A segmented CPC solar concentrator and a method of designing the same

Abstract

The application provides a sectional CPC solar concentrator and a design method thereof. A compound parabolic reflector is fixed in a frame. A flat plate receiving surface is a heat absorbing surface of a flat plate light receiving body. The compound parabolic reflector is symmetrically arranged on both sides of the flat plate receiving surface. The compound parabolic reflector is composed of multiple sub-reflectors. The sub-reflectors are sequentially connected in a head-to-tail mode. The focal lines of the sub-reflectors on the flat plate receiving surface are evenly arranged from the middle to both sides. The focal lines of the sub-reflectors are different and parallel to each other. The sectional design of the traditional trough type parabolic concentrator profile is adopted, so that the energy flow density on the flat plate receiving surface is evenly distributed in multiple focal lines. The uniformity of the energy flow density distribution on the flat plate receiving surface of the concentrator is effectively improved. The thermal stress concentration on the flat plate receiving surface is greatly reduced. The service life of the concentrator is effectively prolonged.

Description

Technical Field

[0001] This invention belongs to the field of solar concentrators, specifically relating to a segmented CPC solar concentrator and its design method. Background Technology

[0002] Solar energy is a clean and renewable energy source that plays an increasingly important role in national economic development and people's daily lives. The solar energy flux density reaching the Earth's surface is relatively low, approximately 1 kW / m². 2 This limits the extent of solar energy utilization and the efficiency of photothermal / photovoltaic conversion. Solar concentrators focus sunlight, increasing the solar energy flux density on the flat-plate receiving surface and laying the foundation for high-temperature solar thermal utilization and concentrated photovoltaic power generation.

[0003] Based on the way light propagates, solar concentrators can be divided into three main categories: reflective concentrators, refractive concentrators, and hybrid concentrators. Among reflective concentrators, tower and dish concentrators focus incident sunlight into a point, concentrating it within a very small area, greatly increasing the solar energy flux density. However, they require two-dimensional tracking of the sun's movement, resulting in high costs for the tracking and control systems. Parabolic trough concentrators, composite parabolic mirror concentrators, and linear Fresnel concentrators focus sunlight into a linear projection onto a flat receiving surface. They require less tracking accuracy, and one-dimensional tracking is sufficient. Among these, the flat-plate composite parabolic mirror concentrator (CPC) is a medium-temperature solar collector. This type of concentrator is designed based on the principle of edge rays, reflecting incident light within a given receiving angle range onto the receiver. Its receiver is flat, and its concentrator structure is simple, with low requirements for the precision of the concentrating surface's linear machining.

[0004] Currently, CPC (Central Photoconcentrator) has been widely adopted and utilized in low- and medium-temperature solar energy applications, such as heating, material drying, and agricultural facility insulation. Sunlight passes through the CPC's light-collecting surface onto the parabolic surface, and after one or more reflections, converges onto the flat receiving surface. Light loss during transmission is minimal, effectively collecting incident light within the receiving angle range. However, due to the structural characteristics of the CPC, the solar energy flow distribution on the flat receiving surface is extremely uneven, exhibiting a pattern of high at both ends and low in the middle, with significant differences. This highly uneven energy flow distribution leads to low efficiency in the photothermal conversion process and causes uneven temperature distribution in the conversion device, making it prone to thermal stress damage. All of these factors affect and limit the promotion of CPC concentrators and the efficient utilization of solar energy. Summary of the Invention

[0005] In traditional CPC operation, the energy flux density distribution on the flat plate receiving surface is uneven, which not only reduces the photothermal efficiency but also makes the large temperature difference of the conversion device prone to thermal stress damage. To address this technical problem, this invention designs the CPC profile in segments, with the focal points of each segment evenly distributed, which greatly improves the uniformity of solar energy flux distribution on the flat plate receiving surface, thereby laying the foundation for the safe and economical operation of CPC.

