Four different views of the heliostat flux density integral

The image due to a single heliostat is represented by its flux density, which can be formulated as an integral over the solid angle of the incoming rays. The initial formulation is transformed into three alternative representations, each having some particular utility. The incoming ray formulation leads to analytic results for flat heliostats with polygonal boundaries. The mirror plane formulation leads to a numerical integration over the mirror plane which can be used to study effects due to distortions of the mirror. The pin-hole view leads to an approximate expression for the flux density integral as a convolution of the image due to a point Sun with respect to the brightness distribution of the real Sun. This formulation allows us to treat the Sun size as though it were a source of guidance errors or alternatively, we can introduce a degraded Sun which includes the guidance errors.     

An analytic evaluation of the flux density due to sunlight reflected from a flat mirror having a polygonal boundary

Computer algorithms for the flux density of reflected sunlight from a heliostat become an essential part of the optical simulation problem for the central receiver system. An exact analytic result is available for heliostats having polygonal boundaries. An analytical method for round heliostats is given in Appendix A, which is extremely complex and requires quartic roots. A useful numerical method is given in Appendix B for heliostats of arbitrary shape. A comparison is made between the analytic method and the Hermite function method, which is much faster but less accurate. The analytic method provides a basis for evaluating all other flux density calculations.     

An analytic function for the flux density due to sunlight reflected from a heliostat

This paper presents an analytical model for the flux density due to a focused heliostat over the receiver plane of a tower solar plant. The main assumptions are: spherical and continuous surface of the mirror, linear conformal transformation in the complex plane equivalent to the reflection mapping between an on-axis aligned heliostat and the objective located on the receiver at the slant range necessary to produce the minimum circle of confusion, circular Gaussian distribution of the effective sunshape and the concentration function constant on the receiver or the image plane. Under the hypotheses presented earlier an exact convolution is obtained. The result, an analytic flux density function, relatively simple and very flexible, is confronted with experimental measurements taken from four heliostat prototypes of second-generation placed at the Central Receiver Test Facility (CRTF), Albuquerque, New Mexico, and compared indirectly with the predictions of the Helios model for the same heliostats. The model is an essential tool in the problem of the determination of collector field parameters by optimization methods.     

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.     

Improving the optical efficiency of a concentrated solar power field using a concatenated micro-tower configuration

The concatenated micro-tower (CMT) is a new configuration for concentrated solar power plants that consists of multiple mini-fields of heliostats. In each mini-field, the heliostats direct and focus sunlight onto designated points along an insulated tube, where thermal receivers are located. The heat transfer fluid, flowing through a multitude of discrete receivers, is combined and directed towards a single power block. The key advantages of CMT are its dual-axis tracking system and dynamic receiver allocation, i.e., the ability of each heliostat to direct sunrays towards receivers from adjacent mini-fields throughout the day according to their optical efficiency. Here we compare between the annual optical efficiencies of a conventional trough, large tower, and CMT configuration, all located at latitude 36 N. For each configuration, we calculated the annual optical efficiency based on the cosine factor and atmospheric transmittance. CMT’s dynamic receiver allocation provides more uniform electricity production during the day and throughout the year and improves the annual optical efficiency by 12-19% compared to conventional trough and large tower configurations.     

Non-axisymmetric reflectors concentrating radiation from an asymmetric heliostat field onto a circular absorber

In solar tower plants, where a rotationally symmetric field of heliostats surrounds the tower, an axisymmetric secondary concentrator such as a compound parabolic concentrator (CPC) or a tailored concentrator or a cone is the obvious choice. For locations at higher latitudes, however, the reflecting area of the heliostats may be used more efficiently if the field of heliostats is located opposite to the sun as seen from the tower. Then the field is asymmetric with regard to the tower. In the case of an asymmetric field, an axisymmetric concentrator necessarily has a concentration significantly lower than the upper limit. Furthermore, the area on the ground from which a tilted axisymmetric concentrator accepts radiation is an ellipse, including also heliostats very distant to the tower producing a large image of the sun. For these reasons we investigate asymmetric secondaries. From the shape of the edge ray reflectors constructed for rays in the central south–north plane we conclude that a skew cone reflector might be appropriate for the field, and optimize its free parameters by means of ray tracing. Asymmetric concentrators may increase the concentration by up to 25% at the same efficiency compared to optimized axisymmetric CPC or cone reflectors.     

