A method for calculating conductor tension sag based on modified simply supported beam theory

Abstract

The invention discloses a method for calculating the conductor tension sag based on the modified simply supported beam theory, which belongs to the technical field of electric power design and construction. The simply supported beam theory is used to accurately solve the line length, suspension point stress and conductor sag of a large-span conductor under the action of non-uniformly distributed loads such as spacers, tension strings, damping wires and anti-vibration hammers. The slope weight gain method is used to correct the deadweight load distribution of the conductor. By decomposing the spatial stress state of the suspension string of the spanning tower, a tension balance relationship equation for the front and rear gears of the spanning tower is established. At the same time, the principle of the constant original line length of the conductor is used to establish the state equation of the average temperature condition of the large-span conductor and each operating condition. The calculation of the tension, spatial position and suspension point tension of the large-span conductor can be completed. The algorithm has high calculation accuracy. In addition to being used for mechanical calculation of large-span conductors, it can also be widely used for the accurate calculation of the tension sag of the ground wire of super and ultra-high transmission lines.

Description

Technical Field

[0001] The invention relates to a conductor tension sag calculation method based on modified simply supported beam theory, belonging to the technical field of electric power design and construction. Background Art

[0002] In the design of overhead transmission line projects, the continuous state equation method is usually used for the mechanical calculation of the ground wire. This method is based on the assumption that there is no longitudinal force difference in the ground wire on the straight tower, the self-weight load of the conductor is evenly distributed along the longitudinal projection of the line, and the influence of the tension string and conductor accessories is not considered. However, the super-large and long-span transmission lines have large spans and large elevation angles. Based on the traditional mechanical calculation of flat parabolas or inclined parabolas, the sag of the conductor of 250m will cause a calculation error of about 5m; at the same time, for super-large and long spans where the average operating tension is controlled by the vibration fatigue of the conductor at the suspension point, in addition to the influence of the spacer rod, the tension string, damping wire and anti-vibration hammer will increase the stress of the aluminum part of the conductor at the suspension point of the large span, resulting in the influence of the accessories on the sag error of up to 2 to 4m. The parabola calculation method and accessories will affect the sag and suspension point tension of super-large and long-span projects to an unacceptable degree. Failure to consider the influence of conductor accessories on the suspension point tension and sag, or overestimating the influence of conductor accessories on the suspension point tension and sag, will cause great investment waste or safety hazards in super-large and long-span construction. Summary of the invention

[0003] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method for calculating the conductor tension sag based on the modified simply supported beam theory. The simply supported beam theory is used to accurately solve the line length, suspension point stress and conductor sag of a large-span conductor under the action of non-uniformly distributed loads such as spacers, tension strings, damping wires and anti-vibration hammers. The slope weight gain method is used to correct the deadweight load distribution of the conductor. By decomposing the spatial stress state of the suspension string of the spanning tower, a tension balance relationship equation for the front and rear gears of the spanning tower is established. At the same time, the principle of the constant original line length of the conductor is used to establish the state equation of the average temperature condition of the large-span conductor and each operating condition. The calculation of the tension, spatial position and suspension point tension of the large-span conductor can be completed. The algorithm has high calculation accuracy. In addition to being used for mechanical calculations of large-span conductors, it can also be widely used for the accurate calculation of the tension sag of the ground wire of super and ultra-high transmission lines.

[0004] To achieve the above object, the present invention is implemented by adopting the following technical solutions:

[0005] In a first aspect, the present invention provides a method for calculating conductor tension sag based on modified simply supported beam theory, comprising:

[0006] Obtain line design data and calculate discretized unit components using the slope weight gain method;

[0007] Calculate the conductor suspension point tension and determine whether the conductor suspension point tension exceeds the allowable force of the conductor fatigue vibration test. If it exceeds, reduce the conductor average temperature allowable tension and recalculate;

[0008] Calculate the average temperature line length of each level through the discretized unit components;

[0009] Set the initial value of the operating tension, and calculate the line length of each gear considering the temperature elastic shrinkage;

[0010] Set the gear spacing of the operating condition, calculate the height difference of the operating condition, and determine whether the line length of the operating condition considering temperature elastic shrinkage of each gear is equal to the line length of the operating condition calculated by the slope weight gain method obtained in advance. If not, reset the gear spacing of the operating condition;

[0011] Determine whether the pre-acquired operating condition tension section length is equal to the original tension section length of the average temperature condition. If not, return to the step of setting the initial tension value of the operating condition.

