Medium and low latitude concentric circle mirror field layout optimization method with heat collection tower as center

Abstract

The invention discloses a medium and low latitude concentric circle mirror field layout optimization method taking a heat collection tower as a center. The method comprises the following steps: preparing before model establishment; sequentially establishing a heliostat reflection model, a heliostat cosine efficiency model, a heliostat shadow shielding efficiency model and a heliostat overflow efficiency model based on the working principle of the tower type solar photo-thermal power station; establishing a concentric circle mirror field layout optimization model taking the heat collection tower as the center; according to the method, an optical efficiency model of the heliostat is established based on a cosine efficiency model, a shadow shielding model and an overflow efficiency model of the heliostat by combining solar apparent motion parameters; a mirror field layout optimization model with a heat collection tower as the center is established, solution searching is carried out with the help of a genetic algorithm, so that an optimal combination scheme of detail parameters of the mirror field is obtained, the highest annual average optical efficiency is 65.9% under the condition that the rated power of the mirror field with the radius of 350 m is 60 MW, and if the rated power is not fixed, the maximum annual average output thermal power can reach 95.119 MW. And the maximum annual average optical efficiency can reach 73.1%.

Description

Technical Field

[0001] The present invention relates to the technical field of solar thermal power generation, and in particular to a method for optimizing the layout of concentric circle mirror fields centered on a heat collecting tower at mid- and low-latitudes. Background Art

[0002] With the advancement and deployment of the national sustainable development strategy, clean energy such as solar energy, wind energy, and tidal energy has gradually become the mainstay of the new energy system. Tower solar thermal power generation is a highly efficient solar energy capture device, but due to its relatively complex system and high overall cost, many scholars are still working hard on the difficult problem of how to improve the solar energy utilization rate of this technology.

[0003] The energy loss of tower-type solar thermal power plants mainly occurs in the energy storage stage and the energy collection stage. This paper mainly studies the energy collection stage of the power generation system. The heliostat field is the energy input unit of the entire system, and its comprehensive efficiency directly determines the highest performance of the power generation system. The significance of heliostat field optimization is to provide a reference for the operation of actual power plants, improve the efficiency of solar thermal power plants, reduce costs, and ensure the smooth, efficient and safe operation of power plants.

[0004] In recent years, most of the research on the layout of heliostat fields has established physical models for the existing initial mirror fields, and simulated and optimized the layout of the mirror fields with the help of programming methods. The current mainstream heliostat field layout methods include EB layout, unobstructed dense layout, DELSOL3 empirical fitting layout, optimized year-round unobstructed layout, etc. The above layout methods pay less attention to detailed parameters such as heliostat size, heliostat installation height, and collector tower installation position, which affects the efficiency of the mirror field and limits its annual maximum average optical efficiency. Summary of the invention

[0005] The purpose of the present invention is to provide a method for optimizing the layout of concentric circle mirror fields centered on a solar collector tower in mid- and low-latitudes. By studying the detailed parameters that affect the annual average output thermal power per unit area of ​​the mirror field, a nonlinear programming model is established, and the optimal concentric circle layout scheme for a 60MW rated power mirror field in mid- and low-latitudes is proposed.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0007] A method for optimizing the layout of concentric circle mirror fields centered on a heat collecting tower at mid- and low-latitudes comprises the following steps:

[0008] 1. Preparation before model establishment; 2. Establish the model, and establish the heliostat reflection model, heliostat cosine efficiency model, heliostat shadow shielding efficiency model and heliostat overflow efficiency model in sequence based on the working principle of the tower solar thermal power station; 3. Establish a concentric circle mirror field layout optimization model centered on the collector tower;

[0009] In step 1, prepare the apparent motion parameters of the sun, the solar declination angle equation, the normal direct radiation irradiance DNI equation, the heliostat field output efficiency equation, the heliostat optical efficiency equation, and the atmospheric transmittance equation;

[0010] Parameters of the Sun's apparent motion

[0011] Sun altitude angle α s It refers to the angle between the incident direction of sunlight and the horizon; the solar azimuth angle γ s That is, the direction of the sun, which can be roughly regarded as the angle between the shadow of a straight line erected on the ground under the sun and the south direction. The calculation method of the solar altitude angle and azimuth angle

[0012]

[0013]

[0014] Where: ω is the solar hour angle; is the local latitude; δ is the solar declination angle.

[0015] Solar Declination Equation

[0016]

[0017] Where: D is the number of days calculated by taking March 21, the spring equinox of 2023, as the 0th day and so on. To simplify the calculation, D only takes the representative 21st day of each month.

[0018] Normal direct radiation irradiance DNI equation

[0019]

[0020] Where: G 0 is the solar constant, which is 1.366kW / m 2 ; H is the altitude (in km). At an altitude of 3 km, 98.5°E, 39.4°N as the center of the heliostat field, the annual average DNI is calculated to be 968W / m 2 .

[0021] Heliostat Field Output Efficiency Equation

[0022]

[0023] Where: N is the total number of heliostats; A i is the lighting area of ​​the i-th heliostat (unit: m 2 );η i is the optical efficiency of the i-th heliostat.

[0024] Therefore, the annual thermal power output equation of the heliostat field is:

[0025]

[0026] Wherein: ST is 6 times every day: 9:00, 10:30, 12:00, 13:30, and 15:00.

[0027] Optical efficiency equation of heliostat

[0028] η=η shadow η cos η at η spill η ref (7)

[0029] Where: η shadow is the shadow occlusion efficiency; η cos is the cosine efficiency; η at is the atmospheric projection rate; η spill is the cutoff efficiency; η ref is the heliostat mirror reflectivity, taken as 0.92

[0030] The optical efficiency equation of this case adds the consideration of shadow blocking efficiency.

[0031] Atmospheric Transmittance Equation

[0032]

[0033] Where: d HR It represents the distance from the center of the mirror to the center of the collector, which can be solved by the coordinate distance of the two points.

[0034] Heliostat reflection model in step 2

[0035] With point D as the center point of the heliostat, establish the ground coordinate system (X so ,Y so ,Z so ), Z so The axis is due north, X so Axis and Y so The plane where the axis is located passes through the center point D of the heliostat, and Q is the center point of the collector tower. is the unit vector pointing from the center of the heliostat to the sun, is the unit vector from the center of the heliostat to the collector tower, for and The heliostat heading vector after superposition,

[0036] Models such as Figure 1 As shown, let point D (x c ,y c ,zc ), Q point (x q ,y q ,z q ), z q is the vertical distance between the height of the collector tower and the heliostat. Combined with the law of the apparent motion of the sun, we can get and

[0037]

[0038]

[0039]

[0040] According to the law of light reflection, the azimuth angle γ of the heliostat can be calculated h and elevation angle α h , laying the foundation for the establishment of subsequent models.

