An overhead line length calculation method based on the far-focus celestial center circle method

Abstract

The present invention relates to a method for calculating the catenary length of overhead lines based on the far-focus celestial center circle method, which includes the following steps: obtaining the length f0 of the sag f and the length L of the catenary span; setting a point far from the catenary and above the catenary as the focus point; when the heights of the two suspension points of the catenary are equal, calculating the horizontal downward inclination angle θ of the line connecting any suspension point and the lowest point of the sag; regarding the catenary as an arc with the focus point as the center, obtaining the arc angle according to the angle θ, calculating the arc length of the arc and making corrections to obtain the equivalent line length of the catenary; when the heights of the two suspension points of the catenary are different, obtaining the height difference h, and initially calculating the equivalent line length L of the catenary without height difference according to the following formula c0 ; according to the equivalent line length L of the catenary without height difference c0 , calculate the equivalent line length L of the catenary with height difference c .

Description

Technical Field

[0001] The present invention relates to a method for calculating the length of overhead lines based on the far - focus celestial circle method, belonging to the technical field of power facility parameter calculation. Background Art

[0002] During the construction of overhead transmission lines, due to complex cross - overs and complex construction meteorological conditions, sometimes the sag of the wire in some spans does not meet the requirements of the acceptance documents during the acceptance by the grid owner. At this time, the strain clamps have been crimped, and it is often necessary to adjust the sag to meet the requirements by increasing or decreasing the length of the wire within the span (by adjusting the length of the hanging hardware). Conventionally, the length of the wire between two towers is usually calculated using the catenary model. This is a hypothetical situation where the wire is considered as a soft and non - rigid rope (ideal catenary model), and its wire length formula is derived using calculus theory. Since the assumption is very consistent with the actual situation (the wire stiffness is approximately 0), the catenary model is used to calculate the sag and stress in actual engineering, and the accuracy is the highest.

[0003] When the suspension points are at the same height, the catenary length is: L c0 = sh(kL) / k;

[0004] The sag formula is: f = [ch(kL) - 1] / (2k)

[0005] Where, sh() is the hyperbolic sine function; ch() is the hyperbolic cosine function; k = p / (2T) is the catenary shape coefficient (1 / m); p is the load per unit length of the overhead line (N / m); T is the tension (N); L is the span (m); f is the sag (m).

[0006] Since the above two formulas are related through the catenary shape coefficient k and contain hyperbolic functions, especially when calculating spans with height differences, the wire stress state equation is very complex and is very inconvenient for practical engineering applications. For example, when using Newton iteration to calculate the stress, due to the relatively complex derivative form of the stress state equation function, sometimes the correct result cannot be obtained (varying with different programming languages). Therefore, in engineering, it is often simplified to the flat parabola model for calculation, but the relationship between the wire length and sag calculated using the flat parabola model is not very accurate for large spans (spans of 1000 m and above). Summary of the Invention

[0007] In order to solve the problems existing in the above - mentioned prior art, the present invention proposes a method for calculating the catenary length of overhead lines based on the far - focus celestial circle method, provides a new calculation method, and simplifies the calculation process of the catenary length.

[0008] The technical solution of the present invention is as follows:

[0009] On the one hand, the present invention proposes a method for calculating the catenary length of overhead lines based on the far - focus center - of - circle method, including the following steps:

[0010] Obtain the length f of the sag f 0 and the catenary span length L;

[0011] Set a point far from the catenary and above the catenary as the focus point;

[0012] When the heights of the two suspension points of the catenary are equal, calculate the horizontal downward inclination angle θ of the connection line between any suspension point and the lowest point of the sag according to the following formula:

[0013] θ = atan(2f 0 / L);

[0014] Regard the catenary as an arc with the focus point as the center of the circle, obtain the arc angle according to the angle θ, calculate the arc length of the arc and make corrections to obtain the equivalent catenary length, specifically as follows:

[0015]

[0016] In the formula, α is half of the arc angle, L c0 is the equivalent catenary length;

[0017] When the heights of the two suspension points of the catenary are different, obtain the height difference h, and initially calculate the equivalent catenary length L without height difference according to the following formula c0 :

[0018]

[0019] In the formula, β is the height - difference angle, and f is the sag length with height difference;

[0020] According to the equivalent catenary length L without height difference c0 , calculate the equivalent catenary length L with height difference c :

[0021]

[0022] In the formula, γ is the equivalent height - difference angle for line - length calculation, and f′ is the sag length converted to the case without height difference; L c is the equivalent catenary length with height difference.

