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.     

塔式太阳能电站聚光镜场的土地利用率研究

塔式太阳能热发电站的聚光镜场大多是由按一定规律排列的矩形定日镜组成,在相邻定日镜间无机械碰撞的情况下,聚光镜场的最大土地利用率仅为58%。文章提出了选用规则交错排列的聚光镜场布置方案,建立不同形状定日镜的土地利用模型,并计算出不同情况下的最大土地利用率。通过仿真得出,矩形定日镜和六边形定日镜在一定长宽比时可获得最大土地利用率,其中六边形定日镜的土地利用率最高,约为100%。     

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。     

Reflectance measurement in solar tower heliostats fields

Knowledge of the mean reflectance of solar thermal central receiver system heliostat fields is highly relevant for both operation and component evaluation. Calculation of the mean reflectance becomes essential to establishing a procedure by which its value can be found without measuring each and every one of the facets that make up the field, since this is a long, time-consuming and not very productive task. This article reports on the results of a statistical reflectance study of the Plataforma Solar de Almería Central Receiver Systems (CRS) heliostats field.     

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.     

EXTENSION OF THE HERMITE EXPANSION METHOD FOR CASSEGRAINIAN SOLAR CENTRAL RECEIVER SYSTEMS

An extension of the Hermite Expansion Method for performance simulation of central receiver plants is presented. This extension allows simulation and parametric study for a solar central receiver plant based on Solar Concentration Off-Tower (SCOT, or Reflective Tower) design. The extension includes mapping the physical receiver aperture into a Virtual Receiver located near the field's aim point, and performing the Hermite Expansion calculation on the Virtual Receiver. The calculation of aperture intercept/spillage and additional losses due to the Tower Reflector's finite size are discussed. Validation of the extension by comparison to ray-tracing simulation is presented for single heliostats, a group of heliostats and a complete surround field. The results match closely, showing the validity of the method and of its implementation.     

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.     

Design and evaluation of esolar’s heliostat fields

Central receiver concentrating solar power plants offer significant performance advantages over line-focus systems. However, the high cost of the heliostat field remains a barrier to the widespread adoption of such plants. eSolar has approached the problem of heliostat field cost by emphasizing small size, low cost, easy installation, and high-volume manufacturing of heliostat field components.During 2008 and 2009, eSolar designed, constructed, and began operation of its demonstration facility, which comprises two towers each with heliostat subfields to the north and the south. These heliostat fields are composed of large numbers of small heliostats, creating an arrangement unlike other central receiver plants. This paper describes the design, construction, startup, and testing of these heliostat fields, showing that they perform well and represent a viable alternative to more traditional fields of large heliostats.     

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.     

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 experimental and numerical study of the gap effect on wind load on heliostat

The main handicap of the concentrating solar power technology is still the higher cost compared with the conventional coal power plant. Heliostat arrays cause about 40% of the costs of central receiver power plants. The cost reduction of heliostats is of crucial importance to central receiver power plants. The reduction of wind load on heliostats will decrease the structural requirement for heliostats, and then cut the cost of heliostats. In this paper, different gap sizes (0–40 mm) between the facets of the heliostats were studied experimentally and numerically. Both of the results showed that the wind load increases slightly with the increase of gap size (0–40 mm). The result of the numerical simulation shows the flow pattern through the gap resembles a jet flow which does not affect the static pressure on the windward surface but does decrease the static pressure on the leeward surface of the facets. Consequently it increases the total drag force on the heliostat. However, the absolute increment of the wind load is very small compared with the overall wind load on the heliostat structure. It is not necessary to take account of the gap size effects on the wind load during the design process of heliostat.     

A new method for the design of the heliostat field layout for solar tower power plant

A new method for the design of the heliostat field layout for solar tower power plant is proposed. In the new method, the heliostat boundary is constrained by the receiver geometrical aperture and the efficiency factor which is the product of the annual cosine efficiency and the annual atmospheric transmission efficiency of heliostat. With the new method, the annual interception efficiency does not need to be calculated when places the heliostats, therefore the total time of design and optimization is saved significantly. Based on the new method, a new code for heliostat field layout design (HFLD) has been developed and a new heliostat field layout for the PS10 plant at the PS10 location has been designed by using the new code. Compared with current PS10 layout, the new designed heliostats have the same optical efficiency but with a faster response speed. In addition, to evaluate the feasibility of crops growth on the field land under heliostats, a new calculation method for the annual sunshine duration on the land surface is proposed as well.     

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.     

Etendue-matched two-stage concentrators with multiple receivers

A possible way to concentrate sun light is by using a Fresnel reflector: a large number of small mirrors (called heliostats) that mimic the behavior of a large concentrator, replacing it. These heliostats can move to track the sun, keeping its light concentrated onto the receiver. Fresnel concentrators, however, may have important losses. If the heliostats are spaced from each other, some light will miss them and be lost. If the heliostats are close to each other, they will block part of each other’s reflected light, also producing losses. One possible way to minimize these losses is to intersect two focusing Fresnel concentrators forming a Compact Linear Fresnel Reflector - CLFR. Although improving on a simple focusing Fresnel concentrator, these optics are still not optimal. Here new geometries for Fresnel reflectors are explored, minimizing their losses and increasing their concentration. This is achieved by changing the overall shape of the primary, making it a wave-shaped trough surface and/or by allowing for a variable size and shape of the heliostats as a function of the position in the heliostat field. These new Fresnel concentrators may also be combined with secondaries significantly improving their total concentration, which now approaches the theoretical maximum.     

