CN110209207B - Method and apparatus for determining lost area of heliostat and machine-readable storage medium - Google Patents
Method and apparatus for determining lost area of heliostat and machine-readable storage medium Download PDFInfo
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Abstract
The embodiment of the invention provides a method and a device for determining the loss area of a heliostat and a machine-readable storage medium, belonging to the field of thermotechnical control and measurement. The method comprises the following steps: determining a loss region corresponding to the first heliostat, wherein the loss region comprises a shadow region and/or a shielding region, the heliostat in the shadow region generates a shadow on the first heliostat, and the heliostat in the shielding region shields light reflected by the first heliostat; determining at least one second heliostat within the loss region; determining at least one projection area of at least one second heliostat on the plane of the first heliostat; determining a union region of the at least one projection region within the surface of the first heliostat; and determining the area of the union region, wherein the area of the union region is a loss area. Therefore, the area of shadow and/or shading loss of the heliostat in a spin angle plus elevation angle control mode is determined.
Description
Technical Field
The invention relates to the field of thermal control and measurement, in particular to a method and a device for determining the loss area of a heliostat and a machine-readable storage medium.
Background
For a light condensing system (heliostat field) of a tower type solar power station, the improvement of the optical performance of the heliostat field and the optimization of parameters of the heliostat field are beneficial to the improvement of the overall performance of the power station and the reduction of the cost, on one hand, the investment cost of the light condensing system accounts for 40% -50% of the overall heliostat field, and on the other hand, the amount of sunlight reflected by the heliostat field directly determines the energy input of a subsequent subsystem.
When simulating a light-gathering system or even a power station, the energy input by the light-gathering system to a subsequent system needs to be known many times, and the energy is mainly determined by three factors: total area of mirror surface, solar illumination intensity and mirror field efficiency. The two are easy to obtain, the mirror field efficiency relates to the optical performance of each heliostat, and the mutual position relation between the surrounding mirror surfaces needs to be considered when the heliostat field efficiency is obtained, so that the heliostat field efficiency is relatively complex, and particularly when the number of the mirror surfaces is large, the calculation amount is very large. When the efficiency of the heliostat on one side is specifically calculated, the main methods are a geometric projection method and a Monte Carlo ray tracing method. The former uses light as parallel light, simplifies the model, and because the optical efficiency is composed of a plurality of component efficiencies, each component efficiency is respectively obtained by a geometric method, and then the comprehensive efficiency of the heliostat and the heliostat field is comprehensively obtained. But due to the simplicity of the model, the accuracy is not sufficient in calculating some fractional efficiencies. For the problem of large calculation amount, a dividing method is proposed to divide a mirror field into blocks, and for a small block of mirror field, only one or more heliostat efficiencies are required to be calculated as a representative, so that the calculation amount is reduced, but the cost of accuracy is sacrificed, and especially when the efficiency change of heliostats at different positions in the mirror field is researched, the result deviation is large. The ray tracing method is more flexible and can simulate non-ideal optical elements, and has the advantage of reproducing the real interaction between photons, thereby giving accurate results. The ray tracing method requires a large amount of computation time and high computation power. In this regard, fast ray tracing methods based on computer architecture have been investigated. A solution idea of combining the two methods is also proposed, and the advantages of the two methods are fully utilized when calculating different score efficiencies.
The total light efficiency of the mirror field includes shadow and occlusion efficiencies. Due to the different arrangement of the heliostat fields, and as the sun operates, the attitude of the heliostat also changes. The attitude control of the current heliostat is divided into two modes, namely an elevation angle + azimuth angle control mode and a spin + elevation angle control mode. Due to different control modes, shadow and occlusion loss calculation methods are different. Shadow and occlusion loss calculations in the elevation + azimuth control mode have been studied. However, shadow and occlusion loss calculations in the spin + elevation mode control are not studied.
Disclosure of Invention
It is an object of the present invention to provide a method and apparatus and machine readable storage medium for determining lost area of heliostats that enables determination of shadow and/or shading lost area of heliostats in a spin plus elevation control mode.
To achieve the above object, an aspect of the present invention provides a method for determining a lost area of a first heliostat, the first heliostat being controlled in a spin plus elevation control manner, the method comprising: determining a loss region corresponding to the first heliostat, wherein the loss region comprises a shadow region and/or an occlusion region, the heliostat in the shadow region generates a shadow on the first heliostat, and the heliostat in the occlusion region occludes light reflected by the first heliostat; determining at least one second heliostat within the loss region; determining at least one projection area of the at least one second heliostat on the plane of the first heliostat; determining a union region of the at least one projection region within the surface of the first heliostat; and determining the area of the union region, wherein the area of the union region is the loss area.
Optionally, determining a union region of the at least one projection region within the surface of the first heliostat and determining an area of the union region comprises: dividing the at least one projection area and a surface area of the first heliostat into squares; marking lattice points on the divided squares, wherein a preset value is marked if a lattice point is in any one of the at least one projection area and the surface area of the first heliostat; summing the marked preset values of each grid point to obtain a marked sum of the grid points, wherein in the surface area of the first heliostat, the area occupied by the grid points with the marked sum being greater than or equal to twice the preset value is the union area; and determining the area of the region occupied by the grid points in the surface region of the first heliostat, wherein the sum of the markers in the surface region of the first heliostat is greater than or equal to two times of the preset value, based on the Pick theorem, wherein the area determined based on the Pick theorem is the area of the union region.
Optionally, the determining at least one projection area of the at least one second heliostat on the plane of the first heliostat includes: determining coordinate values of at least three vertices in the first heliostat and coordinate values of each vertex of each second heliostat in the at least one second heliostat in a first coordinate system, wherein the first coordinate system has the following characteristics: the position of the location surface of the heat collecting tower is a coordinate origin, the east-righting direction is an x axis, and the north-righting direction is a y axis; determining a plane where the first heliostat is located based on coordinate values of at least three vertexes of the first heliostat; determining a straight line where each vertex is located based on the azimuth angle and the elevation angle of the light ray on the first heliostat and the coordinate value of each vertex of each second heliostat in the at least one second heliostat; determining an intersection point of a straight line where each vertex of each second heliostat in the at least one second heliostat is located and a plane where the first heliostat is located; and determining a projection area corresponding to each second heliostat based on the intersection point corresponding to each vertex of each second heliostat in the at least one second heliostat, thereby determining the at least one projection area.
