CN107168381B - Method for analyzing influence of terrestrial shape on sun tracking error of heliostat - Google Patents

Method for analyzing influence of terrestrial shape on sun tracking error of heliostat Download PDF

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CN107168381B
CN107168381B CN201710316060.8A CN201710316060A CN107168381B CN 107168381 B CN107168381 B CN 107168381B CN 201710316060 A CN201710316060 A CN 201710316060A CN 107168381 B CN107168381 B CN 107168381B
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CN107168381A (en
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匡荛
董丽枫
周晓鹏
段梦凡
张超
夏苏恒
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Southeast University
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Abstract

The invention discloses a method for analyzing the influence of a spherical shape on sun tracking errors of a heliostat, which comprises the following steps: (1) determining the normal position, the solar altitude angle and the azimuth angle under the condition that the earth is regarded as an ellipsoid; (2) calculating an incident angle and a reflection angle under the condition that the earth is regarded as an ellipsoid according to the data obtained in the step (1); (3) and (3) comparing the data obtained in the step (1) and the step (2) with the data obtained under the condition that the earth is regarded as a standard sphere, and giving the sun tracking error sizes of different latitudes, different mirror field positions and different time periods. The invention has the beneficial effects that: for a tower-type condensing system with a longer reflection optical path, if the earth is regarded as an ellipsoid to calculate the solar altitude angle, the solar azimuth angle and the solar incident angle, the sun tracking precision can be improved, and the loss of the overflow efficiency can be reduced.

