A heliostat field distribution method based on simulated annealing optimization algorithm

Abstract

The application belongs to the technical field of solar thermal power generation, and particularly discloses a heliostat field distribution method based on a simulated annealing optimization algorithm. The application obtains mirror field parameters, forms a primary distribution mirror field, and optimizes mirror field arrangement through three steps, adjusts the mirror field arrangement according to the annual average output thermal power distribution of each heliostat in the mirror field, and makes the efficiency of the whole mirror field as high as possible while meeting the operation conditions of the mirror field. The application optimizes the coordinates of each heliostat in the primary distribution mirror field by using the simulated annealing optimization algorithm, so as to obtain a high annual average output thermal power per unit mirror area arrangement scheme.

Description

Technical Field

[0001] This invention belongs to the field of solar thermal power generation technology, and specifically introduces a method for heliostat field distribution based on simulated annealing optimization algorithm. Background Technology

[0002] Tower solar power plants, as an innovative application of solar power generation technology, have attracted widespread attention and research in the global energy field. These power plants use advanced technology to generate electricity from solar energy resources. Their main principle is to use a tall tower structure with a large area of ​​solar reflectors to concentrate sunlight onto a collector. Inside the collector, the high-temperature heat energy is used to heat the working fluid to generate steam, which is then used to drive a generator to generate electricity.

[0003] Heliostats are a key component of tower solar power plants, playing a crucial role in receiving solar energy and reflecting it onto the collectors. Their layout strategy significantly impacts the annual average output heat power per unit mirror surface of the tower solar power plant. Existing layout strategies suffer from low improvement rates in annual average output heat power per unit mirror surface and poor applicability. This invention aims to provide a heliostat field distribution method based on simulated annealing optimization algorithms to maximize the annual average output heat power per unit mirror surface of the tower solar power plant, thereby increasing the heat collection capacity. Summary of the Invention

[0004] This invention aims to provide a heliostat field distribution method based on simulated annealing optimization algorithm. This method can maximize the annual average output heat power per unit mirror of a tower solar power plant, thereby increasing the heat collection capacity, given a given annual average output heat power.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for heliostat field distribution based on simulated annealing optimization algorithm includes the following steps:

[0007] Step 1, determine the mirror field parameters:

[0008] Determine the geographical and optical parameters of the mirror field based on the actual situation;

[0009] Step 2, determine the initial distribution of the mirror field:

[0010] Based on the parameters determined in step one, the heliostat field is randomly distributed initially;

[0011] Step 3: Optimize the heliostat field distribution:

[0012] Based on the coordinates of each heliostat field randomly generated in step two, the distribution of the heliostat field is optimized using a simulated annealing algorithm.

[0013] In step one, the various geographical and optical parameters of the mirror field include the solar altitude angle and solar azimuth angle at the location of the mirror field, atmospheric transmittance, shading efficiency, collector cutoff efficiency, specular reflectance at the location of the mirror field, the relative position coordinates of each heliostat and the solar collector tower, the number of heliostats, the height parameters of the solar collector tower, and the height parameters of the solar collector at the top of the solar collector tower.

[0014] In step two, the initial distribution of the heliostat field refers to the distribution coordinates of each heliostat obtained by using a random number arrangement method.

[0015] The simulated annealing optimization algorithm in step three includes the following steps:

[0016] The first step is to determine the decision variables:

[0017] Heliostat side length, installation height, location coordinates, total number of heliostats, absorption tower height:

[0018] {d, h, x, y, N, H}

[0019] The second step is to determine the constraints:

[0020] The heliostat has a side length of a1 to a2m and an installation height of a3 to a4m. It is required that the mirror surface does not touch the ground when rotating, and that the heliostat field reaches its rated power.

[0021]

[0022] The heliostat field must reach its rated power, that is:

[0023] E field =DNI·A'·η=P

[0024] Where A' represents the effective mirror area of ​​the heliostat, and P represents the rated power:

[0025] A'=N·d 2 ·η sb

[0026] Combining the above two equations, we get:

[0027] DNI·K·Nd 2 η sb 2 η cos =P

[0028] The actual total mirror area Nd of the heliostat can be obtained from the above formula. 2 Its average cosine efficiency η cos They are mutually restrictive. In order to maximize the average annual output heat power per unit mirror area, the average cosine efficiency of the heliostat must be maximized.

