High-precision heliostat energy flux density calculation method

Abstract

The application provides a high-precision heliostat energy flow density calculation method, and the calculation method specifically comprises the following steps: S1, determining the position, calculating the incident light and reflected light vector, and the normal vector coordinate of the heliostat; S2, meshing the heliostat and the receiving surface to obtain the mesh coordinate; S3, determining the position coordinate of the intersection point of the reflected sunlight center light of all the heliostat mesh points and the receiving surface; S4, calculating the included angle between the reflected light of the heliostat mesh point and the sunlight center light to obtain the energy flow density of the target mesh point of the receiving surface; S5, adding up the energy flow density contribution of all the heliostat mesh points to the receiving surface mesh point to obtain the calculated energy flow density of the receiving surface mesh point; and S6, repeating the step S4 and the step S5 to calculate the energy flow density of all the mesh points of the receiving surface. The application can quickly and accurately calculate the energy flow density distribution of the focused sunlight of the heliostat on the receiving surface and the interception rate, thereby helping the system design optimization and operation control.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of photovoltaic power generation, and particularly to a high-precision heliostat energy flux density calculation method. BACKGROUND

[0002] Tower system needs to use a large number of heliostats, and the sunlight incident on the heliostats is converged on the receiving surface at the top of the tower, which makes the energy flux density of the receiving surface very high, often thousands of times the solar intensity, and is very easy to overheat and cause the receiving surface to be burned. The energy flux density distribution of the receiving surface must be understood in order to avoid the generation of too high solar radiation energy flux density on the receiving surface of the tower system. Establishing a comprehensive and reliable energy flux density calculation model is an important method for predicting the energy flux density of the receiving surface, and is also the basis for calculating the interception rate and optical efficiency of the system, and provides a basis for the optimal design and evaluation of the tower system.

[0003] The simplest method for calculating the energy flux density is to directly describe the energy flux density distribution on the receiving surface with a function. Collado et al. once proposed the UNIZAR function, and Michael Kiera once proposed the HFCAL function. These two function methods are empirical models summarized from experimental data, and although they are simple and fast to calculate, there are still large errors in the calculation results compared with experimental data. The applicant previously used a Gaussian model to simulate the mirror image function of the heliostat, thereby deriving a Gaussian function. Since an elliptical Gaussian model is used to describe the optical error, the model accuracy exceeds the optical tracking method using a circular Gaussian model compared with experimental data.

[0004] The current methods for calculating the energy flux density of the heliostat mainly include ray tracing and convolution integration.

[0005] Ray tracing is a method for tracing the path of incident light in the system according to the reflection law of light. Ray tracing is a microscopic method that can provide a large amount of numerical information, and its characteristics are that it can track each beam of sunlight and observe its optical behavior in the system. The disadvantage of this method is that the calculation process is very tedious, and the functional relationship is relatively vague, making it difficult to use for system optimization. The advantage of this method is that the physical concept is clear, the basic equation is relatively simple, and it can be solved using an electronic computer, and can solve the simulation calculation of many complex systems.

[0006] Convolution integral method is an indirect integration method, which regards the energy flux density on the mirror image plane as the convolution of the solar radiation distribution function and the heliostat mirror image function, and then projects the energy flux density distribution on the mirror image plane to the receiver plane. Gaussian model is usually used to describe the optical error distribution of the heliostat mirror surface. Convolution integral is an approximation to the actual physical image, including using an approximate function to describe the heliostat mirror image function, and the projection process also introduces errors because it assumes that the sun rays come from the center of the heliostat, rather than being actually reflected by the entire heliostat mirror surface. Although the calculation speed is faster than ray tracing method, sometimes the energy flux density distribution of a single heliostat is not accurate enough.

[0007] Lipps specifically gives four types of convolution integral calculation expressions for energy flux density and summarizes them. Walzel uses polynomial fitting for solar intensity distribution for the reflection of plane mirror, and establishes a convolution integral numerical calculation method. Lipps and Walzel continue to develop analytical methods for solving convolution integrals for plane mirrors of different shapes of polygons. Hennet develops a convolution expression and analytical result for fast solving the energy flux density distribution on the imaging plane without considering the mirror surface error of the heliostat. Lipps considers the solar brightness distribution and elliptical Gaussian optical error distribution, and applies convolution method to solve the energy flux density distribution. Helios system uses two-dimensional Fourier transform to calculate the reflected light distribution under different solar intensity distribution functions using elliptical Gaussian distribution to describe the optical error for calculating the heliostat energy flux density. Using elliptical Gaussian function to describe the optical error distribution is proved to be more consistent with the actual data, so as to improve the calculation accuracy and be suitable for a wider range of conditions. However, the above methods all assume that the optical error of the heliostat at each point is the same or do not consider the optical error, thus introducing errors. Elysayed and Fathalah use separation of variables and superposition technique to develop a numerical program for solving the surface energy flux density distribution of the receiver plane, considering the shadow and blocking effect, suitable for different solar intensity models and concentrating and non-concentrating heliostats.