[0006] The specific technical solution is as follows:

[0007] A segmented CPC solar concentrator includes: a frame, a composite parabolic reflector, a flat receiving surface, an incident surface, a pad, and a glass cover. The composite parabolic reflector is fixed inside the frame. The flat receiving surface is the heat-absorbing surface of a flat concentrator. The composite parabolic reflector is symmetrically placed on both sides of the flat receiving surface. The composite parabolic reflector is composed of multiple sub-reflectors, which are connected end to end in sequence. From bottom to top, the focal lines generated by each sub-reflector on the flat receiving surface are evenly distributed from the middle to both sides. The focal lines of each sub-reflector are at different positions and are parallel to each other.

[0008] A pad is provided below the flat receiving surface, and a glass cover is provided on the top of the frame.

[0009] The specific design method for the multi-segment reflector of the compound parabolic reflector is as follows:

[0010] S1. Determine the number of segments: Given a focusing ratio of C for the concentrator, which is the ratio of the incident surface area to the flat receiving surface area; when sunlight is incident perpendicularly to the incident surface, part of the light directly illuminates the flat receiving surface, while the other part is reflected by the compound parabolic mirror and converges on the flat receiving surface, thus achieving the purpose of focusing the light. Since only the light reflected by the compound parabolic mirror forms a focal line on the flat receiving surface, in order to improve the uniformity of the light distribution on the flat receiving surface, the compound parabolic mirror is designed in segments, with each side having a sub-mirror number of C-1.

[0011] S2. Determine the focal line arrangement: Each sub-mirror segment generates an independent focal line. The compound parabolic mirror is symmetrical on both sides, so the number of focal lines is 2 (C-1), evenly distributed on the flat receiving surface. The sub-mirrors on each side are connected end to end in sequence, and the focal lines generated by the sub-mirrors on the flat receiving surface from bottom to top are evenly distributed from the middle to both sides.

[0012] S3. Equations of the profile of each parabolic segment:

[0013] Given a segmented condenser with a flat receiving surface width of 2L, the sub-mirrors of the compound parabolic reflector are connected end-to-end, with the initial segment fixed to the side of the flat receiving surface. A two-dimensional rectangular coordinate system (XY) is established with the midpoint of the flat receiving surface profile as the origin. The XY coordinate plane is perpendicular to the focal lines of each sub-mirror and the flat receiving surface. The intersection of the XY coordinate plane and the flat receiving surface is the X-axis, and the intersection of the XY coordinate plane and the condenser's symmetry plane is the Y-axis. Starting with the sub-mirrors connected to the flat receiving surface, they are numbered i sequentially from bottom to top, with the initial segment being number 1. Assume the profile equation of the i-th segmented sub-mirror in the XY coordinate system is 2P. i (Yb i )=(Xa i ) 2 The equation of the parabolic profile of the i-th segmental mirror in the XY plane is determined by the following formula:

[0014] (1)

[0015] (2)

[0016] (3)

[0017] The initial x-coordinate of the i-th segmented reflector:

[0018] (4)

[0019] The initial coordinates of the (i+1)th segmented reflector:

[0020] , (5)

[0021] The initial point of the first segmented reflector is known:

[0022] (6)

[0023] In the formula: , Let be the vertex parameters of the parabolic equation expression for the i-th segmented sub-mirror in the XY plane;

[0024] , Let be the initial point parameters for the parabolic equation of the i-th segmented sub-mirror in the XY plane;

[0025] , These are the termination point parameters of the parabolic equation expression for the i-th segmented sub-mirror in the XY plane; they are also the initial point parameters of the parabolic equation expression for the (i+1)-th segmented sub-mirror in the XY plane.

[0026] C represents the focusing ratio of the segmented parabolic concentrator;

[0027] P i Let be the quasi-focal length of the parabolic equation expression of the i-th segmented sub-mirror in the XY plane.

[0028] Substituting equations (6), (2), and (1) into equation (3), we can obtain the parabolic equation of the first segmented sub-mirror in the XY plane. Substituting equation (5) into the equation of the first segmented parabola, we can obtain the initial coordinates of the parabola of the next segmented sub-mirror in the XY plane. Similarly, by iterating in sequence, we can determine the parabolic equation expression of each sub-mirror in the XY two-dimensional rectangular coordinate system, as well as the initial and final coordinates of the intercepts of all parabolic surfaces in the XY two-dimensional rectangular coordinate system. , () , This determines the installation position of the sub-reflector.

