2.1. Mirror official
2.1.1 Basic layout
In the field of tower solar thermal power generation, the radiation grid layout proposed by Laurence et al. is a widely used layout method. This layout method is to alternately place heliostats at constant radii along equal azimuth lines, and as the radial distance increases, the mirror field arrangement also shows a trend from dense to sparse. In order to quantitatively express the positional relationship between the heliostat and the heat-absorbing tower, two parameters, radial spacing ΔR and azimuthal spacing ΔA, are also introduced:
In the formula, HS is the height of the heliostat; WS is the width of the heliostat; L is the height angle of the collector relative to the heliostat; r is the height of the target point (i.e., from the center point of the collector orifice to the heliostat The vertical distance from the center point of the mirror surface) is the horizontal distance from the heliostat to the heat absorption tower when the unit distance is
Based on the idea of radiation grid arrangement, combined with the geometric drawing design method with the goal of avoiding the blocking loss of adjacent heliostats in the same radial direction, EB, No blocking-dense, and DELSOL were later derived. The main difference in the layout of the solar mirror field is that the radial spacing and azimuthal spacing arrangement rules in the near-tower area are different. The formula for calculating the unobstructed radial spacing is as follows:
In the formula, Ht is the optical height of the heat absorber tower; L is the height of the heat absorber; L1 is the length of the line connecting the center point of the heat absorber to the center point of the front row heliostat mirror; L2 is the light reflected by the rear row heliostat. When the light is blocked by the front row heliostat, the horizontal distance between the center point of the line connecting the edge points of the front and rear heliostats and the center point of the front row heliostat mirror; L3 is the heat absorption distance from the center point of the front row heliostat mirror The horizontal distance of the tower; 1 is the angle between the line connecting the center point of the heat absorber to the center point of the front row heliostat mirror and the vertical axis of the heat absorption tower; 2 is the angle between the center point of the heat absorber and the front row heliostat mirror The angle between the line connecting the center point and the line connecting the light reflected from the edge point of the rear heliostat to the center point of the heat absorber when the light reflected from the rear heliostat is just not blocked by the front heliostat; Z0 is the center of the heliostat Height from the horizontal ground; R0 is the radius of the heliostat ring; Ri,j is the radius of the j-th mirror ring in the i-th area of the mirror field; is the light reflected by the rear heliostat that is just not blocked by the front row of heliostats The angle between the reflected light and the axis of the heat absorbing tower. The schematic diagram of the occlusion-free geometric drawing method is shown in Figure 2.1.
The three layouts all stipulate that the azimuth angles of heliostats belonging to the same area must be consistent, so the number of heliostats accommodated in each mirror ring in the same area is the same and the azimuth spacing between heliostats on the same mirror ring is equal. As the radius of the mirror ring increases, the azimuthal spacing of each mirror ring also gradually increases. At this time, the azimuth spacing reset limit factor Arlim will be used to limit the scope of the mirror field in each area to improve land utilization. Otherwise, the azimuth spacing of the mirror ring will continue to increase, causing the mirror field arrangement to become increasingly sparse.
2.1.2 DELSOL layout
DELSOL layout, as shown in Figure 2.2.
In DELSOL, when the ratio of the azimuth distance between the last ring and the first ring of heliostats in a certain area of the mirror field is greater than Arlim, the next mirror field area will start to be arranged. The conditions for arranging a new area of the mirror field are:
In the formula, AZi,1 is the azimuthal spacing of the heliostats in the first ring of the i-th area of the mirror field; AZi,k is the azimuthal spacing of the heliostats in the last ring of the i-th area of the mirror field. The calculation formulas for the characteristic length DM of the heliostat, the azimuth spacing AZi,1 of the first ring heliostats in each region, the azimuth AZ,i of each region, and the number Nhel,i of heliostats in each mirror ring are as follows:
Starting from the first area, it is specified that the radial spacing of the mirror field satisfies ΔR=DM. As the radius of the mirror ring increases, when ΔRi,j=DM does not meet the condition of no occlusion, the j+1 ring in the i-th area begins to experience occlusion loss, and R needs to be increased starting from this ring. At this time, according to The geometric drawing method re-determines the radial spacing, see equations (2.4)-(2.8).
2.1.3 EB layout
EB layout, as shown in Figure 2.3
The calculation formula for the azimuth spacing of the first ring heliostats in each area of the mirror field is:
In the formula, Asf is the azimuthal spacing factor, whose value is mainly related to the tower height, and usually takes a value of 2. Except for the first ring in each area, the azimuth spacing of the heliostats in the remaining rings is calculated from the azimuth angle of the heliostats in the area. The calculation formula is:
In the formula, AZi,j is the azimuth spacing of the j-th ring heliostat in the i-th region of the mirror field. The calculation formula for the heliostat azimuth angle in the i-th mirror field area is:
The calculation formula for the number of heliostats in each mirror ring is shown in Equation (2.13).