Description

Method for analyzing influence of terrestrial shape on sun tracking error of heliostat
Technical Field
The invention relates to the technical field of solar energy utilization, in particular to a method for analyzing influence of a spherical shape on sun tracking errors of a heliostat.
background
In most heliostat sun-tracking control methods, either the azimuth-elevation scheme or the spin-pitch scheme, the earth is regarded as a standard sphere to calculate the correlation angle. However, in practice, the radius of the earth polar region is slightly shorter than that of the equator, and because of the unevenness of the earth surface, the curvature of the earth surface and the curvature of a standard sphere have certain errors, so that the calculation error of the relevant angle is caused. The error is already obviously greater than the precision of the current heliostat in mirror surface manufacturing, installation and sun-tracking mechanical transmission, and although the error has little influence on parabolic trough and disc systems with short reflection optical path, the error can cause large enough focal spot offset for light condensing systems with long reflection optical path, especially tower light condensing systems.
Disclosure of Invention
the invention aims to solve the technical problem of providing an analysis method for the influence of a spherical shape on sun tracking errors of a heliostat, wherein if the earth is regarded as an ellipsoid to calculate the solar altitude angle, azimuth angle and incident angle, the sun tracking precision is improved, and the loss of overflow efficiency is reduced.
In order to solve the technical problem, the invention provides a method for analyzing the influence of a spherical shape on sun tracking errors of a heliostat, which comprises the following steps:
(1) Determining the normal position, the solar altitude angle and the azimuth angle under the condition that the earth is regarded as an ellipsoid;
(2) Calculating an incident angle and a reflection angle under the condition that the earth is regarded as an ellipsoid according to the data measured in the step (1);
(3) And (3) comparing the data obtained in the step (1) and the step (2) with the data obtained under the condition that the earth is regarded as a standard sphere, and analyzing the sun tracking error.
preferably, in the step (1), the determining the position of the normal line specifically includes: the plane of the circle O is the equatorial plane of the earth, the angle FOH is the declination angle delta, and the latitude circle latitude angle of the point B is phi; taking the point B of the latitude as a place at noon, taking B 'as a place at any moment of the same latitude, and then taking the angle BAB' as a time angle omega, wherein the direction of BC is the sunlight direction; BD 'is a ground plane normal of the ground, and a complementary angle of the angle C' B 'D' is a solar altitude angle alpha; if the earth is an ellipsoid, the normal to the tangent plane is the normal to its ground level.
Preferably, in the step (1), the determining the solar altitude angle and the solar azimuth angle specifically includes: when the earth is regarded as an ellipsoid, the semimajor diameter of the ellipsoid is m, the semiminor diameter is n, and an ellipse equation obtained by sectioning the earth through meridian lines can be represented by formula (3):
Ellipse passing through a certain point (x) of the earth0，y0) The tangent equation and the slope are respectively formula (4) and formula (5);
The vector of the B' point tangent plane normal direction is (cos ω, sin ω,) Then, the solar altitude and the solar azimuth, which regard the earth as an ellipse, can be calculated by the equations (6) and (7), respectively:
preferably, in the step (2), the calculating the incident angle specifically includes: assuming that the center of the heat absorption surface and the center of the heliostat are known, the height angle alpha of the reflected lightrAnd an azimuth angle gammaras is known, the incident angle can be calculated by equation (8):
cosλ＝cosαsinγcosαrsinγr+cosαcosγcosαrcosγr+sinαsinαr (8)。
Preferably, in the step (2), the calculating the reflection angle specifically includes: assuming that the central point of a certain heliostat is O ', EO' is incident light of the point, I 'J' is a reflecting surface, the normal line of the heliostat is K 'O', and when no light condensation error exists, the reflected light of the central point of the heliostat is O 'L'; if the earth is taken as a standard sphere to calculate an incident light direction EO ', an included angle between the direction and the incident light direction E ' O calculated by taking the earth as an ellipsoid is equal to EOE '; and at the moment, the normal direction is not changed, the reflected light is changed into L 'O, and the deviation of the reflected light is the included angle LOL'.
The invention has the beneficial effects that: in the sun tracking control, a more accurate calculation angle can be obtained by regarding the earth as an ellipsoid, while regarding the earth as a standard sphere, a calculation error of a reflection angle with an absolute value as high as approximately 1.7mrad (0.1 °) is brought, and even if unfavorable superposition of errors is not considered, a focal spot offset of about 150mm per hundred meters of reflection optical path is caused, that is, for a heliostat with a reflection optical path of up to several hundred meters, the focal spot offset may exceed 1 m. The focal spot is further enlarged if an unfavorable superposition of errors occurs, i.e. the focal spots of different heliostats are deflected in opposite directions, respectively.
in general, in the same mirror field in the months near summer solstice and in the mirror field in the middle latitude area, the larger calculation error of the reflection angle lasts for a longer time. Therefore, for a tower-type condensing system with a long reflection optical path, if the earth is regarded as an ellipsoid to calculate the solar altitude angle, azimuth angle and incident angle, the sun tracking accuracy is improved, and the loss of the overflow efficiency is reduced.
Drawings
FIG. 1 is a schematic diagram of the relationship between the earth and the earth as a standard sphere according to the present invention.
FIG. 2 is a schematic diagram of the relationship between the earth and the earth as an ellipsoid according to the present invention.
FIG. 3 is a schematic diagram of the deflection of the light spot caused by the error of the calculation of the incident angle according to the present invention.
FIG. 4 is a schematic diagram showing the relationship between the mirror field and the position of the heat absorption tower.
FIG. 5(a) is a schematic diagram showing the sun tracking error results for heliostat number 1 of the present invention per month.
FIG. 5(b) is a schematic diagram showing the sun tracking error of heliostat number 2 of the present invention per month.
FIG. 5(c) is a schematic diagram showing the sun tracking error of heliostat number 4 of the present invention per month.
FIG. 5(d) is a schematic diagram showing the sun tracking error of heliostat number 5 of the present invention per month.
FIG. 5(e) is a schematic diagram showing the sun tracking error of heliostat number 7 of the present invention per month.
FIG. 5(f) is a schematic diagram showing the sun tracking error for heliostat number 8 of the present invention per month.
fig. 6(a) is a schematic diagram of the calculation error of the sun tracking of the No. 1 heliostat of the invention using a standard sphere on the autumn equinox day.
fig. 6(b) is a schematic diagram of the calculation error of the sun tracking of the No. 2 heliostat of the invention using a standard sphere on the autumn equinox day.
fig. 6(c) is a schematic diagram of the calculation error of the sun tracking of the No. 4 heliostat of the invention using a standard sphere on the autumn equinox day.