塔式太阳能热发电系统镜场调度方法的研究

提出一种塔式太阳能热发电系统中定日镜调度的方法。根据太阳、定日镜和接收面的光学成像关系,考虑太阳位置、镜面反射率和能见度等因素给出了镜场光能转换效率的计算方法,同时结合定日镜场状态及热力系统所需光功率建立了镜场调度模型。该文将定日镜的调度转化为一个0-1背包问题,设计了一种混合遗传算法来对其求解。采用该调度方法可得到各时刻转换效率最高时所需调用的定日镜数量及其分布,并可调整定日镜瞄准接收靶上分布的目标点,使吸热器上能流分布均匀,降低峰值能流密度,避免过热故障。仿真算例结果表明了该方法的有效性。     

Multi-tower solar array

The multi-tower solar array (MTSA) is a new concept of a point focussing two-axis tracking concentrating solar power plant. The MTSA consists of several tower-mounted receivers which stand so close to each other that the heliostat fields of the towers partly overlap. Therefore, in some sectors of the heliostat field neighbouring heliostats are alternately directed to the receivers on different towers. This allows the MTSA to use radiation which would usually remain unused by a conventional solar tower system due to mutual blocking of the heliostats and permits an MTSA to obtain a high annual ground area efficiency (efficiency of usage of ground area). In the sectors close to the towers, where the shading effect predominates, all heliostats are directed to the nearest tower. In sectors further away from the towers, the heliostats are alternately directed to the receivers on two, three, or four different towers. To reduce dilution of the radiation from the field, the number of towers the heliostats in a specific region can be directed to may be limited to two, which causes almost no losses in the annual ground area efficiency.     

Automated high resolution measurement of heliostat slope errors

A new optical measurement method that simplifies and optimizes the mounting and canting of heliostats and helps to assure their optical quality before commissioning of the solar field was developed. This method is based on the reflection of regular patterns in the mirror surface and their distortions due to mirror surface errors. The measurement has a resolution of about 1 million points per heliostat with a measurement uncertainty of less than 0.2 mrad and a measurement time of about 1 min per heliostat. The system is completely automated and allows the automatic measurement of an entire heliostat field during one night. It was extensively tested at the CESA-1 heliostat field at the Plataforma Solar de Almería. Comparisons of flux simulations based on the measurement results with real flux density measurements were performed. They showed an excellent agreement and demonstrated in a striking manner the high measurement accuracy and high grade of detail in the simulation achieved by this technique.     

An analytical method for reflected flux density calculations

Conception, evaluation and real time control of solar “power tower” systems require the use of fast and accurate computer programs for calculating the flux density distributions on the receiver. Since the classical methods of “cone optics” and “hermite polynomial expansion” have some limitations of speed and accuracy, we have built an analytical model for calculating the convolution of the solar brightness distribution with the principal image of a heliostat (i.e. the fictive image for a “point sun”). We first characterize a principal image of a focusing heliostat by its shape and its geometrical concentration factor. Then this image is projected back onto the central plane (which passes through the center of the mirror), and considered as a flat reflecting surface. And the problem is reduced to density calculation for a flat heliostat. For each point of the receiver, the density of flux reflected by a heliostat is obtained by direct resolution of a convolution integral. The different formulations used to express the density function correspond to the various types of intersections between the image of the solar disk for the considered point and the principal image of the heliostat. Confrontation of this method with a program based on “cone optics” shows a good concordance of results and a strong decrease of computation time. We want to apply this method to the existing “THEMIS” solar plant built in France and to compare our results with real observations. Our density calculation programs will help conceiving fields of focusing heliostats for a new generation of power systems (gaz turbine systems).     