[0023] On the other hand, the present invention also proposes a system for calculating the catenary length of overhead lines based on the far - focus center - of - circle method, including:

[0024] A parameter acquisition module for obtaining the length f of the sag f 0 and the catenary span length L;

[0025] A far - focus setting module for setting a point far from the catenary and above the catenary as the focus point;

[0026] The suspension point equal-height catenary length calculation module is used to calculate the horizontal downward inclination angle θ of the connection line between any suspension point and the lowest point of the sag according to the following formula when the heights of the two suspension points of the catenary are equal:

[0027] θ = atan(2f 0 / L);

[0028] Regarding the catenary as an arc with the focus point as the center of the circle, obtain the arc angle of the arc according to the angle θ, calculate the arc length of the arc and make corrections to obtain the equivalent line length of the catenary, specifically as follows:

[0029]

[0030] In the formula, α is half of the arc angle, and L c0 is the equivalent line length of the catenary;

[0031] The suspension point unequal-height line length calculation module is used to obtain the height difference h when the heights of the two suspension points of the catenary are different, and initially calculate the equivalent line length L of the catenary without height difference according to the following formula c0 :

[0032]

[0033] In the formula, β is the height difference angle, and f is the sag length with height difference;

[0034] According to the equivalent line length L of the catenary without height difference c0 , calculate the equivalent line length L of the catenary with height difference c :

[0035]

[0036] In the formula, γ is the equivalent height difference angle for line length calculation, and f' is the sag length converted to the case without height difference; L c is the equivalent line length of the catenary with height difference.

[0037] On the other hand, the present invention also proposes an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the overhead line catenary length calculation method based on the far-focus celestial center circle method as described in any embodiment of the present invention.

[0038] On the other hand, the present invention also proposes a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it implements the overhead line catenary length calculation method based on the far-focus celestial center circle method as described in any embodiment of the present invention.

[0039] The present invention has the following beneficial effects:

[0040] 1. A method for calculating the catenary length of an overhead line based on the far - focus celestial center circle method. According to the characteristics of the overhead line conductor, imagine that the catenary focuses in the direction of the sky, regard the catenary as an arc, calculate the arc length obtained from this arc and make corrections to obtain the equivalent line length of the catenary. This method does not need to use hyperbolic functions for calculation, but equivalently calculates the line length as a trigonometric function, greatly simplifying the calculation process of the catenary length. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a flowchart of the method according to an embodiment of the present invention;

[0042] Figure 2 It is a schematic diagram of the geometric model of the far - focus celestial center circle method in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0043] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present invention.

[0044] It should be understood that the step numbers used in the text are only for convenient description and do not limit the execution order of the steps.

[0045] It should be understood that the terms used in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the specification of the present invention and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an" and "the" are intended to include the plural forms.

[0046] The terms "comprising" and "including" indicate the presence of the described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or their combinations.

[0047] The term "and / or" refers to any combination and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0048] Embodiment 1:

[0049] Refer to Figure 1 , this embodiment proposes a method for calculating the catenary length of an overhead line based on the far - focus celestial center circle method, which specifically includes the following steps:

[0050] S101. Obtain the length f of the sag f 0and the catenary span length L;

[0051] S102. As shown Figure 2 in the figure, set a point far from the catenary and above the catenary as the focus point; this method assumes that the overhead line catenary focuses in the direction of the sky. Then, a section of conductor is just a small arc (within 5° on both sides of the center point). The arc length calculated from this arc can be obtained and corrected to get the equivalent catenary length; the actual catenary and the arc are in a state of close height. Figure 2 In the figure, the catenary is drawn in a state with a large interval from the arc, which is convenient for those skilled in the art to understand.