Fig. 6(d) is a schematic diagram of the calculation error of the sun tracking of the No. 5 heliostat of the invention using a standard sphere on the autumn equinox day.
Fig. 6(e) is a schematic diagram of the calculation error of the sun tracking of the No. 7 heliostat of the invention using a standard sphere on the autumn equinox day.
Fig. 6(f) is a schematic diagram of the calculation error of the sun tracking of the No. 8 heliostat of the invention using a standard sphere on the autumn equinox day.
Detailed Description
the data recommended by the international association of geodetic surveying and geophysical in 1975 are: the radius of the semi-length is 6378140 meters, the radius of the semi-length is 6356755 meters, and the flat rate is 1: 298.257. Considering that the elevation scale of most optical concentration system installations is not large compared with the difference between the long and short radii of the earth, we consider the earth as an ellipsoid with a long radius (equatorial radius) of 6378km and a short radius (polar radius) of 6357km, and instead consider the earth as a standard sphere with a radius of 6371km, analyze the relevant angles.
Fig. 1 and 2 are the relationship between the earth and the day, and the earth is regarded as a standard sphere and an ellipsoid, respectively. The plane of the circle O (dotted circle) is the equatorial plane of the earth, the angle FOH is the declination angle delta, and the latitude circle latitude angle of the point B is phi. And taking the point B of the latitude as a place at noon, and taking B 'as a place at any moment of the same latitude, wherein the & lt BAB' is a time angle omega. The direction of BC is the direction of sunlight. BD' is the ground plane normal to the ground. The complementary angle of the angle C ' B ' D ' is the solar altitude angle alpha. If the earth is a standard sphere, the normal of the tangent plane of a certain place is the line connecting the center of the earth and the place (i.e. OB ' and B ' D ' are collinear). If the earth is an ellipsoid, the normal to the tangent plane is the normal to its ground level (OB ' is not collinear with B ' D ', the direction of B ' D ' is calculated separately).
When the earth is regarded as a standard sphere, the solar altitude and azimuth can be calculated by the following formulas (1) and (2):
sinα＝cosφcosδcosω+sinφsinδ (1)
When the earth is regarded as an ellipsoid, as shown in fig. 2, the semimajor diameter of the ellipsoid is m, the semiminor diameter is n, and the equation of the ellipse obtained by sectioning the earth through the meridian can be expressed by formula (3):
Ellipse passing through a certain point (x) of the earth0，y0) The tangent equation and the slope are respectively shown in the formulas (4) and (5).
The vector of the B' point tangent plane normal direction is (cos ω, sin ω,) Then, the solar altitude and the solar azimuth, which regard the earth as an ellipse, can be calculated by the equations (6) and (7), respectively:
Assuming that the center of the heat absorption surface and the center of the heliostat are known, the height angle alpha of the reflected lightrAnd an azimuth angle gammarAre known. The angle of incidence can be calculated by equation (8):
cosλ＝cosαsinγcosαrsinγr+cosαcosγcosαrcosγr+sinαsinαr (8)
As shown in fig. 3, assuming that the central point of a certain heliostat is O, EO is the incident light of the point, AB is the reflection surface, and the normal line of the heliostat is CO, when there is no light-gathering error, the reflected light of the central point of the heliostat should be OD.
If the earth is regarded as a standard sphere to calculate an incident light direction EO, the included angle between the direction and the incident light direction E 'O (closer to the real incident light direction) calculated by regarding the earth as an ellipsoid is equal to EOE'. And at the moment, the normal direction is not changed, the reflected light is changed into D 'O, and the deviation of the reflected light is the included angle < DOD'.
It can be seen that the difference exists between the normal of the ground plane of a certain point on the earth surface calculated by adopting the standard sphere and the ellipsoid, so that errors exist between the calculated solar altitude angle and the solar azimuth angle as well as the final reflection angle. In the polar radius direction and the equatorial radius direction, since the normal directions of the two are the same, there is no error, but the magnitude of the actual error value of the remaining latitude position is related to the latitude, the relative position relationship between the heliostat and the heat absorption tower, and the time angle.
Assume a small field of view at a location 31.55 deg. north latitude at one place. A coordinate system is established by taking the base center of the heat absorption tower as an original point, the negative direction of the y axis is positive north, the negative direction of the x axis is positive east, and the xy axes jointly form a horizontal plane, as shown in FIG. 4. The central coordinates of the heat absorption surface of the tower are (0, 0, 30), and the tower is inclined downwards by 36.5 degrees along the due north direction. In order to examine the position deviation of reflected light caused by adopting a standard sphere under different tower-mirror-sun relation conditions, the heliostat with 9 planes in the edge and the middle of a heliostat field is selected to examine the sun tracking calculation errors of all heliostats in the heliostat field. Due to the symmetry in the morning and afternoon, only the results for a 6-sided heliostat are actually given.
The sun tracking errors of heliostats nos. 1,2,4,5,7 and 8 in fig. 4 in each month are calculated according to two different cases, namely a standard sphere and an ellipsoid, and the results are shown in fig. 5(a) to 5 (f). The numbers in the figure indicate 21 days of the month, and "6" indicates 6 months and 21 days.
The calculation result shows that:
1) Heliostats in the north direction of the heat absorption tower have the largest sun tracking error at noon, and the sun tracking error is nearly 1.5 mrad. This error is beyond the present precision of less than 1mrad in condenser profile processing and sun tracking control, resulting in a 150mm focal spot shift for each hundred meters of large reflection path.
2) in the same mirror field, the closer the heliostat is to its northwest or northeast corner relative to the absorber tower, the smaller this calculation error.
3) The larger error lasts for a longer period of time during the day the closer to the summer solstice months, and vice versa the closer to the winter solstice months. This is not very advantageous since solar radiation resources are more abundant in summer than in winter.
4) At the same moment, the deviation values of different heliostats in the same field are opposite in sign, which indicates that the deviation directions may be opposite, and unfavorable superposition is formed, so that the focal spot size is further enlarged.
the heliostat fields are assumed to be located at 10 different latitudes of 0-90 deg. respectively, where 0 deg. and 90 deg. are calculated as 1 deg. and 89 deg. respectively for convenience of expression. The calculation error of the 1 st, 2 nd, 4 th, 5 th, 7 th and 8 th heliostat in the sun tracking on the autumn day using the standard sphere is shown in fig. 6(a) and fig. 6 (f). The numbers in the figure indicate the north hemisphere latitude, and "3" indicates a north latitude of 30 °.
the calculation result shows that:
1) The closer the heliostat is to the heat absorption tower, the smaller the sun tracking error calculated by adopting a standard sphere is.
2) the error of 30-60 degrees in the middle latitude area is large, and the period of the large error lasting every day is also long.
While the invention has been shown and described with respect to the preferred embodiments, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the scope of the invention as defined in the following claims.

