Method for measuring sag of an arc according to spatial coordinates of any three points of the arc

Abstract

The application discloses a method for measuring sag of an arbitrary three-point space coordinate of an overhead curve, wherein a total station is used to observe three arbitrary points on the curve and establish space coordinates, the sag of an arbitrary point located in the middle of the three arbitrary points is calculated preferentially through the three-point coordinates, and then the sag of the curve connected by the three arbitrary points is calculated, the horizontal tension is calculated according to the relationship between the sag and the horizontal tension, and the sag in the overhead curve section is calculated according to the principle that the horizontal tensions of the arbitrary points on the curve are equal. The method can be applied to the sag observation of an extra-high voltage line and a mountainous area line, the applicability of the method is improved, the influence of human factors on the observation is reduced, and the sag observation precision is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of power transmission and transformation, and in particular to a method for measuring sag according to the spatial coordinates of any three points on an overhead curve. Background Art

[0002] Three main methods for sag observation during line construction are the unequal-length method, the equal-length method (parallelogram method), and the angle method. The unequal-length and equal-length methods involve traditional tower-mounted sag plates. These methods require observations on the tower, are time-consuming and labor-intensive, and can result in significant errors. They are currently rarely used. The angle method, however, utilizes a theodolite for ground-based observations, eliminating the need for tower-mounted observations. It is convenient and simple, and is currently the primary sag observation method used during line construction. However, the angle method is complex and slow in calculation, requiring extensive data entry and subject to a high probability of human error. Furthermore, its use is significantly affected by tower height and terrain, potentially preventing sag observations from being performed or leading to significant errors. Therefore, a new sag observation method suitable for UHV and mountainous lines is needed to improve its applicability, reduce the impact of human factors, and enhance sag observation accuracy. Summary of the Invention

[0003] In response to the problems existing in the prior art, the present invention provides a method for measuring sag based on the spatial coordinates of any three points on an overhead curve. The method can be applied to sag observation of ultra-high voltage and mountainous lines, improves the applicability of the method, reduces the influence of human factors on the observation, and improves the accuracy of sag observation.

[0004] The technical solutions adopted to achieve the above objectives are:

[0005] A method for measuring sag based on the spatial coordinates of any three points of an overhead curve, characterized by comprising the following steps:

[0006] (1) Use the total station to build a coordinate system and measure the coordinates of any three points A, B, and C at the appropriate position on the side of the track. The coordinates of point A are (X A , Y A , Z A ), the coordinates of point B are (X B , Y B , Z B ), the coordinates of point C are (X C , Y C , Z C );

[0007] (2) Calculate the vectors CA and BA through the coordinates of the three points A, B, and C, and calculate the value of ∠CAB through the vector and set it as α. Calculate the height difference θ between points A and B AB , where l o is the horizontal distance between any point B and point A, h ois the height difference between any point B and point A, through Calculate the length S, where X is the horizontal distance between points A and C, and calculate l using the coordinates of points A and C. AC and set the value of x;

[0008] (3) Given the values ​​of α, S, and x, calculate the sag f at any point C using the law of cosines. X , the sag f of any point C is known X , according to the arbitrary sag f X and sag f, establish a coordinate system with point A as the origin, and use Calculate the sag f of the AB curve AB , where f X is the sag of any point C, x is the horizontal distance between any point C and point A, l o is the horizontal distance between any point B and point A;

[0009] (4) According to the relationship between sag and horizontal tension, The horizontal tension H can be calculated, where l o is the horizontal distance between any point B and point A, f AB is the sag of the AB curve, θ AB is the height difference between points A and B, is the unit weight of the clue;

[0010] (5) Given the distance l between the two hanging points of the curve and the height difference h between the two hanging points, Calculate the height difference between two suspension points ;

[0011] (6) According to the principle that the horizontal tension at any point on the curve is equal, Calculate the sag f in the curve section DE , where H is the horizontal tension, l is the distance between the two suspension points of the curve, is the unit weight of the clue, is the height difference between the two suspension points, and the sag f in the gear is obtained DE .

[0012] Furthermore, the total station is a high-precision prism-free total station.

[0013] Furthermore, in step (1), point C is any point in the middle of the curve, and points A and B are any points on both sides of point C.

[0014] Furthermore, the value of ∠CAB in step (2) can also be calculated using the law of cosines.

[0015] The beneficial effects of the present invention are:

[0016] The present invention proposes a new sag observation method that can be applied to ultra-high voltage and mountainous lines, which improves the applicability of the method. The method has a simple calculation process. By observing the spatial coordinates of any three points on the overhead curve, the sag of the overhead curve is measured. This method reduces the influence of human factors on the observation and improves the accuracy of sag observation. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is the position diagram of points A, B and C;

[0018] Figure 2 This is a diagram of the position relationship between points A, B, and C and the suspension point. DETAILED DESCRIPTION

[0019] The technical solutions in the embodiments of the present invention will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present invention.

[0020] The present invention provides a method for measuring sag based on the spatial coordinates of any three points on an overhead curve, as shown in Figures 1 and Figure 2 shown.

