Solar array area calculation method based on finite element thought

Abstract

The present disclosure relates to a method for calculating the area of a solar array shielded by a satellite based on the finite element method, which comprises: constructing a finite element calculation model of a satellite shielding a solar array, the model including a satellite body and a solar array; proving the convergence of the finite element calculation model of the satellite shielding the solar array; and calculating the area of the solar array shielded by the satellite body according to the proof result. The method for calculating the area of a solar array shielded by a satellite proposed by the present disclosure divides and calculates the first solar surface of the solar array by using the finite element method, which can effectively calculate the area of the solar array shielded by the satellite body in various attitudes, and the calculation result is basically consistent with the real data of the satellite in orbit.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of space measurement and control, and particularly relates to a solar array area calculation method based on finite element thought. BACKGROUND

[0002] During the space flight, the satellite will present different attitudes, which will cause the mutual occlusion between the surfaces of the satellite body and the solar array, which will affect the current calculation of the satellite solar array. Especially under some extreme conditions, the mutual occlusion will cause the power supply shortage of the solar array, and if the interference caused by the mutual occlusion cannot be excluded, it will make the on-orbit abnormal analysis of the satellite very difficult. Therefore, it is necessary to improve one or more problems existing in the above-mentioned related technical solutions to improve the global estimation accuracy and system fault tolerance performance of the navigation system.

[0003] It should be noted that the information disclosed in the above background section is only used to strengthen the understanding of the background of the present disclosure, and therefore can include information which does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0004] The purpose of the embodiments of the present disclosure is to provide a solar array area calculation method based on finite element thought, which can effectively calculate the area of the solar array occluded by the satellite body under various attitudes of the satellite, and the area calculation result is basically consistent with the real data of the satellite in orbit.

[0005] The embodiments of the present disclosure provide a satellite solar array area calculation method, which comprises the following steps:

[0006] Constructing a finite element calculation model of the satellite solar array, wherein the finite element calculation model comprises a satellite body and a solar array;

[0007] Proving the convergence of the finite element calculation model of the satellite solar array;

[0008] According to the proof result, the area of the solar array occluded by the satellite body is calculated.

[0009] In an exemplary embodiment of the present disclosure, the step of constructing a finite element calculation model of the satellite solar array comprises:

[0010] Establishing a first space rectangular coordinate system with the geometric center of the satellite body as the origin;

[0011] Dividing the surfaces of the satellite body and the solar array into a plurality of blocks respectively, and giving the finite element center coordinates of each surface of the satellite body and the solar array and the division point coordinates of each block;

[0012] Selecting an arbitrary point on the orbit of the satellite, a second space rectangular coordinate system is established according to the position relationship between the sun center point and the geometric center point of the satellite body; and the coordinate conversion is carried out according to the sunlight irradiation direction;

[0013] The center coordinates of each face of the satellite body are compared with the center coordinates of the solar panel, and a plurality of coverage conditions of the satellite body and the solar panel are obtained.

[0014] In an example embodiment of the present disclosure, in the step of establishing the first space rectangular coordinate system with the geometric center of the satellite body as the origin, the length of the satellite body is SFL , the height of the satellite body is SFH , the width of the satellite body is SFW , the wing length of the solar panel is SWL , the wing width of the solar panel is SWW , the total length of the satellite body and the solar panel is ALL , the angle between the solar panel and the plane of the OZ axis of the first space rectangular coordinate system is α, the center axis of the solar panel deviates from the OX axis of the first space rectangular coordinate system by AxiaX , and the center axis of the solar panel deviates from the OY axis of the first space rectangular coordinate system by AxiaY .

[0015] In an example embodiment of the present disclosure, the surfaces of the satellite body and the solar panel are respectively divided into a plurality of blocks, and the center coordinates of each face of the satellite body and the solar panel and the division point coordinates of each block are respectively given.

[0016] The formula of the finite element center coordinates of the satellite body includes:

[0017] (1)

[0018] Wherein, for the satellite body, in the formula of the finite element center coordinates k =0,...,9; j =0,...,9; for the solar panel, in the formula of the finite element center coordinates k =0,...,9; j =0,...,39; n indicates each face of the satellite body and the solar panel; l indicates the coordinates of a certain point on the x axis; m indicates the coordinates of a certain point on the y axis; w indicates the coordinates of a certain point on the z axis; n indicates the coordinates of a certain point on the x axis of the nth face; mn represents the coordinate of a certain point on the nth face along the y-axis; w n represents the coordinate of a certain point on the nth face along the z-axis; x, y and z represent the x-axis, y-axis and z-axis of the first spatial rectangular coordinate system, respectively.

