WO2020240457A1 - Method for optimizing tower-type solar power plants - Google Patents

Method for optimizing tower-type solar power plants Download PDF

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Publication number
WO2020240457A1
WO2020240457A1 PCT/IB2020/055062 IB2020055062W WO2020240457A1 WO 2020240457 A1 WO2020240457 A1 WO 2020240457A1 IB 2020055062 W IB2020055062 W IB 2020055062W WO 2020240457 A1 WO2020240457 A1 WO 2020240457A1
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coverage
heliostats
tower
solar
optimal
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PCT/IB2020/055062
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French (fr)
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Lorenzo PISANI
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Centro Di Ricerca, Sviluppo E Studi Superiori In Sardegna Crs4 Srl Uninominale
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Publication of WO2020240457A1 publication Critical patent/WO2020240457A1/en

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    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24HEATING; RANGES; VENTILATING
    • F24SSOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
    • F24S20/00Solar heat collectors specially adapted for particular uses or environments
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24HEATING; RANGES; VENTILATING
    • F24SSOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
    • F24S20/00Solar heat collectors specially adapted for particular uses or environments
    • F24S2020/10Solar modules layout; Modular arrangements
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24HEATING; RANGES; VENTILATING
    • F24SSOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
    • F24S20/00Solar heat collectors specially adapted for particular uses or environments
    • F24S2020/10Solar modules layout; Modular arrangements
    • F24S2020/16Preventing shading effects
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00Energy generation through renewable energy sources
    • Y02E10/40Solar thermal energy, e.g. solar towers

Definitions

  • the present invention relates to a method for optimizing tower-type solar power plants.
  • the mirrors In known tower-type solar power plants, the mirrors (heliostats) are arranged within an area (solar field) and reflect the solar radiation incident on a receiver (or on multiple receivers in multitower systems) placed on a tower. The solar energy collected in the receiver is then converted into thermal energy, by heating a fluid, and is finally accumulated and/or converted into electric energy.
  • planarity constraint limits the possible applications of the solar tower technology to very specific territories or requires costly earth-moving work to artificially level the ground. Also, the installation of suitably optimized solar fields on non level territories with a favourable exposure relative to the equator would ensure higher efficiency than can be obtained from flat ones.
  • Free-variable optimization techniques as described, for example, in Lutchman SL, Groenwold AA, Gauche P, Bode S,“On using a gradient-based method for heliostat field layout optimization”, Energy Procedia, 2014, 49, 1429-1438, wherein the positions of all the heliostats are variables that need to be optimized, may be an optimum solution for treating systems having non-planar geometries.
  • the huge amount of parameters to be optimized makes such techniques very heavy in computational terms and difficult to use in practice.
  • Figure 1 shows a qualitative block diagram concerning the operations carried out in accordance with known optimization methods for tower-type systems installed on level ground.
  • the (variable) position of the sun and the system type are determined. Then the heliostats are optimally positioned by using structured grid techniques (ray tracing) like those described in the above-mentioned article by Noone CJ.
  • the isotropy of the planar territory ensures that the solution will not depend on the tower position.
  • Figure 2 shows a qualitative block diagram concerning the operations carried out in accordance with known optimization methods for tower-type systems in a general case.
  • the optimal positioning of the heliostats should be done by using non-structured techniques like those described in the above-mentioned article by Lutchman SL.
  • This operation should be repeated after changing the position of the tower; by comparing the best efficiencies obtained in each position, it should be possible to find the optimal solution.
  • all the procedures for optimizing a tower-type solar power plant are executed at a“macroscopic” level by considering the heliostat density as opposed to the exact positions of each heliostat.
  • optimization only requires the evaluation of simple analytical functions that depend on the geometry of the territory and of the tower and on the position of the sun.
  • the basic aspect of the method of the present invention concerns, therefore, the solar energy reflection and collection phase, which translates into a problem of an essentially geometrical nature.
  • the key point of the invention is the execution of all optimization procedures at a“macroscopic” level, considering the optimization of the heliostat density as opposed to the exact positions of each heliostat, on the basis of data about the conformation of the territory, the (variable) position of the sun, the type of plant (essentially the receiver height and the required power) and the position of the tower.
  • the optimization requires the evaluation of some simple analytical functions that depend on the geometry of the territory and of the tower and on the position of the sun. In comparison with the state of the art, this avoids the need for evaluating heliostat-to-heliostat interactions, thus reducing by several orders of magnitude the computational complexity of the optimization process. Only at a subsequent stage the optimal density is used in order to build a quasi-optimal heliostat field, which can finally be validated by using traditional techniques, such as, for example, the“ray tracing” technique.