[0052] S103. Obtain the heights of the two suspension points of the catenary and check whether the heights of the two suspension points are equal.

[0053] S201. If the heights of the two suspension points of the catenary are equal, first calculate the horizontal downward inclination angle θ of the connection line between any suspension point and the lowest point of the sag according to the following formula:

[0054] θ = atan(2f 0 / L) (Formula 1)

[0055] In the formula, the units of f 0 and L are m, and the unit of θ is rad;

[0056] S202. Regard the catenary as an arc with the focus point as the center of the circle. Obtain the arc angle according to the angle θ. Specifically, the arc angle can be deduced according to geometric properties. Calculate the arc length of the arc according to the arc angle and make corrections to obtain the equivalent catenary length, as follows:

[0057]

[0058] In the formula, α is half of the arc angle, the unit is rad, and L c0 is the equivalent catenary length, the unit is m; the specific calculation process of α = 2θ is as follows:

[0059] θ = atan(f / (L / 2));

[0060] f = R*(1 - cos(α));

[0061] L / 2 = R*sin(α);

[0062] tan(θ) = (1 - cos(α)) / sin(α);

[0063] According to the half - angle formula of trigonometric functions:

[0064] (2sin(α / 2)^2) / (2sin(α / 2)cos(α / 2)) = tan(α / 2) = tan(θ). Therefore, α = 2θ;

[0065] In the above formula, Lα 4 The part " / 90" is the correction term. Lα / sin(α) is the arc length of the circular arc. Subtracting a correction term from the arc length is a simple method and can obtain calculation results with extremely high precision.

[0066] S301. If the heights of the two suspension points of the catenary are different, first obtain the height difference h between the two suspension points, and preliminarily calculate the equivalent catenary line length L without height difference according to the following formula c0 :

[0067]

[0068] In the formula, β is the height difference angle, with the unit of rad, f is the sag length with height difference, with the unit of m; some formulas in (Formula 3) are the deformations of the above (Formula 1) and (Formula 2).

[0069] S302. Then, according to the equivalent catenary line length L c0 without height difference, calculate the equivalent catenary line length L c with height difference:

[0070]

[0071] In the formula, γ is the equivalent height difference angle for line length calculation, with the unit of rad, f′ is the sag length converted to the case without height difference, with the unit of m; L c is the equivalent catenary line length with height difference, with the unit of m.

[0072] This method is inspired by the ancient philosophical thought of "round sky and square earth" from the attitude of the overhead line catenary at rest. The sky is far away, so it seems round; the earth is near, so it becomes square. The round represents the smooth will of heaven, and the square formed according to the shape represents the law. According to the characteristics of the overhead line conductor, imagining that the catenary focuses in the direction of the sky, then a span of the conductor is just a small circular arc (the angle is within 5° on both sides of the center point). Assuming that the horizontal downward inclination angle of the line connecting the suspension point and the lowest point of the sag observed nearby is θ, then the angle of this circular arc is 4θ (4θ is generally less than 20°, Figure 2 for a clearer expression of the principle in the figure, it is not drawn according to the actual proportion), and the arc length calculated based on this circular arc is corrected, thus obtaining the name "far-focus celestial center circle method". This is a brand-new method for calculating the catenary line length of the conductor. Instead of using hyperbolic functions for calculation, the line length is equivalent to trigonometric functions for calculation, and the calculation can also be obtained by the method of combining numbers and shapes, greatly simplifying the calculation process of the catenary line length.