[0019] The formula of the segment point coordinate of each of the blocks of the first face of the satellite body includes:

[0020] (2)

[0021] The formula of the segment point coordinate of each of the blocks of the second face of the satellite body includes:

[0022] (3)

[0023] The formula of the segment point coordinate of each of the blocks of the third face of the satellite body includes:

[0024] (4)

[0025] The formula of the segment point coordinate of each of the blocks of the fourth face of the satellite body includes:

[0026] (5)

[0027] The formula of the segment point coordinate of each of the blocks of the fifth face of the satellite body includes:

[0028] (6)

[0029] The formula of the segment point coordinate of each of the blocks of the sixth face of the satellite body includes:

[0030] (7)

[0031] The formula of the segment point coordinate of each of the blocks of one of the solar panels includes:

[0032] (8)

[0033] The formula of the segment point coordinate of each of the blocks of the other solar panel includes:

[0034] (9)

[0035] In which, for the satellite body, in the formula of the segment point coordinate i =0,...,10; j =0,...,10; for the solar panel, in the formula of the segment point coordinate i =0,...,10;j =0,...,40.

[0036] In an example embodiment of the present disclosure, the step of establishing the second space rectangular coordinate system according to the positional relationship between the sun center point and the geometric center point of the satellite body at an arbitrary point on the orbit of the satellite includes:

[0037] The step of establishing the second space rectangular coordinate system according to the positional relationship between the sun center point and the geometric center point of the satellite body at an arbitrary point on the orbit of the satellite includes connecting the geometric center point O of the satellite body and the sun center point M to obtain a vector OM; passing through the point O and the perpendicular plane of the vector OM to obtain ON; and selecting two mutually perpendicular straight lines OP and OQ in the ON plane to establish the second space rectangular coordinate system with the straight line OP as the OX' axis and the straight line OQ as the OY' axis, and the direction of the incident sunlight as the opposite direction of the OZ' axis.

[0038] In an example embodiment of the present disclosure, the step of performing coordinate conversion according to the direction of the incident sunlight includes rotating the original coordinates (x, y, z) of the first space rectangular coordinate system to obtain the rotated coordinates (x', y', z') of the second space rectangular coordinate system, and the formula of the coordinate conversion includes:

[0039] (10) wherein,

[0040] , , are the included angles between the OX' axis and the OX axis, the OY axis and the OZ axis in the original coordinate system, respectively;

[0041] , , are the included angles between the OY' axis and the OX axis, the OY axis and the OZ axis in the original coordinate system, respectively;

[0042] , , are the included angles between the OZ' axis and the OX axis, the OY axis and the OZ axis in the original coordinate system, respectively.

[0043] In an example embodiment of the present disclosure, the step of comparing the center coordinates of each face of the satellite body with the center coordinates of the solar panel to obtain multiple cases in which the satellite body covers the solar panel includes:

[0044] Case 1: The satellite body covers the center point of the solar panel but does not completely cover the solar panel.

[0045] Case 2: The satellite body does not cover the center point of the solar panel and does not completely cover the solar panel.

[0046] In an example embodiment of the present disclosure, the step of proving the convergence of the finite element calculation model of the satellite blocking the solar panel includes:

[0047] According to the case that the satellite body covers the solar panel, the area of the non-blocked part of the solar panel in case 1 is The area of the blocked part of the solar panel in case 2 is Let the true value be When the block in the solar panel is N, the calculated value is , S is the area of the solar panel, then we get:

[0048] (11)

[0049] The blocks on the solar panel in case 1 and case 2 are divided in a way that the number is a multiple of 4N; the length of the solar panel is divided into parts, and the width of the solar panel is divided into parts;

[0050] According to the continuous division results, the convergence of the finite element calculation model of the satellite blocking the solar panel is verified;

[0051] The true value refers to the actual blocked area under certain conditions, and the calculated value refers to the result calculated by the finite element method under the same conditions.

[0052] In an example embodiment of the present disclosure, the process of verifying the convergence of the finite element calculation model of the satellite blocking the solar panel includes:

[0053] ,

[0054] Let That is ,

[0055] When , is less than ,

[0056] When , ;

[0057] Similarly, when , ;

[0058] We get

[0059] Therefore, it is proved that the finite element calculation model of the satellite shielding the solar panel is convergent.