Optionally, the determining the coordinate values of at least three vertices of the first heliostat and the coordinate values of each vertex of each second heliostat of the at least one second heliostat in the first coordinate system comprises: determining coordinate values of a midpoint of each heliostat of the first heliostat and the at least one second heliostat in the first coordinate system; determining coordinate values of a vertex to be used for determining the projection area in each heliostat in a second coordinate system corresponding to each heliostat, wherein the second coordinate system has the following characteristics: the center of the heliostat is a coordinate origin, the normal direction passing through the center of the heliostat is a y-axis, and the rotating shaft corresponding to the elevation angle of the first heliostat is an x-axis; determining a transformation matrix for transforming the second coordinate system to the first coordinate system based on the spin angle, the elevation angle, the altitude angle and the facing angle of the first heliostat; and determining coordinate values of the vertex of each heliostat to be used for determining the projection area in the first coordinate system based on the determined transformation matrix, the coordinate values of the vertex of each heliostat to be used for determining the projection area in the second coordinate system corresponding to each heliostat and the coordinate values of the center of each heliostat in the first coordinate system.
Optionally, the transformation matrix is:
wherein ρ is the spin angle, θ is the elevation angle, λ is the elevation angle of the first heliostat,
is the facing angle.
Accordingly, in another aspect the present invention provides an apparatus for determining the area lost by a first heliostat controlled in a spin plus elevation control mode, the apparatus comprising: a loss region determining module, configured to determine a loss region corresponding to the first heliostat, where the loss region includes a shadow region and/or an occlusion region, a heliostat in the shadow region generates a shadow on the first heliostat, and a heliostat in the occlusion region occludes a light ray reflected by the first heliostat; a loss heliostat determination module to determine at least one second heliostat that is within the loss region; a projection area determination module for determining at least one projection area of the at least one second heliostat on the plane of the first heliostat; a union region determination module for determining a union region of the at least one projection region within the surface of the first heliostat; and a lost area determination module for determining an area of the union region, wherein the area of the union region is the lost area.
Optionally, the determining the union region of the at least one projection region within the surface of the first heliostat by the union region determination module comprises: dividing the at least one projection area and the surface area of the first heliostat into squares; marking lattice points on the divided squares, wherein a preset value is marked if a lattice point is in any one of the at least one projection area and the surface area of the first heliostat; and summing the marked preset values of each grid point to obtain a marked sum of the grid points, wherein in the surface area of the first heliostat, the area occupied by the grid points with the marked sum being greater than or equal to twice the preset value is the union area; the lost area determination module determining the area of the union region comprises: determining the area of the region occupied by the grid points in the surface region of the first heliostat, wherein the sum of the markers in the surface region of the first heliostat is greater than or equal to two times the preset value, based on the Pick theorem, wherein the area determined based on the Pick theorem is the area of the union region.
Optionally, the determining at least one projected area of the at least one second heliostat on the plane of the first heliostat by the projected area determination module includes: determining coordinate values of at least three vertices in the first heliostat and coordinate values of each vertex of each second heliostat in the at least one second heliostat in a first coordinate system, wherein the first coordinate system has the following characteristics: the position of the location surface of the heat collecting tower is a coordinate origin, the east-righting direction is an x axis, and the north-righting direction is a y axis; determining a plane where the first heliostat is located based on coordinate values of at least three vertexes of the first heliostat; determining a straight line where each vertex is located based on the azimuth angle and the elevation angle of the light ray on the first heliostat and the coordinate value of each vertex of each second heliostat in the at least one second heliostat; determining an intersection point of a straight line where each vertex of each second heliostat in the at least one second heliostat is located and a plane where the first heliostat is located; and determining a projection area corresponding to each second heliostat based on the intersection point corresponding to each vertex of each second heliostat in the at least one second heliostat, thereby determining the at least one projection area.
Optionally, the determining the coordinate values of at least three vertices of the first heliostat and the coordinate values of each vertex of each second heliostat of the at least one second heliostat in the first coordinate system comprises: determining coordinate values of a midpoint of each heliostat of the first heliostat and the at least one second heliostat in the first coordinate system; determining coordinate values of a vertex to be used for determining the projection area in each heliostat in a second coordinate system corresponding to each heliostat, wherein the second coordinate system has the following characteristics: the center of the heliostat is a coordinate origin, the normal direction passing through the center of the heliostat is a y-axis, and the rotating shaft corresponding to the elevation angle of the first heliostat is an x-axis; determining a transformation matrix for transforming the second coordinate system to the first coordinate system based on the spin angle and the elevation angle, the altitude angle and the facing angle of the first heliostat; and determining coordinate values of the vertex of each heliostat to be used for determining the projection area in the first coordinate system based on the determined transformation matrix, the coordinate values of the vertex of each heliostat to be used for determining the projection area in the second coordinate system corresponding to each heliostat and the coordinate values of the center of each heliostat in the first coordinate system.
Optionally, the transformation matrix is:
wherein ρ is the spin angle, θ is the elevation angle, λ is the elevation angle of the first heliostat,
is the facing angle.
Additionally, another aspect of the present invention provides a machine-readable storage medium having stored thereon instructions for causing a machine to perform the above-described method.
According to the technical scheme, under the condition that the mode for controlling the first heliostat is a spin angle plus elevation angle control mode, at least one projection area of other heliostats in a loss area of the first heliostat on the plane where the first heliostat is located is determined, a union area of the at least one projection area in the surface of the first heliostat is determined, and the area of the union area is determined, wherein the area of the union area is the loss area of the first heliostat, and the loss area comprises the area of shadow and/or shielding loss.
Additional features and advantages of the invention will be set forth in the detailed description which follows.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the embodiments of the invention without limiting the embodiments of the invention. In the drawings:
FIG. 1 is a schematic diagram of a heliostat attitude control approach;
FIG. 2 is a schematic diagram of a spin plus elevation control scheme;
FIG. 3 is a schematic diagram of a spin plus elevation motion pattern of a heliostat;
FIG. 4 is a flow chart of a method for determining lost area of a first heliostat provided by an embodiment of the invention;
FIG. 5 is a side view of a first heliostat being shaded, according to another embodiment of the invention;
FIG. 6 is a top view of a shadow received by a first heliostat provided in accordance with another embodiment of the invention;
FIG. 7 is a schematic diagram of determining the extent of a shadow region provided by another embodiment of the present invention;
FIG. 8 is a schematic diagram of an exemplary shadow shape provided by another embodiment of the present invention; and
fig. 9 is a block diagram of an apparatus for determining a lost area of a first heliostat according to another embodiment of the invention.