[0008] The applicant proposes two convolution calculation methods in the tower heliostat: one is for circular heliostats, which proposes an analytical solution method, and the calculation is relatively accurate; the other is to apply elliptical Gaussian model, which not only describes the optical error more accurately, but also converts it to one-dimensional integral through analytical conversion, and applies Gauss-Lagrange method to solve it, which is fast in calculation.

[0009] Previous studies show that even if the optical errors of different positions of the heliostat are the same, the optical errors transmitted to the reflected light are different, thereby being different from the actual situation. In the current solar tower system, most of the heliostats use the reflective surface with glass back. Experiments show that the reflected light is mainly divided into three parts, including the light directly reflected from the upper surface of the glass, the main light reflected from the metal reflective surface, and the remaining part of the main reflected light reflected from the upper surface of the glass and then reflected from the metal reflective surface to form the third part of the reflected light, as shown in Figure 1 In the current study of the solar tower system, it is regarded as the same reflected light beam, but it is actually different from the real physical image.

[0010] The existing energy flow density calculation method has good effect in specific cases, but has certain defects in wide use and high-precision calculation. Due to the use of convolution method, errors are introduced; the transmission of optical errors of different points of the heliostat is not considered, in addition, the difference between the upper and lower surfaces of the heliostat is not considered, because the glass back reflector is mainly used in the heliostat, therefore, it is necessary to develop a direct integration model which can not introduce too many assumptions and errors and accurately calculate the solar energy flow density distribution. SUMMARY

[0011] In order to solve the technical problems of poor precision and application limitations of the existing energy flow density calculation method, the present application provides a high-precision heliostat energy flow density calculation method.

[0012] Therefore, the high-precision heliostat energy flow density calculation method provided by the present application specifically includes the following steps:

[0013] S1, according to the sun azimuth and altitude and the positions of the heliostat and the receiver, the incident light and the reflected light vector, and the normal vector coordinate of the heliostat are calculated;

[0014] S2, the heliostat and the receiving surface are gridded, and the coordinate systems thereof are established, and the coordinates of the center points of the heliostat and the receiving surface grid are converted to the global coordinate system;

[0015] S3, the position coordinates of the intersection point of the reflected sun center light of all heliostat grid points and the receiving surface are determined;

[0016] S4, the included angle between the light reflected by the arbitrary heliostat grid point to the target grid point of the receiving surface and the reflected sun center light of the center of the heliostat grid point is calculated, and according to the included angle and the reflected sun light intensity distribution function, the energy flow density of the reflected sun light of the heliostat grid point to the calculated target grid point of the receiving surface is calculated;

[0017] S5, summing up the energy flux density contributions of all heliostat grid points to the receiver grid point, to obtain the calculated energy flux density of the receiver grid point;

[0018] S6, repeating the step S4 and the step S5 to calculate the energy flux density of all grid points of the receiver, to obtain the energy flux density distribution of the entire receiver.

[0019] Preferably, in the step S1, the coordinates (u sun ,v sun ,w sun ) of the incident central solar ray are calculated by the following formula:

[0020] (u sun ,v sun ,w sun ) = (-cosα s sinγ s ,-cosα s sinγ s ,sinα s )

[0021] Wherein, α s is the solar elevation angle, γ s is the solar azimuth angle, which can be determined according to the longitude and latitude of the heliostat installation position and the time, or obtained by measurement;

[0022] The elevation angle α r and the azimuth angle γ r of the reflected central solar ray are calculated by the following formula:

[0023]

[0024]

[0025] Wherein, (x heliostat ,y heliostat ,z heliostat ) and (x receiver ,y receiver ,z receiver ) represent the coordinates of the heliostat center and the receiver center in the global coordinate system respectively;

[0026] The elevation angle α n and the azimuth angle γ n of the heliostat normal vector are calculated by the following formula:

[0027]

[0028] Or,

[0029]

[0030] Preferably, in the step S2, the heliostat and the receiving surface grid are formed into an n x n grid, n = 50 or 100, and the center point of each grid represents the entire grid. In the receiving surface coordinate system, the coordinates of the receiving surface are (x r ,y r ,z r ) receiver , wherein x r and y r are determined according to the uniformly divided grid, and z r = 0 since the receiving surface is a plane. In the heliostat coordinate system, the coordinates of the heliostat are (x h ,y h ,z h ) heliostat , x h and y h are determined according to the uniformly divided grid, and z h is calculated according to the heliostat curved surface shape and the corresponding equation. The normal vector of each heliostat grid center point is calculated.

[0031] The heliostat grid center point coordinates are converted into global grid center point coordinates (x h ,y h ,z h ) global by the following rotation matrix AH and formula:

[0032]

[0033] (x h ,y h ,z h ) global = (x heliostat ,y heliostat ,z heliostat ) global + (x h ,y h ,z h ) heliostat x AH -1

[0034] wherein a n is the elevation angle of the heliostat normal vector, g n is the azimuth angle of the heliostat normal vector, (x heliostat ,y heliostat ,z heliostat ) global represents the heliostat center coordinates in the global coordinate system, and the heliostat grid point normal vectors are converted into the global coordinate system based on the above formula.