[0041]

[0042]

[0043] Heliostat cosine efficiency model

[0044] The cosine efficiency of the heliostat is related to the unit vector that can pass the incident light. With reflected light The dot product calculation of the unit vector of , from the above reflection model, we can get the cosine value of 2 times the incident angle

[0045]

[0046] Finally, the cosine efficiency equation model is established based on the double angle formula in trigonometric functions.

[0047]

[0048] Where θ is the incident angle of the sun on the heliostat.

[0049] Heliostat shadowing efficiency model

[0050] The shadow shading problem is mainly related to the shading of incident light and reflected light. The ray tracing method is used to trace 50*50 rays to calculate the shadow shading efficiency between heliostats.

[0051] (1) In order to track the incidence, reflection, and landing points of light on different planes, the following coordinate system is established

[0052] ① Establish the incident coordinate system (X i ,Y i ,Zi ), Z i The axis is parallel to the sun's chief ray, X i Perpendicular to Z i Axis direction, Y i Axis perpendicular to X i Axis direction;

[0053] ② Establish the mirror coordinate system (X m ,Y m ,Z m ), Z m The axis coincides with the normal line of the heliostat center, X m The axis coincides with the horizontal axis of the heliostat, Y m Axis perpendicular to X m Axis direction;

[0054] ③ With the shadowed heliostat H shaded The center is the origin to establish the shadowed heliostat coordinate system (X o ,Y o ,X o ), Z o The axis points to the zenith, X o The Y axis points due south. o The axis points due east;

[0055] (2) In order to trace the mapping of light in each coordinate system, determine

[0056] Shadow Heliostat H shading For the shadowed heliostat H shaded To improve the occlusion efficiency, the following coordinate transformation matrices are used to realize the conversion of coordinates between different coordinate systems.

[0057] ① The ground coordinate system is mapped to the incident coordinate system (X i ,Y i ,Z i )

[0058]

[0059] ② The ground coordinate system is mapped to the mirror coordinate system (X m ,Y m ,Z m )

[0060]

[0061] ③Incident coordinate system (X i ,Y i ,Z i ) is mapped to the shadowed heliostat coordinate system (X o ,Y o ,Xo )

[0062]

[0063] (3) Determine H shading Is it true for H shaded Create shadows:

[0064] According to the transformation matrix listed above, H shading In the ground coordinate system (X so ,Y so ,Z so ) along the incident direction, projected step by step to H shaded , the shadow condition is

[0065]

[0066] Where: h w ,h l H shaded The width and height of the mirror; Z i H shaded Z coordinate in the incident coordinate system; X mi , Y mi H shading The X and Y coordinates in the coordinate system of the shadowed heliostat;

[0067] If equation (19) is satisfied, the proportion of unblocked rays (num) in the 50*50 ray matrix tracked is counted, and the shadow blocking efficiency is obtained as shown in equation (20). Otherwise, H is calculated. shaded The shadow occlusion efficiency is 1 (no occlusion occurs);

[0068]

[0069] Heliostat spillover efficiency model

[0070] The spillover efficiency model is established by using the integral method;

[0071] In reality, sunlight is a cone of light with a certain cone angle. Based on the mirror imaging principle and the cosine theorem, the imaging equation of the elliptical spot at the center of the collector tower is given:

[0072]

[0073] Where: R is the equivalent circular radius of the square heliostat (unit: m); α τ is the apparent height angle of the collector tower; τ is the azimuth of the heliostat relative to the collector tower.

[0074] The heliostat spillover efficiency equation is established by double integration of the points falling within the collector and the spot ellipse.

[0075]

[0076] Where: σ is the solar half angle, which is 16′.

[0077] Initial mirror field simulation

[0078] In order to facilitate reference when optimizing the heliostat field, the initial mirror field situation before optimization (due to the need to build energy storage and control plant, no heliostats are set within a radius of 100m around the collector tower) is simulated.

[0079] Based on the SolarPILOT simulation software and MATLAB software, the mainstream mirror field layout forms are simulated and analyzed. Through modeling and simulation, the mathematical model and arrangement rules of the layout are analyzed. The number of heliostats and the average annual optical efficiency performance indicators of the heliostat field are compared under the conditions of concentric circle optimization layout, EB layout, DELSOL3 empirical fitting layout and unobstructed intensive layout under a fixed rated power of 60WM.

[0080] Step 3: Establish a concentric circle mirror field layout optimization model centered on the collector tower

[0081] (1) Determine the location of the collector tower

[0082] In order to determine the influence of the movement of the collector tower in the east-west direction (along the x-axis) and the north-south direction (along the y-axis) on the average optical efficiency, MATLAB software was used to simulate the average optical efficiency of different collector tower positions on the vernal equinox (March 21). In the initial mirror field layout data, the horizontal and vertical coordinates were set in the range of [-350, 350], and the step size was set to 50 for traversal.

[0083] Determine the optimal location of the collector tower through the efficiency map.

[0084] When the collector tower coordinates only move along the x-axis, the average optical efficiency of the heliostat field changes very little. Therefore, this case focuses on studying the best efficiency achieved when the collector tower coordinates move along the y-axis. It can be seen intuitively from the efficiency map that when the collector tower vertical coordinate is in the interval [-350, -120], it has a higher average optical efficiency.

[0085] The solar collector tower is traversed in the north-south interval [-350, -120] with a step length of 10 to observe the changes in the average optical efficiency throughout the year. The annual average optical efficiency of the mirror field shows an upward trend in the range of -120 to -280 of the vertical coordinate of the solar collector tower. Since the southernmost installation position of the solar collector tower in the mirror field is (0, -250), the optimal placement coordinate of the solar collector tower is (0, -250).

[0086] (2) Heliostat width and length (l)

[0087] At present, heliostats are generally circular or rectangular. When the spacing is sufficient and there is no mechanical collision, the square has a larger lighting area. Therefore, the mirror field adopts the layout of square heliostats of the same size, with the side length limited to [2m, 8m].

[0088] (3) Heliostat installation height (h)

[0089] The case where the installation height of each heliostat is the same is discussed, and the range of the installation height of the heliostat is limited to [2m, 6m].

[0090] Installation location of the collector tower (CT x ,CT y )The best installation position of the solar tower is (0,-250).

[0091] (4) The distance between the centers of adjacent heliostat bases in each ring of the mirror field (△ dist )

[0092] The △ dist As small as possible, and considering that the heliostat needs to be accessible for maintenance and cleaning, this case is in △ dist At least 5 meters wider than the heliostat width, add △ 1 Meters are optimized.

[0093] △ dist =1+5+△ 1 (△ 1 ∈(0.1m,20m]) (23)

[0094] (5) The spacing between adjacent heliostat rings in the field (△ r )

[0095] Considerations r The value of should be chosen so that the number of heliostat rings is as large as possible while achieving the maximum annual average shadow shielding efficiency, annual average truncation efficiency, and annual average cosine efficiency, while considering the minimum distance constraint between adjacent heliostats in (4.2.4).