Description of the reference numerals
1 loss region determining module 2 loss heliostat determining module
3 projection area determination module 4 union area determination module
5 lost area determination module
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating embodiments of the invention, are given by way of illustration and explanation only, not limitation.
The total optical efficiency of the mirror field includes the atmospheric transmittance ηatCosine efficiency etacosinShadow and occlusion efficiency ηS&BAnd an overflow efficiency ηint. The system can be used for calculating and analyzing the mirror field efficiency.
Of mirror fieldThe optical efficiency is: etafield＝ηat×ηcosin×ηS&B×ηint
Atmospheric transmittance etaat：
ηat＝exp(-0.106×10-4S0) S0> 1000, wherein S0The distance of the mirror field position to the target point.
Cosine efficiency ηcosinThe phenomenon that the radiation of the heliostat actually received is smaller than the theoretical maximum radiation caused by the inclination of the heliostat: etacosinCos θ, where θ is the acute angle between the plane of the heliostat and the plane perpendicular to the incident solar light.
Shadow and occlusion efficiency ηS&BThe proportion of the total area occupied by the "effective" area of the mirror that is not shadowed or otherwise lost from occlusion is shown.
Spill-over efficiency ηintIt is the reflection of solar radiation energy by heliostats that does not reach the collector surface or entrance and the energy loss caused by the escape into the outside atmosphere is called the spill loss.
Due to the different arrangement of the heliostat fields, and as the sun operates, the attitude of the heliostat also changes. The attitude of the heliostat can be controlled in two ways: an elevation angle plus azimuth angle control mode and a spin angle plus elevation angle control mode are different, and the calculation methods of shadow and shielding efficiency are different. The spin angle plus elevation angle control method is shown in fig. 1, wherein a diagram in fig. 1 shows an azimuth angle plus elevation angle control method, and b diagram in fig. 1 shows a spin angle plus elevation angle control method. The control mode of the spin angle plus the elevation angle is mainly characterized in that the spin axis always points to the target heat collector.
The spin plus elevation control scheme is explained below in conjunction with fig. 2. It should be noted that the explanation of the spin angle plus elevation angle control method herein is only for understanding the spin angle plus elevation angle control method, and is not intended to limit the present invention.
In fig. 2, the heliostat or its frame is represented by a plane, O being the central point of the mirror, vector OT pointing to the target point (target collector), OS pointing to the sun, ON being the normal of the mirror. Figure 2 a shows the best instant when the sun is in the same azimuth as the target point (e.g. all in the south), assuming that the mirror is not in the same attitude as the azimuth plus elevation, OT, OS and ON are all in the meridian plane of the optical system perpendicular to the mirror plane, ON is the bisector of the angle between OT and OS, and the mirror plane is left-right symmetric about the meridian plane at that time. The diagram b of fig. 2 shows the case where the sun is in another azimuth, the new tracking mode mirror is not rotated around the azimuth axis perpendicular to the ground, but around the OT axis by an angle denoted by p, which is the spin angle, the spin causing the normal ON to rotate into the plane defined by OT and the new OS (OS '), to OT', while the plane of symmetry of the mirror surface remains the meridian plane. Assuming that the angle between OT and OS ' is 2 θ, the mirror should rotate around another axis parallel to the sagittal line of the mirror while spinning to change the elevation angle of the mirror so that ON ' is at an angle θ with OS '. θ is the incident angle, i.e., the elevation angle, of the sunlight at this time. Further, the directions of movement of the spin angle ρ and the elevation angle θ can be understood with reference to the arrows in fig. 3. In fig. 3, an arrow around T 'T indicates a movement direction of the spin angle ρ, and FF' indicates a movement direction of the elevation angle θ.
One aspect of an embodiment of the present invention provides a method for determining a lost area of a first heliostat. The attitude of the first heliostat is controlled in a spin angle plus elevation angle control mode.
Fig. 4 is a flowchart of a method for determining a lost area of a first heliostat according to an embodiment of the invention. As shown in fig. 4, the method includes the following.
In step S40, a loss region corresponding to the first heliostat is determined, where the loss region includes a shadow region and/or a blocking region, the heliostat in the shadow region generates a shadow on the first heliostat, and the heliostat in the blocking region blocks the light reflected by the first heliostat.
For example, suppose the sun rays areParallel rays, the first heliostat being a rectangular heliostat whose height within the heliostat field is substantially the same. The maximum extent of the shadow zone generated for the first heliostat can be determined by the normal incidence of the solar rays on the first heliostat, wherein the maximum distance of the other heliostats which can shadow the first heliostat from the first heliostat can be seen in fig. 5. Fig. 5 shows a side view in which heliostat a (equivalent to the first heliostat described above) receives a shadow, and d shows the farthest distance from heliostat a in the front-rear direction of heliostat a of another heliostat that can shadow heliostat a. Wherein, as shown in FIG. 5, it can be calculated
L and W are the lengths of two sides of the heliostat a respectively, len is half of the length of a diagonal line of the heliostat,
further, other heliostats in the left-right direction of the heliostat a may also shadow the heliostat a. The shaded area corresponding to heliostat a can be seen in fig. 6, where fig. 6 is a shaded top view of heliostat a. In fig. 6, a region a surrounded by four points a ', B', C ', and D' is a shadow region corresponding to the heliostat a, and the specific range of the shadow region can be determined by determining the seats of the four points a ', B', C ', and D'.
The following description will be given by taking the determination of the coordinates of the point B ' as an example in conjunction with fig. 7, wherein the determination of the coordinates of the points a ', C ', and D ' can be referred to the method of determining the coordinates of the point B '. Let the coordinates of the central point M of the heliostat a be (x, y, H), wherein the heat collecting tower on which the heat collector is installed is the center of the coordinates, the due north direction is the positive y-axis direction, and the due east direction is the positive x-axis direction. B 'U is perpendicular to UM, and angle B' MU is equal toβ-270。
Referring to the method of deriving the coordinates of point B ', it can be found that the coordinates of points a', C ', D' are:
A’：
C’：
D’：
for the occluded regions of the first heliostat, the determination method may refer to the shaded regions. The heliostat in the shielding area shields the light reflected by the first heliostat, and the shielded light cannot be reflected to the heat collector, so that the shielding area of the first heliostat can be determined by referring to the method for determining the shadow area on the assumption that the reflected light is emitted by the heat collector according to the reversibility of the light, namely the heat collector is equivalent to the sun in the shadow area. In this manner, a determination of the region of heliostats that produce shadow losses and/or occlusion losses is achieved.