[0029] The third step is to determine the objective function:

[0030] Maximum annual average heat output per unit mirror area:

[0031]

[0032] The objective function is to maximize the annual average heat output per unit mirror area, where A is the total surface area of ​​the heliostat mirror, and E... field Output thermal power of the heliostat field:

[0033]

[0034] η = η sb η cos η at η trunc η ref

[0035] Among them, the specular reflectivity η ref It is a constant, atmospheric transmittance η at Shadow occlusion efficiency η sb Solar collector cutoff efficiency η trunc DNI represents the irradiance per unit area perpendicular to the direction of sunlight per unit time (unit: kW / m²). 2 Its value is usually affected by factors such as solar altitude angle, weather, atmospheric scattering, and shadowing, making it a dynamic data point. Therefore, an approximate calculation is used.

[0036]

[0037]

[0038] In the formula, H is the local altitude, and G0 is the solar constant, taken as 1.366 kW / m². 2 .

[0039] In optical efficiency η, specular reflectivity η ref It is a constant, atmospheric transmittance η at Shadow occlusion efficiency η sb Solar collector cutoff efficiency η trunc Since the loss has a very small impact and can be approximated as a constant, we define a parameter K, assuming that the parameter K here is a quantifiable constant, such that:

[0040] K = η at η trunc η ref

[0041] Integrating and simplifying the above formulas, we obtain the simplest expression for the objective function:

[0042] maxf(d,h,x,y,N)=DNI·K·η sb 2 ·η cos

[0043] The coordinates of the i-th heliostat in the xoy plane of the mirror field coordinate system:

[0044] {x i y i}

[0045] To maximize the sum of the cosine efficiencies of the heliostats, the average cosine efficiency η is set at the optimal layout. cos The larger the mirror surface area, the greater the annual average heat output per unit area.

[0046] in, In the formula, θ i Let be the angle between the incident ray and the normal to the heliostat mirror. Let be the incident light vector pointing towards the sun. This is the normal vector of the heliostat mirror surface.

[0047] The fourth step is to solve and optimize the objective function.

[0048] Optimal solution initialization. 1000 coordinates symmetric about the y-axis are randomly generated according to the constraints. The maximum mean cosine efficiency is calculated using the simulated annealing algorithm. This operation is performed multiple times to determine the initial mean cosine efficiency.

[0049] The specific approach to implementing random coordinates in MATLAB code is as follows: To maximize the average annual output heat power per unit mirror area, the basic layout of the heliostat should be "more in the north and less in the south, symmetrical east and west".

[0050] Set up n random points, and first give them a 0.9 probability of landing on the north side, i.e. the first and second quadrants. Before landing, it is necessary to determine whether the constraints are met, i.e. whether the heliostat can be placed on the north side and whether the distance between the heliostat and the adjacent heliostat is greater than d+l.

[0051] After maximizing the use of the space on the north side, it will begin to fall into the third and fourth quadrants.

[0052] Determine parameters N and S. (S is the area of ​​the heliostat, its value is equal to d...) 2 For ease of definition, S will be used instead of d below. 2 The value of N·S can be calculated based on the initial average efficiency and the conditions required to achieve P.

[0053] Based on the constant N·S, a series of S and N values ​​are obtained. These S and N values ​​are then substituted into the simulated annealing algorithm to calculate the maximum mean cosine efficiency of the random coordinates under these S and N conditions. The mean cosine efficiencies of this series are compared, and a set of S and N values ​​under the maximum mean efficiency is determined as the parameters for subsequent solutions, ensuring that h > d / 2.

[0054] By continuously improving the minimum cosine efficiency of the judgment condition for each point, and not recording points with a cosine efficiency lower than this, the space of possible points is continuously compressed, and the average cosine efficiency is improved without changing the number of points N.