[0029] When the multiple composite parabolic mirrors are arranged, the starting position of the (i+1)th parabolic mirror is located at the end position of the ith mirror, minimizing the gap between each sub-mirror to the greatest extent.

[0030] This invention provides a segmented CPC solar concentrator and its design method. The traditional parabolic trough concentrator profile is segmented, so that the energy flux density on the flat plate receiving surface is evenly distributed with multiple focal lines. This effectively improves the uniformity of the energy flux density distribution on the flat plate receiving surface of the concentrator, greatly reduces the thermal stress concentration on the flat plate receiving surface, and thus effectively extends the service life of the concentrator. Attached Figure Description

[0031] Figure 1a This is a typical CPC energy flux density distribution diagram;

[0032] Figure 1b This is a diagram showing the energy flux density distribution of the segmented CPC of the present invention.

[0033] Figure 2 This is a structural diagram of the segmented solar collector of the present invention;

[0034] Figure 3 This is a schematic diagram illustrating the principle of light reflection in the segmented parabolic solar concentrator of the present invention.

[0035] Figure 4 This is a schematic diagram of the common CPC focusing principle. Detailed Implementation

[0036] The specific technical solutions of the present invention will be described with reference to the embodiments.

[0037] Under conditions of parallel light incidence, such as Figure 1a In a typical CPC (Central Photoconductive Panel), only the light incident on the reflector produces a focusing effect. To improve the uniformity of the energy flux density on the receiving surface 2-3 of the flat panel, such as... Figure 1b As shown, by comparing the effective and ineffective incident light-gathering areas and using averaging theory, the composite parabolic reflector 2-2 is designed in segments, resulting in segment C-1 sub-reflectors. Based on this, the focal lines of each segment are evenly distributed on the flat receiving surface 2-3, ensuring that the focal lines are parallel to each other and that the distance between any two adjacent focal lines is equal. Given that the width of the flat receiving surface 2-3 in the segmented condenser is 2L, all sub-reflectors are connected sequentially, with an initial segment of sub-reflectors fixed at the end of the flat receiving surface 2-3. A two-dimensional rectangular coordinate system (XY) is established with the midpoint of the shape of the flat receiving surface 2-3 as the origin. The XY coordinate plane is perpendicular to the focal lines of each sub-reflector's reflecting surface and the flat receiving surface 2-3. The intersection of the XY coordinate plane and the flat receiving surface 2-3 is the X-axis, and the intersection of the XY coordinate plane and the condenser's symmetry plane is the Y-axis. Starting from bottom to top, taking the segmented sub-reflectors connected by the flat receiving surface 2-3 as the starting surface, the sub-reflectors are sequentially numbered i, with the initial sub-reflector numbered 1. The coordinates of the initial endpoint of the line segment intercepted by the i-th sub-reflector in the XY coordinate plane are defined as (x... i y i Since adjacent sub-reflectors share a collinear side, the endpoint of the line segment intercepted by the i-th sub-reflector in the XY coordinate plane is the same as the initial endpoint coordinate of the line segment intercepted by the (i+1)-th sub-reflector in the XY coordinate plane, which is (x i+1 y i+1 Assume the equation of the profile of the i-th sub-mirror in the XY coordinate system is expressed as 2P. i (Yb i )=(Xa i ) 2 Since the intersection point of the focal line of the sub-reflector on the XY coordinate plane (referred to as the profile focus) lies on the X-axis, and the focus has the same x-coordinate as the vertex of the sub-reflector, the coordinates of the profile focus of the i-th sub-reflector are (a i According to the properties of a parabola, the vertex and focus lie on the same vertical axis, and the difference between their vertical coordinates is the focal length, which is the approximate focal length P. i One-half of, therefore there is

[0038] (1)