[0035] The receiving surface grid center point coordinates are converted into global grid center point coordinates (x r ,y r ,z r ) global by the following rotation matrix AR and formula:

[0036]

[0037] (x r ,y r ,z r ) global =(x receiver ,y receiver ,z receiver ) global +(x r ,y r ,z r ) receiver ×AR -1

[0038] wherein (x receiver ,y receiver ,z receiver ) global represents the receiving surface center coordinates in the global coordinate system, α rn is the elevation angle of the receiving surface normal vector, γ rn is the azimuth angle of the receiving surface normal vector, and the receiving surface normal vector (u rn ,v rn ,w rn ) is calculated.

[0039] Preferably, in the step S3, the intersection point of the sun center light ray vector reflected by each grid point center (x h ,y h ,z h ) of the heliostat on the receiving surface in the global coordinate system is calculated by the following formula:

[0040]

[0041] x rf =x h +u ray ×t

[0042] y rf =y h +v ray ×t

[0043] z rf =z h +w ray ×t

[0044] wherein (x receiver,y receiver ,z receiver ) represents the center coordinates of the receiving surface in the global coordinate system, (u rn ,v rn ,w rn ) is the normal vector of the receiving surface, (u ray ,v ray ,w ray ) is the direction vector coordinate of the reflected light ray in the global coordinate system, and the specific calculation formula is as follows:

[0045] u ray = 2(u hn u sun +v hn v sun +w hn w sun )u hn -u sun

[0046] v ray = 2(u hn u sun +v hn v sun +w hn w sun )v hn -v sun

[0047] w ray = 2(u hn u sun +v hn v sun +w hn w sun )w hn -w sun

[0048] wherein (u sun ,v sun ,w sun ) is the incident solar central light vector, and (u hn ,v hn ,w hn ) is the normal vector of the heliostat grid point.

[0049] Alternatively, the reflected solar central light equation and the receiving surface equation are solved, and the intersection point (x rf ,y rf ,z rf ) is obtained according to the equation set.

[0050] Preferably, in the step S4, the solar reflected light intensity distribution function is:

[0051]

[0052] wherein σ x and σ y According to the heliostat optical error, the solar light intensity distribution and the optical error transmission theory, θ x and θ y are the components of the angle between the reflected light and the central reflected light of the sun in the x and y directions, respectively, and the specific calculation formula is as follows:

[0053]

[0054]

[0055] wherein:

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062] The formula for calculating the energy flow density of any point on the receiving surface is:

[0063]

[0064] wherein S1 is the projection surface of the heliostat, I is the total intensity of the incident sunlight, β1 and β2 are the incident angles of the reflected light from the grid point of the heliostat to the grid point of the receiving surface and the receiving surface, respectively, wherein

[0065]

[0066]

[0067] wherein, (u rn ,v rn ,w rn ) is the normal vector of the receiving surface, and (u hn ,v hn ,w hn ) is the normal vector of the grid point of the heliostat.

[0068] Preferably, the high-precision heliostat energy flow density calculation method comprises S7, calculating the intercept rate according to the energy flow density distribution, adding the energy flow density in the receiver range, and dividing by the reflected energy flow density.

[0069] Preferably, when the high-precision heliostat energy flux density calculation method is applied to a glass back mirror as a heliostat, the energy of light directly reflected from the upper surface of the glass, the energy of light passing through the glass and reflected by the reflecting surface on the lower surface of the glass, and the energy of light reflected from the lower surface, reflected by the upper surface of the glass, passing through the glass again, and reflected a second time by the reflecting surface on the lower surface are calculated according to Fresnel's theorem. The energy flux density contribution of each of these energy flux density on the receiving surface is calculated using the aforementioned calculation method.

[0070] Compared with the prior art, the present invention has the following beneficial effects:

[0071] Based on the elliptical Gaussian model, this invention calculates the energy flux contribution of all reflections on the heliostat to all points on the receiving surface by integral calculation. For the glass back mirror, the effects of the three main beams generated by the reflections from the upper and lower glass interfaces are considered. Using the circular Gaussian model, the intensity distribution of reflected light can be described more accurately, thereby obtaining the accurate energy flux density distribution and interception rate on the receiving surface, which helps in system design optimization and operation control. Attached Figure Description

[0072] Figure 1 This is a schematic diagram of the light spot formed by the three separate reflected light rays observed in the experiment of this invention;

[0073] Figure 2 This is a schematic diagram of the optical errors at different points of the heliostat of the present invention;

[0074] Figure 3 This is a schematic diagram of the light reflected by the heliostat of the present invention;

[0075] Figure 4 This is a schematic diagram of the amplitude vector decomposition of the rays in this invention;

[0076] Figure 5 This is a schematic diagram of the energy flux density distribution on the receiving surface of the tower heliostat system of the present invention;

[0077] Figure 6 This is a flowchart of the high-precision heliostat energy flux density calculation method of the present invention;

[0078] Figure 7 This is a schematic diagram showing the angle between the reflected light rays and O1O2 in the circular Gaussian model of this invention;

[0079] Figure 8 This is a schematic diagram showing the angle between the reflected light rays of the mesh and O1O2 in the X direction under the elliptical Gaussian model of this invention.