In step S41, at least one second heliostat in the loss zone is determined. Optionally, coordinates of heliostats in the heliostat field may be determined, and whether the coordinates of the heliostats are within the loss region may be determined.
In step S42, at least one projected area of at least one second heliostat onto the plane of the first heliostat is determined. Specifically, if the at least one second heliostat is a heliostat which generates a shadow on the first heliostat, then the at least one heliostat projects in the direction of the sun ray when projecting to the plane where the first heliostat is located; if the at least one second heliostat is a heliostat which shields the light rays reflected by the first heliostat, the at least one heliostat projects along the direction of the reflected light rays when projecting to the plane where the first heliostat is located; if the at least one second heliostat comprises a heliostat in a shadow area and a heliostat in a shielding area, respectively, the projection is carried out to the plane of the first heliostat along the direction of the solar ray and the direction of the reflected ray.
In step S43, a union of the at least one projection area within the surface of the first heliostat, i.e. the intersection of the union of the at least one projection area with the surface area of the first heliostat, is determined, the union of the at least one projection area being the part of the surface area of the first heliostat.
In step 44, the area of the union region of the at least one projection region within the surface of the first heliostat is determined, wherein the determined area of the union region is the loss area.
The method comprises the steps of determining at least one projection area of other heliostats in a loss area of a first heliostat on a plane where the first heliostat is located under the condition that a mode for controlling the first heliostat is a spin angle plus elevation angle control mode, determining a union area of the at least one projection area in the surface of the first heliostat, and determining the area of the union area, wherein the area of the union area is the loss area of the first heliostat, and the loss area comprises the area of shadow and/or shielding loss, so that the shadow and/or shielding loss area of the heliostat under the spin angle plus elevation angle control mode is determined.
In a three-dimensional space, if the attitude of the heliostat is controlled by a spin angle plus elevation angle control method, the movement of the heliostat is complicated, and there are many possible shadow shapes, as shown in fig. 8. It should be noted that fig. 8 only exemplarily lists several possible shadow shapes, and the possible shadow shapes are not limited to these. As can be seen from fig. 8, the shadow shapes are not uniform and vary as the heliostat operates. The same is true of the occluded area. This adds difficulty to calculating the area of the shadow and/or occlusion region.
Optionally, in an embodiment of the present invention, determining a union region of the at least one projection region within the surface of the first heliostat and determining an area of the union region may be determined based on a lattice method, specifically including the following.
The method comprises the steps of dividing at least one projection area and the surface area of a first heliostat into squares, wherein the sizes of the squares can be determined according to actual requirements, and the accuracy is higher when the squares are smaller, so that the calculation accuracy can be controlled by controlling the sizes of the squares.
Marking grid points on the divided squares, wherein a preset value is marked if a grid point is located in any one of the at least one projection area and the surface area of the first heliostat. For example, if the preset value is 1, the at least one second heliostat includes 5 heliostats, and the at least one projection area includes 5 projection areas, the marking of the grid point Q is exemplified to describe the marking of the grid point. When the lattice point Q is positioned in one of the 5 projection areas, marking 1 for the lattice point Q, thus judging whether the lattice point Q is positioned in each of the 5 projection areas one by one, and when the lattice point Q is positioned in one projection area, marking 1 for the lattice point Q; when grid point Q is still in the surface area of the first heliostat, grid point Q is again marked 1.
Summing the marked preset values of each grid point to obtain a marked sum of the grid points, wherein in the surface area of the first heliostat, the area occupied by the grid points with the marked sum being greater than or equal to twice the preset value is a union area. The description continues with the above-mentioned case of the lattice point Q as an example of the marked sum of the lattice points obtained by the summation. Assuming that the grid point Q is located in two projections of the 5 projection regions and in the surface region of the first heliostat, the grid point Q is marked with 3 1 points in total, and the total number of marks of the grid point Q is 3. The labeled sum for each grid point is determined based on a similar manner as finding the labeled sum for grid point Q. Grid point Q is within the surface area of the first heliostat and the sum of the markings of grid point Q is greater than 2, indicating that grid point Q is also within at least one projected area, and thus, grid point Q is within an area that can shadow the first heliostat. Similarly, in the surface area of the first heliostat, the grid points with the price sum of more than or equal to 2 are all in the area which can shadow the first heliostat, so that in the surface area of the first heliostat, the area occupied by the grid points with the price sum of more than or equal to 2 is the union area of at least one projection area in the surface of the first heliostat. In the case where the preset value is not 1, but 2, in the surface area of the first heliostat, the grid points whose total number of markers is greater than or equal to 4 are both within at least one projected area and within the surface area of the first heliostat. Further, in the surface area of the first heliostat, an area occupied by grid points of which the total number of marks is greater than or equal to two times of the preset value is a union area of at least one projection area in the surface area of the first heliostat.
Determining the area of the region occupied by the grid points with the total sum of the markers in the surface region of the first heliostat being greater than or equal to two times the preset value based on the Pick theorem, wherein the area determined based on the Pick theorem is the area of the union region. Continuing with the explanation with the preset value of 1, in the surface area of the first heliostat, the grid points marked with the total sum of 2 are located at the intersection of at least one projection area and the surface area of the first heliostat, that is, on the boundary of the union region, and the grid points marked with the total sum of more than 2 are located inside the union region. Determining the number of grid points whose total number of markers in the surface area of the first heliostat is equal to 2 and the number of grid points whose total number of markers is greater than 2, i.e., determining the total number of grid points located on the border of the union region and the total number of grid points located within the union region. The area of the union region is S ═ a + b ÷ 2-1, where a denotes the total number of lattice points located inside the union region, b denotes the total number of lattice points located on the boundary of the union region, and S denotes the area of the union region.
Optionally, in the embodiment of the present invention, in the case that the union region is determined, the area of the union region may also be determined based on an integration method. Specifically, the union region can be divided into graphs which are convenient for area calculation based on an integral method, and then the area of the union region is determined according to the integral method.
Optionally, in an embodiment of the present invention, determining at least one projection area of at least one second heliostat projected on the plane on which the first heliostat is located includes: determining coordinate values of at least three vertices in a first heliostat and coordinate values of each vertex of each second heliostat in at least one second heliostat in a first coordinate system, wherein the first coordinate system has the following characteristics: the position of the location surface of the heat collecting tower is a coordinate origin, the east-righting direction is an x axis, and the north-righting direction is a y axis; determining a plane where the first heliostat is located based on coordinate values of at least three vertexes of the first heliostat; determining a straight line where each vertex is located based on the azimuth angle and the altitude angle of the light ray on the first heliostat and the coordinate value of each vertex of each second heliostat in at least one second heliostat; determining the intersection point of a straight line where each vertex of each second heliostat in at least one second heliostat is located and a plane where the first heliostat is located; and determining a projection area corresponding to each second heliostat based on the intersection point corresponding to each vertex of each second heliostat in the at least one second heliostat, thereby determining at least one projection area.
