CN114444364A - Calculation method for monitoring internal force of power transmission line - Google Patents

Calculation method for monitoring internal force of power transmission line Download PDF

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CN114444364A
CN114444364A CN202210211769.2A CN202210211769A CN114444364A CN 114444364 A CN114444364 A CN 114444364A CN 202210211769 A CN202210211769 A CN 202210211769A CN 114444364 A CN114444364 A CN 114444364A
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transmission line
formula
parameters
optical fibers
deformation
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胡安龙
薛国斌
夏懿
董倩
冯燕军
魏勇
李惠庸
李婧
孙长昊
尚志鹏
万小花
李敏
李麟鹤
平常
李万伟
张建辉
张伟
陈庆胜
靳攀润
孙亚璐
梁魁
王小文
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State Grid Gansu Electric Power Co Ltd
Economic and Technological Research Institute of State Grid Gansu Electric Power Co Ltd
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State Grid Gansu Electric Power Co Ltd
Economic and Technological Research Institute of State Grid Gansu Electric Power Co Ltd
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Abstract

The invention discloses a calculation method for monitoring internal force of a power transmission line, which specifically comprises the following steps: determining physical and mechanical parameters and material parameters of the overhead transmission line, and defining a coordinate system; installing the distributed optical fibers, and recording initial parameters of the two optical fibers, such as initial installation length lambda 0, initial installation temperature T0, installation positions and the like; measuring original input parameters such as temperature T and deformation delta v1 and delta v2 of 2 corresponding local power transmission lines in real time through two distributed optical fibers; correcting the input parameters; substituting the corrected input parameters delta vE1 and delta vE2 into the model to obtain four parameters of a, b, c, epsilon and the like; and solving the horizontal tension H and the axial tension F of any point of the transmission line according to the four solved parameters. The model of the invention has comprehensive consideration factors and sufficient theoretical basis, so the precision, the calculation efficiency and the reliability are higher, and the real-time monitoring can be realized.

Description

Calculation method for monitoring internal force of power transmission line
Technical Field
The invention relates to a calculation method for feeding back internal force of a transmission line by taking local deformation of the transmission line measured by distributed optical fibers as an input parameter, in particular to a high-precision monitoring method for the internal force of the transmission line.
Background
The monitoring of the power transmission line plays a vital role in the safe operation of a power grid, and accidents such as line breakage, tower collapse and the like caused by the fact that the internal force of the power transmission line exceeds the allowable stress of the power transmission line due to ice and snow loads, wind loads and the like bring huge economic losses at home and abroad. In China, the loss caused by ice coating is the most huge. After the transmission line is iced, the load of the transmission line is increased, so that the internal force of the transmission line is greatly increased and the distribution is uneven, and finally, the power failure accident of the transmission line can be caused by the disconnection and tower falling. Therefore, it is urgent to accurately and efficiently monitor and feed back the operating state of the transmission line in real time.
The existing transmission line internal force measuring methods mainly comprise a finite element method, a strain gauge method and a mechanical calculation method. Finite element method: the method has high safety precision and clear internal force distribution, but the method has limited calculation efficiency and cannot monitor in real time, so the method is not suitable for the safety monitoring of the power transmission line; a strain gauge method: although the method can be used for real-time monitoring, the accuracy is generally inaccurate even if the measurement is often inaccurate, and the reliability is low. Furthermore, it can only measure the partial internal force from the mounting strain gage. Mechanical calculation method: the method has the advantages of sufficient theoretical basis and higher reliability and precision, but the existing calculation model has incomplete consideration factors and unsatisfactory precision. In addition, most of them cannot be effectively applied to real-time monitoring of power transmission lines.
Disclosure of Invention
The invention comprehensively considers the problems, analyzes the stress characteristics of the transmission line from the constitutive model of the transmission line, and comprehensively considers a plurality of factors to research a calculation method which has higher precision and strong reliability and can be used for on-line monitoring.