The radial distance between heliostats at the junction of adjacent mirror field areas is set to RDM.
R1,1 is the radial distance between the first ring and the second ring in the first area of the mirror field . The calculation formula is:
The radial distance between heliostats of adjacent rings in the same area is always set to R1,1. When the mirror field radius increases to a certain value, the corresponding ring heliostat begins to suffer from occlusion loss, and then the radial spacing is re-determined using the geometric drawing method, see Eq.
2.1.4 No blocking-dense layout
No blocking-dense layout, as shown in Figure 2.4.
This layout is composed of Campo layout [23] and EB layout method. Since the loss of various types of optical efficiency in the near-tower area is smaller, the Campo layout is used to generate a dense mirror field in the center area of the mirror field, which requires that the equivalent circles of the heliostats on the mirror ring are arranged tangently, and the adjacent mirror rings are required to be arranged tangently. The helioscopes are also tangent to each other, minimizing the radial distance between them, that is, the azimuthal distance ADM, while specifying the radial distance RDM. However, as the mirror field radius increases, if the Campo layout continues to be arranged, due to the small azimuth angle and radial distance between the heliostats, a large range of shadow occlusion losses will occur, so the EB layout will be used thereafter.
2.2 Mirror field modeling and analysis
2.2.1 Mirror field modeling
1) Optical efficiency of the mirror field.
Since the number of heliostats in the mirror field usually ranges from thousands to tens of thousands, if the mirror field efficiency is simulated and analyzed every day throughout the year, the calculation amount is very huge. , summer solstice, autumnal equinox, winter solstice) for discrete time sampling, calculate the optical efficiency at the corresponding time point and then obtain the annual average optical efficiency [2]. Based on the fact that the opening angle of the mirror field is 15° [23], the solar position algorithm [24] (SPA) is used to calculate the time zone in which the solar altitude angle is greater than 15° during a typical day, and the mirror field is simulated sequentially at half-hour intervals. optical efficiency and received energy.
The optical efficiency of the mirror field is mainly composed of cosine efficiency, atmospheric attenuation efficiency, shadow occlusion efficiency and truncation efficiency [4]. The average annual efficiency of the mirror field under different layouts is shown in Figure 2.7. It can be seen that the overall average annual optical efficiency of the heliostat field with No blocking-dense layout can be as high as 56.40%, the average annual efficiency of the EB layout is slightly lower, at 55.10%, and the DELSOL layout is the lowest at 53.90%. The main reason for this phenomenon is that the first two mirror field arrangements are more compact, and the No blocking-dense layout in the more efficient near-tower area can accommodate more heliostats. It can also be found from Figure 2.7 that no matter which layout method is adopted, the cosine efficiency value is the lowest. This is because its size mainly depends on the position of the sun and the mirror field coordinates, and cosine loss is inevitable. Atmospheric attenuation efficiency and cutoff efficiency are respectively related to the distance between the heliostat and the heat absorption tower and the heliostat tracking accuracy, and their values are generally relatively high. The shadow occlusion efficiency is mainly affected by the arrangement of the mirror field. The basis of these three layouts is radial staggered arrangement and all combine the idea of no occlusion loss, resulting in less interference between heliostats, thus to a large extent The occlusion loss is reduced, but the shadow occlusion efficiency value cannot reach 1. This is because there is still a shadow loss. In addition, due to the layout rules, the first mirror ring in the subsequent mirror field area will always have occlusion loss.
2.2.2.Land utilization rate
The traditional land utilization rate of the mirror field is defined as the ratio of the heliostat area to the mirror field area. Its size mainly depends on the density of the mirror field, which can reflect the number of heliostats accommodated in the unit land area [25]. However, considering that the heliostat is not in a fixed state during operation, but will move in azimuth and pitch, and requires a certain working space during installation and maintenance, in order to express the land utilization more accurately, it was redefined as a fixed state. The ratio of the sun mirror working area to the mirror field area. Among them, the working area of the heliostat is calculated based on the area of the maximum possible rotation range when it is parallel to the ground, that is, the area of the circle with the diagonal of the rectangular heliostat as the diameter. The calculation formulas [22] for the heliostat working area Arec, the mirror field area Aland, and the land utilization rate are as follows:
In the formula, Rmax is the maximum mirror ring radius of the mirror field.