[0096] △ r =1+5+△ 2 (△ 2 ∈(0.1m,20m]) (24)

[0097] Based on the above constraints, determine the number of heliostats N

[0098]

[0099] Where: C is the number of heliostat rings, n iis the number of heliostats on the ith ring. The number of heliostat rings C is related to the interval between adjacent heliostat rings.

[0100]

[0101] From this, we can infer the number of heliostats in each ring.

[0102]

[0103] Where: i is the i-th ring heliostat; θ i is the angle between two adjacent heliostats in the i-th ring; ri is the interval between adjacent heliostats on the ith ring.

[0104] In actual situations, there is a vacuum zone with a cutoff efficiency of 0 near the collector tower, and workshops for installing power generation, energy storage, control and other equipment must be reserved around the collector tower. Therefore, in actual applications, heliostats will not be installed in a circular area with a radius of 100 with the collector tower as the center, and heliostats that meet the following distance conditions should be eliminated.

[0105] d i ≤100 (28)

[0106] Where: d i is the center of the i-th heliostat and (CT x ,CT y ) is the Euclidean distance between .

[0107] (6) Mathematical model for optimizing the layout of concentric circle mirror field with the collector tower as the center

[0108] According to the layout characteristics of heliostats, regular sampling is performed on each heliostat ring, and an optimization solution is obtained based on the genetic algorithm according to the sampling results.

[0109] A nonlinear single-objective programming equation is established to solve the maximum annual average output thermal power per unit area of ​​the mirror under a fixed rated power of 60MW.

[0110]

[0111] Use the MATLAB genetic algorithm toolbox, set the number of iterations to 10, and the population size to 20 for optimization. The optimal solution is

[0112]

[0113] Through formula (30), the detailed design parameters of the optimal mirror field layout under rated power can be calculated.

[0114] If the optimization is continued to seek the maximum annual average thermal output power on the basis of satisfying the rated power of 60MW, the restriction on the range of annual average thermal output power in the nonlinear single-objective programming equation should be removed.

[0115]

[0116]

[0117] Using the MATLAB genetic algorithm toolbox, the genetic algorithm population number was set to 10, the number of iterations was set to 20, and 10 groups of data were taken from the optimal solution at a fixed rated power as the custom initial population. Through the optimization process, it can be inferred that when this layout optimization method seeks the maximum efficiency of the heliostat field, it should ensure that the lighting area of ​​the mirror field is maximized and the installation height of the heliostat is as low as possible.

[0118] The beneficial effects of the present invention are:

[0119] Through the optimization method of concentric circle mirror field layout centered on the collector tower in the middle and low latitudes proposed in this case, the annual average optical efficiency of the optimized concentric circle mirror field layout centered on the collector tower reached 65.9%. Compared with the optimal layout scheme of heliostat size 3.5m*3.5m under the rated power of EB layout simulated by SolarPILOT software, the annual average optical efficiency increased by 2.4%, and the number of heliostats required by this scheme was reduced from 7432 required for EB layout to 1597, and the mirror field structure became more concise and ingenious.

[0120] Compared with the initial mirror field, the optimized mirror field has also achieved significant improvements in comprehensive efficiency and comprehensive power, including an increase of 15.23% in annual average cosine efficiency, 11.05% in annual average shadow shielding efficiency, 7.83% in annual average optical efficiency, and 0.064KW in annual average output thermal power per unit area.

[0121] If the rated power is 60MW, we continue to optimize to seek the maximum annual output thermal power. When the heliostat installation height is 2m, the length and width of the heliostat is 8m, 1 =0,△ 2 =0 (i.e., the distance between adjacent heliostats in the same heliostat ring is 13 m, and the distance between different heliostat rings is 13 m), the maximum annual average output thermal power is 95.119 MW, and the maximum annual average optical efficiency is 73.1%. BRIEF DESCRIPTION OF THE DRAWINGS

[0122] Figure 1 Schematic diagram of a heliostat reflection model in an embodiment of the present invention;

[0123] Figure 2 Schematic diagram of initial mirror field distribution in the present invention;

[0124] Figure 3 Schematic diagram of optical efficiency change;

[0125] Figure 4 This is a schematic diagram of the optimized layout of the embodiment of the present invention. DETAILED DESCRIPTION

[0126] The technical solution will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments.

[0127] (1) Preparation before model establishment

[0128] Parameters of the Sun's apparent motion

[0129] Sun altitude angle α s It refers to the angle between the incident direction of sunlight and the horizon; the solar azimuth angle γ s That is, the direction of the sun, which can be roughly regarded as the angle between the shadow of a straight line erected on the ground under the sun and the south direction. The calculation method of the solar altitude angle and azimuth angle

[0130]

[0131]

[0132] Where: ω is the solar hour angle; is the local latitude; δ is the solar declination angle.

[0133] Solar Declination Equation

[0134]

[0135] Where: D is the number of days calculated by taking March 21, the spring equinox of 2023, as the 0th day and so on. To simplify the calculation, D only takes the representative 21st day of each month.

[0136] Normal direct radiation irradiance DNI equation

[0137]

[0138] Where: G 0 is the solar constant, which is 1.366kW / m 2 ; H is the altitude (in km). At an altitude of 3 km, 98.5°E, 39.4°N as the center of the heliostat field, the annual average DNI is calculated to be 968W / m 2 .

[0139] Heliostat Field Output Efficiency Equation

[0140]

[0141] Where: N is the total number of heliostats; A i is the lighting area of ​​the i-th heliostat (unit: m 2 );η i is the optical efficiency of the i-th heliostat.

[0142] Therefore, the annual thermal power output equation of the heliostat field is:

[0143]

[0144] Wherein: ST is 6 times every day: 9:00, 10:30, 12:00, 13:30, and 15:00.

[0145] Optical efficiency equation of heliostat

[0146] η=η shadow η cos η at η spill η ref (7)

[0147] Where: η shadow is the shadow occlusion efficiency; η cos is the cosine efficiency; η at is the atmospheric projection rate; η spill is the cutoff efficiency; η ref is the heliostat mirror reflectivity, which is taken as 0.92. The optical efficiency equation of this case adds the consideration of shadow shielding efficiency.

[0148] Atmospheric Transmittance Equation

[0149]

[0150] Where: d HR It represents the distance from the center of the mirror to the center of the collector, which can be solved by the coordinate distance of the two points.

[0151] (2) Model building

[0152] According to the working principle of tower solar thermal power station and based on the heliostat reflection model, the heliostat cosine efficiency model, heliostat shadow efficiency model and heliostat overflow efficiency model are established in sequence.