  • Nw dividing said territory into a number of wedges (Nw) having the same opening angle, which is equal to the ratio between the round angle and the number of wedges;
  • each wedge arranging said heliostats along half-lines parallel to the wedge axis, equidistant by a fixed mutual distance (D), the number of half-lines within each wedge increasing with the distance from the tower and being determined by the number of times that the distance between the half-lines can be contained in the side of the regular polygon having a number of sides equal to said number of wedges (Nw), centred at the tower;
  • Figures 1 and 2 are qualitative block diagrams of known methods for optimizing tower-type solar power plants, for planar and non-planar territories, respectively.
  • Figure 3 is a block diagram of the method for optimizing a tower-type solar power plant according to the present invention.
  • Figure 4 shows an exemplary arrangement of heliostats on the territory, obtained by using the method of the invention.
  • the term“solar radiation” refers to the average yearly angular distribution of the incident energy of the sun.
  • the term“receiver” refers to that point, located on the tower, towards which the heliostats will reflect the solar energy (such point may be defined beforehand or it may be subject to optimization).
  • target energy refers to the solar energy to be collected at the receiver in one year.
  • A“cost” of the heliostat surface and a“cost” of the territory area of the solar field are defined.
  • the goal of the invention is to determine, starting from the problem data, a heliostat arrangement within the solar field which permits collecting the target energy at a low cost.
  • the coverage that minimizes the cost is determined.
  • an arrangement of the heliostats within the solar field is determined which allows collecting the target energy at a low cost.
  • the territory of the solar field (plant) must be characterized by a grid of points x, y, and, for each point j defined by the two coordinates x, y, by the corresponding coordinate z and the unitary vector orthogonal to the surface n ' , which can be easily computed from the height data.
  • Solar radiation data are usually provided as a set of energy data measured at regular time intervals, e.g. every hour.
  • time sequence is not relevant, and it is sufficient to consider the time integral of the hourly energies.
  • the yearly incident radiation S year is described as a finite number Ns of solar coordinates Si , each one with a given radiation E,
  • the horizon line changes from one place to another.
  • Said“optimal density” is obtained by computing the minimum value of the cosine of the angle between the normal to the ground at the considered grid point and the direction of the considered solar coordinate and the cosine of the angle between the normal to the ground and the direction of the receiver, and dividing said least value by the cosine of the half-angle between the direction of the solar coordinate and that of the receiver.
  • the optimal heliostat density C opt,ij for each one of the solar coordinates i and at each one of the grid points j can be calculated as follows:
  • Copt,ij min(cos(q Si ),cos(q tj ))/cos(aij) (1)
  • q Si is the angle defined by the vectors .v, and n h q t , is the angle between //, and the vector that identifies the receiver direction, 3 ⁇ 4, and ay is the half-angle between the vectors Si and t j .
  • the energy collected yearly at that point is calculated as the sum of the energetic contributions of each solar coordinate, each one multiplied by the least value of the coverage and the optimal density for the corresponding solar coordinate.
  • the optimal coverage depends on the spatial position (index j) alone, not on the solar coordinate (index i), and is the optimum value that takes into consideration the solar radiation throughout the year, while the optimal density is the optimum value obtained at the instant when the position of the sun coincides with the solar coordinate i.
  • the procedure starts from an empty field and fills it by gradually increasing the coverage at the various grid points j until the collected radiation reaches the required energy, or target.
  • the procedure schematically includes the following steps:
  • Copt,i-l jmax Coptjjmaxj Fi-ljmax - Fijmax j Ri-ljmax — Rijmax
  • the theoretical coverage distribution thereby obtained will ensure an optimal distribution of the reflecting surface in the case of“fluid” heliostats, which can adapt their own shape or position to the solar coordinates.
  • the coverage distribution may turn out to be very irregular, and therefore the structure of the heliostat field should be as flexible as possible. It follows that the known 2D structures, such as the“radial staggered” or the“biomimetic” ones, which can only be adapted to smooth density variations, are unsuitable for this kind of application.
  • the proposed structure is a“quasi-radial” ID structure (fishbone model), see Figure 4.
  • the field area is divided into a predefined number of wedges Nw, with respect to the tower position; within each wedge, equidistant and“quasi-radial” half-lines are drawn parallel to the wedge axis, along which the heliostats are arranged.
  • the wedges are centred in the tower position and have all the same opening angle, which is equal to the ratio between the round angle and the number of wedges.
  • a 2 /Nw.
  • the distance D between the half-lines of adjacent heliostats is set in a manner such as to avoid any contact between heliostats.
  • D S*sqrt(2).
  • the number of half-lines within each wedge grows with the distance from the tower and is determined by the number of times that the distance between the half-lines can be contained in the side of the regular polygon with Nw sides centred at the tower.