[0080] Figure 9 This is a schematic diagram showing the angle between the reflected light rays of the grid and O1O2 in the Y direction under the elliptical Gaussian model of this invention. Detailed Implementation

[0081] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described with reference to the accompanying drawings.

[0082] To better understand this invention, the principles behind the high-precision heliostat energy flux density calculation method will be explained in detail.

[0083] Sunlight rays from different locations, after being reflected by a point on a heliostat, will reach different positions on the receiving surface. For example... Figure 2 As shown, optical errors at different points on the heliostat will cause the reflected light to deviate from the ideal orientation. By integrating all reflection points on the heliostat, the contribution of reflected sunlight to the energy flux density at a point on the receiving surface can be calculated. Similarly, the energy flux density distribution across the entire receiving surface can be calculated.

[0084] like Figure 3 As shown, a heliostat is a glass back-reflector, meaning the back of the glass is covered with a metal coating as the main reflecting surface. The reflected light is mainly divided into three parts: I1, I2, and I3. The incident light first reaches the upper surface of the glass of the heliostat, and the part directly reflected is I1, accounting for about 5%. The remaining light passes through the glass, is reflected by the metal reflecting surface, and then passes through the upper surface again. This part is the main reflected light, namely I2, which accounts for about 91.5% when the incident angle is small. The remaining part is reflected again by the upper surface of the glass and then by the metal reflecting surface again. The part that finally passes through the upper surface is I3, accounting for about 3%. The remaining light still propagates inside the glass, but the proportion of this part is negligible.

[0085] The focal points of the reflected light from these three parts are different, but the I2 part mainly determines the energy flux density distribution on the receiving surface. Therefore, in a practical solar tower system, the position of the central ray of the I2 part hitting the receiving surface is consistent with the center of the receiving surface. When the distance between the receiving surface and the heliostat is large enough, the difference in the focal position of these three parts can be ignored. However, the I1 and I3 parts also make a significant contribution to the energy flux density. When a more accurate energy flux density distribution is required, the optical errors of these two parts and the differences in energy flux density distribution from the I2 part should be considered. When calculating the interception rate, if the I1 and I3 parts are not considered, the curvature of the interception rate curve will differ significantly from the actual situation, especially when the interception rate reaches 90%.

[0086] The ratios of I1, I2, and I3 are related to the angle of incidence. The reflection and refraction of light on the glass surface are also affected by polarization changes. The amplitude vector of the ray can be decomposed into two directions: the component perpendicular to the incident surface is called the S-component, and the component parallel to the incident surface is called the P-component. For example... Figure 4As shown, the P and S components have the same amplitude in natural light, with an incident angle of i1. The ratio of the refractive indices on both sides of the reflective glass interface is n1 and n2, respectively. According to the law of refraction, the angle of refraction inside the glass can be calculated as i2. According to Fresnel's equations, the amplitude reflection coefficient and amplitude transmission coefficient of the light ray can be calculated.

[0087]

[0088]

[0089]

[0090]

[0091] In the above formula, r p and t p These are the amplitude reflection coefficient and amplitude transmission coefficient of the P component, respectively, r s and t s These are the amplitude reflection coefficient and amplitude transmission coefficient of the S component, respectively. Further calculations are made of the reflectivity of the reflected light in the P and S components:

[0092]

[0093]

[0094] Further calculations were performed on the transmittance of reflected light in the P and S components:

[0095]

[0096]

[0097] The incident ray is natural light with intensity I0, and it has the same amplitude in both the P and S components. Therefore, for natural light, the intensities of the P and S components are equal. Thus, the energy of the reflected and refracted light after one reflection or refraction is:

[0098]

[0099]

[0100] When light strikes the reflective surface of a metal, i.e., the silver plating, it reacts with the silver during refraction and reflection. The light refracted into the silver plating is essentially lost.

[0101]

[0102]

[0103] and i is the reflectivity of light in the P and S components of the silver plating layer. i3 is the angle of incidence reaching the silver plating layer. n3 is the refractive index of the silver plating layer relative to the glass, which is equal to 0.03416 here. k is the dielectric constant, which is equal to 3.9046 here. The wavelength of the incident light is taken as 587.6 nm.

[0104] When light passes through glass, some of it is absorbed. Heliostats typically use ultra-clear glass; according to experimental results, approximately 1% of the light is absorbed when it passes perpendicularly through the glass, mainly due to absorption by impurities in the glass mirror.

[0105] By solving for the energy distribution of reflected and refracted rays at each interface boundary, the energy of the three parts of the reflected light from the glass surface can be obtained. Finally, the proportion of each of the three parts of the reflected light can be calculated.

[0106]

[0107]

[0108]

[0109] Where R p and R s R' represents the reflectivity of the first reflection from the P component and the S component, respectively. p and R' s T represents the reflectivity of the second reflection occurring on the P and S components, respectively. p and T s T' represents the transmittance of the glass in the P and S components, respectively. p and T' s These are the transmittances of the glass transmitted through the P and S components, respectively. α is the absorption rate of the glass, calculated using the following formula:

[0110]

[0111] Where d is the thickness of the glass and ε is the absorption coefficient, which should be determined based on the test data of a specific reflector.