[0153] Heliostat Reflectance Model

[0154] With point D as the center point of the heliostat, establish the ground coordinate system (X so ,Y so ,Z so ), Z so The axis is due north, X so Axis and Y soThe plane where the axis is located passes through the center point D of the heliostat, and Q is the center point of the collector tower. is the unit vector pointing from the center of the heliostat to the sun, is the unit vector from the center of the heliostat to the collector tower, for and The heliostat heading vector after superposition,

[0155] Models such as Figure 1 As shown, let point D (x c ,y c ,z c ), Q point (x q ,y q ,z q ), z q is the vertical distance between the height of the collector tower and the heliostat. Combined with the law of the apparent motion of the sun, we can get and

[0156]

[0157]

[0158]

[0159] According to the law of light reflection, the azimuth angle γ of the heliostat can be calculated h and elevation angle α h , laying the foundation for the establishment of subsequent models.

[0160]

[0161]

[0162] Heliostat cosine efficiency model

[0163] The cosine efficiency of the heliostat is related to the unit vector that can pass the incident light. With reflected light The dot product calculation of the unit vector of , from the above reflection model, we can get the cosine value of 2 times the incident angle

[0164]

[0165] Finally, the cosine efficiency equation model is established based on the double angle formula in trigonometric functions.

[0166]

[0167] Where θ is the incident angle of the sun on the heliostat.

[0168] Heliostat shadowing efficiency model

[0169] The shadow shading problem is mainly related to the shading of incident light and reflected light. The ray tracing method is used to trace 50*50 rays to calculate the shadow shading efficiency between heliostats.

[0170] (1) In order to track the incidence, reflection, and landing points of light on different planes, the following coordinate system is established

[0171] ① Establish the incident coordinate system (X i ,Y i ,Z i ), Z i The axis is parallel to the sun's chief ray, X i Perpendicular to Z i Axis direction, Y i Axis perpendicular to X i Axis direction;

[0172] ② Establish the mirror coordinate system (X m ,Y m ,Z m ), Z m The axis coincides with the normal line of the heliostat center, X m The axis coincides with the horizontal axis of the heliostat, Y m Axis perpendicular to X m Axis direction;

[0173] ③ With the shadowed heliostat H shaded The center is the origin to establish the shadowed heliostat coordinate system (X o ,Y o ,X o ), Z o The axis points to the zenith, X o The Y axis points due south. o The axis points due east;

[0174] (2) In order to trace the mapping of light in each coordinate system, determine

[0175] Shadow Heliostat H shading For the shadowed heliostat H shaded To improve the occlusion efficiency, the following coordinate transformation matrices are used to realize the conversion of coordinates between different coordinate systems.

[0176] ① The ground coordinate system is mapped to the incident coordinate system (X i ,Y i ,Z i )

[0177]

[0178] ② The ground coordinate system is mapped to the mirror coordinate system (Xm ,Y m ,Z m )

[0179]

[0180] ③Incident coordinate system (X i ,Y i ,Z i ) is mapped to the shadowed heliostat coordinate system (X o ,Y o ,X o )

[0181]

[0182] (3) Determine H shading Is it true for H shaded Create shadows:

[0183] According to the transformation matrix listed above, H shading In the ground coordinate system (X so ,Y so ,Z so ) along the incident direction, projected step by step to H shaded , the shadow condition is

[0184]

[0185] Where: h w ,h l H shaded The width and height of the mirror; Z i H shaded Z coordinate in the incident coordinate system; X mi , Y mi H shading The X and Y coordinates in the coordinate system of the shadowed heliostat;

[0186] If equation (19) is satisfied, the proportion of unblocked rays (num) in the 50*50 ray matrix tracked is counted, and the shadow blocking efficiency is obtained as shown in equation (20). Otherwise, H is calculated. shaded The shadow occlusion efficiency is 1 (no occlusion occurs);

[0187]

[0188] Heliostat spillover efficiency model

[0189] There are two mainstream methods for calculating the heliostat spillover efficiency. One method uses the Monte Carlo ray tracing method to simulate the focusing process of the heliostat field; the other method simulates the spot image on the receiver plane and uses the integral method to obtain the spillover efficiency. If the first calculation method is used, higher accuracy will be obtained, but it involves complex tracking processes and mirror condition analysis, and the calculation cost is very expensive, and it does not have the ability to handle large-scale mirror field rapid optimization tasks.

[0190] Therefore, this case adopts the more practical integral method to establish the spillover efficiency model.

[0191] In reality, sunlight is a cone of light with a certain cone angle. Based on the mirror imaging principle and the cosine theorem, the imaging equation of the elliptical spot at the center of the collector tower is given:

[0192]

[0193] Where: R is the equivalent circular radius of the square heliostat (unit: m); α τ is the apparent height angle of the collector tower; τ is the azimuth of the heliostat relative to the collector tower.

[0194] The heliostat spillover efficiency equation is established by double integration of the points falling within the collector and the spot ellipse.

[0195]

[0196] Where: σ is the solar half angle, which is 16′.

[0197] (3) Initial mirror field simulation

[0198] In order to facilitate the reference when optimizing the heliostat field, this case uses the parameter information listed in Table 1 as the initial mirror field situation before optimization (due to the need to build energy storage and control plant, no heliostats are set within a radius of 100m around the collector tower). Figure 3 At this time, there are 1745 heliostats, with an annual average cosine efficiency of 76%, an annual average shadowing efficiency of 88.9%, an annual average truncation efficiency of 96.7%, an annual average optical efficiency of 58.1%, and an annual average thermal output per unit area of ​​0.567kW / m 2 The average annual thermal output power is 35.59MW.

[0199] Table 1 Initial mirror field parameters

[0200]

[0201]

[0202] Simulate and analyze the mainstream mirror field layout based on SolarPILOT simulation software

[0203] Mirror field layout modeling

[0204] DELSOL3 empirical fitting layout method

[0205] This layout method is based on DELSOL3 software, combining multiple factors that affect the spacing between heliostats, such as the radial distance from the heliostat to the collector tower, the height of the heliostat, the area of ​​the heliostat, the shape of the heliostat, etc., and through continuous simulation fitting, the radial distance and azimuth distance of the heliostat are determined.

[0206] EB layout method

[0207] The principle of the EB layout is to change the radial distance between adjacent rings to ensure that the reflected light of the far heliostat will not be blocked by the near heliostat between two radially adjacent heliostats, and at the same time to ensure that the heliostats on the same ring will not interfere with each other. In the EB layout, as the radial distance increases, the elevation angle of the tangent will gradually decrease. To avoid blocking, the EB layout increases the distance between the heliostats on adjacent rings. At this time, the adjacent heliostats on adjacent rings will have a certain offset to reduce the mutual interference between each heliostat.