The following description will be given of determining at least one projection area of at least one second heliostat on the plane on which the first heliostat is located, taking a heliostat of a heliostat field, which is a rectangular heliostat, as an example. Specifically, the description will be given taking an example in which heliostat b (i.e., the second heliostat as described above) generates a shadow on heliostat a (i.e., the first heliostat as described above).
Establishing a coordinate system S ', wherein in the coordinate system S', the position of the heat collection tower where the heat collector is installed is set as the origin (0, 0, 0) of coordinates, the positive north direction of the heat collection tower is the positive y-axis direction, and the positive east direction is the positive x-axis direction.
And determining coordinate values of three vertexes of the heliostat a and four vertexes of the heliostat b in the coordinate system S'. And determining a plane equation M of the heliostat a according to the coordinate of three vertexes of the heliostat a according to the principle that three points determine a plane.
The intersection point of the straight line and the plane can be determined according to the straight line equation and the plane equation, and the intersection point of the four vertexes of the heliostat b projected in the plane of the heliostat a is determined based on the principle. When the projection area of the heliostat b on the plane of the heliostat a is determined, the projection is performed along the solar ray, and when the projection area of the heliostat b on the plane of the heliostat a is determined, the vertex of the heliostat b is positioned on the solar ray. And determining the intersection point of the four vertexes of the heliostat b projected in the plane of the heliostat a, namely determining the intersection point of the four vertexes of the heliostat b and the plane of the heliostat a along the straight line of the solar ray.
The following description will be given taking as an example the determination of the point on the plane where the heliostat a is located along the solar ray at the vertex P of the heliostat b. Determining the points where the other three vertices of heliostat b project on the plane of heliostat a can be seen in the method of determining the points where vertices P project on the plane of heliostat a.
And determining the altitude angle alpha and the azimuth angle beta of the solar ray on the heliostat a so as to determine the attitude of the heliostat a. The altitude angle alpha of the sun is an included angle between the sun ray and the tangent line of the earth surface, the azimuth angle beta of the sun is an included angle between the projection of the sun ray on the ground plane and the local meridian, and can be approximately regarded as an included angle between the shadow of a straight line erected on the ground in the sun and the south. The azimuth angle beta is zero in the positive north direction of the target object, gradually increases in the clockwise direction, and ranges from 0 to 360 degrees. The coordinate of the vertex P is set to (x)b，yb，zb) Along the linear equation L of the vertex P of the solar rayPIs composed of
Simultaneous plane equation M and linear equation LPThe coordinate value of the point where the vertex P is projected on the plane of the heliostat a along the solar ray can be found. Based on the same principle, the intersection points of the other three vertexes of the heliostat b projected on the heliostat a are determined.
The area surrounded by the intersection points of the four vertexes of the heliostat b projected on the plane of the heliostat a is the projection area of the heliostat b projected on the plane of the heliostat a. Similarly, a projection area of other heliostats which can shadow the heliostat a on the plane of the heliostat a is determined.
For determining the projection area of the other heliostat which shields the first heliostat and projects on the plane where the first heliostat is located, according to the reversibility of light, the reflected light is emitted by the heat collector, the intersection point of the other heliostat along the emitted light and projecting on the plane where the first heliostat is located is determined, the projection area of the other heliostat and projecting on the plane where the first heliostat is located is determined, and specifically, the method for determining the projection area of the heliostat b and projecting on the plane where the heliostat a is located can be referred to.
Optionally, in an embodiment of the present invention, determining the coordinate values of at least three vertices in the first heliostat and the coordinate value of each vertex in each second heliostat in at least one second heliostat in the first coordinate system includes the following. And determining coordinate values of the middle point of each heliostat in the first coordinate system in the first heliostat and the at least one second heliostat. For example, the at least one second heliostat includes 5 second heliostats, coordinate values of the center of each heliostat of the first heliostat and the 5 second heliostats in the first coordinate system are determined. And determining coordinate values of the vertexes of the heliostats to be used for determining the projection area in a second coordinate system corresponding to each heliostat, wherein the second coordinate system has the following characteristics: the center of the heliostat is a coordinate origin, the normal direction passing through the center of the heliostat is a y-axis, and the rotating shaft corresponding to the elevation angle of the first heliostat is an x-axis. Continuing with the example of the 5 second heliostats, determining the projection area requires using at least three vertices of the first heliostat and each vertex of each second heliostat of the 5 second heliostats. And establishing a second coordinate system based on the first heliostat and the 5 second heliostats respectively, and determining at least three vertexes of the first heliostat and the coordinate value of each vertex of each second heliostat in the 5 second heliostats in the corresponding second coordinate systems. Determining a conversion matrix for converting a second coordinate system to a first coordinate system based on the spin angle, the elevation angle, the altitude angle and the facing angle of the first heliostat; and determining coordinate values of the vertex of each heliostat to be used for determining the projection area in the first coordinate system based on the determined transformation matrix, the coordinate values of the vertex of each heliostat to be used for determining the projection area in the second coordinate system corresponding to each heliostat and the coordinate values of the center of each heliostat in the first coordinate system. The height angle of the first heliostat is a relative height, and for the first heliostat, the target heat collector and the first heliostat are 0 degree on the same horizontal plane, and 10 means 10 degrees clockwise of a horizontal line. The facing angle of the first heliostat is a direction relation, the north and the south of the target heat collector at the center of the first heliostat are 0 degree, and the west and the north of the target heat collector at the first heliostat are 90 degrees. As shown in FIG. 2, the height angles of the targets T and O in the same horizontal plane are 0 degrees, and 10 means that the horizontal line is 10 degrees clockwise; the north of the point O of T is 0 degree, and the west of T is 90 degrees.
Optionally, in an embodiment of the present invention, the conversion matrix is:
wherein ρ is a spin angle, θ is an elevation angle, λ is a height angle of the first heliostat,
is a facing angle.
The following description will be given taking as an example the coordinate values of the vertexes of the heliostat a (equivalent to the first heliostat described above) specified in the first coordinate system. It is assumed that all heliostats in the heliostat field are rectangular heliostats. Setting the parallel edge of the heliostat a with the ground as a long edge and the length as L; the other side of the heliostat a is a wide side with a width of W.