[0060] In an example embodiment of the present disclosure, the area calculation process of the satellite body shielding the solar panel comprises:

[0061] calculating the area of each block in the satellite body shielding the solar panel,

[0062] The area calculation formula of each block in the satellite body shielding the solar panel comprises:

[0063] (12)

[0064] determining that the result calculated by the calculation formula satisfies

[0065] (13) The number of values satisfying the condition is N',

[0066] obtaining the total area of the satellite body shielding the solar panel, and the total area calculation formula of the satellite body shielding the solar panel is: S 总遮挡 =N'x S 遮挡

[0067] wherein, l n’ represents the coordinate on the x-axis after the conversion of the nth face; m n’ represents the coordinate on the y-axis after the conversion of the nth face; & represents the meaning of "and"; p represents the number of blocks representing the finite element center of the satellite body, and q represents the number of blocks representing the satellite body segmentation point.

[0068] The technical solution provided by the present disclosure can include the following beneficial effects:

[0069] In the embodiment of the present disclosure, a calculation method for the area of the satellite shielding the solar panel is proposed, which adopts the finite element idea to divide and calculate the first sun-facing surface of the solar panel, and can effectively calculate the area of the solar panel shielded by the satellite body in various attitudes. The area calculation result is basically consistent with the real data of the satellite in orbit. BRIEF DESCRIPTION OF DRAWINGS

[0070] The accompanying drawings, which are incorporated herein and constitute part of this specification, illustrate embodiments consistent with the present disclosure and, together with the description, further serve to explain the principles of the present disclosure. It is to be understood that the drawings are only schematic, and that they do not necessarily represent a limiting case of the present disclosure. For a better understanding of the present disclosure, reference will now be made to the accompanying drawings, in which:

[0071] Figure 1 a-4a shows a schematic diagram of the method for calculating the area of the sun shield of the satellite in the exemplary embodiment of the present disclosure;

[0072] Figure 2 a-5a shows a schematic diagram of the first space rectangular coordinate system established with the geometric center of the satellite body as the origin in the exemplary embodiment of the present disclosure;

[0073] Figure 3 a-6a shows a schematic diagram of the principle of the satellite body covering the sun shield in the exemplary embodiment of the present disclosure;

[0074] Figure 4 a-4d shows a schematic diagram of various cases of the satellite body covering the sun shield in the exemplary embodiment of the present disclosure;

[0075] Figure 5 a-5b shows a schematic diagram of the third face being perpendicular to the first face in the exemplary embodiment of the present disclosure; Figure 3 c and Figure 3 d being divided in a manner of 4N times;

[0076] Figure 6 a-6b shows a schematic diagram of the satellite body covering the sun shield in the exemplary embodiment of the present disclosure; when reaching the maximum;

[0077] Figure 7 a-7b shows a schematic diagram of the center point coordinate of the seventh face after conversion being perpendicular to the third face in the exemplary embodiment of the present disclosure DETAILED DESCRIPTION

[0078] Example implementations will now be described more fully with reference to the accompanying drawings. Example implementations may, however, be implemented in many different forms and should not be construed as limited to the implementations set forth herein; rather, these implementations are provided so that this disclosure will be thorough and complete, and will fully convey the scope of example implementations to those skilled in the art. Features described in the description, structures, or characteristics may be combined in any suitable manner in one or more implementations.

[0079] In addition, the accompanying drawings are merely schematic and are not necessarily drawn to scale. Like reference numerals in the drawings denote like or similar parts, and so repeated description thereof will be omitted. Some of the block diagrams shown in the drawings are functional entities that do not necessarily have to correspond to physically or logically independent entities. These functional entities can be implemented in the form of software, or in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0080] A method for calculating the area of a satellite-shielded solar array is provided in the present example embodiment, which can include the following steps, as shown in Figure 1

[0081] Step S101: constructing a finite element calculation model of a satellite-shielded solar array, which includes a satellite body and a solar array;

[0082] Step S102: proving the convergence of the finite element calculation model of the satellite-shielded solar array;

[0083] Step S103: calculating the area of the satellite-shielded solar array according to the proof result.

[0084] The method for calculating the area of a satellite-shielded solar array provided in the present embodiment adopts the finite element idea to divide and calculate the first sun-facing surface of the solar array, and can effectively calculate the area of the solar array shielded by the satellite body in various attitudes, and the calculation result of the area is basically consistent with the real data of the satellite in orbit.

[0085] Next, each step of the calculation method in the present example embodiment will be described in more detail.

[0086] In the present embodiment, a regular hexahedral satellite is selected as an example for illustration.

[0087] In step S101, the present disclosure utilizes the finite element idea to construct a finite element calculation model of a satellite-shielded solar array, which includes a satellite body and two solar arrays, and this step includes the following sub-steps:

[0088] Step S1011: establishing a first space rectangular coordinate system with the geometric center of the satellite body as the origin.

