Quick evaluation of the annual heliostat field efficiency

The recent world wide interest in solar power tower justifies the presentation of a simplified model that allows quick evaluations of the annual overall energy collected by a surrounding heliostat field, which is sent to the electric power generating system (EPGS). The model is the combination of an analytical model of the flux density produced by a heliostat from Zaragoza University, an optimized mirror density distribution developed by University of Houston for the Solar One project and molten salt receiver efficiencies measured during the Solar Two project. The abilities of the model are successfully compared against the scarce open data about the next Solar Tres demonstration plant-a 15 MWe solar tower with molten salts storage. This simplified model could be valid for rather preliminary optimizations, although it should not substitute much more accurate discrete evaluations that manage thousands of individual heliostats with their actual shadowing and blockings, performed every few minutes using actual meteorological data.     

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.     

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.     

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.     

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 approximate model for sizing and costing a solar thermal collector-central receiver system

An approximate generalized theoretical model is presented for the geometry and energy transfer of a solar thermal collector-central receiver system. Equations permit sizing the receiver, tower, and heliostat field. Cost functions correlate data from Department of Energy studies. Based on a set of assumed conditions, simplified, optimized sizing equations yield the minimum capital cost. The costs of the tower and central receiver will change with plant and equipment cost indices, while heliostat costs are expected to diminish as annual production increases. The heliostat cost is the major cost component even at lowest projected unit cost; therefore optimization tends toward minimum heliostat area. The model permits order-of-magnitude cost estimates to be made very quickly, compared to detailed simulation.     

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).     

Low-profile heliostat design for solar central receiver systems

Heliostat designs intended to reduce costs and the effect of adverse wind loads on the devices were developed. Included was the low-profile heliostat consisting of a stiff frame with sectional focusing reflectors coupled together to turn as a unit. The entire frame is arranged to turn angularly about a center point. The ability of the heliostat to rotate about both the vertical and horizontal axes permits a central computer control system to continuously aim the sun's reflection onto a selected target. A schematic of the heliostat design is shown in Fig. 1. An engineering model of the basic device was built and is being tested. Control and mirror parameters, such as roughness and need for fine aiming, are being studied. The fabrication of these prototypes is in process. The model was also designed to test mirror focusing techniques, heliostat geometry, mechanical functioning, and tracking control. The model can be easily relocated to test mirror imaging on a tower from various directions. In addition to steering and aiming studies, the tests include the effects of temperature changes, wind gusting and weathering. The results of economic studies on this heliostat are also presented.     

Optical analysis for simplified astigmatic correction of non-imaging focusing heliostat

In the previous work, non-imaging focusing heliostat that consists of m × n facet mirrors can carry out continuous astigmatic correction during sun-tracking with the use of only (m + n − 2) controllers. For this paper, a simplified astigmatic correction of non-imaging focusing heliostat is proposed for reducing the number of controllers from (m + n − 2) to only two. Furthermore, a detailed optical analysis of the new proposal has been carried out and the simulated result has shown that the two-controller system can perform comparably well in astigmatic correction with a much simpler and more cost effective design.     

Performance of low cost solar reflectors for transferring sunlight to a distant collector

Efficiency of reflection and optical transmission to a distant collector is a critical parameter, along with cost per unit area, in the selection of a heliostat design for the Central Collector Solar Electric Plant. Efficient optical transmission is not easily accomplished because of the large distance to be spanned in a multi-MW facility. Depending on heliostat location, the transmission distance may vary from a few hundred to thousands of feet.Design conditions which influence optical transmission over these long distances are: heliostat pointing accuracy; spreading of the reflected solar beam due to the finite size of the Sun's image; beam spreading due to reflector misalignment or waviness; aberration present if curved heliostat reflectors are used and beam spreading due to microscopic irregularities (characteristic length less than 0.1 mm) in the reflective surface. These factors increase in importance as the transmission distance from heliostat to collector increases. Even the most preliminary heliostat design activity requires a detailed evaluation of beam spreading before the most cost effective heliostat concept, or family or concepts depending on transmission distance, can be defined.Data are presented here which will be of value in assessing one of the factors causing beam spreading. An experimental method has been utilized to determine beam spreading due to microscopic surface irregularities prevalent with “mill finished” materials. The test method provides a nearly independent measure of the effect of surface imperfections.Data are presented for five candidate materials and, as reference, an optical quality first surface mirror.     