An artificial vision-based control system for automatic heliostat positioning offset correction in a central receiver solar power plant

This paper presents the development of a simplified and automatic heliostat positioning offset correction control system using artificial vision techniques and common CCD devices. The heliostats of a solar power plant reflect solar radiation onto a receiver (in this case, a volumetric receiver) placed at the top of a tower in order to provide a desired energy flux distribution correlated with the coolant flow (in this case air mass flow) through the receiver, usually in an open loop control configuration. There exist error sources that increase the complexity of the control system, some of which are systematic ones, mainly due to tolerances, wrong mirror facets alignment (optical errors), errors due to the approximations made when calculating the solar position, etc., that produce errors (offsets) in the heliostat orientation (aiming point). The approximation adopted in this paper is based on the use of a B/W CCD camera to correct these deviations in an automatic way imitating the same procedure followed by the operators. The obtained images are used to estimate the distance between the sunbeam centroid projected by the heliostats and a target placed on the tower, this distance thus is used for low accuracy offset correction purposes. Basic threshold-based image processing techniques are used for automatic correction.     

Site selection for hillside central receiver solar thermal plants

In this article, a new tool is introduced for the purpose of locating sites in hillside terrain for central receiver solar thermal plants. Provided elevation data at a sufficient resolution, the tool is capable of evaluating the efficiency of a heliostat field at any site location. The tool also locates suitable sites based on efficiency and average annual normal insolation. The field efficiency, or ratio of radiation incident to the receiver to direct normal solar radiation, is maximized as a result of factors including projection losses and interference between heliostats, known respectively as cosine efficiency, shading, and blocking. By iteratively defining the receiver location and evaluating the corresponding site efficiency by sampling elevation data points from within the defined heliostat field boundary, efficiency can be mapped as a function of the receiver location. The case studies presented illustrate the use of the tool for two field configurations, both with ground-level receivers and hillside heliostat layouts. While both configurations provide acceptable efficiencies, results from case studies show that optimal sites for ground-level receivers are ones in which the receiver is at a higher elevation than the heliostat field. This result is intuitive from the perspective of minimizing cosine losses but is nevertheless a novel configuration.     

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.     

One-point fitting of the flux density produced by a heliostat

Accurate and simple models for the flux density reflected by an isolated heliostat should be one of the basic tools for the design and optimization of solar power tower systems. In this work, the ability and the accuracy of the Universidad de Zaragoza (UNIZAR) and the DLR (HFCAL) flux density models to fit actual energetic spots are checked against heliostat energetic images measured at Plataforma Solar de Almería (PSA). Both the fully analytic models are able to acceptably fit the spot with only one-point fitting, i.e., the measured maximum flux. As a practical validation of this one-point fitting, the intercept percentage of the measured images, i.e., the percentage of the energetic spot sent by the heliostat that gets the receiver surface, is compared with the intercept calculated through the UNIZAR and HFCAL models. As main conclusions, the UNIZAR and the HFCAL models could be quite appropriate tools for the design and optimization, provided the energetic images from the heliostats to be used in the collector field were previously analyzed. Also note that the HFCAL model is much simpler and slightly more accurate than the UNIZAR model.     

Impact of heliostat curvature on optical performance of Linear Fresnel solar concentrators

The present paper gives a numerical investigation of the effect of mirror curvature on optical performance of a Linear Fresnel Reflector solar field installed recently in Morocco. The objective is to highlight and discuss the effect of mirror curvature on the flux density distribution over the receiver and the system optical efficiency. For this purpose, a Monte Carlo-ray tracing simulation tool is developed and used to optimize the optical design taking into account the curvature degree of the heliostat field. In order to assess the accuracy of the numerical code developed and the validity of simulation results, a set of verification tests were developed and detailed within this article. Then, the optical performance of the system is evaluated as a function of mirror curvature and receiver height. The major challenge of this study is to find a trade-off between heliostat curvature and receiver height since lower and smaller receivers may reduce the system cost. It has been found that the flux distribution over the receiver and the optical efficiency of the system are relatively sensitive to the mirror curvature. We have demonstrated quantitatively how the use of curved mirrors can enhance the optical performance and reduce the required receiver size.     