[0089] Referring to Figure 2 A first space rectangular coordinate system is established with the collection center of the hexahedral satellite as the origin, with the direction through the faces 5-6 of the hexahedral satellite as the direction of the OX axis, with the direction through the faces 2-4 of the hexahedral satellite as the direction of the OY axis, and with the direction through the faces 1-3 of the hexahedral satellite as the direction of the OZ axis.​

[0090] Step S1012: respectively dividing the surface of the satellite body and the solar panel into multiple blocks, and respectively giving the finite element center coordinates of each face of the satellite body and the solar panel and the coordinates of the division points of each block;

[0091] Here, the six faces of the satellite are respectively divided into 10x10 blocks (i.e. 100 blocks), and each solar panel is divided into 10x40 blocks (i.e. 400 blocks). It is specified that the length of the satellite body is SFL , the height of the satellite body is SFH , the width of the satellite body is SFW , the wing length of the solar panel is SWL , the wing width of the solar panel is SWW , the total length of the satellite body and the two solar panels is ALL , the angle between the solar panel and the face of the OZ axis of the first space rectangular coordinate system is a, the deviation of the central axis of the solar panel from the OX axis of the first space rectangular coordinate system is AxiaX , and the deviation of the central axis of the solar panel from the OY axis of the first space rectangular coordinate system is AxiaY .

[0092] As shown in Figure 2 , the satellite body and the solar panel of the hexahedral satellite are divided into 8 faces by the first space rectangular coordinate system, and are respectively represented by the numbers 1-8 in Figure 2 , wherein the satellite body includes 6 faces (face 1 to face 6), and the solar panel includes 2 faces (face 7 and face 8). Here, the finite element center coordinates of each face and the coordinates of each division point are established.

[0093] Suppose the finite element center coordinates of the first face of the satellite body are , p=0,...,99, and the coordinates of each division point of the first face are , q=0,...,120. Then the coordinates of each division point in the first face can be expressed as:

[0094] (2)

[0095] Then the finite element center coordinates of the first face of the satellite body can be expressed as:

[0096]

[0097] Similarly, suppose the finite element center coordinates of the second face of the satellite body are , p=0,...,99, and the coordinates of each division point of the second face are , q=0,...,120. Then the coordinates of each division point in the second face can be expressed as:

[0098] (3)

[0099] Then the finite element center coordinates of the second face of the satellite body can be expressed as:

[0100]

[0101] Suppose the finite element center coordinates of the third face of the satellite body are , p = 0,..., 99, and the coordinates of each partition point of the third face are , q = 0,..., 120. Then the coordinates of each partition point in the third face can be expressed as:

[0102] (4)

[0103] Then the finite element center coordinates of the third face of the satellite body can be expressed as:

[0104]

[0105] Suppose the finite element center coordinates of the fourth face of the satellite body are , p = 0,..., 99, and the coordinates of each partition point of the fourth face are , q = 0,..., 120. Then the coordinates of each partition point in the fourth face can be expressed as:

[0106] (5)

[0107] Then the finite element center coordinates of the fourth face of the satellite body can be expressed as:

[0108]

[0109] Suppose the finite element center coordinates of the fifth face of the satellite body are , p = 0,..., 99, and the coordinates of each partition point of the fifth face are , q = 0,..., 120. Then the coordinates of each partition point in the fifth face can be expressed as:

[0110] (6)

[0111] Then the finite element center coordinates of the fifth face of the satellite body can be expressed as:

[0112]

[0113] Suppose the finite element center coordinates of the sixth face of the satellite body are , p = 0,..., 99, and the coordinates of each partition point of the sixth face are , q = 0,..., 120. The coordinates of each partition point in the sixth face can be expressed as:

[0114] (7)

[0115] The finite element center coordinates of the sixth face of the satellite body can be expressed as:

[0116]

[0117] Assuming that the finite element center coordinates of the seventh face (the upper solar panel) are , p = 0,..., 399, the coordinates of each partition point of the seventh face are , q = 0,..., 440. The coordinates of each partition point in the seventh face can be expressed as:

[0118] (8)

[0119] The finite element center coordinates of the seventh face can be expressed as:

[0120]

[0121] Assuming that the finite element center coordinates of the eighth face (the lower solar panel) are , p = 0,..., 399, the coordinates of each partition point of the eighth face are , q = 0,..., 440. The coordinates of each partition point in the eighth face can be expressed as:

[0122] (9)

[0123] The finite element center coordinates of the eighth face can be expressed as:

[0124]

[0125] This embodiment is a regular hexahedral satellite with two solar panels. If it is extended to a regular n-hedron, the formula of the finite element center coordinates is:

[0126] (1)