The invention provides a calculation method for monitoring internal force of a power transmission line, wherein a calculation model comprises the following steps:
step S1, firstly, determining physical and mechanical parameters and material parameters of the overhead transmission line, specifically including horizontal span L, vertical height difference h, initial cross-sectional area A, elastic modulus E and linear expansion coefficient R of the flexible conductor, and defining a coordinate system;
step S2, installing the distributed optical fiber, recording the initial installation length lambda of two optical fibers0Initial installation temperature T0And mounting position x1、x11、x12、x2、x21、x22；
Step S3, the temperature T and the deformation delta v of the 2 sections of local power transmission lines corresponding to the two distributed optical fibers at any time T are monitored in real time through the two distributed optical fibers1、Δv2；
In step S4, the input parameters are corrected. For measured Δ v1、Δv2Correction is made to remove a portion Δ v due to temperature changeT1、ΔvT2To obtain the direct input parameter Deltav of the model of the inventionE1、ΔvE2。
Step S5, inputting parameter delta v after correctionE1、ΔvE2And an initial parameter x1、x2、Δx1、Δx2Substituting the following formula:
Figure BDA0003532975060000021
in the formula: l is a horizontal span of the transmission line; h is a vertical height difference; Δ vE1、ΔvE2For two corrected inputsA parameter representing an elastic deformation portion in the measured deformations of the two distribution fibers; x is the number of1、x2Is the horizontal coordinate of two optical fibers, Δ x1、Δx2Is the horizontal length of two optical fibers; and a, b, c are catenary coefficients. In addition, in the case of the present invention,
Figure BDA0003532975060000022
wherein: h is the horizontal force of any point on the catenary; e is the transmission line elastic modulus; a is the cross-sectional area of the transmission line,
and solving the 4-element 4-degree equation set of the equation set to obtain four unknown parameters of a, b, c and epsilon.
In step S6, a, b, c, and e obtained based on the model of the present invention are substituted into H ═ EA,
Figure BDA0003532975060000023
Figure BDA0003532975060000024
And the horizontal force H and the axial tension F at any position of the transmission line are obtained through the equal formulas.
Further, x in step S21、x11、x12、x2、x21、x22Wherein:
Figure BDA0003532975060000025
Figure BDA0003532975060000026
Δx2＝x22-x21。
further, in step S3, the distributed optical fiber monitors the deformation Δ v in real time1、Δv2Involving both elastic deformation and deformation due to temperature change, i.e. Deltav1＝ΔvE1+ΔvT1,Δv2＝ΔvE2+ΔvT2In the formula: Δ vE1、ΔvE2An elastically deformed portion of the local deformations measured for the two distributed optical fibers; Δ vT1、ΔvT2Measured for two distributed optical fibresDeformation portion caused by temperature change in local deformation.
Further, in step S4, the measured Δ v is measured1、Δv2Corrected to remove Δ vT1、ΔvT2Obtaining an input parameter Δ vE1、ΔvE2I.e. Δ vE1＝Δv1-ΔvT1,ΔvE2＝Δv2+ΔvT2，
The calculation formula of the local deformation caused by the temperature is as follows: Δ vT ═ λ0R(T-T0)；
Then the correction Δ v1、Δv2Is Δ vE1、ΔvE2The calculation formula utilized is: Δ vE1＝Δv1-λ0R(T-T0)、ΔvE2＝Δv2-λ0R(T-T0)，
In the formula: lambda [ alpha ]0An initial installation length for the optical fiber; r is the linear expansion coefficient of the transmission line; t is the temperature of the transmission line at any time; t is0The temperature of the transmission line when the optical fiber is installed.
Further, in step S5, the corrected input parameter Δ v is correctedE1、ΔvE2And an initial parameter x1、x2、Δx1、Δx2Substituting the following formula
Figure BDA0003532975060000031
And the system of equations is represented by the following equation:
Figure BDA0003532975060000032
the method is simplified by a reduced order formula and a Taylor expansion formula, wherein the reduced order formula is as follows:
cosh2x＝1+cosh2x
the Taylor expansion used is:
Figure BDA0003532975060000033
and the four equations in the second equation set can be divided into 2 types of equations:
Figure BDA0003532975060000034
and
Figure BDA0003532975060000035
further, in step S6, the formula for solving the horizontal force H and the axial tension F at any position of the transmission line includes:
formula of transmission line horizontal force H: h ═ Epsilon EA;
formula of axial tension F at any position of power transmission line:
Figure BDA0003532975060000041
in the formula: e is the elastic modulus of the transmission line; a represents a cross-sectional area of the power transmission line; the rest parameters are the same as above.