From the mirror field modeling results, the number of heliostats in three layout modes can be obtained, among which the DELSOL layout contains 4585 heliostats, the EB layout contains 5027 heliostats, and the No blocking-dense layout contains 4856 heliostats. The land utilization rate, area and total heliostat area data of the mirror field under different layouts are shown in Figure 2.8. As can be seen,
The No blocking-dense layout has the highest land utilization rate at 34.49%; the EB layout is second at 33.24%; the DELSOL layout is the lowest at 29.56%. It is not difficult to find from the radial and azimuthal spacing layout rules of the three layouts that the No blocking-dense layout is more compact in the mirror field near the tower area than the EB layout, while the DELSOL layout is sparser. This layout method is also certain. To a certain extent, it affects the land utilization rate of the mirror field. At the same time, because the number of heliostats in the densely packed area of the No blocking-dense layout is determined by the height of the heat-absorbing tower, when the tower height is constant, as the scale of the mirror field increases, the land utilization rate of the mirror field under this layout will continue to increase. Close to EB layout.
(3) Mirror field energy analysis.
Based on the known annual average optical efficiency of the mirror field, select typical days to simulate the optical performance of the mirror field to explore which layout can generate more energy under conditions that limit the mirror field boundary. The initial conditions for the simulation are the same as for the mirror field optical efficiency simulation. Through optical performance simulation, a typical solar mirror field heat absorption tower received energy curve is obtained, as shown in Figure 2.9. It can be seen that the EB layout generates the highest energy among all modes, and DELSOL is the lowest. The reason is that the optical efficiency of the three layouts The difference is not big, so when the difference in the number of heliostats between the EB layout and the No blocking-dense layout is large, the energy received by the EB mirror field is higher.
2.2.3 Shadow occlusion efficiency
(1) Determine the range in which the problem heliostat exists.
The shadow occlusion efficiency is actually the product of the heliostat shadow efficiency and occlusion efficiency. The shadow loss is the loss caused by the incident light of the target heliostat being blocked by surrounding heliostats. Blockage The loss is the loss caused by the reflected light of the target heliostat being blocked by surrounding heliostats [32]. When solving the shadow occlusion efficiency, it is first necessary to determine the possible range of the heliostat's center point on the two-dimensional plane (called the target range) that will cause shadow loss and occlusion loss to the target heliostat. After that, first search for other heliostats besides the target heliostat (called problem heliostats) within the shadow target range of the target heliostat, and find the target heliostat among the identified problem heliostats. Calculate the shadow efficiency of the heliostat that actually causes shadow loss; calculate the coordinate points of the actual lighting part of the heliostat after the shadow loss, and find the problem heliostat that actually causes the shadow loss within the occlusion target range to calculate the occlusion efficiency; The shadow occlusion efficiency is obtained by multiplying the shadow efficiency and occlusion efficiency of the target heliostat.
To solve the problem when shadow occurs, the area where the heliostat is located needs to be solved according to the maximum range, as shown in Figures 3.6 and 3.7. The equivalent circle in the figure represents the maximum motion trajectory that the heliostat's vertex may form on the XY plane when it rotates (this motion trajectory can be produced when the heliostat does not pitch and only rotates horizontally, and the characteristic length of the heliostat is is the diameter of the equivalent circle), the auxiliary line passing through the equivalent circle of the target heliostat is tangent to the problem heliostat according to the reverse component of the incident light ray in the XY plane, and starting from the center of the problem heliostat circle is parallel to the auxiliary line and The equal straight line L2 determines the range P1P2P3P4 where the problem heliostat may exist.
Figure 3.6 The area where the heliostat is located when it is shadowed
In order to facilitate calculation, it is stipulated that the z coordinate of all heliostat center points is 0, the coordinates of the target heliostat are (x, y, 0), and the calculation formula for the area where the problem heliostat is located when a shadow occurs is:
In the same way, the possible range of the problem heliostat when occlusion loss occurs can be solved. That is, after changing the incident light to reflected light, the solution can be solved according to the idea of solving the problem heliostat range when shadows are solved.
(2) Plate projection method to solve S&B loss.
After determining the range of the problem heliostat when shadow or occlusion loss occurs, search for the heliostat number within the range and obtain the vertex coordinates of the corresponding problem heliostat. By pressing the incident Or the reflected light will project the problem heliostat to the target heliostat plane and whether it intersects with the target heliostat to determine whether the problem heliostat has a real shadow or occlusion loss with the target heliostat.