[0112] Finally, the energy distribution coefficients of the three parts of the reflected light can be calculated:

[0113]

[0114] Although the energy density distributions formed by the three parts of the reflected light are different, the calculation process for the energy flux density of each part is similar. It is only necessary to calculate the energy flux density on the receiving surface of a single part, and then multiply it by the energy distribution coefficient to obtain the energy flux density values ​​of the light rays in the three parts. Finally, the energy flux density distribution of the entire receiving surface can be calculated.

[0115]

[0116] In the formula F i This represents the energy flux density of a single portion of the light reflected.

[0117] In a tower-type heliostat system, the receiving surface is a sufficiently large square plane mirror, and the heliostat itself is a rectangular spherical mirror, such as... Figure 5 As shown, the x-axis points due east, the y-axis points due north, and the z-axis points to the zenith. Calculate the energy flux density distribution across the entire receiving surface. Assume the area of ​​the heliostat's reflecting surface is S1, the area of ​​the receiving surface is S2, n1 and n2 are the normals to the infinitesimal surfaces on the heliostat and receiving surface, O1 and O2 are points on each infinitesimal surface, and β1 and β2 are the angles between the line connecting O1 and O2 and each normal. Then, the analytical expression for the energy flux density at point O2 on the receiving surface is:

[0118]

[0119] In the formula, r = |O1O2| is the distance from the reflection point to the receiving point, I is the total intensity of the reflected light in a single part, and B is the intensity distribution of the reflected light, which is calculated by convolving the solar intensity distribution with the optical error.

[0120] To calculate the distribution of reflected light intensity, it is necessary to first determine the solar light intensity distribution, which is described using a circular Gaussian model. Due to the influence of various factors (such as the sun's position and atmospheric absorption), the solar light intensity distribution is constantly changing, but the standard deviation parameter σ of the solar light intensity distribution... sun It can be determined by the direct light intensity I D Decide:

[0121]

[0122] Then, the optical errors of the reflected rays from multiple parts are determined. An elliptic Gaussian function is used to describe the slope error of the heliostat. Since the light is reflected from both the top and bottom surfaces of the mirror, the equation for calculating the optical error differs for each part of the reflected ray.

[0123] For the first portion I1 of the reflected light ray, which is directly reflected by the upper surface of the glass, the optical error at each point is calculated as follows:

[0124]

[0125]

[0126] Where, σ slopex and σ slopey These are the slope errors in the X and Y directions, respectively.

[0127] For the second part I2 of the reflected light, it will be refracted by the upper surface and reflected by the lower surface. Since the manufacturing technology of glass mirrors used to reflect sunlight is relatively mature, the slope errors of the upper and lower surfaces of the mirror can be assumed to be equal. Therefore, the standard deviation of the optical error at each point is calculated as follows:

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134] Where n0 is the ratio of the refractive index of glass to that of air, typically 1.51. λ and β are the incident angle and azimuth angle of the heliostat's reflection point, respectively. Thus, the standard deviation of the total optical error in both directions can be calculated:

[0135] σ sx 2 =σ x1 2 +σ x2 2 +σ x3 2 (29)

[0136] σ sy 2 =σ y1 2 +σ y2 2 +σ y3 2 (30)

[0137] For the third part of the reflected ray I3, the ray continues to propagate within the glass, so its optical error is twice as large as that of the reflected ray I2.

[0138] σ sx 2 =σ x1 2 +3σ x2 2 +σ x3 2 (31)

[0139] σ sy 2 =σ y12 +3σ y2 2 +σ y3 2 (32)

[0140] The total error of the reflected light at each point of the heliostat is calculated by convolving the errors of the three Gaussian functions, as shown in the following formula:

[0141] σ x 2 =σ sun 2 +σ sx 2 +σ trx 2 (33)

[0142] σ y 2 =σ sun 2 +σ sy 2 +σ try 2 (34)

[0143] Where σ trx and σ try These are the tracking errors in the X and Y directions. All models in this chapter have a tracking error of 0.

[0144] In the elliptic Gaussian model, the distribution of reflected light intensity can be calculated as follows:

[0145]

[0146] Where, θ x Let θ be the angle between the component of O1O2 in the X direction and the reflected rays from the center points of each infinitesimal element on the heliostat. y Let σ be the angle between the component of O1O2 in the Y direction and the reflected rays from the center points of each infinitesimal element on the heliostat. x and σ y These are the total errors in the X and Y directions, respectively.

[0147] In the circular Gaussian model, the reflected ray is no longer divided into three parts, but is calculated as a single reflected ray. For the mirror surface, the optical errors at each point are no longer considered separately, but only the average slope error of the mirror surface is used instead, and the slope error σ is expressed as... slope Simplified to radial, and considering the tracking error σ tr The total error is then calculated as follows:

[0148] σ 2 =σ sun 2 +σ slope2 +σ tr 2 (36)

[0149] In the circular Gaussian model, the intensity distribution function of the reflected light can be expressed as:

[0150]

[0151] θ is the angle between O1O2 and the reflected light from the center of each heliostat unit, and σ is the total error.