The invention has the beneficial effects that:
the invention is based on the catenary model, and comprehensively considers the elastic deformation of the transmission line and the deformation caused by temperature change, thereby having the advantage of high precision.
The invention starts from the constitutive model of the transmission line, deduces the mathematical model for solving the internal force of the transmission line, does not need iterative computation or finite element modeling analysis, and can obtain the result only by substituting the monitored input parameters into the mathematical model of the invention, so the invention has the advantage of high computational efficiency.
Because the input parameter of the mathematical model is the local deformation of the power transmission line, and the input parameter shape can be obtained in real time through the distributed optical fiber, the internal force of any point on the power transmission line can be fed back in real time through 2 sections of distributed optical fibers arranged on the power transmission line.
The invention relates to a method for measuring the deformation of a local power transmission line in real time by using a distributed optical fiber, and the internal force of any point on the whole power transmission line is fed back by the method.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a feedback flow diagram of the model of the present invention;
FIG. 2 is a schematic representation of a model of the present invention;
FIG. 3 is a schematic view of the distributed fiber installation of the present invention 1;
FIG. 4 is a schematic illustration of the distributed fiber installation of the present invention 2;
FIG. 5 is a schematic illustration of the distributed fiber installation of the present invention 3;
fig. 6 is a schematic illustration of the input variable, i.e. the local deformation, according to the invention.
Detailed Description
The present invention is further described in detail below with reference to the attached drawings so that those skilled in the art can implement the invention by referring to the description text.
It will be understood that terms such as "having," "including," and "comprising," as used herein, do not preclude the presence or addition of one or more other elements or groups thereof.
As shown in fig. 1, an embodiment of the present invention is a method for calculating an internal force of an overhead transmission line based on an elastic catenary model, where the method uses local deformation measured by a distributed optical fiber as an input parameter, and includes the following steps:
step S1, firstly, determining physical and mechanical parameters and material parameters of the overhead transmission line, specifically including horizontal span L, vertical height difference h, cross-sectional area A of the flexible conductor, elastic modulus E and linear expansion coefficient R of the flexible conductor. Then, a coordinate system is defined, and as shown in fig. 2, the coordinate system is established with the suspension point on the left side of the wire as the origin O.
Step S2, installing the distributed optical fiber, recording the initial installation length lambda of two optical fibers0Initial installation temperature T0And mounting position x1、x11、x12、x2、x21、x22As shown in figures 3 to 5, the,
Figure BDA0003532975060000051
Δx1＝x12-x11,
Figure BDA0003532975060000052
Figure BDA0003532975060000053
Δx2＝x22-x21。
step S3, the temperature T and the deformation delta v of the 2 sections of local transmission lines corresponding to the two distributed optical fibers at any time T are monitored in real time through the two distributed optical fibers1、Δv2，Δv1、Δv2It is the initial input parameter for the model.
In step S4, the input parameters are corrected. Local transmission line deformation Deltav measured directly by optical fiber includes elastic deformation DeltavEAnd deformation Δ v caused by temperature deformationTCommon composition, i.e. Δ v ═ Δ vE+ΔvTWhile the direct input parameter of the model is the local elastic deformation DeltavETherefore, the distortion Δ v directly measured by the optical fiber needs to be corrected. Deformation Deltav caused by temperature change at any time tTComprises the following steps:
ΔvT＝λ0R(T-T0) (1)
in the formula: lambda [ alpha ]0An initial installation length for the optical fiber; r is the linear expansion coefficient of the transmission line; t is the temperature of the transmission line at any time; t is0Is the temperature of the transmission line when the optical fiber is installed,
so that the corrected input parameter, i.e. the local elastic deformation Δ vEComprises the following steps:
ΔvE＝Δv-λ0R(T-T0) (2)
in the formula: lambda [ alpha ]0An initial installation length for the optical fiber; r is the linear expansion coefficient of the transmission line; t is the temperature of the transmission line at any time; t is0The temperature of the transmission line when the optical fiber is installed.