  • the positioning of the heliostats along the lines is determined starting from the optimal coverage, calculated in the previous step. Since the parallel lines within each wedge lie at a fixed distance D, the positioning of the heliostats along the lines can be carried out by simply considering that the local coverage c(x,y), obtainable as the value of optimal coverage Cmaxj at the grid point j closest to the point (x,y), is defined as the ratio between the heliostat area Ah and the corresponding surface. In practice, after the first heliostat has been positioned at the beginning of the line, the next one will lie at a quasi-radial distance equal to the ratio between the heliostat area and the local coverage multiplied by the distance D between the lines. In mathematical terms:
  • Such a“fishbone” structure can be built very easily, as shown in Fig. 4.
  • Nw equidistant“generation” points (solid circles) are placed. From each one of them, two half lines (continuous lines) start in the direction - p /Nw and + p /Nw relative to the radial direction. Along these lines, the heliostats (squares) are arranged at mutual distances R(c).
  • the present invention can advantageously be implemented by means of a computer program, which comprises coding means for implementing one or more steps of the method when said program is executed by a computer. It is understood, therefore, that the protection scope extends to said computer program and also to computer-readable means that comprise a recorded message, said computer-readable means comprising program coding means for implementing one or more steps of the method when said program is executed by a computer.

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Abstract

Method for optimizing the arrangement of heliostats on the territory of a tower-type solar power plant, the territory including a discrete grid of points (j=x, y, z) whereon a coverage (Cj) is defined as the ratio between the mirroring surface installed at said points and the corresponding territory area, the yearly solar radiation concerning a discrete grid of solar coordinates, zenith and azimuth (i=zen, azi), above a local horizon line, contributing to the usable radiation for the plant, comprising the following steps: - for each one of said points and solar coordinates, calculating an optimal density Copt ij, of the heliostats as the maximum specific mirroring area that can be covered at the considered grid point without the heliostats shading each other, thereby blocking the incident or reflected radiation; - for each one of said points, calculating the yearly collected energy as the sum of the energetic contributions of each solar coordinate, each one multiplied by the least value of the coverage and the optimal density for the corresponding solar coordinate; - for each one of said points, calculating an increase in the collected radiation resulting from increased coverage (Cj,) as the ratio between said collected energy and said coverage at that point; - calculating an optimal coverage Cmax.j with reference to the position of said tower, progressively increasing the coverage at said grid points until a target energy value (Rmax) is obtained; - determining a distribution of the positions of the heliostats that complies with said optimal coverage relative to said tower, by means of the following steps: - dividing said territory into a number of wedges (Nw) having the same opening angle, which is equal to the ratio between the round angle and the number of wedges; - within each wedge, arranging said heliostats along half-lines parallel to the wedge axis, equidistant by a fixed mutual distance (D), the number of half-lines within each wedge increasing with the distance from the tower and being determined by the number of times that the distance between the half-lines can be contained in the side of the regular polygon having a number of sides equal to said number of wedges (Nw), centred at the tower; - positioning the first heliostat at the beginning of the line and positioning the other ones at a distance equal to the ratio between the heliostat area and the local optimal coverage multiplied by said distance (D) between the lines.

Description

TITLE
“Method for optimizing tower-type solar power plants”
DESCRIPTION
Field of the invention
The present invention relates to a method for optimizing tower-type solar power plants.
Background art
In known tower-type solar power plants, the mirrors (heliostats) are arranged within an area (solar field) and reflect the solar radiation incident on a receiver (or on multiple receivers in multitower systems) placed on a tower. The solar energy collected in the receiver is then converted into thermal energy, by heating a fluid, and is finally accumulated and/or converted into electric energy.
The optimization of a heliostat field in a tower-type system must take into account:
1. A large number of heliostats (up to 10,000), which can mutually interact by blocking incident rays (shading) or reflected rays (blocking).
2. The relative position of the sun, which moves during the day and between days during the year.
3. The irregular profile of the territory, resulting in the tower position being an additional parameter that must be optimized.
Such elements make the heliostat positioning optimization problem extremely complex.
In the current state of technological development, such complexity is reduced by installing solar fields on level grounds only. This constraint allows positioning the heliostats at nodes of structured grids, so that quasi-optimal arrangements can be obtained by optimizing just a few numerical parameters.
On the other hand, the planarity constraint limits the possible applications of the solar tower technology to very specific territories or requires costly earth-moving work to artificially level the ground. Also, the installation of suitably optimized solar fields on non level territories with a favourable exposure relative to the equator would ensure higher efficiency than can be obtained from flat ones.