Establishing a first coordinate system S ', wherein in the first coordinate system S', the position of the heat collection tower where the heat collector is installed is set as the origin (0, 0, 0) of coordinates, the north direction of the heat collection tower is the positive y-axis direction, and the east direction is the positive x-axis direction. The height of the center of the heliostat a from the ground is H, and the coordinates of the center of the heliostat a in the first coordinate system S' are (x, y, H).
A second coordinate system S is established, where the center of the heliostat a is taken as the origin of coordinates (0, 0, 0), the normal direction passing through the center of the heliostat a is taken as the y-axis, and the rotation axis corresponding to the elevation motion of the heliostat a is taken as the x-axis, where the positive directions of the x-axis and the y-axis can be set according to the actual situation, and when the positive directions of the x-axis and the y-axis are set there, the description will be given with reference to fig. 3. As shown in fig. 3, FF 'is an x-axis, FF' is a rotation axis corresponding to the elevation motion of heliostat a, F-direction F 'is a positive x-axis direction, TT' is a y-axis, TT 'is a normal direction passing through the center of heliostat a, and T-direction T' is a positive y-axis direction. Further, an upward axis passing through the origin of the mirror surface of the heliostat a is defined as a z-axis, and an upward direction is defined as a positive direction. Note that, the positive directions of the x axis and the y axis in the second coordinate system corresponding to the heliostat a are described here by way of example only, and the setting of the positive directions of the x axis and the y axis is not limited to this, and when setting other positive directions of the x axis and the y axis, the coordinate values may be determined by the method for determining coordinate values described here.
The four vertexes of heliostat a are set to A, B, C, D, respectively, and as shown in fig. 3, in the second coordinate system S, the coordinates of point a are (L/2, 0, W/2), the coordinates of point B are (-L/2, 0, W/2), the coordinates of point C are (-L/2, 0, -W/2), and the coordinates of point D are (L/2, 0, -W/2).
The coordinate transformation of the coordinate system from the second coordinate system S to the first coordinate system S' is a total of three transformations.
The x axis and the y axis of the first conversion into the second coordinate system S are centered on the y axis, and the coordinate system S is obtained by rotating the angle rho towards the negative direction of the z axis1Where ρ is a spin angle of the heliostat a, and the first conversion matrix T is:
second conversion into a coordinate system s1The y-axis and the z-axis of the coordinate system are centered on the x-axis, and the negative direction rotation angle to the z-axis is theta + lambda, so as to obtain a coordinate system s2And theta is the self-rotating angle of the heliostat a, lambda is the height angle of the heliostat a, and the height angle is the formed height angle between the heat collector of the heat collecting tower and the center of the heliostat. The height angle is a relative height, for example, the height may be 0 degree on the same horizontal plane with the center of the heliostat, and 10 degrees is equal to 10 degrees, which means that the horizontal line is 10 degrees clockwise. The second transformation matrix is:
third conversion to coordinate system s2The x-axis and the y-axis of the optical disk rotate in the negative direction of the y-axis (counterclockwise when viewed from the negative direction to the positive direction of the z-axis) around the z-axis
Obtaining a coordinate system s3Wherein, in the step (A),
is a facing angle. The facing angle is the direction relation between the heat collecting tower and the heliostat. For example, the heat collecting tower may be 0 degree in the true north of the heliostat and 90 degrees in the true west of the heliostat. The third transformation matrix is:
in determining a coordinate system s3Thereafter, the coordinate system s is set3Translating to the central point (x, y, H) of the heliostat a to obtain a first coordinate system S',
according to the above transformation process, the transformation matrix from the second coordinate system S to the first coordinate system S' is:
wherein ρ is a spin angle, θ is an elevation angle, λ is a height angle,
is a facing angle.
The conversion relationship of the coordinate value of the point of the heliostat a in the second coordinate system S to the first coordinate system S' is as follows:
where S represents a coordinate value of a point on heliostat a in the first coordinate system S, and S 'is a coordinate value of a point on heliostat a in the second coordinate system S'.
In the second coordinate system S, the coordinates of the point a are (L/2, 0, W/2), the coordinates of the point B are (-L/2, 0, W/2), the coordinates of the point C are (-L/2, 0, -W/2), the coordinates of the point D are (L/2, 0, -W/2), and by substituting the above transformation relationship, the coordinate values of the four vertexes of the heliostat a in the first coordinate system S' can be determined as:
coordinates of point A:
b point coordinates are as follows:
c point coordinate:
d, point coordinates:
for determining the coordinate values of the points on at least one second heliostat (for example, the points to be used for determining the projection area) in the first coordinate system, the method for determining the coordinate values of the points on heliostat a in the first coordinate system can be referred to above, a corresponding second coordinate system S is established for each second heliostat in at least one second heliostat, and then based on the similar coordinate transformation as above, the transformation relationship of the second coordinate system S corresponding to each second heliostat to the first coordinate system S' is found, and then the coordinate values of the points on each second heliostat in the first coordinate system are determined. In this way, the calculation of real-time coordinates of heliostats in a heliostat field is achieved.
It should be noted that the solar rays are emitted on the first heliostat, and the reflected rays can be regarded as being emitted by the collector according to the reversibility of the rays, and all relevant contents for determining the occlusion loss can be understood and realized by referring to the relevant contents for determining the shadow loss.
Accordingly, another aspect of embodiments of the present invention provides an apparatus for determining a lost area of a first heliostat. Fig. 9 is a block diagram of an apparatus for determining a lost area of a first heliostat according to another embodiment of the invention. And the mode for controlling the first heliostat is a spin angle plus elevation angle control mode. As shown in fig. 9, the apparatus includes a loss region determining module 1, a loss heliostat determining module 2, a projection region determining module 3, a union region determining module 4, and a loss area determining module 5. The loss region determining module 1 is configured to determine a loss region corresponding to the first heliostat, where the loss region includes a shadow region and/or a shielding region, the heliostat in the shadow region generates a shadow on the first heliostat, and the heliostat in the shielding region shields light reflected by the first heliostat; the loss heliostat determination module 2 is used for determining at least one second heliostat in a loss area; the projection area determining module 3 is used for determining at least one projection area of at least one second heliostat projected on the plane where the first heliostat is located; the union region determining module 4 is used for determining a union region of at least one projection region in the surface of the first heliostat; the lost area determining module 5 is configured to determine an area of a union region, where the area of the union region is a lost area.