The measured delta v of the two distributed optical fibers can be obtained by the above formula (2)1、Δv2Successful correction to Δ vE1、ΔvE2These two models are directly input parameters.
Step S5, substituting the input parameters into the model of the present invention, the model of the present invention is derived as follows:
as indicated above: o, C are the left and right suspension points of the catenary, point A is the lowest point of the catenary, and point B is any point on the catenary. H is the horizontal pulling force that the minimum A point goes out, and F is the pulling force of arbitrary point B point department on the rope, and theta is the contained angle of B point tangential direction and horizontal direction, and q is the plane load, and s is the arc length between AB, then has:
Figure BDA0003532975060000061
in the formula, F represents the axial tension of any point on the catenary; theta represents the included angle between the tangent direction of any point on the catenary and the horizontal direction; q represents the uniform load on the catenary vertical plane; s represents the length between any point on the catenary (point B) and its lowest point (point a), i.e., the arc length between AB in fig. 2; h represents the horizontal pulling force at the point of nadir a,
while
Figure BDA0003532975060000062
Therefore, it is not only easy to use
Figure BDA0003532975060000063
Then, the following formula (4) is obtained by twice deriving the formula
Figure BDA0003532975060000064
In the formula: x and y respectively represent the horizontal and vertical coordinates of any point B on the catenary, as shown in FIG. 2; the other parameters are the same as the above parameters,
and because of
Figure BDA0003532975060000065
If order
Figure BDA0003532975060000066
Substituting the formula (4) to obtain the catenary equation:
Figure BDA0003532975060000067
in the above equation (5), b and c are integral constants, so that the three parameters a, b and c in the catenary equation are collectively referred to as catenary parameters.
As can be seen from the above formula (3), the tensile force at any point on the catenary is F ═ H sec θ
Figure BDA0003532975060000068
Then
Figure BDA0003532975060000069
And because of
Figure BDA00035329750600000610
And is
Figure BDA00035329750600000611
Therefore, the axial tension F at any point on the catenary is as follows:
Figure BDA0003532975060000071
in the formula: the parameters are the same as the above parameters,
it is generally accepted that the elastic deformation of a transmission line satisfies Hooke's law, let s0Is the original length of the transmission line, s is the length after deformation, E is the elastic modulus of the transmission line, then：
Figure BDA0003532975060000072
In the formula: e is the elastic modulus of the transmission line; a represents a cross-sectional area of the power transmission line; the other parameters are the same as the above parameters,
according to series expansion
Figure BDA0003532975060000073
The following can be obtained:
Figure BDA0003532975060000074
in the formula: the parameters are the same as the above parameters,
so approximately consider
Figure BDA0003532975060000075
Substituting it into the above formula (7) gives:
Figure BDA0003532975060000076
in the formula: the parameters are the same as the above parameters,
from fig. 3, it can be seen that dv-ds0V denotes the deformation, which is derived from Hooke's Law and should be dv in the strict senseE＝ds-ds0，vEIndicating elastic deformation. And then substituting formula (6) for formula (9):
Figure BDA0003532975060000077
in the formula: v. ofERepresenting elastic deformation; the other parameters are the same as the above parameters,
order to
Figure BDA0003532975060000078
And is
Figure BDA0003532975060000079
Then, according to the finite difference concept, the above-mentioned infinitesimal elements are replaced by sufficiently small difference values to obtain the core model of the present invention, which is expressed as the following formula (11)
Figure BDA00035329750600000710
In the formula: Δ vEAnd Δ x represents the elastic deformation of the local catenary and its horizontal projected length, respectively, as shown in FIG. 6;
Figure BDA00035329750600000711
the other parameters are the same as the above parameters,
it can be seen that there are 3 unknowns such as a, b, epsilon, etc. in the above formula (11), it is obvious that the input quantities measured by two optical fibers can only construct two equations, and 3 unknowns cannot be solved. However, as shown in FIG. 1, point O (0,0) is on the catenary with point C (L, h) and thus satisfies equation (5) above, and equation (5) has unknown parameters a, b, C, so equation (5) shares four unknowns, a, b, C, ε, etc. with equation (11), and O, C can construct an equation 2 from two points, plus the two equations, exactly four unknowns, as in equation (12) below
Figure BDA0003532975060000081