[0127] wherein, for the satellite body, in the formula of the finite element center coordinates k = 0,..., 9; j = 0,..., 9; for the solar panels, in the formula of the finite element center coordinates k = 0,..., 9; j = 0,..., 39; n indicates each face of the satellite body and the solar panels; l indicates the coordinates of a certain point on the x-axis.m represents the coordinate of a certain point on the y-axis; w represents the coordinate of a certain point on the z-axis; n represents the coordinate of a certain point on the x-axis of the nth face; m n represents the coordinate of a certain point on the y-axis of the nth face; w n represents the coordinate of a certain point on the z-axis of the nth face; x, y and z respectively represent the x-axis, the y-axis and the z-axis of the first spatial rectangular coordinate system.

[0128] Step S1013: selecting an arbitrary point of the satellite on the running track, establishing a second spatial rectangular coordinate system according to the positional relationship between the sun center point and the geometric center point of the satellite body; and performing coordinate conversion according to the sunlight incidence direction;

[0129] In step S1013, first, an arbitrary point of the satellite on the running track is selected, and the geometric center point O of the satellite body and the sun center point M are connected according to the positional relationship between the sun center point and the geometric center of the satellite body, to obtain a vector OM, for example (3, 1, 17). The ON plane is perpendicular to the O (0, 0, 0) point and the OM vector, and two mutually perpendicular straight lines OP and OQ are selected in the ON plane. The straight line OP is taken as the OX' axis, and the straight line OQ is taken as the OY' axis to establish a second spatial rectangular coordinate system. At this time, the sunlight incidence direction can be approximately regarded as the opposite direction of the OZ' axis.

[0130] Secondly, the step of performing coordinate conversion according to the sunlight incidence direction includes: rotating the original coordinates (x, y, z) of the first spatial rectangular coordinate system to obtain the rotated coordinates (x', y', z') of the second spatial rectangular coordinate system, and the formula of the coordinate conversion is:

[0131] (10) wherein,

[0132] , , are the included angles of the OX' axis with the OX axis, the OY axis and the OZ axis in the original coordinate system, respectively;

[0133] , , are the included angles of the OY' axis with the OX axis, the OY axis and the OZ axis in the original coordinate system, respectively;

[0134] , , are the included angles of the OZ' axis with the OX axis, the OY axis and the OZ axis in the original coordinate system, respectively.

[0135] Step S1014 compares the center coordinates of each face of the satellite body with the center coordinates of the solar panel to obtain various coverage conditions of the satellite body and the solar panel

[0136] In step S1014, it can be known according to geometric principles that the blocks of the same face cannot cover each other, so it is not necessary to compare the blocks of the same face with each other; and it can be known from the characteristics of the regular hexahedron that the sun can only illuminate three faces at most, so it is only necessary to compare the blocks of the three faces obtained according to the illumination direction of the sun.

[0137] It should be noted that, as shown in Figure 3 , the comparison between two faces means that the first block of the first face is compared with all the blocks of the second face, then the second block of the first face is compared with all the blocks of the second face, and so on until all the blocks of the two faces are compared once. The comparison is performed by projecting the coordinates of all the points onto the same plane, and the basis is whether the center coordinates of the block of the first face are contained in a block of the second face. The basis for the center point of the block of the second face being contained in the block of the first face is the coverage block.

[0138] As shown in Figure 3 , assuming that the length of the block is Length and the width is Width, then the distance from the center point L1 of a block of the first face to a block of the second face to form a straight line M1M2 is less than or equal to the length Length, and the distance to form a straight line I1I2 is less than or equal to Width, which indicates that the center point L1 of the block is covered, i.e., the block is covered.

[0139] It can be seen that, in step S1014, according to the above discussion, it can be known that the center point being covered indicates that the block is covered, and the center point not being covered indicates that the block is not covered. Thus, there will be some errors because the center point being covered does not mean that the entire block is covered, and the center point not being covered does not mean that the block is not covered at all, so the following situations occur, as shown in Figure 4 a-4d:

[0140] Case 1: The satellite body covers the center point of the solar panel but does not completely cover the solar panel.

[0141] Case 2: The satellite body does not cover the center point of the solar panel and does not completely cover the solar panel.

[0142] Case 1 can be represented by Figure 4 a and Figure 4 c, Figure 4 a is a special case of Figure 4 c; and case 2 can be represented by Figure 4 b and Figure 4 d, Figure 4b is Figure 4 Special case of d.