[0208] Unobstructed dense layout

[0209] The non-blocking dense layout is a variant of the EB layout. The spacing between the rings in the EB layout is determined by calculating the radial distance of each row of rings from the collector tower. However, for heliostats that are closer to the collector tower (inner circle), the radial spacing is usually determined by the maximum radius to avoid collision. While ensuring that the reflected light of the heliostat is not affected by the shading of other heliostats, the inner circle heliostats are arranged as closely as possible. As the radial distance between the rings increases, until the shadow shading efficiency decreases, the EB layout is replaced. Compared with the EB layout, the non-blocking dense layout can effectively improve the land utilization rate of the mirror field.

[0210] Mirror field layout design and optimization

[0211] The tower CSP power station simulation optimization software SolarPILOT was used to model and simulate the above three layout methods of the mirror field, and the mathematical model and arrangement rules of the layout were studied and analyzed. The performance indicators such as the number of heliostats and annual average optical efficiency of the heliostat field under the three different layouts were compared.

[0212] According to the software, simulation research is carried out. The specific ideas are to select the mirror field layout model, input design parameters, generate the initial mirror field layout, set constraints, calculate the objective function, and complete the mirror field layout design. According to the DNI and other parameters obtained above, the SolarPILOT software is used to automatically calculate and generate the mirror field. At the same time, the three layout methods are compared, and the layout method with the highest efficiency is selected. The annual average optical efficiency η of the mirror field is used as the objective function, and the annual output thermal power of the heliostat field is used as the constraint condition for calculation and analysis. Find the layout with the highest annual average efficiency of the mirror field under the condition of meeting the rated output power of the heliostat.

[0213] The constraint function of the mirror field layout is shown in formula (23):

[0214]

[0215] The objective function of the mirror field layout, that is, the average annual efficiency of the mirror field, is given by formula (24).

[0216]

[0217] Where: is the annual average optical efficiency of heliostat i.

[0218] The simulation results of SolarPILOT software show that each layout is symmetrical from east to west. The heliostats with higher efficiency are concentrated in the northern and inner areas of the mirror field, while the annual average optical efficiency in the southern and outer areas of the mirror field is lower.

[0219] Combined with the position of the sun, the heliostats distributed in the northern part of the mirror field have higher cosine efficiency than those in the southern part, because the angle between the incident solar light and the normal of the heliostat surface is smaller; the heliostats in the inner circle of the mirror field also have higher cosine efficiency than those in the outer circle, so the overall annual average optical efficiency is higher.

[0220] In addition, by observing the distribution of optical efficiency, it is found that the efficiency of the heliostats is very low where the various areas in the mirror field intersect, because the intersection area is greatly affected by shadows and occlusion losses.

[0221] Comparison and analysis of three mirror field layouts

[0222] Through the above mirror field simulation results, the differences between the three mirror field layouts are compared to find the best mirror field layout. The relevant data comparison data of each layout are as follows: the number of heliostats in the EB layout is 7432, and the annual average optical efficiency is 63.5%; the number of heliostats in the unobstructed dense layout is 7621, and the annual average optical efficiency is 63.2%; the number of heliostats in the DELSOL3 empirical fitting layout is 7508, and the annual average optical efficiency is 62.9%.

[0223] Analysis of the number of heliostats in different layouts

[0224] According to the comparison results of the number of heliostats under different mirror field layouts, the EB layout has the least number of heliostats, followed by the DELSOL3 empirical fitting layout, and the unobstructed dense layout has the largest number of heliostats.

[0225] The main reasons for this result are as follows: When the size of the heliostats is small, there is basically no difference between the EB layout and the unobstructed dense layout. The heliostats in the unobstructed dense layout are arranged more densely and the annual average optical efficiency is lower, so there are more heliostats. The annual average optical efficiency of the DELSOL3 empirical fitting layout is the lowest. In order to achieve the output thermal power of the heliostat field, a large number of heliostats are required.

[0226] Analysis of annual average optical efficiency of different layouts

[0227] 2) Analysis of annual average optical efficiency of different layouts In the unobstructed intensive layout, the mirrors are arranged more compactly and the shadow blocking efficiency is taken into account, so the annual average efficiency is higher. However, in the DELSOL3 empirical fitting layout, the heliostats are more dispersed in distribution and the heliostats are far away from the collector tower, so the cosine efficiency is lower, resulting in low efficiency of the DELSOL3 empirical fitting layout.

[0228] Based on the above analysis of the three layout methods, the following conclusions can be drawn:

[0229] The DELSOL3 empirical fitting layout has the lowest optical efficiency and requires a large number of heliostats. The heliostat field requires a high cost but low optical efficiency, resulting in a low annual average thermal output power, which is significantly different from the other two layouts. It is concluded that the unobstructed dense layout and EB layout are better than the DELSOL3 empirical fitting layout. Compared with the EB layout, the unobstructed dense layout has a denser arrangement of heliostats in the inner circle, and the optics of the inner circle are also lower. Combined with the actual situation, the inner circle heliostats of the unobstructed dense layout are too dense, which is not conducive to the cleaning, disassembly and replacement of the heliostats, and will also affect the traffic efficiency of the vehicles repairing the inner circle of the heliostats.

[0230] Except for the atmospheric attenuation efficiency, the other efficiencies of the EB layout are slightly higher than those of the unobstructed dense layout, and the annual average optical efficiency of the EB layout is also higher than that of the unobstructed dense layout. Taking into account the optical efficiency, layout conditions and other factors, the EB layout is the best among the three mainstream layout methods.

[0231] The SolarPILOT software can simulate the detailed layout of a high-efficiency solution when the heliostat size, latitude, rated power and other parameters are specified. However, it is difficult to optimize key parameters such as heliostat size, height, and spacing.

[0232] In order to explore the optimal position of the solar tower and the optimal distance between the center points of the heliostats under different conditions, scholars have conducted a lot of research. Lipps and Vanthull from the University of Houston in the United States proposed a heliostat layout plan based on radial grid distribution. This distribution design usually arranges the reflectors in order on concentric circles with the center of the bottom of the solar tower as the center while ensuring a radial spacing, so as to achieve the effect of reducing shading losses.

[0233] Subsequently, Pylkanen optimized the sorting method by drawing pictures and proposed a layout plan that was unobstructed throughout the year.

[0234] The year-round unobstructed layout plan stipulates that the distance between the first row of reflectors and the tower is the tower height, ensuring that the front row does not block the reflected light of the rear row of heliostats.

[0235] The radial grid distribution and the year-round unobstructed layout can effectively solve the problem of obstruction of reflected light in the radial direction between heliostats to a certain extent. However, since the time variation has a great influence on the solar azimuth, the above two methods are difficult to solve the problem of incident light being blocked.

[0236] Based on the year-round unobstructed layout plan, a technician proposed an optimization method, which uses concentric circles drawn based on efficiency to optimize the mirror field layout. According to their research on efficiency and latitude distribution, it is known that the high-efficiency distribution area of ​​heliostats is related to latitude. Low-latitude areas can be fitted into a circle, mid-latitude areas can be fitted into a fan shape, and areas close to the equator can be fitted into an ellipse. The design steps are as follows.