In the formula: Δ vE1、ΔvE2And Δ x1And Δ x2Respectively representing the elastic deformation of 2 sections of local catenary and the horizontal projection length thereof, as shown in FIG. 6, wherein a, b and c are catenary parameters; the rest parameters are the same as above;
since the formula (12) is a high-order equation and the solution is complex, the equation is firstly based on cosh2Decreasing equation (12) by 1+ cosh2 x:
Figure BDA0003532975060000082
in the formula: the parameters are the same as the above parameters,
the formula in the formula (12) is changed into a 1-order equation through the formula (13), but the formula is still a hyperbolic cosine function, namely a transcendental function, the direct solution can reduce the calculation efficiency of the model, so that the Taylor formula is further utilized to improve the efficiency of the model
Figure BDA0003532975060000083
The above formulas (12) and (13) are simplified to obtain the following formula (14)
Figure BDA0003532975060000084
In the formula: the parameters are the same as the above parameters,
correcting the horizontal span L and the vertical height difference h of the transmission line to obtain an input parameter delta vE1、ΔvE2And the position of the unknown parameter is substituted into the above formula (14), and a 4-element 4-degree equation system of the above formula is solved to obtain four unknown parameters of a, b, c, epsilon and the like.
And step S6, solving the horizontal force H and the axial tension F at any position of the transmission line according to the four parameters solved in the step S5.
From the above formula (11):
Figure BDA0003532975060000085
the horizontal force H of the transmission line is therefore:
H＝εEA (15)
in the formula: e is the elastic modulus of the transmission line; a represents a cross-sectional area of the power transmission line; the other parameters are the same as the above parameters,
according to the formula (6), the axial tension F at any point of the power transmission line is as follows:
Figure BDA0003532975060000091
in the formula: e is the elastic modulus of the transmission line; a represents a cross-sectional area of the power transmission line; the rest parameters are the same as above.
Therefore, the real-time feedback of the internal force of the transmission line through the local transmission line deformation monitored by the two distributed optical fibers is completed.
While embodiments of the invention have been disclosed above, it is not limited to the applications listed in the description and the embodiments. It can be applied to all kinds of fields suitable for the present invention. Additional modifications will readily occur to those skilled in the art. Therefore, the present invention is not limited to the above-mentioned embodiments, which are only illustrative and not restrictive, and those skilled in the art can make many forms without departing from the spirit and scope of the present invention as claimed in the appended claims.

Claims (7)

1. A computational method for monitoring forces within a power transmission line, wherein the computational model comprises the steps of:
step S1, firstly, determining physical and mechanical parameters and material parameters of the overhead transmission line, and defining a coordinate system;
step S2, installing the distributed optical fiber, recording the initial installation length lambda of two optical fibers0Initial installation temperature T0And mounting position x1、x11、x12、x2、x21、x22；
Step S3, the temperature T and the deformation delta v of the 2 sections of local power transmission lines corresponding to the two distributed optical fibers at any time T are monitored in real time through the two distributed optical fibers1、Δv2；
Step S4, correcting the input parameters, and measuring the delta v1、Δv2Correction is made to remove a portion Δ v due to temperature changeT1、ΔvT2To obtain the direct input parameter Deltav of the model of the inventionE1、ΔvE2；
Step S5, inputting parameter delta v after correctionE1、ΔvE2And an initial parameter x1、x2、Δx1、Δx2Substituting the following formula:
Figure FDA0003532975050000011
in the formula: l is a horizontal span of the transmission line; h is a vertical height difference; Δ vE1、ΔvE2Two corrected input parameters representing the elastic deformation portions of the two distribution optical fibers in the measured deformation; x is a radical of a fluorine atom1、x2Is the horizontal coordinate of two optical fibers, Δ x1、Δx2Is the horizontal length of two optical fibers; and a, b, c are catenary coefficients, and further,
Figure FDA0003532975050000012
wherein: h is the horizontal force of any point on the catenary; e is the transmission line elastic modulus; a is the cross-sectional area of the transmission line;
solving a 4-element 4-order equation set of the formula to obtain four unknown parameters of a, b, c and epsilon;
in step S6, based on a, b, c, and ∈ obtained by the above models, H ═ EA, and ∈ EA are substituted,
Figure FDA0003532975050000013
And solving the horizontal force H and the axial tension F of any position of the transmission line by a formula.