[0152] Therefore, for a certain portion of the reflected light, the energy flux density distribution function of a point on the receiving surface of the heliostat can be transformed into:

[0153] Circular Gaussian model:

[0154]

[0155] A more accurate calculation method uses an elliptic Gaussian model:

[0156]

[0157] like Figure 6 As shown, the high-precision heliostat energy flux density calculation method includes the following steps:

[0158] S1. Determine the location based on the solar altitude angle α. s and solar azimuth γ s Calculate the coordinates of the incident ray at the center of the sun, i.e., (u sun ,v sun ,w sun Solar altitude angle α s and solar azimuth γ s The location can be determined based on the longitude and latitude of the heliostat's installation position and the time, or it can be obtained through actual measurement:

[0159] (u sun ,v sun ,w sun )=(-cosα s sinγ s ,-cosα s sinγ s sinα s (40)

[0160] Based on the positions of the heliostat and the receiving surface, the elevation angle α of the reflected solar rays can be calculated. r and azimuth γ r :

[0161]

[0162]

[0163] Among them, (x heliostat ,y heliostat ,z heliostat ) and (x receiver ,y receiver ,z receiver ) represent the coordinates of the heliostat center and the center of the receiving surface in the global coordinate system, respectively.

[0164] The elevation angle α of the normal vector of the heliostat n and azimuth γ n Also, the following should be calculated:

[0165] or,

[0166]

[0167] S2. Grid the heliostat and receiving surface, and establish their respective coordinate systems. Transform the coordinates of the center points of the grids on the heliostat and receiving surface to the global coordinate system. Specifically, grid the heliostat and receiving surface into a 100×100 grid, or alternatively a 50×50 grid. Use the center point of each grid (the grid point) to represent the entire grid. The area of ​​the square grid on the heliostat is represented by Δhg, and the area of ​​the square grid on the receiving surface is represented by Δrg. Based on this, calculate the coordinates of the heliostat and receiving surface in the global coordinate system. In the receiving surface coordinate system, the coordinates of the receiving surface are (x... r ,y r ,z r ) receiver , where x r and y r It is determined based on a uniformly divided grid, because the receiving surface is a plane, so z r The coordinates are always 0. In the heliostat coordinate system, the coordinates of the heliostat are (x... h ,y h ,z h ) heliostat , where x h and y h It is determined based on a uniformly divided grid. Based on the shape of the heliostat surface and the corresponding equation, z is calculated. h Since a heliostat is part of a sphere, it can be calculated using the equation of the sphere. Then, the normal vector at the center point of each heliostat grid is calculated. Specifically, z... h The coordinates are:

[0168]

[0169] After meshing the heliostat and receiving surface, the coordinate systems of the heliostat and receiving surface are transformed into the global coordinate system. The total rotation matrix from the global coordinate system to the heliostat coordinate system is shown below:

[0170]

[0171] Therefore, the coordinates of the heliostat grid points in the global coordinate system are as follows:

[0172] (x h ,y h ,z h ) global =(x heliostat ,y heliostat ,z heliostat ) global +(x h ,y h ,z h ) heliostat ×AH -1 (47)

[0173] Where, α n γ is the elevation angle of the heliostat normal vector. n Let x be the azimuth angle of the heliostat normal vector, (x) heliostat ,y heliostat ,z heliostat ) global This represents the coordinates of the heliostat center in the global coordinate system.

[0174] Similarly, the rotation matrix from the global coordinate system to the receiving surface coordinate system is:

[0175]

[0176] (x r ,y r ,z r ) global =(x receiver ,y receiver ,z receiver ) global +(x r ,y r ,z r ) receiver ×AR -1 (49)

[0177] Among them, (x receiver ,y receiver ,z receiver ) global α represents the coordinates of the center of the receiving surface in the global coordinate system. rn γ is the elevation angle of the normal vector of the receiving surface. rnThe azimuth angle is the normal vector of the receiving surface.

[0178] S3. To calculate the energy flux density reaching a certain grid point on the receiver, first determine the coordinates of the receiving point when the sunlight reflected from all the heliostat grid points hits the receiving surface. Specifically, determine the coordinates of the center of the heliostat sphere:

[0179] x spherical =x heliostat +2hf(-cosα n sinγ n (50)

[0180] y spherical =y heliostat +2hf(-cosα n cosγ n (51)

[0181] z spherical =z heliostat +2hf sinα n (52)

[0182] Determine the normal vectors of each point on the heliostat:

[0183]

[0184]

[0185]

[0186] Among them, l so The distance from a grid point of the heliostat to the center of the heliostat sphere is calculated using the following formula:

[0187]

[0188] Then, based on the incident vector (u) sun ,v sun ,w sun ) and the normal vector (u) of the heliostat grid points hn ,v hn ,w hn The coordinates of the reflected ray in the global coordinate system are calculated using the following formula:

[0189] u ray =2(u hn u sun +v hn v sun +w hn w sun )u hn -u sun (57)

[0190] v ray =2(u hn u sun +v hn v sun +w hn w sun )v hn -v sun (58)

[0191] w ray =2(u hn u sun +v hn v sun +w hn w sun )w hn -w sun (59)

[0192] When the reflected ray reaches the receiving surface, the coordinates of the receiving point in the global coordinate system can be obtained using the following formula:

[0193]

[0194] x rf =x h +u ray ×t (61)

[0195] y rf =y h +v ray ×t (62)

[0196] z rf =z h +w ray ×t (63)

[0197] Among them, (u rn ,v rn ,w rn (x) is the normal vector of the receiving surface. h ,y h ,z h ) represents the coordinates of the heliostat in the global coordinate system.

