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.     

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).     

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.     

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.     

A solar furnace using a horizontal heliostat array

A two-component solar furnace, condenser-heliostat combination, is described in which the condenser faces downward at 30° towards a heliostat comprised of numerous rows of plane mirrors mounted on a horizontal turntable. It is shown that for a south-facing condenser, with the angle of the final flux beam limited to 30° below the horizontal, the rows of heliostat mirrors may be mounted so they overlap, resulting in a reduction of the edge losses occurring when the heliostat mirrors are all held in a single plane. The over-all size of the heliostat turntable is calculated for a 6-hour workday throughout the year, and a suggestion is made for using the heliostat control mechanism to provide shutter action. The saving in flux possible by the elimination of an independent shutter is estimated at about eight per cent.     

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.     

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.     

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.     

Flux and temperature distribution in the receiver of parabolic solar furnaces

In this study, a mathematical analysis is presented on the complete interface problem between solar concentration systems and high temperature thermochemical processes. This includes the thermal process starting from the incoming solar radiation up to the heat transfer to a heat carrier fluid or reactants in a given reactor. The system considered comprises a heliostat, a parabolic concentrator and a receiver. The hourly incoming radiation, the hourly reflection and absorption losses on the heliostat and concentrator systems, the radiation flux density distribution in the receiver space, the solar and IR bands radiation exchange and the useful heat transfer are all considered in the analysis. The parameters such as temperature distribution in the receiver as well as thermal efficiency can be calculated for a given case. The model has been verified using the experimental results obtained in two different systems. In addition, a parametric study has been carried out on the global receiver efficiency with respect to temperature.     

Solar flux distribution on central receivers: A projection method from analytic function

This paper presents a methodology to project the flux distribution from the image plane into the panels of any central receiver in Solar Power Tower plants. Since analytic functions derived from the convolution approach are conveniently defined on the image plane, its oblique projection solves the distorted spot found in actual receivers. Because of its accuracy describing the flux distribution due to rectangular focusing heliostats, we make use of the analytic function on the image plane by Collado et al. (1986). Based on the projection method, we have developed a computer code successfully confronted against PSA measurements and SolTrace software, either for flat plate or multi-panel cylindrical receivers. The validated model overcomes the computation time limitation associated to Monte Carlo technique, with a similar accuracy and even higher level of resolution. For each heliostat in a field, the spillage is computed besides the rest of optical losses; parallel projection is used for shading and blocking. The resulting optical performance tool generates the flux map caused by a whole field of heliostats. A multi-aiming strategy is investigated on the basis of the radius of the reflected beams, estimated from error cone angles.     

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。     

Preliminary design of surrounding heliostat fields

Recently, the author has shown elsewhere a simplified model that allows quick evaluations of the annual overall energy collected by a surrounding heliostat field. This model is the combination of an analytical flux density function produced by a heliostat, developed by the own author, and an optimized mirror density distribution developed by University of Houston for the Solar One Project. As main conclusion of this previous work, it was recognized that such pseudo-continuous simplified model should not substitute much more accurate discrete evaluations, which manage thousands of individual heliostat coordinates. Here in this work, the difficulty of generating a preliminary discrete layout of a large number of heliostats is addressed. The main novelty is the direct definition of thousands of heliostat coordinates through basically two parameters i.e. a simplified blocking factor and an additional security distance. Such procedure, which was formerly theoretically suggested by the author, is put into practice here, showing examples and commenting their problems and advantages. Getting a previous set of thousands of heliostat coordinates would be a major first step in the complex process of designing solar power tower (SPT).     

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.     

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.     

Tracking formulas and strategies for a receiver oriented dual-axis tracking toroidal heliostat

A 4 m × 4 m toroidal heliostat with receiver oriented dual-axis tracking, also called spinning-elevation tracking, was developed as an auxiliary heat source for a hydrogen production system. A series of spinning-elevation tracking formulas have been derived for this heliostat. This included basic tracking formulas, a formula for the elevation angle for heliostat with a mirror-pivot offset, and a more general formula for the biased elevation angle. This paper presents the new tracking formulas in detail and analyzes the accuracy of applying a simplifying approximation. The numerical results show these receiver oriented dual-axis tracking formula approximations are accurate to within 2.5 × 10⁻⁶ m in image plane. Some practical tracking strategies are discussed briefly. Solar images from the toroidal heliostat at selected times are also presented.     

Modelling of the receiver transient flux distribution due to cloud passages on a solar tower thermal power plant

As more and more solar tower thermal power plants are being operated, built or planned, effort is put both on the development and research to bring costs down and increase the plant efficiency. In those plants, the central receiver is one of the key components, accounting for a large investment share. Receivers have to sustain strong thermal stresses caused by irradiation transients, mainly due to cloud passages. To avoid premature failures, increase the receiver cyclic life, and allow longer daily operation periods, an anticipation of the most likely or the worst situations is required. First the calculation of the receiver incident flux distribution is performed, second the cloud and cloud passage characteristics are identified for a given location, third the most likely case is simulated by covering and uncovering the heliostat field, then a worst case configuration is presented, and finally a strategy for the start-up/shut-down of the heliostats is proposed. The value of terms such as the heat flux peak, the maximal flux gradient, the fastest flux transient and total power transients are needed to choose the control strategies regarding heliostat orientation and the receiver operation, as well as the elimination of some bad plant layouts during the design phase.     

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.     

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.     

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.     

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.