2. A calculation method for monitoring the internal force of a transmission line according to claim 1, characterized in that the physical and mechanical parameters and material parameters include the horizontal span L of the flexible conductor, the vertical height difference h, the initial cross-sectional area a of the conductor, the elastic modulus E, and the coefficient of linear expansion R of the conductor.
3. The calculation method for monitoring the internal force of a power transmission line according to claim 1, wherein in step S2,
Figure FDA0003532975050000021
Δx1＝x12-x11
Figure FDA0003532975050000022
Δx2＝x22-x21。
4. the method according to claim 3, wherein the step S3 is implemented by monitoring the deformation Δ ν in real time through the distributed optical fiber1、Δv2Involving both elastic deformation and deformation due to temperature change, i.e. Deltav1＝ΔvE1+ΔvT1,Δv2＝ΔvE2+ΔvT2In the formula: Δ vE1、ΔvE2An elastically deformed portion of the local deformations measured for the two distributed optical fibers; Δ vT1、ΔvT2The deformation caused by temperature variation in the local deformation measured for the two distributed optical fibers.
5. The method of claim 4, wherein the step S4 is performed on the measured Δ ν1、Δv2Corrected to remove Δ vT1、ΔvT2Obtaining an input parameter Δ vE1、ΔvE2I.e. Δ vE1＝Δv1-ΔvT1,ΔvE2＝Δv2+ΔvT2；
The calculation formula of the local deformation caused by the temperature is as follows: Δ vT＝λ0R(T-T0)；
Then the correction Δ v1、Δv2Is Δ vE1、ΔvE2The calculation formula utilized is: Δ vE1＝Δv1-λ0R(T-T0)；ΔvE2＝Δv2-λ0R(T-T0)；
In the formula: lambda0An initial installation length for the optical fiber; r is the linear expansion coefficient of the transmission line; t is the temperature of the transmission line at any time; t is0For optical fibre installationThe wire temperature.
6. A calculation method for monitoring the internal force of a power transmission line according to claim 5, characterized in that said step S5 is implemented by modifying said input variable Δ νE1、ΔvE2And an initial parameter x1、x2、Δx1、Δx2Substituting the following formula
Figure FDA0003532975050000023
And the system of equations is represented by the following equation:
Figure FDA0003532975050000031
the method is simplified by a reduced order formula and a Taylor expansion, wherein the reduced order formula is as follows:
cosh2x＝1+cosh2x
the Taylor expansion used is:
Figure FDA0003532975050000032
and the four equations in the second equation set can be divided into 2 types of equations:
Figure FDA0003532975050000033
and
Figure FDA0003532975050000034
7. the method of claim 6, wherein the solving formula of the horizontal force H and the axial tension F at any position of the transmission line in the step S6 comprises:
formula of transmission line horizontal force H: h ═ EA;
formula of axial tension F at any position of power transmission line:
Figure FDA0003532975050000035
in the formula: e is the elastic modulus of the transmission line; a represents the cross-sectional area of the transmission line.
CN202210211769.2A 2022-03-04 2022-03-04 Calculation method for monitoring internal force of power transmission line Pending CN114444364A (en)

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