The method comprises the steps of determining at least one projection area of other heliostats in a loss area of a first heliostat on a plane where the first heliostat is located under the condition that a mode for controlling the first heliostat is a spin angle plus elevation angle control mode, determining a union area of the at least one projection area in the surface of the first heliostat, and determining the area of the union area, wherein the area of the union area is the loss area of the first heliostat, and the loss area comprises the area of shadow and/or shielding loss.
Optionally, in an embodiment of the present invention, the determining the union region of the at least one projection region in the surface of the first heliostat includes: dividing at least one projection area and the surface area of the first heliostat into squares; marking lattice points on the divided squares, wherein if a lattice point is in any one of the at least one projection area and the surface area of the first heliostat, a preset value is marked; and summing the marked preset values of each grid point to obtain a marked sum of the grid points, wherein in the surface area of the first heliostat, the area occupied by the grid points with the marked sum being greater than or equal to twice the preset value is a union area; the lost area determination module determining the area of the union region comprises: determining the area of the region occupied by the grid points in the surface region of the first heliostat, wherein the sum of the marks in the surface region of the first heliostat is greater than or equal to two times of the preset value, based on the Pick theorem, wherein the area determined based on the Pick theorem is the area of the union region.
Optionally, in an embodiment of the present invention, the determining, by the projected area determining module, at least one projected area of at least one second heliostat projected on the plane where the first heliostat is located includes: determining coordinate values of at least three vertices in a first heliostat and coordinate values of each vertex of each second heliostat in at least one second heliostat in a first coordinate system, wherein the first coordinate system has the following characteristics: the position of the location surface of the heat collecting tower is a coordinate origin, the east-righting direction is an x axis, and the north-righting direction is a y axis; determining a plane where the first heliostat is located based on coordinate values of at least three vertexes of the first heliostat; determining a straight line where each vertex is located based on the azimuth angle and the altitude angle of the light ray on the first heliostat and the coordinate value of each vertex of each second heliostat in at least one second heliostat; determining an intersection point of a straight line where each vertex of each second heliostat in at least one second heliostat is located and a plane where the first heliostat is located; and determining a projection area corresponding to each second heliostat based on the intersection point corresponding to each vertex of each second heliostat in the at least one second heliostat, thereby determining at least one projection area.
Optionally, in an embodiment of the present invention, determining the coordinate values of at least three vertices of the first heliostat and the coordinate values of each vertex of each second heliostat of the at least one second heliostat in the first coordinate system includes: determining coordinate values of the middle point of each heliostat in the first coordinate system in the first heliostat and the at least one second heliostat; and determining coordinate values of the vertexes of the heliostats to be used for determining the projection area in a second coordinate system corresponding to each heliostat, wherein the second coordinate system has the following characteristics: the center of the heliostat is a coordinate origin, the normal direction passing through the center of the heliostat is a y axis, and the rotating shaft corresponding to the elevation angle of the first heliostat is an x axis; determining a transformation matrix for transforming the second coordinate system to the first coordinate system based on the spin angle, the elevation angle, the altitude angle and the facing angle of the first heliostat; and determining coordinate values of the vertex of each heliostat to be used for determining the projection area in the first coordinate system based on the determined transformation matrix, the coordinate values of the vertex of each heliostat to be used for determining the projection area in the second coordinate system corresponding to each heliostat and the coordinate values of the center of each heliostat in the first coordinate system.
Optionally, in an embodiment of the present invention, the conversion matrix is:
wherein ρ is a spin angle, θ is an elevation angle, λ is a height angle,
is a facing angle.
The specific working principle and benefits of the apparatus for determining the lost area of the first heliostat provided in the embodiment of the present invention are similar to those of the method for determining the lost area of the first heliostat provided in the embodiment of the present invention, and will not be described again here.
In addition, another aspect of the embodiments of the present invention also provides a machine-readable storage medium, on which instructions are stored, and the instructions are used for causing a machine to execute the method described in the embodiments.
In summary, in the case that the mode for controlling the first heliostat is the spin angle plus elevation angle control mode, at least one projection area of other heliostats in the loss area of the first heliostat on the plane where the first heliostat is located is determined, a union area of the at least one projection area in the surface of the first heliostat is determined, and the area of the union area is determined, where the area of the union area is the loss area of the first heliostat, and the loss area includes the area of shadow and/or shielding loss, so that the shadow and/or shielding loss area of the heliostat in the spin angle plus elevation angle control mode is determined. In addition, the coordinates of each vertex of the first heliostat and each vertex of each second heliostat of the at least one second heliostat can be determined, and thus, the coordinate values of the vertices of the heliostats can be determined in real time.
Although the embodiments of the present invention have been described in detail with reference to the accompanying drawings, the embodiments of the present invention are not limited to the details of the above embodiments, and various simple modifications can be made to the technical solutions of the embodiments of the present invention within the technical idea of the embodiments of the present invention, and the simple modifications all belong to the protection scope of the embodiments of the present invention.
It should be noted that the various features described in the foregoing embodiments may be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, the embodiments of the present invention do not describe every possible combination.
Those skilled in the art will understand that all or part of the steps in the method according to the above embodiments may be implemented by a program, which is stored in a storage medium and includes several instructions to enable a single chip, a chip, or a processor (processor) to execute all or part of the steps in the method according to the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
In addition, any combination of various different implementation manners of the embodiments of the present invention is also possible, and the embodiments of the present invention should be considered as disclosed in the embodiments of the present invention as long as the combination does not depart from the spirit of the embodiments of the present invention.
Claims (9)
1. A method for determining lost area of a first heliostat, wherein the first heliostat is controlled in a spin plus elevation control mode, the method comprising:
determining a loss region corresponding to the first heliostat, wherein the loss region comprises a shadow region and/or an occlusion region, the heliostat in the shadow region generates a shadow on the first heliostat, and the heliostat in the occlusion region occludes light reflected by the first heliostat;
determining at least one second heliostat within the loss region;
determining at least one projection area of the at least one second heliostat on the plane of the first heliostat;
determining a union region of the at least one projection region within the surface of the first heliostat; and
determining an area of the union region, wherein the area of the union region is the loss area,
wherein the determining at least one projection area of the at least one second heliostat onto the plane of the first heliostat comprises:
determining coordinate values of at least three vertices in the first heliostat and coordinate values of each vertex of each second heliostat in the at least one second heliostat in a first coordinate system, wherein the first coordinate system has the following characteristics: the position of the location surface of the heat collecting tower is a coordinate origin, the east-righting direction is an x axis, and the north-righting direction is a y axis;
determining a plane where the first heliostat is located based on coordinate values of at least three vertexes of the first heliostat;
determining a straight line where each vertex is located based on the azimuth angle and the elevation angle of the light ray on the first heliostat and the coordinate value of each vertex of each second heliostat in the at least one second heliostat;
determining an intersection point of a straight line where each vertex of each second heliostat in the at least one second heliostat is located and a plane where the first heliostat is located; and
determining a projection area corresponding to each second heliostat based on the intersection point corresponding to each vertex of each second heliostat in the at least one second heliostat, thereby determining the at least one projection area.