[0143] According to the coverage, step S102: the convergence of the finite element calculation model of the satellite blocking the solar panel is proved; including the following steps:

[0144] In step S1021, Figure 3 The part of c that is not blocked is called The part of d that is blocked is called Figure 3 The part of d that is blocked is called , the true value is When the block in the solar panel is N, the calculated value is , S The area of the solar panel is

[0145] (11)

[0146] The true value refers to the actual blocked area under certain conditions, and the calculated value refers to the result calculated by the finite element method under the same conditions.

[0147] In step S1022, the blocks of c and 3d are taken to further divide the blocks of the solar panel: as shown in Figure 3 a and Figure 5 b, Figure 5 a is the schematic diagram after case 1 division, Figure 5 b is the schematic diagram after case 2 division. As can be seen, as the number of blocks N increases, Figure 5 is gradually reduced, is also gradually reduced. Now the number of blocks of the solar panel light receiving area is divided by 4N times, and the initial division of 10 40 (wide long) can be known, the solar wing is divided into parts, the wing width of the solar panel is divided into parts, as shown in . The boundary line of the regular hexahedral satellite blocking surface passes through all the blocks Figure 6 c. Figure 3

[0148] In step S1023, the convergence of the finite element calculation model of the satellite blocking the solar panel is verified according to the continuous division result. The proof process is as follows:

[0149] ,

[0150] Let , that is ​

[0151] When , less than ,

[0152] then when , ;

[0153] Similarly, when , ;

[0154] get

[0155] Therefore, it is proved that the finite element calculation model of the satellite shielding solar panel is convergent.

[0156] As Figure 5 shown, Figure 5 a, the length and width of the regular hexahedral satellite shielding surface are less than the wing length and wing width of the solar panel; obviously ; Figure 5 b, the maximum number of diagonal crossing blocks is equal to the wing length of the solar panel (the number of blocks crossed by the sun diagonal is equal to the number of blocks divided by the wing length of the solar panel), so also satisfies

[0157] Step S103: according to the convergence proof result, the area of the satellite body shielding the solar panel is calculated. The calculation process is as follows:

[0158] 1. First, the area calculation process of the satellite body shielding the solar panel includes:

[0159] calculating the area of each block in the satellite body shielding the solar panel,

[0160] the area calculation formula of each block in the satellite body shielding the solar panel includes:

[0161] (12)

[0162] determine whether the result calculated by the formula satisfies

[0163] (13) the number of numerical values of the condition is N',

[0164] get the total area of the satellite body shielding the solar panel, the total area calculation formula of the satellite body shielding the solar panel is: S 总遮挡 =N' × S 遮挡

[0165] where, l n’This represents the x-coordinate of the nth face after transformation; m n’ This represents the y-coordinate of the nth face after transformation; & It means "and"; p This indicates the number of blocks representing the finite element center of the satellite body, and q This indicates the number of blocks representing the segmentation points of the satellite body.

[0166] This explanation uses the coordinates (3, 1, 17) of the Sun's center point relative to the satellite's body coordinate system as an example. Ignoring factors such as sunlight reflecting off the Earth, the surfaces illuminated by the Sun are the 3rd, 4th, 6th, 7th, and 8th faces. The body coordinates of each point on each face, converted to solar coordinates, are (x...). 3’ ,y 3’ ,z 3’ ), (x 4’ ,y 4’ ,z 4’ ), (x 6’ ,y 6’ ,z 6’ ), (x 7’ ,y 7’ ,z 7’ ) and (x 8’ ,y 8’ ,z 8’ The coordinates of each dividing point after the third face transformation can be denoted as (). , , ), where q=0,...,120; the coordinates of the dividing points after the transformation of the fourth face can be denoted as ( , , ), q=0,...,120; the coordinates of the dividing points after the transformation of the sixth face can be denoted as ( , , ), q=0,...,120; the coordinates of the center point after the transformation of the seventh face can be denoted as ( , , ), p=0,...,399; The coordinates of the center point after the transformation of the eighth face can be denoted as ( , , ), p=0,...,399.

[0167] Based on the above discussion, let's now take the coordinates of a certain center point after the transformation of the seventh face (the... i For example, (one) Figure 7 As shown, its X-axis and Y-axis coordinates are located in the middle of the coordinates of the four cut points on the third face. Then, the module represented by the coordinates of this center point (the first cut point) is...i The block is occluded by the third face, i.e. as satisfying the formula The block is occluded by the third face, i.e. as satisfying the formula i The block is occluded by the third face.

[0168] Assuming SWL=20, SWW=5.3, ALL=54, a=0, SFL=5, SFW=7, SFH=9, three groups of calculations are respectively performed, and the calculation results obtained according to formula (12) are shown in Tables 1-3.