[0021] A method for measuring sag based on the spatial coordinates of any three points on an overhead curve comprises the following steps:

[0022] (1) If Figure 1 As shown, a high-precision prism-free total station is used to build a self-built coordinate system. The coordinates of any three points A, B, and C are measured at the appropriate position on the side of the curve. Point C is any point in the middle of the curve, and points A and B are any points on both sides of point C. The coordinates of point A are (X A , Y A , Z A ), the coordinates of point B are (X B , Y B , Z B ), the coordinates of point C are (X C , Y C , Z C );

[0023] (2) Calculate the vectors CA and BA through the coordinates of the three points A, B, and C, and calculate the value of ∠CAB through the vector and set it as α. Calculate the height difference θ between points A and B AB ,in,

[0024] l o is the horizontal distance between any point B and point A;

[0025] h o is the height difference between any point B and point A;

[0026] pass Calculate the length S, where

[0027] X is the horizontal distance between points A and C;

[0028] Calculate l by the coordinates of points A and C AC and set the value of x;

[0029] (3) Given α, S, l AC The value of the arc sag f at any point C is calculated according to the cosine theorem. X , the sag f of any point C is known X , according to the arbitrary sag f X and the relationship between sag f, establish a coordinate system with point A as the origin as follows Figure 1 and through Calculate the sag f of the AB curve AB ,in,

[0030] f X is the sag of any point C;

[0031] x is the horizontal distance between any point C and point A;

[0032] l o is the horizontal distance between any point B and point A;

[0033] (4) According to the relationship between sag and horizontal tension, The horizontal tension H can be calculated, where

[0034] l o is the horizontal distance between any point B and point A;

[0035] f AB is the sag of the AB curve;

[0036] θ AB is the height difference between points A and B;

[0037] is the unit weight of the clue;

[0038] (5) If Figure 2 As shown, the distance l between the two suspension points D and E of the known curve and the height difference h between the two suspension points D and E are obtained by Calculate the height difference between two suspension points ;

[0039] (6) According to the principle that the horizontal tension at any point on the curve is equal, Calculate the sag f in the curve section DE ,in,

[0040] H is the horizontal tension;

[0041] l is the distance between the two suspension points of the curve;

[0042] is the unit weight of the clue;

[0043] is the height difference between the two suspension points;

[0044] Then we can get the sag f in the gear DE .

[0045] Table 1 below shows the calculation results of overhead curve sag using this method:

[0046] Table 1 List of calculation results

[0047]

[0048] This method of measuring sag based on the spatial coordinates of any three points on the overhead curve observes any three points on the overhead curve, establishes spatial coordinates for the observed three points, preferentially calculates the sag of any point in the middle of the curve among the three points through the coordinates of the three points, and then calculates the sag of the curve formed by the three points, calculates the horizontal tension according to the relationship between sag and horizontal tension, and calculates the sag within the overhead curve according to the principle that the horizontal tension at any point on the curve is equal. This method is suitable for sag observation of various ultra-high voltage and mountainous lines, thereby improving the applicability of the method, and this method reduces the limitation of the observation, and only needs to observe any three points on the curve, reducing the influence of human factors on the observation, improving the efficiency and accuracy of sag observation, can be widely used in current line construction, and sag observation software is written to facilitate on-site promotion and application.

[0049] In the description of the present invention, it should be understood that the terms "center", "front", "back", "left", "right", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the protection content of the present invention.

[0050] If words such as "first" and "second" are used in this document to limit components, those skilled in the art should know that the use of "first" and "second" is only for the convenience of describing the present invention and simplifying the description. Unless otherwise stated, the above words have no special meaning.

[0051] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for measuring sag based on the spatial coordinates of any three points on an overhead curve, characterized in that: The following steps are involved: (1) Use the total station to build a coordinate system and measure the coordinates of any three points A, B, and C at the appropriate position on the side of the track. The coordinates of point A are (X A , Y A , Z A ), the coordinates of point B are (X B , Y B , Z B ), the coordinates of point C are (X C , Y C , Z C ); (2) Calculate the vectors CA and BA through the coordinates of the three points A, B, and C, and calculate the value of ∠CAB through the vector and set it as α. Calculate the height difference θ between points A and B AB , where l o is the horizontal distance between any point B and point A, h o is the height difference between any point B and point A, through Calculate the length S, where X is the horizontal distance between points A and C, and calculate l using the coordinates of points A and C. AC and set the value of x; (3) Given the values ​​of α, S, and x, calculate the sag f at any point C using the law of cosines. X , the sag f of any point C is known X , according to the arbitrary sag f X and sag f, establish a coordinate system with point A as the origin, and use Calculate the sag f of the AB curve AB , where f X is the sag of any point C, x is the horizontal distance between any point C and point A, l o is the horizontal distance between any point B and point A; (4) According to the relationship between sag and horizontal tension, The horizontal tension H can be calculated, where l o is the horizontal distance between any point B and point A, f AB is the sag of the AB curve, θ AB is the height difference between points A and B, is the unit weight of the clue; (5) Given the distance l between the two hanging points of the curve and the height difference h between the two hanging points, Calculate the height difference between two suspension points ; (6) According to the principle that the horizontal tension at any point on the curve is equal, Calculate the sag f in the curve section DE , where H is the horizontal tension, l is the distance between the two suspension points of the curve, is the unit weight of the clue, is the height difference between the two suspension points, and the sag f in the gear is obtained DE .

2. The method for measuring sag based on the spatial coordinates of any three points on an overhead curve according to claim 1, characterized in that: The total station is a high-precision prism-free total station.

3. The method for measuring sag based on the spatial coordinates of any three points on an overhead curve according to claim 1, characterized in that: In step (1), point C is any point in the middle of the curve, and points A and B are any points on both sides of point C.

4. The method for measuring sag based on the spatial coordinates of any three points on an overhead curve according to claim 1, characterized in that: The value of ∠CAB in step (2) can also be calculated using the law of cosines.

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