2. The method of claim 1, wherein determining a union region of the at least one projection region within the surface of the first heliostat and determining an area of the union region comprises:
dividing the at least one projection area and a surface area of the first heliostat into squares;
marking lattice points on the divided squares, wherein a preset value is marked if a lattice point is in any one of the at least one projection area and the surface area of the first heliostat;
summing the marked preset values of each grid point to obtain a marked sum of the grid points, wherein in the surface area of the first heliostat, the area occupied by the grid points with the marked sum being greater than or equal to twice the preset value is the union area; and
determining the area of the region occupied by the grid points in the surface region of the first heliostat, wherein the sum of the markers in the surface region of the first heliostat is greater than or equal to two times the preset value, based on the Pick theorem, wherein the area determined based on the Pick theorem is the area of the union region.
3. The method of claim 1, wherein determining the coordinate values of at least three vertices of the first heliostat and each vertex of each of the at least one second heliostat in the first coordinate system comprises:
determining coordinate values of a midpoint of each heliostat of the first heliostat and the at least one second heliostat in the first coordinate system;
determining coordinate values of a vertex to be used for determining the projection area in each heliostat in a second coordinate system corresponding to each heliostat, wherein the second coordinate system has the following characteristics: the center of the heliostat is a coordinate origin, the normal direction passing through the center of the heliostat is a y-axis, and the rotating shaft corresponding to the elevation angle of the first heliostat is an x-axis;
determining a transformation matrix for transforming the second coordinate system to the first coordinate system based on the spin angle, the elevation angle, the altitude angle and the facing angle of the first heliostat; and
and determining coordinate values of the vertex of each heliostat to be used for determining the projection area in the first coordinate system based on the determined transformation matrix, the coordinate values of the vertex of each heliostat to be used for determining the projection area in the second coordinate system corresponding to each heliostat and the coordinate values of the center of each heliostat in the first coordinate system.
4. The method of claim 3, wherein the transformation matrix is:
wherein ρ is the spin angle, θ is the elevation angle, λ is the elevation angle of the first heliostat,
is the facing angle.
5. An apparatus for determining lost area of a first heliostat in which the first heliostat is controlled in a spin plus elevation control mode, the apparatus comprising:
a loss region determining module, configured to determine a loss region corresponding to the first heliostat, where the loss region includes a shadow region and/or an occlusion region, a heliostat in the shadow region generates a shadow on the first heliostat, and a heliostat in the occlusion region occludes a light ray reflected by the first heliostat;
a loss heliostat determination module to determine at least one second heliostat within the loss region;
a projection area determination module for determining at least one projection area of the at least one second heliostat on the plane of the first heliostat;
a union region determination module for determining a union region of the at least one projection region within the surface of the first heliostat; and
a lost area determination module for determining an area of the union region, wherein the area of the union region is the lost area,
wherein the projected area determination module determining at least one projected area of the at least one second heliostat projected onto the plane of the first heliostat comprises:
determining coordinate values of at least three vertices in the first heliostat and coordinate values of each vertex of each second heliostat in the at least one second heliostat in a first coordinate system, wherein the first coordinate system has the following characteristics: the position of the location surface of the heat collecting tower is a coordinate origin, the east-righting direction is an x axis, and the north-righting direction is a y axis;
determining a plane where the first heliostat is located based on coordinate values of at least three vertexes of the first heliostat;
determining a straight line where each vertex is located based on the azimuth angle and the elevation angle of the light ray on the first heliostat and the coordinate value of each vertex of each second heliostat in the at least one second heliostat;
determining an intersection point of a straight line where each vertex of each second heliostat in the at least one second heliostat is located and a plane where the first heliostat is located; and
determining a projection area corresponding to each second heliostat based on the intersection point corresponding to each vertex of each second heliostat in the at least one second heliostat, thereby determining the at least one projection area.
6. The apparatus of claim 5,
the union region determination module determining a union region of the at least one projection region within the surface of the first heliostat includes:
dividing the at least one projection area and a surface area of the first heliostat into squares;
marking lattice points on the divided squares, wherein a preset value is marked if a lattice point is in any one of the at least one projection area and the surface area of the first heliostat; and
summing the marked preset values of each grid point to obtain a marked sum of the grid points, wherein in the surface area of the first heliostat, the area occupied by the grid points with the marked sum being greater than or equal to twice the preset value is the union area;
the lost area determination module determining the area of the union region comprises:
determining the area of the region occupied by the grid points in the surface region of the first heliostat, wherein the sum of the markers in the surface region of the first heliostat is greater than or equal to two times the preset value, based on the Pick theorem, wherein the area determined based on the Pick theorem is the area of the union region.
7. The apparatus of claim 5, wherein determining the coordinate values of at least three vertices of the first heliostat and each vertex of each of the at least one second heliostat in the first coordinate system comprises:
determining coordinate values of a midpoint of each of the first heliostat and the at least one second heliostat in the first coordinate system;
determining coordinate values of a vertex to be used for determining the projection area in each heliostat in a second coordinate system corresponding to each heliostat, wherein the second coordinate system has the following characteristics: the center of the heliostat is a coordinate origin, the normal direction passing through the center of the heliostat is a y-axis, and the rotating shaft corresponding to the elevation angle of the first heliostat is an x-axis;
determining a transformation matrix for transforming the second coordinate system to the first coordinate system based on the spin angle, the elevation angle, the altitude angle and the facing angle of the first heliostat; and
and determining coordinate values of the vertex of each heliostat to be used for determining the projection area in the first coordinate system based on the determined transformation matrix, the coordinate values of the vertex of each heliostat to be used for determining the projection area in the second coordinate system corresponding to each heliostat and the coordinate values of the center of each heliostat in the first coordinate system.
8. The apparatus of claim 7, wherein the transformation matrix is:
wherein ρ is the spin angle, θ is the elevation angle, λ is the elevation angle of the first heliostat,
is the facing angle.
9. A machine-readable storage medium having stored thereon instructions for causing a machine to perform the method of any one of claims 1-4.
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