[0169] When x3=3, y3=1, z3=17, the calculation results shown in Table 1 are obtained as follows:

[0170] Table 1: First group of calculation results table

[0171]

[0172] When x3=3, y3=1, z3=7, the calculation results shown in Table 2 are obtained as follows:

[0173] Table 2: Second group of calculation results table

[0174]

[0175] When x3=3, y3=3, z3=3, the calculation results shown in Table 3 are obtained as follows:

[0176] Table 3: Third group of calculation results table

[0177]

[0178] As can be seen from the proof result of convergence, the calculation results are approximately convergent, which is consistent with the conclusion of the theoretical proof. Meanwhile, the calculation results obtained are basically reasonable compared with the real conditions of the satellite in orbit, thereby proving that the method of the present disclosure can effectively calculate the area of the solar sail occluded by the satellite body under various attitudes of the satellite.

[0179] It should be noted that although the steps of the method in the present disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in this specific order, or that all the steps shown must be performed to achieve the desired results. In addition to or alternatively, some steps can be omitted, a plurality of steps can be combined into one step, and / or one step can be divided into a plurality of steps, etc. In addition, it is also easy to understand that these steps can be executed synchronously or asynchronously, for example, in multiple modules / processes / threads.

[0180] It should be noted that, although several units of the system for action execution are mentioned in the foregoing detailed description, such division is not mandatory. In fact, according to embodiments of the present disclosure, features and functions of two or more units described above can be embodied in one unit. Conversely, features and functions of one unit described above can be further divided into units embodied by multiple units. Part or all of the units can be selected to achieve the purpose of the present disclosure according to actual needs. Those skilled in the art can understand and implement without creative labor.

[0181] Other embodiments of the present disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the application disclosed herein. It is intended that the present disclosure cover any and all variations of the present disclosure that come within the scope of the following claims and their equivalents. It is intended that the specification and examples be considered exemplary only, with the true scope and spirit of the present disclosure being indicated by the following claims.

Claims

1. A method for calculating the shading area of ​​solar panels based on the finite element method, characterized in that, Includes the following steps: A finite element model of a satellite blocking a solar panel is constructed, the finite element model including the satellite body and the solar panel; wherein, A first spatial rectangular coordinate system is established with the geometric center of the satellite body as the origin; The surfaces of the satellite body and the solar panel are divided into multiple blocks, and the finite element center coordinates of each surface of the satellite body and the solar panel and the coordinates of the dividing point of each block are given respectively; Select any point on the satellite's orbit and establish a second spatial rectangular coordinate system based on the positional relationship between the sun's center point and the satellite's geometric center point; then perform coordinate transformation according to the direction of sunlight illumination. By comparing the center coordinates of each facet of the satellite body with the center coordinates of the solar panel, various coverage scenarios of the satellite body and the solar panel are obtained, including: Scenario 1: The satellite body covers the center point of the solar panel but does not completely cover the solar panel; Scenario 2: The satellite body does not cover the center point of the solar panel, nor does it completely cover the solar panel; The convergence of the finite element calculation model of the satellite blocking the solar panel is proven, including: Based on the situation where the satellite body covers the solar panel, the area of ​​the unobstructed portion of the solar panel in situation 1 is defined as follows: The area of ​​the solar panel that is blocked in scenario 2 is... Let the true value be... When the number of blocks in the solar panel is N, the calculated value is , S Given the area of ​​the solar panel, we get: （11） The sections on the solar panel in cases 1 and 2 are divided in multiples of 4N; the wing length of the solar panel is then divided into sections. The width of the solar panel is converted into portions. share; The convergence of the finite element calculation model of the satellite blocking the solar panel is verified based on the continuous division results. The true value refers to the actual shading area under certain conditions, while the calculated value refers to the result calculated by the finite element method under the same conditions. The process of verifying the convergence of the finite element calculation model of the satellite blocking the solar panel includes: ， make ,Right now , when hour, Less than , Then when hour, ; Similarly, when hour, ; get Therefore, it is proven that the finite element calculation model of the satellite blocking the solar panel is convergent; Based on the proof results, the area of ​​the solar panel obscured by the satellite body was calculated.

2. The method for calculating the shading area of ​​a solar panel based on the finite element method as described in claim 1, characterized in that, In the step of establishing a first spatial rectangular coordinate system with the geometric center of the satellite body as the origin, the length of the satellite body is... SFL The height of the satellite body is SFH The width of the satellite body is SFW The wingspan of the solar panel is SWL The width of the solar panel is SWW The total length of the satellite body and the solar panels is [length missing]. ALL The angle between the solar panel and the plane containing the OZ axis of the first spatial rectangular coordinate system is α, and the central axis of the solar panel deviates from the OX axis of the first spatial rectangular coordinate system by α. AxiaX The central axis of the solar panel deviates from the OY axis of the first spatial rectangular coordinate system by: AxiaY .