[0073] To further illustrate the superiority and effectiveness of the method proposed in this embodiment, the following provides a specific application example:

[0074] For a certain line with a span between 300 - 800 m, when determining the sag f using the catenary shape coefficient k = 0.00027 / m, calculate the line length error calculated by the far - focus celestial - center circle method and the ideal catenary method when the sag remains unchanged. The catenary line lengths and relative errors calculated according to the method of this embodiment are shown in Tables 1 and 2 below:

[0075] Table 1 Line length errors calculated by the far - focus celestial - center circle method and the ideal catenary method (no height difference)

[0076]

[0077]

[0078] Table 2 Line length errors calculated by the far - focus celestial - center circle method and the ideal catenary method (with height difference)

[0079]

[0080] As can be seen from the above two tables, as the span increases, the relative error gradually expands. However, within the main span range of the project (300 - 800), the maximum relative error is only 1.03E - 09, and the error at an 800 - m span is approximately at the 0.824 - micron level. For a transmission line, the millimeter level is already precise enough. Therefore, it can be known that the far - focus celestial - center circle method and the ideal catenary method proposed in this embodiment can be completely interchanged in actual projects and can be selected according to the needs of the project. Since the geometric model of the method proposed in this embodiment is simple, it is very convenient to calculate the adjustment of the construction catenary line length, facilitating the use of an ordinary calculator with trigonometric functions for calculation at the construction site, and the design scheme can be completed without carrying a computer. Therefore, it can improve the efficiency of designers in solving on - site actual construction problems. Designers or constructors can determine the construction scheme by simply hand - drawing geometric figures and combining data and graphics using trigonometric functions, which is also safer and more reliable.

[0081] Embodiment 2:

[0082] This embodiment proposes an overhead line catenary line length calculation system based on the far - focus celestial - center circle method, including:

[0083] A parameter acquisition module for acquiring the length f of the sag f 0 and the catenary span length L; this module is used to implement the function of step S101 in the embodiment and will not be elaborated here;

[0084] A far - focus setting module for setting a point far from the catenary and above the catenary as the focus point; this module is used to implement the function of step S102 in the embodiment and will not be elaborated here;

[0085] Suspension point equal-height catenary length calculation module, which is used to implement the functions of steps S103 to S302 in the embodiment, and will not be elaborated here. When the heights of the two suspension points of the catenary are equal, it is used to calculate the horizontal dip angle θ of the connection line between any suspension point and the lowest point of the sag according to the following formula:

[0086] θ = atan(2f 0 / L);

[0087] Regard the catenary as an arc with the focus point as the center of the circle, obtain the arc angle according to the angle θ, calculate the arc length of the arc and make corrections to obtain the equivalent line length of the catenary, specifically as follows:

[0088]

[0089] In the formula, α is half of the arc angle, and L c0 is the equivalent line length of the catenary;

[0090] Suspension point unequal-height line length calculation module, which is used to obtain the height difference h when the heights of the two suspension points of the catenary are different, and preliminarily calculate the equivalent line length L of the catenary without height difference according to the following formula c0 :

[0091]

[0092] In the formula, β is the height difference angle, and f is the sag length with height difference;

[0093] According to the equivalent line length L of the catenary without height difference c0 , calculate the equivalent line length L of the catenary with height difference c :

[0094]

[0095] In the formula, γ is the equivalent height difference angle for line length calculation, and f' is the sag length converted to the case without height difference; L c Equivalent line length of the catenary with height difference.

[0096] Example 3:

[0097] This example proposes an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the overhead line catenary length calculation method based on the far-focus celestial center circle method as described in any embodiment of the present invention.

[0098] Example 4:

[0099] The present invention also proposes a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it implements the overhead line catenary length calculation method based on the far-focus celestial center circle method as described in any embodiment of the present invention.

[0100] In the embodiments of the present application, "at least one" means one or more, and "a plurality" means two or more. "And / or" describes the association relationship of associated objects, indicating that three relationships can exist. For example, A and / or B can represent the cases of A existing alone, A and B existing simultaneously, and B existing alone. Where A and B can be singular or plural. The character " / " generally represents an "or" relationship between the associated objects before and after. "At least one of the following" and its similar expressions refer to any combination of these items, including any combination of single items or plural items. For example, at least one of a, b, and c can represent: a, b, c, a and b, a and c, b and c, or a and b and c, where a, b, and c can be single or multiple.