[0237] Step 1: According to the total efficiency of the heliostats in the north-south direction of the collector tower, the efficiency is greater than 70%, and the approximate range is obtained.

[0238] Step 2: According to the interval range of Step 1, draw a circle M through the minimum and maximum values ​​so that the diameter of the circle falls in the due south and due north directions; if the interval range is a union, it is necessary to draw a circle N through the second largest and second smallest values ​​of the interval, and finally take the M circle range obtained by excluding the range where the N circle is located as the preferred range of the heliostat.

[0239] Step 3: Take the center of circle M as the reference, draw several concentric circles, and the difference of the radius of the concentric circles is a fixed value, so as to determine the number of heliostat rings.

[0240] Step 4: Determine the number of heliostats in each ring by taking the horizontal spacing between the center points of two heliostats as 3 times the width of the heliostat.

[0241] Step 5: Set the heliostat width and tower height. Through the above steps, the radial spacing, the number of heliostat rings, and the number of heliostats can be obtained, and finally the distribution of heliostats can be obtained.

[0242] MATLAB software was used to simulate and analyze the results. MATLAB software was used to simulate and discuss the layout of the solar collector tower when it was located in the center of the mirror field and when it was located 85 meters south of the center of the mirror field. It was found that the optical efficiency and the annual average output thermal power of the heliostat field can be significantly improved by adjusting the position of the solar collector tower. Therefore, the optimal installation position of the solar collector tower is given priority, and the size of the heliostat and the distance between the heliostats are optimized under the premise of comprehensively considering the annual average shadow shielding efficiency, the annual average cosine efficiency and the annual average truncation efficiency. The optimal layout scheme for the mid- and low-latitude mirror field at a rated power of 60MW is proposed.

[0243] Establishing a concentric circle mirror field layout optimization model centered on the collector tower

[0244] 1. Determine the location of the solar tower

[0245] In order to determine the influence of the movement of the collector tower in the east-west direction (along the x-axis) and the north-south direction (along the y-axis) on the average optical efficiency, MATLAB software was used to simulate the average optical efficiency of different collector tower positions on the vernal equinox (March 21). In the initial mirror field layout data, the horizontal and vertical coordinates were set in the range of [-350, 350], and the step size was set to 50 for traversal.

[0246] Through the efficiency map ( Figure 3 (a) It can be seen intuitively that when the collector tower coordinates only move along the x-axis, the average optical efficiency of the heliostat field changes very little. Therefore, we focus on studying the best efficiency achieved when the collector tower coordinates move along the y-axis. It can be seen intuitively from the efficiency map that when the collector tower ordinate is in the interval [-350, -120], it has a higher average optical efficiency.

[0247] The collector tower is traversed in the north-south interval [-350, -120] with a step length of 10, and the change of the average optical efficiency throughout the year is observed ( Figure 3 (b)), the annual average optical efficiency of the mirror field shows an upward trend in the range of -120 to -280 of the vertical coordinate of the solar collector tower. Since the southernmost installation position of the solar collector tower in this mirror field is (0, -250), the optimal placement coordinate of the solar collector tower is (0, -250).

[0248] Heliostat width and length (l)

[0249] At present, heliostats are generally circular or rectangular. When the spacing is sufficient and there is no mechanical collision, the square has a larger lighting area. Therefore, this case mainly studies the layout of square heliostats of the same size in the mirror field, with a side length range of [2m, 8m].

[0250] Heliostat installation height (h)

[0251] The case where the installation height of each heliostat is the same is discussed, and the range of the installation height of the heliostat is limited to [2m, 6m].

[0252] Installation location of the collector tower (CT x ,CT y )The best installation position of the solar tower is (0,-250).

[0253] The distance between the centers of adjacent heliostat bases in each ring of the mirror field (△ dist )

[0254] The △ dist As small as possible, and considering that the heliostat needs to be accessible for maintenance and cleaning, this case is in △ dist At least 5 meters wider than the heliostat width, add △ 1 Meters are optimized.

[0255] △ dist =1+5+△ 1 (△ 1 ∈(0.1m,20m]) (25)

[0256] The spacing between adjacent heliostat rings in the mirror field (△ r )

[0257] Considerations r The value of should be chosen so that the number of heliostat rings is as large as possible while achieving the maximum annual average shadow shielding efficiency, annual average truncation efficiency, and annual average cosine efficiency, while considering the minimum distance constraint between adjacent heliostats in (4.2.4).

[0258] △ r =1+5+△ 2 (△ 2 ∈(0.1m,20m]) (26)

[0259] Based on the above constraints, determine the number of heliostats N

[0260]

[0261] Where: C is the number of heliostat rings, n iis the number of heliostats on the ith ring. The number of heliostat rings C is related to the interval between adjacent heliostat rings.

[0262]

[0263] From this, we can infer the number of heliostats in each ring.

[0264]

[0265] Where: i is the i-th ring heliostat; θ i is the angle between two adjacent heliostats in the i-th ring; ri is the interval between adjacent heliostats on the ith ring.

[0266] In actual situations, there is a vacuum zone with a cutoff efficiency of 0 near the collector tower, and workshops for installing power generation, energy storage, control and other equipment must be reserved around the collector tower. Therefore, in actual applications, heliostats will not be installed in a circular area with a radius of 100 with the collector tower as the center, and heliostats that meet the following distance conditions should be eliminated.

[0267] d i ≤100 (30)

[0268] Where: d i is the center of the i-th heliostat and (CT x ,CT y ) is the Euclidean distance between .

[0269] Mathematical model for optimizing the layout of concentric circle mirror field with the collector tower as the center

[0270] Considering that there are many factors that affect the annual average thermal output power of the mirror field, the amount of calculation is extremely large. If the traversal method is used to solve it, it will take a very long time to calculate. Therefore, according to the characteristics of the heliostat layout, this case conducts regular sampling on each heliostat ring, and optimizes the solution based on the genetic algorithm according to the sampling results.

[0271] Table 2 Layout parameters

[0272]

[0273] The nonlinear single-objective programming equation for finding the maximum annual average thermal output power per unit area of ​​the mirror is established under the parameter conditions in Table 2.

[0274]

[0275] Use the MATLAB genetic algorithm toolbox, set the number of iterations to 10, and the population size to 20 for optimization. The optimal solution is

[0276]

[0277] Through formula (32), the detailed design parameters of the optimal mirror field layout under rated power can be calculated. The heliostat size is 7.78m*7.78m, the heliostat installation height is 2.92m, the total number of heliostats is 1597, and the distribution of the mirror field layout ( Figure 4 ). As shown in Table 3, the annual average optical efficiency of the optimized concentric circle mirror field layout centered on the collector tower reached 65.9%. Compared with the optimal layout scheme of 3.5m*3.5m heliostat size at rated power of EB layout simulated by SolarPILOT software, the annual average optical efficiency increased by 2.4%, and the number of heliostats required by this scheme was reduced from 7432 required for EB layout to 1597, and the mirror field structure became more concise and ingenious.