[0012] Calculate the tension, spatial position and suspension point tension of long-span conductors corresponding to operating conditions.

[0013] Furthermore, the line design data includes original span, tower hanging point height, conductor parameters, suspension string and tension string parameters.

[0014] Furthermore, the calculation of the discretized unit components by using the slope weight gain method includes:

[0015] Calculate the initial coordinate components;

[0016] The correction steps include: correcting the deadweight of the conductor by using a slope weight increase method;

[0017] The beam theory is used to calculate the coordinate components of the average temperature, and whether the coordinate accuracy is satisfied is determined. If not, the correction step is returned.

[0018] Compute the discretized element components.

[0019] Furthermore, the slope weight gain method is used to correct the deadweight of the wire, and the formula is as follows:

[0020]

[0021] Among them, p i,j is the original comprehensive load per unit length of the jth section of the i-th stage conductor or tension string; p′ i,j Δx is the comprehensive load per unit length after correction by the slope weight increase method for the jth section of the i-th gear or tension string; i,j is the longitudinal component of the jth conductor unit of the i-th gear after discretization; Δy i,j It is the vertical component of the j-th conductor unit in the i-th gear after discretization.

[0022] Furthermore, when calculating the tension of the wire suspension point, the vertical force R of the suspension point A at the starting point of the i-th gear i,A and the vertical force R at the end suspension point B i,B , the calculation formula is:

[0023]

[0024]

[0025] The calculation formula for the tension of the starting suspension point and the ending suspension point of the i-th gear is:

[0026]

[0027]

[0028] Among them, l i is the i-th gear distance; h i is the height difference of the i-th level (large height minus small height); T i is the wire tension of the i-th gear.

[0029] Furthermore, the average temperature line length of each level is calculated by the discretized unit component, and the calculation formula is:

[0030]

[0031] Furthermore, the calculation formula for obtaining the line length of each gear using the operating condition considering temperature elastic shrinkage is:

[0032]

[0033] Among them, L′ i , T′ i , t′ are the line length, tension and air temperature of the operating condition to be determined; a and E are the temperature coefficient and elastic modulus of the conductor respectively.

[0034] Furthermore, the tension section length under the operating condition and the original tension section length under the average temperature condition satisfy the following formula:

[0035]

[0036] Among them l i , l′ i They are the original gear span under average temperature condition and the gear span under operating condition respectively.

[0037] Furthermore, the calculation of the tension, spatial position, and suspension point tension of the long-span conductor corresponding to the operating condition includes:

[0038] The coordinates of the wire are calculated with the starting suspension point A as the origin as shown in the following formula:

[0039]

[0040]

[0041] Where Δx′ i,j is the longitudinal component of the jth section conductor unit of the i-th gear after discretization during the operation condition, Q′ i,j-1 , Q′ i,j are respectively the shear forces at the head and the end of the conductor unit of the i-th gear and the j-th section calculated according to the prior art and corrected by the slope weight gain method under the operating condition;

[0042] Vertical force R′ at the suspension point A at the starting point of the i-th gear in the operating condition i,A and the vertical force R′ at the end suspension point B i,B , the calculation formula is:

[0043]

[0044]

[0045] Among them, l i is the i-th gear distance; h i is the height difference of the i-th level; T i is the conductor tension of the i-th gear; Q i,j-1 , Q i,j They are respectively the shear forces at the beginning and end of the j-th section conductor unit of the i-th gear calculated according to the prior art.