[0198] S4. Calculate the angle between the ray reflected from any heliostat grid point to the receiving surface grid point and the ray reflected from the center of the sun at the center of the heliostat grid point. Based on the angle and the reflected solar intensity distribution function, calculate the energy flux density of the sunlight reflected from the heliostat grid point to the calculated receiving surface grid point. Specifically, transform the receiving point O3 on the receiving surface from the global coordinate system to the receiving surface coordinate system:

[0199] (x rf ,yrf ,z rf ) receiver =(x rf -x receiver ,y rf -y receiver ,z rf -z receiver ) global ×AR (64)

[0200] The coordinates of grid point O1 on the heliostat are transformed from the global coordinate system to the receiving surface coordinate system:

[0201] (x h ,y h ,z h ) receiver =(x h -x receiver ,y h -y receiver ,z h -z receiver ) global ×AH (65)

[0202] The calculation of the angle between the reflected rays from the grid and the reflected rays from the center of the sun involves the following steps:

[0203] S41. The distance between receiving point O3 and heliostat grid point O1 is:

[0204]

[0205] l in the X and Y directions hrfx and l hrfy They are respectively:

[0206]

[0207]

[0208] S42. The distance between receiving point O3 and receiving surface grid point O2 is:

[0209]

[0210] l rfr The components in the X and Y directions are as follows:

[0211]

[0212]

[0213] S43. The distance between heliostat grid point O1 and receiver surface grid point O2 is:

[0214]

[0215] l rh The components in the X and Y directions are as follows:

[0216]

[0217]

[0218] S44. Calculate the angle between the reflected ray and O1O2 for each grid, such as... Figures 7-9 As shown:

[0219]

[0220]

[0221]

[0222] The intensity distribution function of reflected sunlight is:

[0223]

[0224] Where, σ x and σ y Based on the optical error of heliostats, the distribution of solar intensity, and the theory of optical error propagation, θ is determined. x and θ y These are the x and y components of the angle between the reflected ray and the ray reflected from the center of the sun.

[0225] The formula for calculating the energy flux density at any point on the receiving surface is:

[0226]

[0227] S1 is the projection surface of the heliostat, I is the total intensity of the incident sunlight, and β1 and β2 are the angles of incidence between the reflected rays from the grid points on the heliostat to the grid points on the receiving surface and the heliostat and the receiving surface, respectively. The specific calculation formula is as follows:

[0228]

[0229]

[0230] in,

[0231] S5. By summing the energy flux density contributions of all heliostat grid points to the receiving surface grid points, the energy flux density of the receiving surface grid points can be obtained.

[0232] S6. Repeat S4 and S5 to calculate the energy flux density at all grid points on the receiving surface. Integrate over the heliostat to obtain the energy flux density distribution across the entire receiving surface.

[0233] S7. Calculate the interception rate based on the energy flux density distribution F. The interception rate is calculated by summing the energy flux densities within the receiver's range and dividing by the reflected energy flux density. The formula for calculating the interception rate is:

[0234]

[0235] Where Δrg is the size of the square after the receiving surface is gridded, and E is the total incident energy I.

[0236] To verify the effectiveness of this invention, the accuracy of the calculation results was verified using the root mean square error (RMSE) calculation formula:

[0237]

[0238] Here, F1(u,v) and F2(u,v) represent the energy flux density calculated using the above method and the energy flux density calculated from measured data, respectively. Compared with measured data from ten heliostats, the average error in calculating the interception rate is only 1.13%, far less than Soltrace's calculation error of 2.36%. The average error in calculating the energy flux density at the receiving surface is only 2.83%, far less than Soltrace's calculation error of 3.50%.

[0239] This invention, based on an elliptical Gaussian model, integrally calculates the energy flux contribution of all reflections on the heliostat to all points on the receiving surface. For the glass back mirror, it considers the effects of the three main beams generated by reflections from the upper and lower glass interfaces. Using a circular Gaussian model, it can accurately describe the reflected light intensity distribution, thereby quickly obtaining an accurate energy flux density distribution and interception rate on the receiving surface, thus aiding in system design optimization and operational control.

[0240] The above description discloses only preferred embodiments of the present invention and should not be construed as limiting the scope of the invention. It should be noted that any equivalent variations made to the present invention by those skilled in the art without departing from its design structure and principles are considered within the scope of protection of the present invention.