[0101] Those of ordinary skill in the art can realize that the various units and algorithm steps described in the embodiments disclosed herein can be implemented by a combination of electronic hardware, computer software, and electronic hardware. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. Professional technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of the present application.

[0102] Those skilled in the art can clearly understand that for the convenience and conciseness of description, the specific working processes of the systems, devices, and units described above can refer to the corresponding processes in the foregoing method embodiments and will not be elaborated herein.

[0103] In several embodiments provided by the present application, if any function is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present application. The foregoing storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (hereinafter referred to as ROM), random access memories (hereinafter referred to as RAM), magnetic disks, or optical discs that can store program codes.

[0104] The above are only embodiments of the present invention, and do not limit the patent scope of the present invention accordingly. Any equivalent structure or equivalent process transformation made by using the content of the specification and drawings of the present invention, or directly or indirectly applied in other related technical fields, shall be similarly included in the patent protection scope of the present invention.

Claims

1. A calculation method for the catenary length of overhead lines based on the far - focus celestial center circle method, characterized in that, it includes the following steps: Obtain the length f of the sag f 0 and the length L of the catenary span; Set a point far from the catenary and above the catenary as the focus point; When the heights of the two suspension points of the catenary are equal, calculate the horizontal downward inclination angle θ of the line connecting any suspension point and the lowest point of the sag according to the following formula: θ = atan(2f 0 / L); Regard the catenary as an arc with the focus point as the center of the circle, obtain the arc angle according to the angle θ, calculate the arc length of the arc and make corrections to obtain the equivalent catenary length, specifically as follows: where α is half of the arc angle, and L c0 is the equivalent line length of the catenary; When the heights of the two suspension points of the catenary are different, obtain the height difference h, and initially calculate the equivalent line length L of the catenary without height difference according to the following formula c0 : In the formula, β is the height difference angle, and f is the sag length with height difference; According to the catenary equivalent line length L without elevation difference c0 , calculate the catenary equivalent line length L with elevation difference c : Where γ is the equivalent height difference angle for line length calculation, f′ is the sag length after conversion to the case without height difference; L c The equivalent catenary line length with height difference.

2. A calculation system for the catenary length of overhead lines based on the far - focus celestial center circle method, characterized in that, it includes: A parameter acquisition module, configured to acquire the length f of the sag f 0 and the length L of the catenary span; A far - focus setting module for setting a point far from the catenary and above the catenary as the focus point; A catenary length calculation module for equal - height suspension points, when the heights of the two suspension points of the catenary are equal, calculate the horizontal downward inclination angle θ of the line connecting any suspension point and the lowest point of the sag according to the following formula: θ = atan(2f 0 / L); Regard the catenary as an arc with the focus point as the center of the circle, obtain the arc angle according to the angle θ, calculate the arc length of the arc and make corrections to obtain the equivalent catenary length, specifically as follows: where α is half of the arc angle, and L c0 is the equivalent line length of the catenary; The suspension point unequal height catenary length calculation module is used to obtain the height difference h when the heights of the two suspension points of the catenary are different, and initially calculate the equivalent catenary length L without height difference according to the following formula c0 :[[]]END]] In the formula, β is the height difference angle, and f is the sag length with height difference; According to the catenary equivalent line length L without height difference c0 , calculate the catenary equivalent line length L with height difference c : Where γ is the equivalent elevation angle for calculating the line length, f′ is the sag length converted to the case without elevation difference; L c The equivalent catenary line length with elevation difference.

3. An electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, when the processor executes the program, it implements the calculation method for the catenary length of overhead lines based on the far - focus celestial center circle method as described in claim 1.

4. A computer - readable storage medium, on which a computer program is stored, characterized in that, when the program is executed by the processor, it implements the calculation method for the catenary length of overhead lines based on the far - focus celestial center circle method as described in claim 1.

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