The state of the art of optimization of tower-type systems is dominated by methods based on regular patterns such as Fermat’s spirals, e.g. of the type described in the article by Noone CJ, Torrilhon M, Mitsos A, “Heliostat field optimization: A new computationally efficient model and biomimetic layout”, Solar Energy, 2012, 86, 792-803, or of the“radial staggered” type, e.g. as described in Lipps FW, Vant-Hull LL,“A CELLWISE METHOD FOR THE OPTIMIZATION OF LARGE CENTRAL RECEIVER SYSTEMS”, Solar Energy, 1978, 20, 505-512, wherein the number of parameters that need to be optimized is reduced to just a few. The drawback of such methods is that the rigidity of the structure makes them unsuitable for irregular grounds.
Those optimization methods which are based on progressive filling of the solar field by arranging one heliostat at a time (growth methods), e.g. as described in Sanchez M, Romero M,“Methodology for generation of heliostat field layout in central receiver systems based on yearly normalized energy surfaces”, Solar Energy, 2006, 80, 861-874, can be adapted to the territory, but are computationally expensive and cannot lead to a really optimal layout.
“Free-variable” optimization techniques, as described, for example, in Lutchman SL, Groenwold AA, Gauche P, Bode S,“On using a gradient-based method for heliostat field layout optimization”, Energy Procedia, 2014, 49, 1429-1438, wherein the positions of all the heliostats are variables that need to be optimized, may be an optimum solution for treating systems having non-planar geometries. However, the huge amount of parameters to be optimized makes such techniques very heavy in computational terms and difficult to use in practice.
Figure 1 shows a qualitative block diagram concerning the operations carried out in accordance with known optimization methods for tower-type systems installed on level ground.
First of all, the (variable) position of the sun and the system type (receiver height, required power) are determined. Then the heliostats are optimally positioned by using structured grid techniques (ray tracing) like those described in the above-mentioned article by Noone CJ. The isotropy of the planar territory ensures that the solution will not depend on the tower position.
Figure 2 shows a qualitative block diagram concerning the operations carried out in accordance with known optimization methods for tower-type systems in a general case.
Given the conformation of the territory, the (variable) position of the sun, the system type (receiver height, required power) and the position of the tower, the optimal positioning of the heliostats should be done by using non-structured techniques like those described in the above-mentioned article by Lutchman SL.
This operation should be repeated after changing the position of the tower; by comparing the best efficiencies obtained in each position, it should be possible to find the optimal solution.
The use of free-variable optimization techniques and the necessity of repeating the calculation for different tower positions make the schematized procedure extremely complex.
In the current state of technological development, no computational solutions exist which are easy to use in practice for managing the design and the optimization of large heliostat fields in territories with generic shape and profile.
Summary of the invention
It is therefore the object of the present invention to propose a method for optimizing tower-type solar power plants, which can overcome all of the above-mentioned drawbacks.
According to a basic aspect of the present invention, all the procedures for optimizing a tower-type solar power plant are executed at a“macroscopic” level by considering the heliostat density as opposed to the exact positions of each heliostat. At such a macroscopic level, optimization only requires the evaluation of simple analytical functions that depend on the geometry of the territory and of the tower and on the position of the sun.
In comparison with the state of the art, this avoids the need for evaluating heliostat- to-heliostat interactions, thus reducing by several orders of magnitude the computational complexity of the optimization process. Only at a subsequent stage the optimal density is used in order to build a quasi-optimal heliostat field, which can finally be validated by using traditional techniques.
The basic aspect of the method of the present invention concerns, therefore, the solar energy reflection and collection phase, which translates into a problem of an essentially geometrical nature.
With reference to the operative flow chart of Figure 3, the key point of the invention is the execution of all optimization procedures at a“macroscopic” level, considering the optimization of the heliostat density as opposed to the exact positions of each heliostat, on the basis of data about the conformation of the territory, the (variable) position of the sun, the type of plant (essentially the receiver height and the required power) and the position of the tower.
At such a macroscopic level, the optimization requires the evaluation of some simple analytical functions that depend on the geometry of the territory and of the tower and on the position of the sun. In comparison with the state of the art, this avoids the need for evaluating heliostat-to-heliostat interactions, thus reducing by several orders of magnitude the computational complexity of the optimization process. Only at a subsequent stage the optimal density is used in order to build a quasi-optimal heliostat field, which can finally be validated by using traditional techniques, such as, for example, the“ray tracing” technique.