[0055] After repeating the loop, the set of coordinates with the highest average cosine efficiency is selected as the coordinates for subsequent calculations. Finally, the coordinates are optimized through multiple fine-tuning iterations (10,000 times), that is, by slightly changing the position of one coordinate and observing whether the cosine efficiency changes. If it increases, it is retained; otherwise, it remains unchanged. Attached Figure Description

[0056] Figure 1 Flowchart for optimizing the heliostat field distribution in this invention;

[0057] Figure 2 This is a diagram showing the field distribution of the heliostat in Example 1. Detailed Implementation

[0058] The following provides specific descriptions of some embodiments based on the technical solutions of the present invention. However, the scope of protection of the present invention is not limited to the following embodiments. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

[0059] A method for heliostat field distribution based on simulated annealing optimization algorithm includes the following steps:

[0060] Step 1, determine the mirror field parameters:

[0061] Determine the geographical and optical parameters of the mirror field based on the actual situation;

[0062] Step 2, determine the initial distribution of the mirror field:

[0063] Based on the parameters determined in step one, the heliostat field is randomly distributed initially;

[0064] Step 3: Optimize the heliostat field distribution:

[0065] Based on the coordinates of each heliostat field randomly generated in step two, the distribution of the heliostat field is optimized using a simulated annealing algorithm.

[0066] In step one, the various geographical and optical parameters of the mirror field include the solar altitude angle and solar azimuth angle at the location of the mirror field, atmospheric transmittance, shading efficiency, collector cutoff efficiency, specular reflectance at the location of the mirror field, the relative position coordinates of each heliostat and the solar collector tower, the number of heliostats, the height parameters of the solar collector tower, and the height parameters of the solar collector at the top of the solar collector tower.

[0067] In step two, the initial distribution of the heliostat field refers to the distribution coordinates of each heliostat obtained by using a random number arrangement method.

[0068] The simulated annealing optimization algorithm in step three includes the following steps:

[0069] The first step is to determine the decision variables:

[0070] Heliostat side length, installation height, location coordinates, total number of heliostats, absorption tower height:

[0071] {d, h, x, y, N, H}

[0072] The second step is to determine the constraints:

[0073] The heliostat has a side length of a1 to a2m and an installation height of a3 to a4m. It is required that the mirror surface does not touch the ground when rotating, and that the heliostat field reaches its rated power.

[0074]

[0075] The heliostat field must reach its rated power, that is:

[0076] E field =DNI·A'·η=P

[0077] Where A' represents the effective mirror area of ​​the heliostat, and P represents the rated power:

[0078] A'=N·d 2 ·η sb

[0079] Combining the above two equations, we get:

[0080] DNI·K·Nd 2 η sb 2 η cos =P

[0081] The actual total mirror area Nd of the heliostat can be obtained from the above formula. 2 Its average cosine efficiency η cos They are mutually restrictive. In order to maximize the average annual output heat power per unit mirror area, the average cosine efficiency of the heliostat must be maximized.

[0082] The third step is to determine the objective function:

[0083] Maximum annual average heat output per unit mirror area:

[0084]

[0085] The objective function is to maximize the annual average heat output per unit mirror area, where A is the total surface area of ​​the heliostat mirror, and E... field Output thermal power of the heliostat field:

[0086]

[0087] η = η sb η cos η at η trunc η ref

[0088] Among them, the specular reflectivity η ref It is a constant, atmospheric transmittance η at Shadow occlusion efficiency η sb Solar collector cutoff efficiency η trunc DNI represents the irradiance per unit area perpendicular to the direction of sunlight per unit time (unit: kW / m²). 2 Its value is usually affected by factors such as solar altitude angle, weather, atmospheric scattering, and shadowing, making it a dynamic data point. Therefore, an approximate calculation is used.

[0089]

[0090]

[0091] In the formula, H is the local altitude, and G0 is the solar constant, taken as 1.366 kW / m². 2 .

[0092] In optical efficiency η, specular reflectivity η ref It is a constant, atmospheric transmittance η at Shadow occlusion efficiency η sb Solar collector cutoff efficiency η trunc Since the loss has a very small impact and can be approximated as a constant, we define a parameter K, assuming that the parameter K here is a quantifiable constant, such that:

[0093] K = η at η trunc η ref

[0094] Integrating and simplifying the above formulas, we obtain the simplest expression for the objective function:

[0095] maxf(d,h,x,y,N)=DNI·K·η sb 2 ·η cos

[0096] The coordinates of the i-th heliostat in the xoy plane of the mirror field coordinate system:

[0097] {x i y i}

[0098] To maximize the sum of the cosine efficiencies of the heliostats, the average cosine efficiency η is set at the optimal layout. cos The larger the mirror surface area, the greater the annual average heat output per unit area.