[0039] To reduce material costs per sub-reflector while ensuring the effective light-receiving area of ​​each sub-reflector remains constant, the focal line of the left sub-reflector can be positioned on the right half of the symmetrical plane of the flat receiving surface 2-3, and the focal line of the right sub-reflector on the left half of the symmetrical plane of the flat receiving surface 2-3 (this reduces the arc length of the parabolic profile). Since there are i sub-reflectors on each side, there are a total of 2i focal lines on the flat receiving surface 2-3. Assuming the width of the flat receiving surface 2-3 is 2L, the distance between two adjacent focal lines is... n is the total number of single-sided sub-mirrors. Therefore, the focal coordinates of the profile corresponding to the i-th sub-mirror are: The foci of the profile are taken as positive on the right side of the y-axis and negative on the left side. The x-coordinate of the vertex is the same as the x-coordinate of the foci, so the x-coordinates of the vertex are:

[0040] (2)

[0041] The initial x-coordinate of the i-th segmented reflector:

[0042] (4)

[0043] like Figure 3 It can be seen that the initial point of each segment is a connection point. Let... , Let be the initial point parameters of the parabolic equation expression for the i-th sub-mirror in the XY plane. , Let be the termination point parameters of the parabolic equation expression for the i-th sub-mirror in the XY plane. Then, the initial parameters of the i-th sub-mirror segment are the initial point parameters of the parabolic equation expression for the (i+1)-th sub-mirror segment in the XY plane.

[0044] The initial coordinates of the (i+1)th segmented reflector:

[0045] , (5)

[0046] The first segment of the reflector intersects the line in the XY plane, passing through the endpoint A of the line intersected by the receiving surface of the flat plate in the XY plane. Therefore:

[0047] X1=L, Y1=0 (6)

[0048] Given the concentration ratio, substitute equations (6), (2), and (1) into the overall parabolic equation. The parabola equation of the first sub-mirror in the XY plane can be obtained. Substituting equation (5) into the equation of the first sub-mirror, the initial coordinates of the parabola of the next sub-mirror in the XY plane can be obtained. Similarly, by iterating in sequence, the parabola equation of each sub-mirror in the XY two-dimensional rectangular coordinate system can be determined, as well as the initial and final coordinates of the intercepts of all parabolic surfaces in the XY two-dimensional rectangular coordinate system. , () , This determines the installation position of the sub-reflector.

[0049] Advantages of this invention compared to existing technologies: such as Figure 4 As shown, the mirror profiles on both sides of a traditional CPC concentrator are complete parabolic curves. When sunlight is incident parallel to the surface, each mirror profile produces only one focal point on the flat receiving surface, located at the endpoint of the profile. This invention segments the traditional CPC profile, resulting in a multi-focal distribution of energy flux density on the flat receiving surface. This significantly improves the uniformity of energy flux density distribution, reduces thermal stress concentration, and extends the device's lifespan. By importing models of a traditional CPC solar concentrator with a concentration ratio of 6 and a segmented CPC solar concentrator into TracePro software for optical tracing simulation, the energy flux density distribution on the flat receiving surface can be obtained. When the solar irradiance of each ray is 700 W / m²... 2 Figure 1 shows the energy flux density distribution on the receiving surfaces of the two types of concentrators. As can be seen from Figure 1, the energy flux density on the receiving surface of the traditional CPC concentrator exhibits a distribution trend of high at both ends and low in the middle, with the highest energy flux density reaching 5.88 × 10⁻⁶ at both ends. 10 W / m 2 The lowest point is only 5.6×10 8 W / m 2 The energy flux density range is 5.82 × 10⁻⁶. 10 W / m 2 The energy flux density of the flat receiving surface of the segmented CPC concentrator exhibits an approximately sinusoidal distribution, with the energy flux density near each focal point being roughly the same, at 1.25 × 10⁻⁶. 10 W / m 2 The minimum value is 5.25 × 10⁻⁶. 8 W / m 2 The range is 1.1975 × 10⁻⁶. 10 W / m 2 Therefore, the energy flux density difference on the segmented CPC flat plate receiving surface is much smaller than that on the traditional CPC flat plate receiving surface. This indicates that under the same operating conditions, the energy flux density distribution uniformity of the segmented CPC solar concentrator proposed in this invention is much higher than that of the traditional CPC concentrator, thereby effectively improving the safety and economy of the CPC concentrator.