A new code for the design and analysis of the heliostat field layout for power tower system

A new code for the design and analysis of the heliostat field layout for power tower system is developed. In the new code, a new method for the heliostat field layout is proposed based on the edge ray principle of nonimaging optics. The heliostat field boundary is constrained by the tower height, the receiver tilt angle and size and the heliostat efficiency factor which is the product of the annual cosine efficiency and the annual atmospheric transmission efficiency. With the new method, the heliostat can be placed with a higher efficiency and a faster response speed of the design and optimization can be obtained. A new module for the analysis of the aspherical heliostat is created in the new code. A new toroidal heliostat field is designed and analyzed by using the new code. Compared with the spherical heliostat, the solar image radius of the field is reduced by about 30% by using the toroidal heliostat if the mirror shape and the tracking are ideal. In addition, to maximize the utilization of land, suitable crops can be considered to be planted under heliostats. To evaluate the feasibility of the crop growth, a method for calculating the annual distribution of sunshine duration on the land surface is developed as well.     

Tracking and ray tracing equations for the target-aligned heliostat for solar tower power plants

The tracking and ray tracing equations for the target-aligned heliostat for solar tower power plants have been derived in this paper. Based on the equations, a new module for analysis of the target-aligned heliostat with an asymmetric surface has been developed and incorporated in the code HFLD. To validate the tracking and ray tracing equations, a target-aligned heliostat with a toroidal surface is designed and modeled. The image of the target-aligned heliostat is calculated by the modified code HFLD and compared with that calculated by the commercial software Zemax. It is shown that the calculated results coincide with each other very well. Therefore, the correctness of the tracking and ray tracing equations for the target-aligned heliostat is proved.     

Measurements of solar flux density distribution on a plane receiver due to a flat heliostat

An experimental facility is designed and manufactured to measure the solar flux density distribution on a central flat receiver due to a single flat heliostat. The tracking mechanism of the heliostat is controlled by two stepping motors, one for tilt angle control and the other for azimuth angle control. A x-y traversing mechanism is also designed and mounted on a vertical central receiver plane, where the solar flux density is to be measured. A miniature solar sensor is mounted on the platform of the traversing mechanism, where it is used to measure the solar flux density distribution on the receiver surface. The sensor is connected to a data acquisition card in a host computer. The two stepping motors of the heliostat tracking mechanism and the two stepping motors of the traversing mechanism are all connected to a controller card in the same host computer. A software “TOWER” is prepared to let the heliostat track the sun, move the platform of the traversing mechanism to the points of a preselected grid, and to measure the solar flux density distribution on the receiver plane. Measurements are carried out using rectangular flat mirrors of different dimensions at several distances from the central receiver. Two types of images were identified on the receiver plane—namely, apparent (or visible) and mirror-reflected radiation images. Comparison between measurements and a mathematical model validates the mathematical model.     

Modeling and simulation of absorption–desorption cyclic processes for hydrogen storage-compression using metal hydrides

This work is aimed to develop and analyze reduced and simplified lumped models of cyclic processes for hydrogen storage and thermal compression using metal hydrides. Rigorous models involve several thousands of variables whereas reduced models we are interested in involve only several tens of variables. The models here presented reproduce the main dynamic behavior of rigorous models and experimental data found in the literature. Furthermore, the main tradeoffs arisen in process design are well described with these models, which is always an objective of optimal process design.In the first part of the work, a simplified lumped model is developed and validated by comparing the simulations outcome with numerical results and experimental measurements obtained from the literature for absorption and desorption individual processes. Our model is then used to simulate the process behavior using real parameters and constraints required by continuous recovery and compression systems such as those found in the metal treatment industry. The simulation results are used to improve the process performance by adjusting some key parameters of the system. These results are also used to perform a sensitivity analysis, i.e. evaluate the storage/compression system behavior when introducing variations to parameters such as operating conditions, reactor design, and material properties.Finally, we further reduce the model by considering that the inlet and outlet hydrogen flow is approximately constant. This particular specification is usually required by continuous processes in the metal treatment industry where hydrogen flow must remain constant. This requirement allows considering reaction rate as a constant. The constant reaction rate constraint allows integrating the ordinary differential equations; hence the system no longer has differential and algebraic equations but just algebraic equations. As a consequence of the simplification, the number of equations to be solved is reduced from over 15,000 to less than 50, maintaining an excellent match in the results.     

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.     

Modeling and simulation of the pioneer 1 MW solar thermal central receiver system in China

DAHAN, the pioneer 1 MWe CRS (central receiver system) funded by Ministry of Sciences and Technology (MOST), which can be regarded as the milestone in solar thermal power development in China, is now under construction at the foot of The Great Wall nearby Beijing. The major objective of the design and construction of DAHAN is to demonstrate the operation of CRS in China. A software tool HFLD is developed for heliostat field layout design and performance calculation. The simulation results from HFLD approximately agree very well with the published heliostat field efficiency data from Spain PS10. Based on that, the heliostat field layout of DAHAN is designed using HFLD and the whole CRS performance is simulated in the TRNSYS plant model. The modeling and simulation of this plant is presented in this paper.     