[0046] In a second aspect, the present invention provides a computing device comprising one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include instructions for executing any of the methods described in any of the foregoing.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] The invention provides a method for calculating the conductor tension sag based on the modified simply supported beam theory. The state equations of the installation condition and each operating condition are established by utilizing the principle of constant original line length and the tension balance relationship between the front and rear steps of the spanning tower. The slope weight gain method and the simply supported beam theory can be used to accurately calculate the influence of non-uniformly distributed loads or concentrated loads such as tension strings, spacers, damping wires and anti-vibration hammers on the long-span sag, line length and support force. The calculation of the conductor tension, spatial position and suspension point tension of the long-span conductor can be completed. The algorithm has high calculation accuracy. In addition to being used for mechanical calculation of long-span conductors, it can also be widely used for accurate calculation of the tension sag of the ground wire of super and ultra-high transmission lines. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flow chart of a method for calculating conductor tension sag based on modified simply supported beam theory provided by an embodiment of the present invention;

[0050] Figure 2 is a flow chart of calculating a discretization unit using a slope weight gain method provided by an embodiment of the present invention;

[0051] Figure 3 It is a schematic diagram for decomposing the spatial stress state of a suspension string across a tower provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0052] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0053] Example 1

[0054] This embodiment introduces a method for calculating conductor tension sag based on modified simply supported beam theory, including:

[0055] Obtain line design data and calculate discretized unit components using the slope weight gain method;

[0056] Calculate the conductor suspension point tension and determine whether the conductor suspension point tension exceeds the allowable force of the conductor fatigue vibration test. If it exceeds, reduce the conductor average temperature allowable tension and recalculate;

[0057] Calculate the average temperature line length of each level through the discretized unit components;

[0058] Set the initial value of the operating tension, and calculate the line length of each gear considering the temperature elastic shrinkage;

[0059] Set the gear spacing of the operating condition, calculate the height difference of the operating condition, and determine whether the line length of the operating condition considering temperature elastic shrinkage of each gear is equal to the line length of the operating condition calculated by the slope weight gain method obtained in advance. If not, reset the gear spacing of the operating condition;

[0060] Determine whether the pre-acquired operating condition tension section length is equal to the original tension section length of the average temperature condition. If not, return to the step of setting the initial tension value of the operating condition.

[0061] Calculate the tension, spatial position and suspension point tension of long-span conductors corresponding to operating conditions.

[0062] like Figure 1 As shown, the conductor tension sag calculation method based on the modified simply supported beam theory provided in this embodiment specifically involves the following steps:

[0063] S01, read the meteorological conditions of the long span, the original span, the tower hanging point height, the conductor parameters, the suspension string and the tension string parameters; the meteorological conditions include the minimum temperature, the average temperature, icing, strong wind, installation and high temperature, etc.; the above average temperature condition is the large span control condition, and the other conditions are the commonly used operating conditions for the large span.

[0064] S02, it is assumed that no longitudinal deviation occurs in the suspension string across the tower under the average temperature condition, and the average temperature tension of the conductor and meteorological conditions are used as the initial control conditions.

[0065] S03, discretize each conductor and tension string in the tension section along the longitudinal direction of the line, consider the non-uniform loads such as tension string, spacer, damping wire and anti-vibration hammer, and use the coordinate method to correct the weight gain of uniform conductor on the slope. The slope weight gain method is used to calculate the discretized unit component. Figure 2 .

[0066] The calculation formula of the self-weight after correction by slope weight gain method is:

[0067]

[0068] Among them, p i,j is the original comprehensive load per unit length of the jth section of the i-th stage conductor or tension string; p′ i,j Δx is the comprehensive load per unit length after correction by the slope weight increase method for the jth section of the i-th gear or tension string; i,j is the longitudinal component of the jth conductor unit of the i-th gear after discretization; Δy i,j It is the vertical component of the j-th conductor unit in the i-th gear after discretization.