CRS4-2: A numerical code for the calculation of the solar power collected in a central receiver system

The analysis of the solar power collected at the receiver in solar tower systems requires the use of efficient and accurate numerical codes. This paper presents a new Fortran computer program, CRS4-2 (an acronym for Crs4 Research Software for Central Receiver Solar System SimulationS), for the simulation of the optical performance of a central receiver solar plant. The implemented mathematical algorithm allows for the calculation of cosine, shading and blocking effects for heliostats arbitrarily arranged in the solar field. Special attention has been given to ensure the maximum flexibility concerning the number, dimension, shape, and position of the heliostats. In the present implementation, the solar field can be composed of both square and circular heliostats possibly mixed together, each one of them characterized by the size and height from the ground. The modular design of CRS4-2 allows the extension to heliostats of arbitrary shape with only minor modifications of the code. Shading and blocking effects are computed by a tessellation of the heliostats: therefore, the numerical accuracy depends only on the refinement of the tessellation. The application to actual systems has shown that the approach is stable and general.     

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.     

A solar flux density calculation for a solar tower concentrator using a two-dimensional hermite function expansion

The calculation of flux density on the central receiver due to a large number of flat polygonal reflectors having various orientations is a basic part of the system simulation problem for the tower concept of solar energy collection. A two-dimensional Hermite function expansion is adapted to the simulation problem, and numerical results are contrasted with an analytic integration of the solar flux density at specific nodes on an image plane. Various measures of error in the flux density calculation are monitored vs distance to the image plane and orientation of the reflector. The flux densities predicted by the statistical method compare favorably with those of the analytic model and require approximately one-tenth the computer time.     

A cellwise method for the optimization of large central receiver systems

The total number of heliostats in the collecter field determines the approach to the optical simulation problem. For large central receiver systems, it is desirable to introduce a cell model which establishes an array of representative heliostats (see Ref.[1] for central receiver systems). We now have an arsenal of computer programs which allows us to optimize the arrangement of heliostats in the collector field subject to the approximations of the cell model. Each cell contains an arbitrary regular two dimensional array of heliostats. For practical reasons we have limited our current study of the 100 MWe commercial model to four categories of heliostats arrangement; (1) radial cornfields, (2) radial staggers, (3) N.-S. cornfields, and (4) N.-S. staggers.

The most important results from the 100 MWe commercial model optimization study are:

1. (1) Staggers are better than cornfields.

2. (2) The increased cost of the tower and receiver subsystems has moved the solution to a larger cell size and a shorter tower.

3. (3) No panels should be deleted from the south side of the cykindrical receiver, and

4. (4) The collector field trims to a 360° configuration.

The center of the collector field is north of the tower and some compromise may be made to prevent excessive panel power asymmetry. Currently, this problem is solved by using preheat panels in the southern part of the receiver.     

太阳能热发电系统中腔式吸热器的光学性能

建立了球形、圆柱形、圆锥形和平顶圆锥形4种典型腔式吸热器与抛物面聚光器的三维模型,利用蒙特卡洛光线追踪法预测了4种典型腔式吸热器内部辐射能流的分布,其中球形吸热器内部的辐射能流分布均匀性最好,且辐射峰值最小,具有较好的光学性能。通过统计逸出腔口的反射光计算出这4种腔式吸热器的反射光损,其中球形吸热器的反射光损最小。在聚光器反射率为0.9,腔体内壁吸收率为0.9时,球形吸热器反射光损仅为0.66%,聚光器/球形吸热器的光学效率为88.9%。