During the incident process, the incident light that should originally hit the target heliostat is blocked by the problem heliostat, as shown in Figure 3.8. Among them, M is the target heliostat. After solving the area where the problematic heliostat is located when shadow occurs, three problematic heliostats W1, W2, and W3 were found. W3 did not block the incident light of M heliostat. In many shadow occlusion efficiency calculations, the geometric projection method or the Monte Carlo ray tracing method is usually used. In the calculation of the geometric projection method, because this type of efficiency loss is mainly caused by adjacent heliostats, the problem heliostat is usually considered to be parallel to the target heliostat in the calculation. However, in fact, the heliostats are larger in size and separated from each other. The distance is also large, and when the problem heliostat is projected to the target heliostat plane along the incident light, the projection surface is not a rectangle, but an irregular quadrilateral, so the error of this method is large; while in Monte In the Carlo ray tracing method, the denser the tracing rays are set, the more accurate the results will be, but conversely the amount of calculation and calculation time will also increase [33]. Therefore, this paper uses an improved geometric projection method to calculate shadow occlusion efficiency. The specific calculation process is as follows:
The center point of the mirror surface of the problem heliostat A is OA (xA, yA, 0), and the four vertices are PA1~PA4. The center point of the target heliostat M is OM (xM, yM, 0), and the four vertices are The order is PM1~PM4. First, the problem heliostat should be projected along the incident light to the target heliostat plane. Combine the incident light and the three-dimensional plane formula to determine the projection distance and thus the projection point. Draw a plane A* parallel to the mirror surface M through the vertex PA1. The three-dimensional expressions of the two planes are:
Taking point PA1 as an example, the x, y, z values of the original coordinate point plus the corresponding component values of the projection distance on the three coordinate axes are its projection point *1,A xP on the problem plane, and the mirror surface The coordinates of the projection points of other vertices on A can also be obtained by this method. The calculation formula is:
Although the projected mirror A* and the target heliostat M are on the same plane, their vertex coordinates are still three-dimensional coordinate data (as shown in Figure 3.9), which is not conducive to calculation of the intersection area, so the projected mirror needs to be The coordinates of the mirror and the problem mirror are transferred to the same plane coordinate system to calculate the area of the overlapping part. The vertex coordinates can be converted from the spatial coordinate system to a new coordinate system with the center point of the target heliostat mirror as the origin and the mirror normal vector direction as the z-axis. That is, the XY plane of the converted spatial coordinate system is the target heliostat plane. , and the z coordinates of the transformed coordinate points are all 0.
The above purpose can be achieved by rotating the global coordinate system at a certain angle. Specifically, the Euler rotation change of the coordinate system can be calculated. First, the rotation angles of the three components in the global coordinate system need to be found. It is stipulated that the rotations are performed around the x-axis, y-axis, and z-axis in sequence. The rotation angles are , , and . When the coordinate system rotates around the x-axis, the angle from the positive direction of the y-axis to the positive direction of the z-axis; when rotating around the y-axis, the angle from the positive direction of the z-axis to the positive direction of the x-axis; when rotating around the z-axis, the angle from the positive direction of the x-axis The angle from the positive direction of the axis to the positive direction of the y-axis. As shown in Figure 3.10.
The corresponding rotation matrices in turn are:
At this time, the directions of the x, y, and z axes of the rotated new coordinate system are consistent with the target coordinate system, but the new coordinate system still takes the origin of the original global coordinate system as its origin, and the origin of the target coordinate system is essentially the target date. The center point of the mirror surface. Therefore, the three-dimensional problem can be converted into a two-dimensional problem by subtracting the new coordinates of each projection point obtained in the new coordinate system from its corresponding target heliostat mirror center point, that is, the final obtained coordinates of each point are The z values are all 0.
After coordinate conversion, a two-dimensional schematic diagram of the target heliostat and the problem heliostat projected on the same plane is obtained, as shown in Figure 3.11. In actual situations, when the sun's altitude angle is low, it is easy for multiple heliostats to block the incident light of the same target heliostat. At this time, the blocked parts may overlap. Therefore, we still need to make detailed calculations for the situation where multi-faceted heliostats cause occlusion at the same time.
The specific calculation method is to determine the mathematical expressions of its four sides based on the projected quadrilateral, determine the intersection of each side with the four sides of the target heliostat and find the intersection point, and then determine the projection of the problematic heliostat in the target heliostat. point and the vertex of the target heliostat within the projection of the problem heliostat, thereby determining the vertex coordinates of the intersection between the two. After successively finding the vertex coordinates of the blocked parts of each problem heliostat projected on the target heliostat, we can then use the above method to find out whether the blocked parts intersect with each other, and find the vertex coordinates of the polygon after the overlap of the blocks. , and then find the area of the blocked part to determine the shadow loss. The occlusion loss can also be solved according to the above method.
The overall solution for the shadow occlusion efficiency is as follows:
