angle their concentration surpasses that of other solar concentrators by a factor of two to four, but a rather large reflector area is required. The number of reflections varies with angle of incidence, with an average value around one in most cases of interest. In order to help provide a rational basis for deciding which concentrator type is best suited for a particular application, we have compared a variety of solar concentrators in terms of their most important general characteristics, namely concentration, acceptance angle, sensitivity to mirror errors, size of reflector area and average number of reflections.The connection between concentration, acceptance angle and operating temperature of a solar collector is analysed in simple intuitive terms, leading to a straightforward recipe for designing collectors with maximal concentration (no radiation emitted by the absorber must be allowed to leave the concentrator outside its acceptance angle). We propose some new concentrators, including the use of compound parabolic concentrators as second stage concentrators for conventional parabolic or Fresnel mirrors. Such a combination approaches the performance of an ideal concentrator without demanding a large reflector; it may offer significant advantages for high temperature solar systems.     

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.     

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.     

Concentrating sunlight with an immobile primary mirror and immobile receiver: Ray-tracing results

Using a combination of custom computer code and commercially available ray-tracing software, we explore variations of concentrator geometries where sunlight is first incident onto a stationary primary mirror of circular cross section. The reflected radiation is incident onto a smaller, secondary moveable mirror, which focuses the radiation onto a stationary target. Simulations for this trough geometry show peak concentrations of 38 solar equivalents.     

Optimal geometries of plane mirror solar collectors

This paper presents an analytical study of a stationary plane mirror solar concentrator. It is composed of an array of East-West oriented trapezoidal channels with two sided reflecting walls and a tubular absorber as a receiver at the base. We have analysed and identified the most practical design parameters for a trough like concentrator. The one- and two-faceted plane side wall configurations with tubular receiver at the base of the trough have been studied in detail. It has been concluded that large savings in reflecting surfaces are possible while sacrificing some reduction in concentration. A theoretical prediction for the dependance of absorber efficiency on temperature has been obtained.     

太阳时角对槽式聚光器焦线位置的影响

在讨论太阳时角对槽式聚光器焦线位置影响的基础上,建立了因焦线运动导致太阳辐射损失的理论模型.通过对昆明晴天不同节气下的焦线运动和太阳辐射损失的分析和计算,得到了焦线随时角变化的一般规律以及瞬时太阳辐射强度损失和不同时段的太阳辐射相对损失率,并与实验进行了对比.针对焦线运动的特点,提出了对槽式集热系统接收器的改进措施和建议,认为对于大规模的槽式聚光集热器利用,因焦线运动造成的太阳辐射损失可不必考虑.     

太阳能热发电定日镜旋转角度算法研究

通过使用太阳的高度角和方位角两个参数,推导出槽式太阳能热发电技术中聚光镜的旋转公式和塔式太阳能热发电技术中定日镜的旋转公式,为后续针对太阳能热发电技术镜场控制的仿真模拟和控制系统的硬件设计提供了基础。     

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.     

Optimal geometries of a seasonally adjusted discrete-mirror solar concentrator employing a tubular absorber

The geometrical profile of a seasonally adjusted solar concentrator composed of plane mirror elements and employing a tubular absorber has been optimized. The procedure maximizes concentration for any specified number of mirror elements, and for acceptance angle, with the height of the concentrator or the reflector area as a constraint. The geometrical characteristics of the optimal concentrators have been analysed in detail. The results for a tubular absorber are compared with those for a flat horizontal absorber. Detailed results for a wide range of number of mirror elements, reflector heights, and reflector areas are provided as a design aid. Designs using a glazed tubular absorber are also considered.     

Optimum cell size for concentrated-sunlight silicon solar cells

The photovoltaic power conversion efficiency of a silicon solar cell varies with the concentration of sunlight on the solar cell. It is shown that, for a given grid structure and cell design, the variation in cell efficiency with sunlight concentration depends on the size of the solar cell and that for a given sunlight concentration there is an upper limit to the solar cell size required to obtain a given cell efficiency.     

Solar flux density distributions on central tower receivers

An analytical formulation of the solar flux density distributions produced on the surface of a central tower receiver by large mirror fields is developed which accounts for dispersion, shading and screening effects of mirrors, and for degradation of insolation levels. In the case of symmetrical geometries involving circular mirror fields and vertical cylindrical receivers, a general method of calculation yields closed-form solutions for the concentration ratios in terms of normalized parameters describing the mirror field configuration, the receiver dimensions, the insolation levels, the mirror characteristics, and the time of the day. Aiming strategies of mirror focusing are devised to reshape the solar flux in accordance with desired distributions. Mirror field asymmetries created by the configuration itself or by operational conditions blanking a portion of the field (due, for instance, to maintenance or cloud cover) are shown to set up flux gradients around the receiver which can be computed using a flux superposition technique. The methodology elaborated in the case of the vertical cylindrical receiver for simplicity and insight of treatment is applicable to many other geometries presently envisioned in receiver studies for solar power tower systems.