[0278] Compared with the initial mirror field, the optimized mirror field has also achieved significant improvements in comprehensive efficiency and comprehensive power. The annual average cosine efficiency has increased by 15.23%, the annual average shadow shielding efficiency has increased by 11.05%, the annual average optical efficiency has increased by 7.83%, and the annual average output thermal power per unit area has increased by 0.064KW.

[0279] If the rated power is 60MW, the optimization is continued to seek the maximum annual average thermal output power (see the optimization equation in formula 33), the number of genetic algorithm populations is set to 10, the number of iterations is set to 20, and 10 groups of data are taken from the optimal solution obtained in formula 32 as the custom initial population. It can be found from Table 4 that: Since this study is based on an unobstructed layout throughout the year, it should be ensured that △ 1 ,△ 2 The parameters and the installation height of the heliostat are as low as possible and the size of the heliostat is as large as possible to achieve the maximum number of heliostats and the maximum lighting area. 1 =0,△ 2 =0 (i.e., the distance between adjacent heliostats in the same heliostat ring is 13 m, and the distance between different heliostat rings is 13 m), the maximum annual average output thermal power is 95.119 MW, and the maximum annual average optical efficiency is 73.1%.

[0280]

[0281]

[0282] Table 3 Annual average optical efficiency and output power

[0283]

[0284] Table 4 Genetic algorithm optimization process table

[0285]

[0286] The present invention uses the linear relationship between the detailed parameters of the mirror field layout and the annual average output thermal power per unit area of ​​the mirror surface to establish a concentric circle layout optimization model centered on the collector tower. Compared with the initial mirror field, the optical efficiency of the optimized mirror field is improved by 15%, and at a rated power of 60MW, the optical efficiency of this layout method is 2.4%, 2.7%, and 3% higher than that of the EB layout, the unobstructed intensive layout, and the ELSOL3 empirical fitting layout, respectively.

[0287] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in the technical field, several improvements can be made without departing from the principles of the present invention. These improvements should also be regarded as the scope of protection of the present invention without paying creative labor.

Claims

1. A method for optimizing the layout of concentric circle mirror fields centered on a heat collecting tower at mid- and low-latitudes, characterized by: It includes the following steps: (1) Preparation before model establishment; (2) Model establishment, based on the working principle of tower solar thermal power station, establish the heliostat reflection model, heliostat cosine efficiency model, heliostat shadow shielding efficiency model and heliostat overflow efficiency model in sequence; (3) Establish a concentric circle mirror field layout optimization model centered on the collector tower; In step (1), the apparent motion parameters of the sun, the solar declination angle equation, the normal direct radiation irradiance DHI equation, the heliostat field output efficiency equation, the heliostat optical efficiency equation, and the atmospheric transmittance equation are prepared; Heliostat shadow shading efficiency model in step (2) The shadow occlusion problem is mainly related to the occlusion of incident light and reflected light. The ray tracing method is used to trace 50*50 rays to calculate the shadow occlusion efficiency between heliostats. In order to track the incidence, reflection and landing points of light on different planes, the following coordinate system is established: ① Establish the incident coordinate system (X i ,Y i ,Z i ), Z i The axis is parallel to the sun's chief ray, X i Perpendicular to Z i Axis direction, Y i Axis perpendicular to X i Axis direction; ② Establish the mirror coordinate system (X m ,Y m ,Z m ), Z m The axis coincides with the normal line of the heliostat center, X m The axis coincides with the horizontal axis of the heliostat, Y m Axis perpendicular to X m Axis direction; ③ With the shadowed heliostat H shaded The center is the origin to establish the shadowed heliostat coordinate system (X o ,Y o ,X o ), Z o The axis points to the zenith, X o The Y axis points due south. o The axis points due east; In order to trace the mapping of light in each coordinate system, determine the shadow heliostat H shading For the shadowed heliostat H shaded To improve the occlusion efficiency, the following coordinate transformation matrices are used to realize the conversion of coordinates between different coordinate systems. ① The ground coordinate system is mapped to the incident coordinate system (X i ,Y i ,Z i ) ② The ground coordinate system is mapped to the mirror coordinate system (X m ,Y m ,Z m ) ③Incident coordinate system (X i ,Y i ,Z i ) is mapped to the shadowed heliostat coordinate system (X o ,Y o ,X o ) Judge H shading Is it true for H shaded Create shadows: According to the transformation matrix listed above, H shading In the ground coordinate system (X so ,Y so ,Z so ) along the incident direction, projected step by step to H shaded , the shadow condition is Where: h w ,h l H shaded The width and height of the mirror; Z i H shaded Z coordinate in the incident coordinate system; X mi , Y mi H shading The X and Y coordinates in the coordinate system of the shadowed heliostat; If the above formula is satisfied, the proportion of unblocked light in the 50*50 light matrix tracked is counted, and the shadow blocking efficiency is obtained as shown in the following formula. Otherwise, H is calculated. shaded The shadow occlusion efficiency is 1; Step (3) includes ①Determine the location of the solar tower In order to determine the effect of the movement of the solar collector tower in the east-west and north-south directions on the average optical efficiency, MATLAB software was used to simulate the average optical efficiency of different solar collector tower positions during the spring equinox. In the initial mirror field layout data, the horizontal and vertical coordinates were set within the range of [-350, 350], and the step size was set to 50 for traversal; the optimal location of the solar collector tower was determined through the efficiency map; ②Width and length of heliostat The mirror field adopts a layout of square heliostats of the same size, with a side length limit of [2m, 8m]; ③ Heliostat installation height The range of heliostat installation height is limited to [2m, 6m]; ④ The distance between the centers of adjacent heliostat bases in each ring of the mirror field△ dist The △ dist As small as possible, and considering that the heliostat needs to be accessible for maintenance and cleaning, this case is in △ dist At least 1 meter is added to the basic condition of 5 meters more than the width of the heliostat for optimization; △ dist =l+5+△1(△1∈(0.1m,20m]) ⑤ The interval between adjacent heliostat rings in the mirror field △ r Considerations r The value of should be chosen so that the number of heliostat rings is as large as possible while achieving the maximum annual average shadow shielding efficiency, annual average truncation efficiency, and annual average cosine efficiency, while considering the minimum distance constraint between adjacent heliostats; △ r =l+5+△2(△2∈(0.1m,20m]) Based on the above constraints, determine the number of heliostats N Where: C is the number of heliostat rings, n i is the number of heliostats on the ith ring. The number of heliostat rings C is related to the interval between adjacent heliostat rings; From this, we can infer the number of heliostats in each ring. Where: i is the i-th ring heliostat; θ i is the angle between two adjacent heliostats in the i-th ring; ri is the interval between adjacent heliostats on the ith ring; In actual situations, there is a vacuum zone with a cutoff efficiency of 0 near the collector tower, and workshops for installing power generation, energy storage, control and other equipment must be reserved around the collector tower. Therefore, in actual applications, heliostats will not be installed in a circular area with a radius of 100 with the collector tower as the center, and heliostats that meet the following distance conditions should be eliminated d i ≤100 Where: d i is the center of the i-th heliostat and (CT x ,CT y ) between ; ⑥ Mathematical model for optimizing the layout of concentric circle mirror field with the collector tower as the center According to the layout characteristics of heliostats, regular sampling is performed on each heliostat ring, and an optimization solution is obtained based on the genetic algorithm according to the sampling results.