3. The method for calculating the shading area of ​​a solar panel based on the finite element method as described in claim 1, characterized in that, In the steps of dividing the surfaces of the satellite body and the solar panels into multiple blocks, and providing the center coordinates of each face of the satellite body and the center coordinates of each block, when the satellite body is a hexahedron and each end contains two solar panels, Formula for the finite element center coordinates of the satellite body include: （1） Among them, for the satellite body, the formula for the finite element center coordinates is as follows: k =0,...,9; j =0,...,9; For solar panels, the formula for the center coordinates of the finite element method is as follows: k =0,...,9; j =0,...,39; n The x-axis represents the various surfaces of the satellite body and solar panels; l represents the coordinates of a point on the x-axis. m This represents the coordinates of a point on the y-axis; w Represents the coordinates of a point on the z-axis; l n This represents the coordinates of a point on the x-axis of the nth plane; m n This represents the coordinates of a point on the y-axis of the nth plane; w n Let x represent the coordinates of a point on the z-axis of the nth plane; x, y, and z represent the x-axis, y-axis, and z-axis of the first spatial rectangular coordinate system, respectively. The formula for the coordinates of the dividing points of each block on the first surface of the satellite body includes: （2） The formula for the coordinates of the dividing points of each block on the second surface of the satellite body includes: （3） The formula for the coordinates of the dividing points of each block on the third surface of the satellite body includes: （4） The formula for the coordinates of the dividing points of each block on the fourth surface of the satellite body includes: （5） The formula for the coordinates of the dividing points of each block on the fifth surface of the satellite body includes: （6） The formula for the coordinates of the dividing points of each block on the sixth surface of the satellite body includes: （7） The formula for the coordinates of the dividing points of each block of one of the solar panels includes: （8） The formula for the coordinates of the dividing points of each of the other said solar panels includes: （9） Among them, for the satellite body, the formula for the coordinates of the segmentation points is as follows: i =0,...,10; j =0,...,10; For solar panels, the formula for the coordinates of the dividing points is... i =0,...,10; j =0,...,40.

4. The method for calculating the shading area of ​​a solar panel based on the finite element method as described in claim 1, characterized in that, The steps for selecting any point on the satellite's orbit and establishing a second spatial rectangular coordinate system based on the positional relationship between the solar center and the geometric center of the satellite body include: Select any point on the satellite's orbit. Based on the positional relationship between the solar center and the geometric center of the satellite body, connect the geometric center point O of the satellite body with the solar center point M to obtain vector OM. The plane perpendicular to vector OM through point O is ON. In the ON plane, take any two mutually perpendicular lines OP and OQ. Establish the second spatial rectangular coordinate system with line OP as the OX' axis and line OQ as the OY' axis. The direction of sunlight incident is the opposite direction of the OZ' axis.

5. The method for calculating the shading area of ​​a solar panel based on the finite element method as described in claim 4, characterized in that, The steps for coordinate transformation based on the direction of sunlight include: rotating the original coordinates (x, y, z) of the first spatial rectangular coordinate system to obtain the rotated coordinates (x', y', z') of the second spatial rectangular coordinate system. The formula for the coordinate transformation includes: (10) Among them, , , These are the angles between the OX' axis and the OX, OY, and OZ axes in the original coordinate system, respectively. , , These are the angles between the OY' axis and the OX, OY, and OZ axes in the original coordinate system, respectively. , , These are the angles between the OZ' axis and the OX, OY, and OZ axes in the original coordinate system, respectively.

6. The method for calculating the shading area of ​​a solar panel based on the finite element method as described in claim 1, characterized in that, The calculation process for the area of ​​the solar panel obstructed by the satellite body includes: Calculate the area of ​​the solar panels obstructed by each block within the satellite body. The formula for calculating the area of ​​the solar panel obstructed by each block in the satellite body includes: （12） Determine if the result obtained by this formula satisfies: (13) The number of numerical values ​​in the condition is N'. The total area of ​​the solar panel obscured by the satellite body is obtained. The formula for calculating the total area of ​​the solar panel obscured by the satellite body is: S 总遮挡 =N'×S 遮挡 Among them, l n’ This represents the x-coordinate of the nth face after transformation; m n’ This represents the y-coordinate of the nth face after transformation; & It means "and"; p This indicates the number of blocks representing the finite element center of the satellite body, and q This indicates the number of blocks representing the segmentation points of the satellite body.

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