[0050] The invention will now be described in detail with reference to examples. Frame 2-1, composite parabolic reflector 2-2, flat receiving surface 2-3, incident surface 2-4, pad 2-5, glass cover 2-6;

[0051] A schematic diagram of a segmented CPC solar collector with a concentration ratio of 6 is provided for reference. Figure 2 The solar collector consists of a frame 2-1, a flat plate receiver 2-3, and a composite parabolic reflector 2-2. As shown in Figure 1, the composite parabolic reflector 2-2 is placed inside the frame 2-1. A glass cover plate 2-6 is added to the upper end of the frame 2-1 to reduce convective heat transfer between the environment and the flat plate receiver. The composite parabolic reflector 2-2 adopts a uniform segmented design, including multiple sub-reflectors, so that the parabolic focal lines of each sub-reflector segment are evenly distributed on the flat plate receiver 2-3. All light reflected by the composite parabolic reflector 2-2 is evenly distributed on the flat plate receiver 2-3, achieving a uniform energy flux density distribution on the flat plate receiver. The segments of the composite parabolic reflector 2-2 are connected in a row according to their numbers. The end of the sub-reflector of the previous segment is connected to the beginning of the next segment to form a whole. The initial segment of the whole is fixed to one segment of the flat plate receiver 2-3 to maximize its placement stability.

[0052] like Figure 3 As shown, a two-dimensional rectangular coordinate system is established using the XY coordinate plane, which is perpendicular to the focal line of the parabolic reflecting surface of each segmented sub-mirror and the receiving surface of the flat plate receiver, as shown. Figure 3 With point O as the origin, the vertical axis is the Y-axis, and the horizontal axis is the X-axis. Regardless of whether a tracking device is added, the incident light at noon is perpendicular to the receiving surface of the flat plate (2-3), and this is used as the analysis time for the condenser. The segmented CPC profile on the XY coordinate plane consists of five segments: AB, BC, CD, DE, and EF. The focal lines of the parabolic surfaces of each segment's sub-reflector are on the same plane, and the vertical axes of each segment's parabolic surface are perpendicularly upward and parallel to each other. Taking the leftward direction of the Y-axis as the positive direction, the sub-reflectors are numbered i sequentially, with segment AB being the starting number 1. The initial x-coordinate of the i-th segment's sub-reflector is defined as X... i The vertical axis is Y i Therefore, the initial coordinates (X) of the i-th sub-mirror are given. i Y i Given initial conditions AO=40 and concentration ratio C=6, the incident plane FF'=240. Dividing the incident plane into equal segments, the initial coordinates of the first segment are (20, 0), and the initial x-coordinates of subsequent segments are... Since the focal points are evenly distributed on the receiving surface 2-3 of the flat plate, the coordinates of each focal point segment can be obtained sequentially as (-2, 0), (-6, 0), (-10, 0), (-14, 0), and (-18, 0). The vertical axes of the parabolic surfaces of each sub-reflector are perpendicular and parallel to each other, so the x-coordinate of the vertex of the sub-reflector parabola is consistent with the x-coordinate of the focal point.

[0053] Assume the equation of the profile of the i-th sub-mirror 2-1 in the XY coordinate system is 2P. i (Yb i )=(Xa i ) 2 The equation of the parabolic profile of the i-th sub-mirror in the XY plane is determined by the following formula:

[0054] (1)

[0055] (2)

[0056] (3)

[0057] The initial x-coordinate of the i-th segmented reflector:

[0058] (4)

[0059] The initial coordinates of the (i+1)th segmented reflector:

[0060] (5)

[0061] The initial point of the first segmented reflector is known:

[0062] (6)

[0063] In the formula: , Let be the vertex parameters of the parabolic equation of the i-th sub-mirror in the XY plane.

[0064] , Let be the initial point parameters of the parabolic equation expression for the i-th sub-mirror in the XY plane.