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.     

Concentrated solar power on demand

A concentrating solar power system is presented which uses hillside mounted heliostats to direct sunlight into a volumetric absorption molten salt receiver with integral storage. The concentrated sunlight penetrates and is absorbed by molten salt in the receiver through a depth of 4-5 m, making the system insensitive to the passage of clouds. The receiver volume also acts as the thermal storage volume eliminating the need for secondary hot and cold salt storage tanks. A small aperture and refractory-lined domed roof reduce losses to the environment and reflect thermal radiation back into the pond. Hot salt is pumped from the top of the tank through a steam generator and then returned to the bottom of the tank. An insulated barrier plate is positioned within the tank to provide a physical and thermal barrier between the thermally stratified layers, maintaining hot and cold salt volumes required for continuous operation. As a result, high temperature thermal energy can be provided 24/7 or at any desired time.The amount of storage required depends on local needs and economic conditions. About 2500 m³ of nitrate salt is needed to operate a 4 MW_e steam turbine 24/7 (7 h sunshine, 17 h storage), and with modest heliostat field oversizing to accumulate energy, the system could operate for an additional 24 h (1 cloudy day). Alternatively, this same storage volume can supply a 50 MW_e turbine for 3.25 h without additional solar input. Cosine effect losses associated with hillside heliostats beaming light downwards to the receiver are offset by the elimination of a tower and separate hot and cold storage tanks and their associated pumping systems. Reduced system complexity also reduces variable costs. Using the NREL Solar Advisor program, the system is estimated to realize cost-competitive levelized production costs of electricity.     

Optical performance analysis of an innovative linear focus secondary trough solar concentrating system

The parabolic trough solar concentrating system has been well developed and widely used in commercial solar thermal power plants. However, the conventional system has its drawbacks when connecting receiver tube parts and enhancing the concentration ratio. To overcome those inherent disadvantages, in this paper, an innovative concept of linear focus secondary trough concentrating system was proposed, which consists of a fixed parabolic trough concentrator, one or more heliostats, and a fixed tube receiver. The proposed system not only avoids the end loss and connection problem on the receiver during the tracking process but also opens up the possibility to increase the concentration ratio by enlarging aperture. The design scheme of the proposed system was elaborated in detail in this paper. Besides, the optical performance of the semi and the whole secondary solar trough concentrator was evaluated by using the ray tracing method. This innovative solar concentrating system shows a high application value as a solar energy experimental device.     

Assessment of the potential improvement due to multiple apertures in central receiver systems with secondary concentrators

When striving for maximum efficiencies in solar thermal central receiver systems (CRS) the use of gas turbines with bottoming cycles is inevitable. Pressurized volumetric receivers have proven their feasibility and good performance, and their integration into gas turbine cycles has been demonstrated. One disadvantage of this system is the necessity to use secondary concentrators. The sunlight has to be concentrated into the relatively small glass windows of the receiver, which leads to a limited view cone. This means that of all the possible heliostat positions around the tower, only those within the ellipse, resulting from the section boundary of the view cone with the ground plane, are usable.For small systems, for which tower costs are small, the resulting heliostat field layout is similar, with or without secondary concentrator. For large systems, which are more cost-effective, tower costs become significant, and the losses due to atmospheric attenuation and spillage dominate over the cosine losses. Thus, the purely North-oriented fields become increasingly sub-optimal.This article shall demonstrate at what power levels this problem can be alleviated by not using a single, North-oriented aperture, but up to six apertures—each of them associated with a separate heliostat field.     

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.     

An analysis of the terminal concentrator concept for solar central receiver systems

One of the most interesting approaches to the large scale development of solar energy for electric power production is the Central Receiver System Concept. The Central Receiver System contains a large number of individually guided heliostats that reflect sunlight towards a central receiver high above the field of heliostats. The system resembles a giant Fresnel mirror and provides a substantial concentration of the solar beam. If high concentration is desired, a terminal concentrator may be included.The terminal concentrator is a device designed to increase the concentration of solar flux reflected from the collector field. Our study depends on two assumptions: (1) the beam width formula for the reflected beams and (2) the uniformly bright collector field which is a gross simplification allowing us to deal with the terminal concentrator. We obtained the necessary design relations, including a lower bound for the rim angle φ_m, the average fraction reflected $\text{?}\text{(φ}{}_{\mathrm{m}}\text{)}$, a radiative stagnation temperature for the aperature, and the concentration ratios. The temperature and concentration ratio curves determine the optimum rim angle φ_m for each of several designs. When designed to provide maximum concentration, the terminal concentrator becomes excessively large. Consequently, we consider a design which produces 90 per cent of the maximum concentration and reduces the size of the conical reflector by 5–6 times. The effectiveness of this compromise design permits us to conclude that a practical terminal concentrator of the conical variety can almost double the concentration without any appreciable loss of total power. There will be losses due to reflectivity but not due to beam spillage because of the reduced aperture. The terminal concentrator will be economically desirable for small central receiver systems if it is cheaper than the incremental cost of the heliostat field due to the additional focusing required to produce the same concentration.