[0069] S04, calculate the tension of the conductor suspension point, and determine whether the tension of the conductor suspension point exceeds the allowable force of the conductor fatigue vibration test. If it exceeds, reduce the allowable tension of the conductor average temperature and recalculate. i,A and the vertical force R at the end suspension point B i,B , the calculation formula is:

[0070]

[0071]

[0072] The calculation formula for the tension of the starting suspension point and the ending suspension point of the i-th gear is:

[0073]

[0074]

[0075] Among them, l i is the i-th gear distance; hi is the height difference of the i-th level (large height minus small height); T i is the wire tension of the i-th gear.

[0076] S05, using the discretized unit components, calculate the average temperature line length of each level, the calculation formula is:

[0077]

[0078] S06, assume the initial value of tension under operating conditions (such as minimum temperature, icing, strong wind, installation and high temperature).

[0079] S07, without considering the influence of elastic deformation and temperature deformation of the tension string, only considering the elastic deformation and temperature deformation of the conductor, calculate the line length of each operating condition. The calculation formula is:

[0080]

[0081] Among them, L′ i , T′ i , t′ are the line length, tension and air temperature of the operating condition to be determined; a and E are the temperature coefficient and elastic modulus of the conductor respectively.

[0082] S08, based on the principle of the original line length being constant within the span, the tension balance equation of the spans before and after the spans was established, and the spatial stress state of the spanning tower suspension string was decomposed to see Figure 3 . Assume the gear spacing of the operating condition, calculate the height difference of the operating condition, and determine whether the line length of the operating condition considering temperature elastic shrinkage is equal to the line length of the operating condition calculated by the slope weight gain method. If they are not equal, re-assume the gear spacing of the operating condition.

[0083] S09, determine whether the tension section length under the operating condition is equal to the original tension section length under the average temperature condition, if not equal, return to step S06. The tension section length satisfies the following formula:

[0084]

[0085] Among them l i , l′ i They are the original gear span under average temperature condition and the gear span under operating condition respectively.

[0086] S10, calculate the tension, spatial position, and suspension point tension of the long-span conductor corresponding to the operating conditions. The conductor coordinates are calculated with the starting suspension point A as the origin as shown in the following formula:

[0087]

[0088]

[0089] Where Δx′i,j is the longitudinal component of the jth section conductor unit of the i-th gear after discretization during the operation condition, Q′ i,j-1 , Q′ i,j They are respectively the shear forces at the beginning and end of the conductor unit of the i-th gear and the j-th section calculated after correction by the slope weight gain method according to the prior art during the operating condition.

[0090] Vertical force R′ at the suspension point A at the starting point of the i-th gear in the operating condition i,A and the vertical force R′ at the end suspension point B i,B , the calculation formula is:

[0091]

[0092]

[0093] Among them, l i is the i-th gear distance; h i is the height difference of the i-th level (large height minus small height); T i is the conductor tension of the i-th gear; Q i,j-1 , Q i,j They are respectively the shear forces at the beginning and end of the j-th section conductor unit of the i-th gear calculated according to the prior art.

[0094] Example 2

[0095] This embodiment provides a computing device, including one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include instructions for executing any of the methods described in any one of Embodiment 1.

[0096] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for calculating conductor tension sag based on modified simply supported beam theory. It is characterized in that include: Obtain line design data and calculate discretized unit components using the slope weight gain method; Calculate the conductor suspension point tension and determine whether the conductor suspension point tension exceeds the allowable force of the conductor fatigue vibration test. If it exceeds, reduce the conductor average temperature allowable tension and recalculate; Calculate the average temperature line length of each level through the discretized unit components; Set the initial value of the operating tension, and calculate the line length of each gear considering the temperature elastic shrinkage; Set the gear spacing of the operating condition, calculate the height difference of the operating condition, and determine whether the line length of the operating condition considering temperature elastic shrinkage of each gear is equal to the line length of the operating condition calculated by the slope weight gain method obtained in advance. If not, reset the gear spacing of the operating condition; Determine whether the pre-acquired operating condition tension section length is equal to the original tension section length of the average temperature condition. If not, return to the step of setting the initial tension value of the operating condition. Calculate the tension, spatial position and suspension point tension of long-span conductors corresponding to operating conditions.