[0065] , , which represents the termination point parameter of the parabolic equation expression of the i-th sub-mirror in the XY plane, and also the initial point parameter of the parabolic equation expression of the (i+1)-th sub-mirror segment in the XY plane.

[0066] C represents the focusing ratio of the segmented parabolic concentrator;

[0067] P i Let be the quasi-focal length of the parabolic equation of the i-th sub-mirror in the XY plane.

[0068] Substituting equations (6), (2), and (1) into equation (3), the parabolic equation of the first sub-mirror in the XY plane can be obtained. Substituting equation (5) into the equation of the first sub-mirror, the initial coordinates of the parabola of the next sub-mirror in the XY plane can be obtained. Similarly, by iterating in sequence, the parabolic equation expression of each sub-mirror in the XY two-dimensional rectangular coordinate system can be determined, as well as the initial and final coordinates of the intercepts of all parabolic surfaces in the XY two-dimensional rectangular coordinate system. , () , This determines the installation position of the sub-reflector. Specific parameters for the example are shown in Table 1 below:

[0069] Table 1. Parameters of each segment of the reflector

[0070] initial point coordinates End point coordinates Vertex coordinates Focus coordinates <![CDATA[Quasi-focal length p i > First paragraph （20，0） （40，29.090） （-2，-11） （-2，0） 22 Second paragraph （40，29.090） (60，73.296） （-6，-12.667） （-6，0） 25.334 Third paragraph (60，73.296） （80，130.325） （-10，-14.068） （-10，0） 28.136 Fourth paragraph （80，130.325） （100，198.830） （-14，-15.181） （-14，0） 30.362 Fifth paragraph （100，198.830） （120，277.895） （-18，-16.189） （-18，0） 32.378

[0071] The first part of the equation is: 44(y+11) = (x+2) 2

[0072] The second equation is: 50.668(y+12.667)=(x+6) 2

[0073] The third equation is: 56.272(y+14.068) = (x+10) 2

[0074] The fourth equation: 60.724(y+15.181) = (x+14) 2

[0075] The fifth equation: 64.756(y+16.189)=(x+18) 2

[0076] The above description is merely a preferred embodiment of this disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this disclosure is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features disclosed in this disclosure that have similar functions.

Claims

1. A segmented CPC solar concentrator, characterized in that, The utility model relates to a kind of segmented parabolic concentrator, including: Frame (2-1), compound parabolic reflector (2-2), flat plate receiving surface (2-3), incident surface (2-4); Compound parabolic reflector (2-2) is fixed in frame (2-1);Compound parabolic reflector (2-2) is symmetrically placed on both sides of flat plate receiving surface (2-3); The flat plate receiving surface (2-3) is the heat-absorbing surface of flat plate-like light-receiving body; Compound parabolic reflector (2-2) is composed of multiple sub-mirrors, each sub-mirror is sequentially connected head to tail, and the focal line generated by each sub-mirror on flat plate receiving surface (2-3) is evenly arranged from the middle to both sides, and the focal line positions of each sub-mirror are different, and the focal lines are parallel to each other.

2. A segmented CPC solar concentrator according to claim 1, characterized in that, The flat plate receiving surface (2-3) is provided with a backing plate (2-5) below, and the frame (2-1) is provided with a glass cover plate (2-6) on the top.