Design optimization of a solar tower power plant heliostat field by considering different heliostat shapes

The present study focuses on the optimization of solar tower power plant heliostat field by considering different heliostat shapes including rectangular, square, pentagon, hexagon, heptagon, octagon, and circular heliostat shapes. The optimization is carried out using an in-house developed code-based MATLAB program. The developed in-house code is validated first on a well-known PS10 Solar Thermal Power plant having rectangular heliostats shape and the resulting yearly unweighted heliostat field efficiency of about 64.43% could be obtained. The optimized PS10 heliostat field using different heliostat shapes showed that the circular and octagon heliostat shapes provide better efficiency with minimum land area. The yearly efficiency is increased from 69.65% for the rectangular heliostat shape to 70.96% and 71% for the octagon and circular shapes, respectively. In addition, the calculated field area (land area) is reduced for the case of circular and octagon heliostat shapes with a gain of about 11.10% and 10.93% (about 42.0436 × 10³ and 41.4036 × 10³ m²), respectively, in comparison with the PS10 field area.     

Sensor-controlled heliostat with an equatorial mount

A heliostat having a photo-sensor sun-tracking system was developed and evaluated. The sensor was composed of a set of two photo-cells placed side by side on the bottom of the small box. Sun-tracking can be achieved by rotating the heliostat equipped with the sensor, while maintaining the two photo-cells under illumination by the sun through a slit in the box. A preliminary tracking evaluation of the sensor was carried out with the aid of a mirror-telescope system, and the tracking error was estimated to be less than 0.6 mrad in clear weather. The developed heliostat employed an equatorial mount system that permits the rotating speed of the right-ascension axis to be nearly constant for the diurnal motion of the sun. The use of two additional sensors, a cloud sensor and a primary sensor, permitted stable tracking with high accuracy even in a cloudy sky. Field tests of the heliostat revealed that an angular error within 2 mrad was achieved in fine weather. In cloudy weather, the heliostat operated stably with the cloud sensor within an error of 10 mrad.     

Mathematical formulation of a graphical method for a no-blocking heliostat field layout

The graphical method for a no-blocking radial staggered layout was introduced within the joint work between the Center For Solar Energy Studies (CSES), Tripoli, and Atlantis Energy Ltd, Bern. It locates the heliostats in the field of a solar central receiver plant so that they provide no blocking losses over the year. In this method the field is divided into certain groups to increase the efficient use of land. The method is a simple one when compared to cell-wise procedures, making it more suitable for preliminary design of heliostat fields. At the same time, the method can be represented by a set of mathematical equations, consequently facilitating its computer implementation. In this paper a mathematical formulation of the method will be introduced, as well as its algorithm. Also, a criterion for the transfer to a new heliostat group is proposed based on mirror density.     

Rose pattern for heliostat field optimization with a dynamic speciation-based mutation differential evolution

Concentrated solar power technology is one of the most promising technologies in energy field. Arguably, the heliostat field layout is a crucial component in solar power tower system. Numerous studies have been developed for heliostat field optimization. However, most of the existing layouts which utilize radial staggered patterns are based on only two or four variables, leading to relatively rigid modes due to strong configuration constraints. In this article, we propose a new method called rose layout, which divides the regular radial staggered pattern into six sectors and they are optimized separately. Therefore, the radial increments between consecutive rows are not restricted to zones or rows, only relevant to which sector they belong to. This arrangement is more flexible and also efficient. Furthermore, a new differential evolution algorithm with a dynamic speciation-based mutation strategy (DSM-DE) is developed to solve this high-dimensional problem. In order to validate the proposed rose pattern and DSM-DE, three sets of comparative experiments were carried out. The first set of tests were operated with the conventional four optimization variables, the second series optimized total 43 radial increments between consecutive rows, whereas the third series employed the rose layout. All sets of cases were optimized by four competitive variants of differential evolution algorithm, ie, JADE, SHADE, EB-LSHADE, and DSM-DE. Experimental results verified that the rose layout can obtain higher overall optical efficiency and less land coverage than previous methods and DSM-DE is superior to other DE variants for this high-dimensional problem. The heliostat field studied in this article is simulated in Qinghai, China. By integrating rose layout with DSM-DE, the field unweighted efficiency progressed from 44.386% to 53.972%, and the annual weighted efficiency reached 59.091%, which was 0.318% higher than the 43-variable optimization.