The present invention relates to a method for optimizing the arrangement of heliostats on the territory of a tower-type solar power plant, the territory including a discrete grid of points (j=x, y, z) whereon a coverage ( ) is defined as the ratio between the mirroring surface installed at said points and the corresponding territory area, the yearly solar radiation concerning a discrete grid of solar coordinates, zenith and azimuth (i=zen, azi), above a local horizon line, contributing to the usable radiation for the plant, comprising the following steps:
- for each one of said points and solar coordinates, calculating an optimal density Copt ij, of the heliostats as the maximum specific mirroring area that can be covered at the considered grid point without the heliostats shading each other, thereby blocking the incident or reflected radiation;
- for each one of said points, calculating the yearly collected energy as the sum of the energetic contributions of each solar coordinate, each one multiplied by the least value of the coverage and the optimal density for the corresponding solar coordinate;
- for each one of said points, calculating an increase in the collected radiation resulting from increased coverage ( ,) as the ratio between said collected energy and said coverage at that point;
- calculating an optimal coverage Cmaxj with reference to the position of said tower, progressively increasing the coverage at said grid points until a target energy value (Rmax) is obtained;
- determining a distribution of the positions of the heliostats that complies with said optimal coverage relative to said tower, by means of the following steps:
- dividing said territory into a number of wedges (Nw) having the same opening angle, which is equal to the ratio between the round angle and the number of wedges;
- within each wedge, arranging said heliostats along half-lines parallel to the wedge axis, equidistant by a fixed mutual distance (D), the number of half-lines within each wedge increasing with the distance from the tower and being determined by the number of times that the distance between the half-lines can be contained in the side of the regular polygon having a number of sides equal to said number of wedges (Nw), centred at the tower;
- positioning the first heliostat at the beginning of the line and positioning the other ones at a distance equal to the ratio between the heliostat area and the local optimal coverage multiplied by said distance (D) between the lines.
It is a particular object of the present invention to provide a method for optimizing tower-type solar power plants, and a tower-type solar power plant realized by applying said method, as further set out in the claims, which are an integral part of the present description.
Brief description of the drawings
Further objects and advantages of the present invention will become apparent from the following detailed description of a preferred embodiment (and variants) thereof and from the annexed drawings, which are supplied merely by way of non-limiting example, wherein:
Figures 1 and 2 are qualitative block diagrams of known methods for optimizing tower-type solar power plants, for planar and non-planar territories, respectively.
Figure 3 is a block diagram of the method for optimizing a tower-type solar power plant according to the present invention.
Figure 4 shows an exemplary arrangement of heliostats on the territory, obtained by using the method of the invention.
In the drawings, the same reference numerals and letters identify the same items or components.
Detailed description of some embodiments of the invention The following will describe the method for optimizing a tower-type solar power plant according to the present invention.
The term“solar field” refers to the territory area available for heliostat installation.
The term“solar radiation” refers to the average yearly angular distribution of the incident energy of the sun.
The term“receiver” refers to that point, located on the tower, towards which the heliostats will reflect the solar energy (such point may be defined beforehand or it may be subject to optimization).
The term“target energy” refers to the solar energy to be collected at the receiver in one year.
A“cost” of the heliostat surface and a“cost” of the territory area of the solar field are defined.
The goal of the invention is to determine, starting from the problem data, a heliostat arrangement within the solar field which permits collecting the target energy at a low cost.
Having defined the“coverage”, in each area of the solar field, as the ratio between the mirroring surface installed in that area and the area of the region, a procedure is proposed herein which permits achieving the above-defined goals in two major steps.
In the first step, starting from the problem data, the coverage that minimizes the cost is determined. In the second step, starting from such coverage, an arrangement of the heliostats within the solar field is determined which allows collecting the target energy at a low cost.
First step - determining the optimal coverage
1) Given the solar field, it is geometrically discretized and characterized.
The territory of the solar field (plant) must be characterized by a grid of points x, y, and, for each point j defined by the two coordinates x, y, by the corresponding coordinate z and the unitary vector orthogonal to the surface n ' , which can be easily computed from the height data.
2) Given the solar radiation, an angular grid of solar coordinates is defined in order to discretize it.
The sun moves relative to ground orography, tower position and heliostat position. Solar radiation data (DNI) are usually provided as a set of energy data measured at regular time intervals, e.g. every hour. In order to evaluate the yearly collected energy, the time sequence is not relevant, and it is sufficient to consider the time integral of the hourly energies. Overall, the spatial distribution of solar energy over one year has the shape of a big arc in the sky, which can be represented as a discrete grid of zenith and azimuth values (i=zen, azi), each one associated with an energy value obtained by summing up the solar energies coming from the nearest sky area. In formal terms, the yearly incident radiation Syear is described as a finite number Ns of solar coordinates Si , each one with a given radiation E,
Figure imgf000009_0001
On uneven terrains, the horizon line changes from one place to another. In order to take orographic shading into account, it is necessary to identify, at each point of the spatial grid, the subset of solar coordinates located above the local horizon line, since they are the only ones that contribute to the collected radiation. In practice, from each point j of the spatial grid and for each one of the Ns solar coordinates i, it is necessary to calculate the possible intersections between the half-lines starting from j in the direction Si and the orographic surface and, in case of intersection, the coordinate i must be removed from the set of local solar coordinates. This procedure requires a description of the territory profile which is more extended than the region under examination, because it must include the“real” horizon line, which may be very far.