3. A method of designing a segmented CPC solar concentrator according to claim 1 or 2, characterized in that, The utility model relates to a kind of segmented parabolic concentrator, including the following steps: S1, determine the number of segments: Given the segmented parabolic concentrator ratio C, i.e. the ratio of the area of incident surface (2-4) to the area of flat plate receiving surface (2-3) is C;The number of sub-mirrors on each side of flat plate receiving surface (2-3) is C-1; S2, determine the focal line arrangement: Each sub-mirror generates an independent focal line, and compound parabolic reflector (2-2) is symmetric on both sides, with 2 (C-1) focal lines evenly distributed on flat plate receiving surface (2-3);Each sub-mirror on one side is sequentially connected head to tail, and the focal line generated by each sub-mirror on flat plate receiving surface (2-3) is evenly arranged from the middle to both sides; S3, the equation of each parabolic segment line: The width of the flat receiving surface (2-3) in the given segmented concentrator is 2L, the sub-mirrors of the compound parabolic mirror (2-2) are connected end to end in turn, and the initial segment is fixed at the side of the flat receiving surface (2-3); the X-Y two-dimensional rectangular coordinate system is established with the midpoint of the flat receiving surface (2-3) as the origin, the X-Y coordinate plane is perpendicular to the focal line of each sub-mirror and the flat receiving surface (2-3), the intersection line of the X-Y coordinate plane and the flat receiving surface (2-3) is the X axis, and the intersection line of the X-Y coordinate plane and the symmetry plane of the concentrator is the Y axis; the sub-mirrors are numbered i from bottom to top, the starting segment is No. 1, and the coordinates of the initial endpoint of the intersection segment of the i-th sub-mirror on the X-Y coordinate plane are defined as (x i , y i ), since the adjacent sub-mirrors have a side in a straight line, the terminal point of the intersection segment of the i-th sub-mirror on the X-Y coordinate plane and the initial endpoint of the intersection segment of the i+1-th sub-mirror on the X-Y coordinate plane have the same coordinates (x i+1 , y i+1 ); assuming that the equation of the profile line of the i-th segmented sub-mirror on the X-Y coordinate system is 2P i (Y-b i )=(X-a i ) 2 , since the focal point of the sub-mirror focal line on the X-Y coordinate plane is on the X axis, and the focal point and the vertex of the sub-mirror have the same horizontal coordinate, the focal point coordinates of the i-th sub-mirror are (a i , 0), according to the properties of the parabola, the vertex and the focal point are located on the same vertical axis, and the difference in vertical coordinates is the focal length, which is half of the focal length P i ; the parabolic profile equation of the i-th segmented sub-mirror on the X-Y plane is determined by the following formula: （1） The focal line of the left sub-reflector is arranged at the right half of the symmetric plane of the flat receiving surface (2-3), and the focal line of the right sub-reflector is arranged at the left half of the symmetric plane of the flat receiving surface (2-3); since there are i sub-reflectors on each side, there are 2i focal lines on the flat receiving surface (2-3), and the width of the flat receiving surface (2-3) is 2L, so the distance between the adjacent two focal lines is ; n is the total number of single-sided sub-reflectors; therefore, the focal point coordinates of the i-th sub-reflector are , the focal point of the profile line is positive on the right side of the y-axis and negative on the left side; the vertex horizontal coordinate is consistent with the focal point horizontal coordinate, so the vertex horizontal coordinate is: （2） （3） The horizontal coordinate of the initial point of the i-th segmented sub-mirror: （4） The coordinate of the initial point of the i+1-th segmented sub-mirror: ， （5） The initial point of the first segmented sub-mirror is known: （6） In the formula: , is the vertex parameter of the parabolic equation expression of the ith segment sub-mirror on the X-Y plane; , Xi is the initial point parameter of the parabolic equation expression of the i-th segment sub-mirror on the X-Y plane; , is the termination point parameter of the parabolic equation expression of the ith segmented sub-mirror on the X-Y plane; it is also the initial point parameter of the parabolic equation expression of the (i+1)th segmented sub-mirror on the X-Y plane; P i focal length of the parabolic equation expression of the i-th segment sub-mirror in the X-Y plane; Substitute formula (6)(2)(1) into formula (3), the parabolic equation of the first sub-reflector in X-Y plane can be obtained; Substitute formula (5) into the first parabolic equation, the initial coordinates of the next sub-reflector in X-Y plane can be obtained, and the parabolic equation expression of each sub-reflector in X-Y two-dimensional rectangular coordinate system and the initial and final coordinates of the section line in X-Y two-dimensional rectangular coordinate system can be determined by iteration, thereby determining the installation position of the sub-reflector , ( , ), thereby determining the installation position of the sub-reflector When the multiple compound parabolic reflectors (2-2) are arranged, the starting position of the i+1-th parabolic mirror is located at the end position of the i-th mirror.

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