2. According to the method for calculating conductor tension sag based on modified simply supported beam theory of claim 1, Features: The line design data includes original span, tower hanging point height, conductor parameters, suspension string and tension string parameters.

3. The method for calculating conductor tension sag based on modified simply supported beam theory according to claim 1, Features: The method of calculating the discretized unit components by using the slope weight gain method includes: Calculate the initial coordinate components; The correction steps include: correcting the deadweight of the conductor by using a slope weight increase method; The beam theory is used to calculate the coordinate components of the average temperature, and whether the coordinate accuracy is satisfied is determined. If not, the correction step is returned. Compute the discretized element components.

4. The method for calculating conductor tension sag based on modified simply supported beam theory according to claim 1, Features: The slope weight increase method is used to correct the deadweight of the conductor, and the formula is as follows: Among them, p i,j is the original comprehensive load per unit length of the jth section of the i-th stage conductor or tension string; p' i,j Δx is the comprehensive load per unit length after correction by the slope weight increase method for the jth section of the i-th gear or tension string; i,j is the longitudinal component of the jth conductor unit of the i-th gear after discretization; Δy i,j is the vertical component of the j-th conductor unit in the i-th gear after discretization.

5. The method for calculating conductor tension sag based on modified simply supported beam theory according to claim 1, Features: When calculating the tension of the wire suspension point, the vertical force R i,A and the vertical force R at the end suspension point B i,B , the calculation formula is: The calculation formula for the tension of the starting suspension point and the ending suspension point of the i-th gear is: Among them, l i is the i-th gear distance; h i is the height difference of the i-th level, that is, the large elevation minus the small elevation; T i is the wire tension of the i-th gear.

6. The method for calculating conductor tension sag based on modified simply supported beam theory according to claim 1, Features: The average temperature line length of each level is calculated by the discretized unit component, and the calculation formula is:

7. The method for calculating conductor tension sag based on modified simply supported beam theory according to claim 1, Features: The calculation formula for obtaining the line length of each gear using the operating condition considering temperature elastic shrinkage is: Among them, L' i , T i ', t' are the line length, tension and air temperature of the operating condition to be determined; a, E are the temperature coefficient and elastic modulus of the conductor respectively.

8. The method for calculating conductor tension sag based on modified simply supported beam theory according to claim 1, Features: The tension section length under the operating condition and the original tension section length under the average temperature condition satisfy the following formula: Among them l i , l i ' are the original gear span under average temperature condition and the gear span under operating condition respectively.

9. The method for calculating conductor tension sag based on modified simply supported beam theory according to claim 1, Features: The calculation of the tension, spatial position, and suspension point tension of the long-span conductor corresponding to the operating condition includes: The coordinates of the wire are calculated with the starting suspension point A as the origin as shown in the following formula: Where Δx' i,j is the longitudinal component of the jth section conductor unit of the i-th gear after discretization during the operation condition, Q' i,j-1 , Q' i,j are respectively the shear forces at the head and the end of the conductor unit of the i-th gear and the j-th section calculated according to the prior art and corrected by the slope weight gain method under the operating condition; Vertical force R' at the suspension point A at the starting point of the i-th gear in the operating condition i,A and the vertical force R' at the end suspension point B i,B , the calculation formula is: Among them, l i is the i-th gear distance; h i is the height difference of the i-th level; T i is the conductor tension of the i-th gear; Q i,j-1 , Q i,j They are respectively the shear forces at the beginning and end of the j-th section conductor unit of the i-th gear calculated according to the prior art.

10. A computing device, Features: The method comprises one or more processors, a memory and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include instructions for executing any one of the methods described in any one of claims 1 to 9.

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