3) For each solar coordinate and grid point there is an“optimal heliostat density” that expresses the maximum specific area of mirroring surface that can be covered at the considered grid point, for the considered solar coordinate, without the heliostats shading each other, thereby blocking either the incident or the reflected radiation. Said“optimal density” is obtained by computing the minimum value of the cosine of the angle between the normal to the ground at the considered grid point and the direction of the considered solar coordinate and the cosine of the angle between the normal to the ground and the direction of the receiver, and dividing said least value by the cosine of the half-angle between the direction of the solar coordinate and that of the receiver.
In mathematical terms, the optimal heliostat density Copt,ij for each one of the solar coordinates i and at each one of the grid points j can be calculated as follows:
Copt,ij = min(cos(qSi),cos(qtj))/cos(aij) (1)
where qSi is the angle defined by the vectors .v, and nh qt, is the angle between //, and the vector that identifies the receiver direction, ¾, and ay is the half-angle between the vectors Si and tj .
4) In order to proceed with the optimization, the sun coordinates must be sorted in order of increasing optimal density value at each grid point. In mathematical terms, for each grid point“j” the following can be written:
Figure imgf000010_0001
where the tilde indicates that the indices of the sun coordinates have been locally re sorted.
5) The“collected energy”
Given a coverage value, for each grid point the energy collected yearly at that point is calculated as the sum of the energetic contributions of each solar coordinate, each one multiplied by the least value of the coverage and the optimal density for the corresponding solar coordinate.
In mathematical terms, calling“j” the grid point, and for each solar coordinate“L”, the collected energy corresponding to a coverage of Copt,Lj can be written as:
Figure imgf000010_0002
6) Variation
In order to be able to optimize the heliostat distribution, it is necessary to know how the collected radiation increases with coverage at each point. This information is obtained as the ratio between collected energy, calculated as described above, and coverage at that point.
In mathematical terms:
Figure imgf000010_0003
which decreases with L.
7) Filling cycle.
After having assessed the optimal heliostat density Copt,ij at each grid point j, the collected energy and the variation as envisaged in steps 3, 5 and 6, and having sorted the solar coordinates as envisaged in step 4, it is possible to compute the optimal heliostat coverage Cmaxj by progressively increasing the coverage at the various grid points until the target energy is obtained.
The optimal coverage depends on the spatial position (index j) alone, not on the solar coordinate (index i), and is the optimum value that takes into consideration the solar radiation throughout the year, while the optimal density is the optimum value obtained at the instant when the position of the sun coincides with the solar coordinate i.
The procedure starts from an empty field and fills it by gradually increasing the coverage at the various grid points j until the collected radiation reaches the required energy, or target.
Defining the collected radiation as Rtot and the target as Rmax, the procedure schematically includes the following steps:
i. Initially zeroing the collected radiation and the coverage matrix: Rtot=0; =0 ii. Finding the point (jmax) in the spatial grid where the energy/coverage ratio reaches the maximum value: /'i jmax^' i.j
iii. Assigning, at the grid point determined during the previous step, a new coverage value equal to the first element of the optimal density: Cjmax=C0pt,ijmax iv. Adding the collected energy to the total radiation: Rtot = Rtot+Ri jmax
v. Updating the vectors R, F and Copt of the point jmax in the grid as follows:
Copt,i-l jmax Coptjjmaxj Fi-ljmax - Fijmax j Ri-ljmax Rijmax
vi.If the total radiation is lower than the target (Rtot<Rmax), returning to step ii. vii. Assigning, at each grid point j, Cmax,j=Cj
viii.End.
At the end of the procedure, the theoretical coverage distribution thereby obtained will ensure an optimal distribution of the reflecting surface in the case of“fluid” heliostats, which can adapt their own shape or position to the solar coordinates.
In the case of normal, rigid and fixed heliostats, such coverage may be excessive in that it cannot completely prevent shading and blocking. Higher efficiency can be obtained by reducing the theoretical coverage by a certain quantity. A reduction parameter S is thus introduced, which multiplies the coverage in Eq. (3). The optimal value of such parameter is strongly dependent on the heliostats’ characteristics, and decreases gradually from the value 1 for“fluid” heliostats to lower values for rectangular heliostats rotating about their own axis, for circular heliostats and for square heliostats. It can be demonstrated that S=0.7 is a good value for square heliostats.
In the case of flat ground, optimal coverage and cost are only dependent on the height of the receiver, and not on its position in the horizontal plane. On non-level ground, on the contrary, different optimal coverage and cost correspond to each position of the receiver. Therefore, coverage optimization must be repeated several times by moving the receiver within the territory until that point is found where the cost is minimized. An in-depth analysis may require a large number of optimizations, resulting in higher computational complexity and making a fast algorithm like the one described above even more valuable.