Claims

1. A high-precision method for calculating the energy flux density of a heliostat, characterized in that... Specifically, it includes the following steps: S1. Determine the location. Based on the sun's azimuth and altitude, as well as the positions of the heliostat and receiver, calculate the incident ray and reflected ray vectors, and the coordinates of the heliostat's normal vector. S2. Grid the heliostat and the receiving surface, and establish their respective coordinate systems. Transform the coordinates of the center points of the grid of the heliostat and the receiving surface to the global coordinate system. S3. Determine the coordinates of the points where the reflected solar rays from all heliostat grid points intersect with the receiving surface; S4. Calculate the angle between the light rays reflected from any heliostat grid point to the target grid point on the receiving surface and the central sunlight reflected from the center of the heliostat grid point. Based on the angle and the reflected sunlight intensity distribution function, calculate the energy flux density of the sunlight reflected from the heliostat grid point to the calculated target grid point on the receiving surface. S5. Sum the energy flux density contributions of all heliostat grid points to the receiving surface grid points to obtain the calculated energy flux density of the receiving surface grid points; S6. Repeat steps S4 and S5 to calculate the energy flux density of all grid points on the receiving surface and obtain the energy flux density distribution of the entire receiving surface. In step S4, the intensity distribution function of the reflected sunlight is: ； Where, σ x and σ y Based on the optical error of heliostats, the distribution of solar intensity, and the theory of optical error propagation, θ is determined. x and θ y These are the x and y components of the angle between the reflected ray and the ray reflected from the center of the sun, respectively, calculated using the following formulas: ； ； in: ； ； ； ； ； ； The formula for calculating the energy flux density at any point on the receiving surface is: ； Where S1 is the heliostat projection surface, and I is the total intensity of incident sunlight. and These are the reflected rays from the grid points on the heliostat to the grid points on the receiving surface, and the angles of incidence of the heliostat and the receiving surface, respectively. ； ； in, , , , Let be the normal vector of the receiving surface. is the normal vector of the heliostat grid points.

2. The high-precision heliostat energy flux density calculation method according to claim 1, characterized in that, In step S1, the coordinates of the incident solar ray at the center are calculated using the following formula. : ； in, The solar altitude angle, The solar azimuth angle can be determined based on the longitude and latitude of the heliostat's installation location and the time, or it can be obtained through actual measurement. The altitude angle of the reflected solar rays is calculated using the following formula. and azimuth : ； ； in, and These represent the coordinates of the heliostat center and the center of the receiving surface in the global coordinate system, respectively, which are determined by their actual relative positions. The elevation angle of the heliostat normal vector is calculated using the following formula. and azimuth : ； or, ; 。 3. The high-precision heliostat energy flux density calculation method according to claim 1, characterized in that, In step S2, the heliostat and the receiving surface are meshed into an n×n grid, where n=50 or 100. The center point of each grid represents the entire grid. In the receiving surface coordinate system, the coordinates of the receiving surface are... , where x r and y r Based on a uniformly divided grid, since the receiving surface is a plane, z r =0, in the heliostat coordinate system, the coordinates of the heliostat are x h and y h It is determined based on a uniformly divided grid, and z is calculated based on the shape of the heliostat surface and the corresponding equation. h Calculate the normal vector of the center point of each heliostat grid; The coordinates of the heliostat grid center point are converted to the coordinates of the global grid center point using the following rotation matrix AH and formula. : ； ； in, The elevation angle is the normal vector of the heliostat. Let be the azimuth angle of the heliostat normal vector. This represents the coordinates of the heliostat center in the global coordinate system. Based on the above formula, the normal vectors of each grid point of the heliostat are transformed to the global coordinate system. The coordinates of the receiving surface mesh center point are converted to the global mesh center point coordinates using the following rotation matrix AR and formula. : ； ； in, This represents the coordinates of the center of the receiving surface in the global coordinate system. The elevation angle of the receiving surface normal vector. Calculate the normal vector of the receiving surface to find the azimuth angle of the receiving surface normal vector. .

4. The high-precision heliostat energy flux density calculation method according to claim 1, characterized in that, In step S3, the center of each grid point of the heliostat is calculated using the following formula. The coordinates of the intersection point of the reflected solar ray vectors on the receiving surface in the global coordinate system are as follows: ； ； ； ； in, This represents the coordinates of the center of the receiving surface in the global coordinate system. Let be the normal vector of the receiving surface. The direction vector coordinates of the reflected ray in the global coordinate system are given by the following formula: ； ； ； in, The vector of the incident ray at the center of the sun. The normal vector of the heliostat grid points; Alternatively, solve the equations for the reflected solar rays from the center and the receiving surface, and then solve for their intersection using the system of equations to obtain (x). rf ,y rf ,z rf ).

5. The high-precision heliostat energy flux density calculation method according to claim 1, characterized in that, The high-precision heliostat energy flux density calculation method includes S7, which calculates the interception rate based on the energy flux density distribution, that is, summing the energy flux densities within the receiver range and dividing by the reflected energy flux density.

6. The high-precision heliostat energy flux density calculation method according to claim 1, characterized in that, When the high-precision heliostat energy flux density calculation method is applied to a glass back mirror as a heliostat, the energy of light directly reflected from the upper surface of the glass, the energy of light passing through the glass and reflected by the reflecting surface on the lower surface of the glass, and the energy of light reflected from the lower surface, reflected by the upper surface of the glass, passing through the glass again, and reflected a second time by the reflecting surface on the lower surface are calculated according to the Fresnel theorem. The energy flux density contribution of each of these energy flux density on the receiving surface is calculated using the aforementioned calculation method.

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