[0099] in, In the formula, θ i Let be the angle between the incident ray and the normal to the heliostat mirror. Let be the incident light vector pointing towards the sun. This is the normal vector of the heliostat mirror surface.

[0100] Fourth step, solving the objective function.

[0101] Optimal solution initialization. 1000 coordinates symmetric about the y-axis are randomly generated according to the constraints. The maximum mean cosine efficiency is calculated using the simulated annealing algorithm. This operation is performed multiple times to determine the initial mean cosine efficiency.

[0102] The specific approach to implementing random coordinates in MATLAB code is as follows: To maximize the average annual output heat power per unit mirror area, the basic layout of the heliostat should be "more in the north and less in the south, symmetrical east and west".

[0103] Set up n random points, and first give them a 0.9 probability of landing on the north side, i.e. the first and second quadrants. Before landing, it is necessary to determine whether the constraints are met, i.e. whether the heliostat can be placed on the north side and whether the distance between the heliostat and the adjacent heliostat is greater than d+l.

[0104] After maximizing the use of the space on the north side, it will begin to fall into the third and fourth quadrants.

[0105] Determine parameters N and S. S is the area of ​​the heliostat, which is equal to d. 2 For ease of definition, S will be used instead of d below. 2The value of N·S can be calculated based on the initial average efficiency and the condition for achieving P. Based on the constant N·S, a series of S and N values ​​are obtained. These S and N values ​​are then substituted into the simulated annealing algorithm to calculate the maximum average cosine efficiency of the random coordinates under these S and N conditions. The series of average cosine efficiencies are compared, and a set of S and N values ​​under the maximum average efficiency is determined as the parameters for subsequent solutions, ensuring that h > d / 2.

[0106] By continuously improving the minimum cosine efficiency of the judgment condition for each point, and not recording points with a cosine efficiency lower than this, the space of possible points is continuously compressed, and the average cosine efficiency is improved without changing the number of points N.

[0107] After repeating the loop, the set of coordinates with the highest average cosine efficiency is selected as the coordinates for subsequent calculations. Finally, the coordinates are optimized through 10,000 fine-tuning iterations, that is, by slightly changing the position of one coordinate and observing whether the cosine efficiency changes. If it increases, it is retained; otherwise, it remains unchanged.

[0108] Example 1

[0109] A circular heliostat field with a radius of 350m is established on an open area at 98.5°E, 39.4°N, and an altitude of 3000m. A coordinate system for the field is established with the center of this area as the origin, where the positive x-axis points east, the positive y-axis points north, and the positive z-axis points vertically upwards.

[0110] At the center of the heliostat field is an absorption tower. Within a 100-meter radius of this tower, buildings are constructed to house power generation, energy storage, and control equipment. Above the absorption tower is a cylindrical, externally oriented solar collector, 7 meters in diameter and 8 meters high. The heliostat itself is a rectangular plane; its two sides are called the mirror height, and its two top and bottom sides are always parallel to the ground and are called the mirror width. Generally, the latter is greater than or equal to the former. The side length is between 2 and 8 meters, and the installation height is between 2 and 6 meters, ensuring that the bottom of the mirror does not touch the ground. For maintenance and access purposes, the distance between the centers of adjacent heliostats must be at least 5 meters greater than the mirror width.

[0111] For ease of calculation, all "annual average" indicators are calculated based on local time at 9:00, 10:30, 12:00, 13:30, and 15:00 on the 21st of each month. By designing parameters such as the location coordinates of the absorption towers, the number and location of heliostats, and the dimensions and installation height of the heliostat field, the goal is to maximize the annual average output heat power per unit mirror area while achieving a rated power of 60MW.

[0112] The relevant calculation results obtained after applying the aforementioned invention content are shown in Table 1:

[0113]

[0114] The distribution of the heliostat field is as follows Figure 2 .

[0115] The relevant calculation results based on the original heliostat coordinates are shown in Table 2:

[0116]

[0117] The table shows that the average annual heat output per unit area of ​​the mirror increases by 12%.