Second step - Building of the heliostat field
Once the optimal position of the tower and the optimal heliostat coverage Cmaxj have been selected, it is necessary to determine a quasi-optimal distribution of the heliostats’ positions that will reflect the theoretical optimal coverage while at the same time keeping the shading between adjacent heliostats at a low level. To this end, it is necessary to define a geometrical structure with a free parameter that will permit imposing the equality between the local density and the optimal coverage determined in the previous step.
Because the goal of the present invention is to treat territories with generic elevation profiles, the coverage distribution may turn out to be very irregular, and therefore the structure of the heliostat field should be as flexible as possible. It follows that the known 2D structures, such as the“radial staggered” or the“biomimetic” ones, which can only be adapted to smooth density variations, are unsuitable for this kind of application.
Although it is true that there is only one strictly optimal solution, the number of quasi- optimal solutions is virtually infinite. One of such solutions will now be proposed, which has the required flexibility characteristics and is easy to implement.
The proposed structure is a“quasi-radial” ID structure (fishbone model), see Figure 4. The field area is divided into a predefined number of wedges Nw, with respect to the tower position; within each wedge, equidistant and“quasi-radial” half-lines are drawn parallel to the wedge axis, along which the heliostats are arranged.
The wedges are centred in the tower position and have all the same opening angle, which is equal to the ratio between the round angle and the number of wedges. In mathematical terms: a=2 /Nw.
The distance D between the half-lines of adjacent heliostats is set in a manner such as to avoid any contact between heliostats. For square heliostats with side S, D=S*sqrt(2).
The number of half-lines within each wedge grows with the distance from the tower and is determined by the number of times that the distance between the half-lines can be contained in the side of the regular polygon with Nw sides centred at the tower. In mathematical terms, for one wedge to contain NL parallel lines, the minimum distance from the tower is Rmin=(2*NL+l)*Rm; where Rm=D/(2*sin(u /Nw)).
The positioning of the heliostats along the lines is determined starting from the optimal coverage, calculated in the previous step. Since the parallel lines within each wedge lie at a fixed distance D, the positioning of the heliostats along the lines can be carried out by simply considering that the local coverage c(x,y), obtainable as the value of optimal coverage Cmaxj at the grid point j closest to the point (x,y), is defined as the ratio between the heliostat area Ah and the corresponding surface. In practice, after the first heliostat has been positioned at the beginning of the line, the next one will lie at a quasi-radial distance equal to the ratio between the heliostat area and the local coverage multiplied by the distance D between the lines. In mathematical terms:
R(c)=Ah/(c(x,y)*D). (4)
Such a“fishbone” structure can be built very easily, as shown in Fig. 4.
This figure shows the inner region of a heliostat field generated for a planar ground with a fishbone structure with Nw=30 in order to illustrate the building procedure.
On the N circles with radius Rm, 3Rm, 5Rm, ... , (2N-l)Rm centred at the tower, Nw equidistant“generation” points (solid circles) are placed. From each one of them, two half lines (continuous lines) start in the direction - p /Nw and + p /Nw relative to the radial direction. Along these lines, the heliostats (squares) are arranged at mutual distances R(c).
It can also be observed that the lines along which the heliostats are arranged are straight and equidistant, so that the space between them can be used for cleaning and maintaining the heliostats.
The advantage offered by heliostats aligned with the tower in the radial direction lies in the fact that blocking only occurs between heliostats on the same line and can be easily controlled. In the fishbone structure, however, the direction of the lines is not exactly radial, since it can deviate by p /Nw at most from the tower direction, and some blocking may occur between different heliostat lines; this phenomenon can be kept low by choosing a sufficiently high number Nw. On the other hand, local coverage is exact by construction along the inner lines within each wedge, whereas at the edges it may fail because the distance between such line and the next line of the other wedge is not well defined (is not parallel). The optimal number of wedges derives, therefore, from a trade-off between “being as radial as possible” (high Nw) and“minimizing the interfaces between wedges” (low Nw). Nw=30 has proven to be an acceptable value.
The present invention can advantageously be implemented by means of a computer program, which comprises coding means for implementing one or more steps of the method when said program is executed by a computer. It is understood, therefore, that the protection scope extends to said computer program and also to computer-readable means that comprise a recorded message, said computer-readable means comprising program coding means for implementing one or more steps of the method when said program is executed by a computer.
The elements and features shown in the various preferred embodiments may be combined together without however departing from the protection scope of the present invention.
From the above description, those skilled in the art will be able to produce the object of the invention without introducing any further construction details.

Claims

1. Method for optimizing the arrangement of heliostats on the territory of a tower- type solar power plant, the territory including a discrete grid of points (j=x, y, z) whereon a coverage (Q) is defined as the ratio between the mirroring surface installed at said points and the corresponding territory area, the yearly solar radiation concerning a discrete grid of solar coordinates, zenith and azimuth (i=zen, azi), above a local horizon line, contributing to the usable radiation for the plant,
the method being characterized in that it comprises the following steps:
- for each one of said points and solar coordinates, calculating an optimal density Copt ij, of the heliostats as the maximum specific mirroring area that can be covered at the considered grid point without the heliostats shading each other, thereby blocking the incident or reflected radiation;
- for each one of said points, calculating the yearly collected energy as the sum of the energetic contributions of each solar coordinate, each one multiplied by the least value of the coverage and the optimal density for the corresponding solar coordinate;
- for each one of said points, calculating an increase in the collected radiation resulting from increased coverage (Q,) as the ratio between said collected energy and said coverage at that point;
- calculating an optimal coverage Cmaxj with reference to the position of said tower, progressively increasing the coverage at said grid points until a target energy value (Rmax) is obtained;
- determining a distribution of the positions of the heliostats that complies with said optimal coverage relative to said tower, by means of the following steps:
- dividing said territory into a number of wedges (Nw) having the same opening angle, which is equal to the ratio between the round angle and the number of wedges;
- within each wedge, arranging said heliostats along half-lines parallel to the wedge axis, equidistant by a fixed mutual distance (D), the number of half-lines within each wedge increasing with the distance from the tower and being determined by the number of times that the distance between the half-lines can be contained in the side of the regular polygon having a number of sides equal to said number of wedges (Nw), centred at the tower;
- positioning the first heliostat at the beginning of the line and positioning the other ones at a distance equal to the ratio between the heliostat area and the local optimal coverage multiplied by said distance (D) between the lines.
2. Method for optimizing the arrangement of heliostats according to claim 1, wherein said optimal density Copt i j, of the heliostats is obtained by calculating the least value of the cosine of the angle between the normal to the ground at the considered grid point and the direction of the considered solar coordinate and the cosine of the angle between the normal to the ground and the direction of the receiver, and dividing said least value by the cosine of the half-angle between the direction of the solar coordinate and that of the receiver.
3. Method for optimizing the arrangement of heliostats according to claim 1, wherein said yearly collected energy, corresponding to a coverage of Copt,Lj, is calculated by means of the following expression:
Figure imgf000016_0001
“j” being the grid point, and for each solar coordinate“L”.
4. Method for optimizing the arrangement of heliostats according to claim 3, wherein said increase in the collected radiation is calculated by means of the following expression, which decreases with L:
FL.J= ¾./ fsptlj
5. Method for optimizing the arrangement of heliostats according to claim 1, wherein said optimal coverage Cmaxj is calculated by means of the following steps, where Rtot is the collected radiation and Rmaxis the target:
- zeroing the collected radiation and the coverage matrix: Rtot=0; =0
- finding the point (jmax) in the spatial grid where the energy/coverage ratio reaches the maximum value: FijmaxMhj
- assigning, at the grid point determined during the previous step, a new coverage value equal to the first element of the optimal density: Cjmax=Copt,ijmax
- adding the collected energy to the total radiation: Rt0t = Rtot+Rijmax
- updating the vectors R, F and Copt of the point jmax in the grid as follows: Copt,i-ijmax CoPt,ijmaxj Fi-l jmax Fijmax j Ri-1 jmax Rijmax
- if the total radiation is lower than the target (Rtot<Rmax), returning to step ii,
- assigning, at each grid point j, Cmaxj=Cj.
6. Method for optimizing the arrangement of heliostats according to claim 1, wherein said fixed mutual distance (D), for square heliostats with sides S, is D=S*sqrt(2).
7. Method for optimizing the arrangement of heliostats according to claim 1, wherein the number of half-lines within each wedge increases with the distance from the tower and is determined by the number of times that the distance between the half-lines can be contained in the side of the regular polygon with Nw sides centred at the tower;
- for a wedge to contain NL parallel lines, the minimum distance from the tower is Rmin=(2*NL+l)*Rm; where Rm=D/(2*sin(u /Nw)).
8. Method for optimizing the arrangement of heliostats according to claim 1, wherein, since the parallel lines within each wedge lie at a fixed distance D from each other, the positioning of the heliostats on the lines is effected by considering that the local coverage c(x,y), obtainable as the value of the optimal coverage Cmaxj at the grid point j that is closest to the point (x,y), is defined as the ratio between the heliostat area (Ah) and the corresponding surface, so that the following relationship is fulfilled:
R(c)=Ah/(c*D).
9. Tower-type solar power plant comprising a number of heliostats on the territory of the plant, characterized in that the heliostats are arranged on the territory by using a method according to any one of the preceding claims.
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