Claims (1)

1. A method for analyzing the influence of a spherical shape on sun tracking errors of a heliostat is characterized by comprising the following steps: (1) determining the normal position, the solar altitude angle and the azimuth angle under the condition that the earth is regarded as an ellipsoid;
The specific steps for determining the position of the normal line are as follows: the plane of the circle O is the equatorial plane of the earth, the angle FOI is the declination angle delta, and the latitude circle latitude angle of the point B is phi; taking the point B of the latitude as a place at noon, taking B 'as a place at any moment of the same latitude, and then taking the angle BAB' as a time angle omega, wherein the direction of BC is the sunlight direction; BD 'is a ground plane normal of the ground, and a complementary angle of the angle C' B 'D' is a solar altitude angle alpha; if the earth is an ellipsoid, the normal of the ground tangent plane is the normal of the ground horizontal plane;
the specific steps for determining the solar altitude angle and the solar azimuth angle are as follows: when the earth is regarded as an ellipsoid, the semimajor diameter of the ellipsoid is m, the semiminor diameter is n, and an ellipse equation obtained by sectioning the earth through meridian lines can be represented by formula (3):
ellipse passing through a certain point (x) of the earth0，y0) The tangent equation and the slope are respectively formula (4) and formula (5);
The vector of the normal direction of the B' point tangent plane isthen, the solar altitude and the solar azimuth, which regard the earth as an ellipse, can be calculated by the equations (6) and (7), respectively:
(2) Calculating an incident angle and a reflection angle under the condition that the earth is regarded as an ellipsoid according to the data obtained in the step (1);
The calculation of the incident angle is specifically: assuming that the center of the heat absorption surface and the center of the heliostat are known, the height angle alpha of the reflected lightrand an azimuth angle gammarAs is known, the incident angle can be calculated by equation (8):
cosλ＝cosαsinγcosαrsinγr+cosαcosγcosαrcosγr+sinαsinαr (8)；
The calculation of the reflection angle specifically comprises: assuming that the central point of a certain heliostat is O ', EO' is incident light of the point, I 'J' is a reflecting surface, the normal line of the heliostat is K 'O', and when no light condensation error exists, the reflected light of the central point of the heliostat is O 'L'; if the earth is taken as a standard sphere to calculate an incident light direction EO ', an included angle between the direction and the incident light direction E ' O calculated by taking the earth as an ellipsoid is equal to EOE '; and at the moment, the normal direction is unchanged, the reflected light is changed into L 'O, and the deviation of the reflected light is the included angle < LOL';
(3) and (3) comparing the data obtained in the step (1) and the step (2) with the data obtained under the condition that the earth is regarded as a standard sphere, and giving the sun tracking error sizes of different latitudes, different mirror field positions and different time periods.
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CN109189104B (en) * 2018-10-16 2021-08-27 旭孚（北京）新能源科技有限公司 Automatic tracking control method and system for heliostat
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