Claims

1. A method for heliostat field distribution based on simulated annealing optimization algorithm, characterized in that, Includes the following steps: Step 1, determine the mirror field parameters: Determine the geographical and optical parameters of the mirror field based on the actual situation; Step 2, determine the initial distribution of the mirror field: Based on the parameters determined in step one, the heliostat field is randomly distributed initially; Step 3: Optimize the heliostat field distribution: Based on the coordinates of each heliostat field randomly generated in step two, the distribution of the heliostat field is optimized using the simulated annealing algorithm; The simulated annealing optimization algorithm in step three includes the following steps: The first step is to determine the decision variables: Heliostat side length, installation height, location coordinates, total number of heliostats, absorption tower height: {d, h, x, y, N, H}; The second step is to determine the constraints: The heliostat has a side length of a1~a2m and an installation height of a3~a4m. It is required that the mirror surface does not touch the ground when rotating, and that the heliostat field reaches its rated power. The heliostat field must reach its rated power, that is: in, This indicates the effective mirror area of ​​the heliostat. Indicates rated power; Combining the above two equations, we get: The actual total mirror area of ​​the heliostat can be obtained from the above formula. Its average cosine efficiency They are mutually restrictive. In order to maximize the average annual output heat power per unit mirror area, the average cosine efficiency of the heliostat must be maximized. The third step is to determine the objective function: in, In the formula, Let be the angle between the incident ray and the normal to the heliostat mirror. Let be the incident light vector pointing towards the sun. This is the normal vector of the heliostat mirror surface; The fourth step is to initialize the optimal solution. A spatial rectangular coordinate system is established with the solar collector in the mirror field as the origin. 1000 coordinates symmetrical about the y-axis are randomly generated according to the constraints. The maximum average cosine efficiency is calculated according to the simulated annealing algorithm. This operation is repeated multiple times to determine the initial average cosine efficiency. The specific idea of ​​implementing the random coordinates in MATLAB code is as follows: In order to maximize the annual average output heat power per unit mirror area, the basic layout of the heliostat should be "more in the north and less in the south, symmetrical in the east and west". The fifth step is to set up n random points, and firstly, let them fall on the north side with a probability of 0.9, that is, the first and second quadrants. Before the landing point, it is necessary to determine whether the constraint conditions are met, that is, whether the heliostat can be placed on the north side and whether the distance between it and the adjacent heliostat is greater than the distance d+l in the field setting parameters. The sixth step is to maximize the use of the space on the north side, and then begin to fall into the third and fourth quadrants; Step 7: Determine parameters N and S, where S is the area of ​​the heliostat, and its value is equal to... Based on the initial average efficiency and the conditions required to achieve P, we can calculate... The value; Step 8, based on the fixed value A series of S and N values ​​are obtained. These S and N values ​​are then substituted into the simulated annealing algorithm to calculate the maximum average cosine efficiency of the random coordinates under these S and N conditions. The average cosine efficiencies of this series are compared, and a set of S and N values ​​under the maximum average efficiency is determined as the parameters for subsequent solutions. It is ensured that h > d / 2, i.e., the rotation does not touch the ground. In the ninth step, the space of possible points is continuously compressed by continuously increasing the minimum cosine efficiency of the judgment condition for each point. Points with a cosine efficiency lower than this are not recorded. At the same time, the average cosine efficiency is increased without changing the number of points N. Step 10: After repeating the loop, select the set of coordinates with the highest average cosine efficiency as the coordinates for subsequent calculations. Finally, optimize the coordinates by fine-tuning 10,000 times. That is, slightly change the position of one coordinate and observe whether the cosine efficiency changes. If it increases, keep it; otherwise, leave it unchanged.

2. The heliostat field distribution method based on simulated annealing optimization algorithm according to claim 1, characterized in that: In step one, the various geographical and optical parameters of the mirror field include the solar altitude angle and solar azimuth angle at the location of the mirror field, atmospheric transmittance, shading efficiency, collector cutoff efficiency, specular reflectance at the location of the mirror field, the relative position coordinates of each heliostat and the solar collector tower, the number of heliostats, the height parameters of the solar collector tower, and the height parameters of the solar collector at the top of the solar collector tower.

3. The heliostat field distribution method based on simulated annealing optimization algorithm according to claim 1, characterized in that: In step two, the initial distribution of the heliostat field refers to the distribution coordinates of each heliostat obtained by using a random number arrangement method.

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