2. The method for optimizing the layout of concentric circle mirror fields centered on the heat collecting tower at mid- and low-latitudes according to claim 1 is characterized in that: In step (3), a nonlinear single-objective programming equation is established to solve the maximum annual average output thermal power per unit area of ​​the mirror under a fixed rated power of 60MW: Use the MATLAB genetic algorithm toolbox, set the number of iterations to 10, and the population size to 20 for optimization. The optimal solution is Through the above formula, the detailed design parameters of the optimal mirror field layout under rated power can be calculated.

3. The method for optimizing the layout of concentric circle mirror fields centered on the heat collecting tower at mid- and low-latitudes according to claim 2 is characterized in that: If the optimization is continued to seek the maximum annual average thermal output power on the basis of satisfying the rated power of 60MW, the restriction on the range of annual average thermal output power in the nonlinear single-objective programming equation should be removed. The MATLAB genetic algorithm toolbox was used to set the genetic algorithm population number to 10 and the number of iterations to 20. Ten groups of data were taken from the optimal solution at a fixed rated power as the custom initial population. The layout optimization method can be deduced through the optimization process. When seeking the maximum efficiency of the heliostat field, the lighting area of ​​the field should be maximized and the installation height of the heliostat should be low enough.

4. The method for optimizing the layout of concentric circle mirror fields centered on the heat collecting tower at mid- and low-latitudes according to claim 1 is characterized in that: The optical efficiency equation of the heliostat in step (1) is the=the shadow or cos or at or spill or ref Where: η shadow for shadow occlusion efficiency; η cos is the cosine efficiency; η at is the atmospheric projection rate; η spill is the cutoff efficiency; η ref is the heliostat mirror reflectivity, which is taken as 0.

92.

5. The method for optimizing the layout of concentric circle mirror fields centered on the heat collecting tower at mid- and low-latitudes according to claim 4 is characterized in that: The apparent motion parameters of the sun in step (1) Sun altitude angle α s It refers to the angle between the incident direction of sunlight and the horizon; the solar azimuth angle γ s That is, the direction of the sun, which can be roughly regarded as the angle between the shadow of a straight line erected on the ground under the sun and the south direction. The calculation method of the solar altitude angle and azimuth angle Where: ω is the solar hour angle; is the local latitude; δ is the solar declination angle; Solar Declination Equation Where: D is the number of days calculated by taking March 21, the spring equinox of 2023, as the 0th day and so on. To simplify the calculation, D only takes the representative 21st day of each month; Normal direct radiation irradiance DNI equation a=0.4237-0.00821(6-H) 2 , b=0.5055+0.00595(6.5-H) 2 , c=0.2711+0.01858(2.5-H) 2 , Where: G0 is the solar constant, which is 1.366kW / m 2 ; H is the altitude (in km); at an altitude of 3 km, 98.5°E, 39.4°N, the heliostat field is centered, and the annual average DNI is calculated to be 968W / m 2 ; Heliostat Field Output Efficiency Equation Where: N is the total number of heliostats; A i is the lighting area of ​​the i-th heliostat (unit: m 2 );η i is the optical efficiency of the i-th heliostat; Therefore, the annual thermal power output equation of the heliostat field is: Where: ST is 6 times a day: 9:00, 10:30, 12:00, 13:30, 15:00; Atmospheric Transmittance Equation Where: d HR It represents the distance from the center of the mirror to the center of the collector, which can be solved by the coordinate distance of the two points.

6. The method for optimizing the layout of concentric circle mirror fields centered on the heat collecting tower at mid- and low-latitudes according to claim 1 is characterized in that: Heliostat reflection model in step (2) With point D as the center point of the heliostat, establish the ground coordinate system (X so ,Y so ,Z so ), Z so The axis is due north, X so Axis and Y so The plane where the axis is located passes through the center point D of the heliostat, and Q is the center point of the collector tower. is the unit vector pointing from the center of the heliostat to the sun, is the unit vector from the center of the heliostat to the collector tower, for and The heliostat heading vector after superposition, let point D (x c ,y c ,z c ), Q point (x q ,y q ,z q ), z q is the vertical distance between the height of the collector tower and the heliostat. Combined with the law of the apparent motion of the sun, we can get and According to the law of light reflection, the azimuth angle γ of the heliostat can be calculated. h and elevation angle α h , laying the foundation for the establishment of subsequent models.

7. The method for optimizing the layout of concentric circle mirror fields centered on the heat collecting tower at mid- and low-latitudes according to claim 6 is characterized in that: Heliostat cosine efficiency model in step (2) The cosine efficiency of the heliostat is related to the unit vector that can pass the incident light. With reflected light The dot product of the unit vector of is calculated, and the cosine value of twice the incident angle can be obtained from the above reflection model; finally, the cosine efficiency equation model is established according to the double angle formula in the trigonometric function; Heliostat spillover efficiency model The spillover efficiency model is established by using the integral method; In reality, sunlight is a cone of light with a certain cone angle. Based on the mirror imaging principle and the cosine theorem, the imaging equation of the elliptical spot at the center of the solar tower is given: Where: R is the equivalent circular radius of the square heliostat (unit: m); α τ is the apparent height angle of the collector tower; τ is the azimuth angle of the heliostat relative to the collector tower; The heliostat spillover efficiency equation is established by double integration of the points falling within the collector and the spot ellipse. Where: σ is the solar half angle, which is 16′.

8. The method for optimizing the layout of concentric circle mirror fields centered on the heat collecting tower at mid- and low-latitudes according to claim 1 is characterized in that: In order to facilitate reference when optimizing the heliostat field, the initial field conditions before optimization and the mainstream layout of the industry are simulated; Based on the SolarPILOT simulation software and MATLAB software, the mainstream mirror field layout forms are simulated and analyzed. Through modeling and simulation, the mathematical model and arrangement rules of the layout are analyzed. The number of heliostats and the average annual optical efficiency performance indicators of the heliostat field are compared under the conditions of concentric circle optimization layout, EB layout, DELSOL3 empirical fitting layout and unobstructed intensive layout under a fixed rated power of 60WM.

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