CN105760561B - It is a kind of consider conductor spacer damping parameter bundle conductor breeze vibration determine method - Google Patents
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Abstract
The present invention relates to a kind of bundle conductor breeze vibrations for considering conductor spacer damping parameter to determine method, it is described that analysis and experimental study are calculated based on wire clamp of conductor spacer damping parameter, in conjunction with average span calculation method of conductor spacer, the true damping in interval is applied to the suitable position of split conductor, the solution of bundle conductor breeze vibration is finally realized using finite element method, so that it is determined that bundle conductor breeze vibration is horizontal, reference is provided for the Anti-vibration Design of route.This method can make up for it the deficiency that bundle conductor breeze vibration is solved based on traditional discount coefficient method.
Description
Technical field:
The present invention relates to a kind of bundle conductor breeze vibrations to determine method, is more particularly to a kind of consideration conductor spacer damping ginseng
Several bundle conductor breeze vibrations determine method.
Background technique:
Since reform and opening-up, China's power industry is fast-developing.Especially in recent years, with the lasting high speed of power demand
Increase, electric power development speed is further speeded up.Power industry is the basic industry to involve the interests of the state and the people.Optimization energy resources are matched
It sets, ensures national energy security, provide high-quality, reliable power supply for national economy and social development, be power industry clothes
It is engaged in the important mission built a harmonious socialist society.
Overhead transmission line split conductor is easy to induce the vibration of diversified forms under the action of natural wind, wherein gentle breeze
Vibration is a kind of most commonly seen vibration mode, has the characteristics that amplitude is small, frequency is high, the duration is long.Long-term gentle breeze vibration
It is visibly moved to easily lead to the major accidents such as conducting wire fatigue stranded, fitting damage, or even generation broken string, seriously threaten the safety fortune of route
Row, it is necessary to adopt an effective measure and be prevented and treated.For split conductor, usually pass through installation damper, conductor spacer, damping wire
Equal antihunting devices are horizontal come the aeolian vibration for reducing conducting wire.Traditional aeolian vibration, which is calculated, handles conductor spacer using discount coefficient method
To the inhibiting effect of conducting wire aeolian vibration, i.e., by the level of vibration under single conductor state by the different multiplied by 1/3-1/6 of division number
Equal reduction coefficient does not carry out the level of vibration of equivalent corresponding split conductor.Although this method can satisfy the need of engineering calculation
It wants, but the accuracy calculated is not high, needs to deeply consider the damping action of conductor spacer, improve what bundle conductor breeze vibration calculated
Accuracy.
This patent is based on wire clamp of conductor spacer damping parameter and calculates analysis and experimental study, in conjunction with average span meter of conductor spacer
The true damping in interval is applied to the suitable position of split conductor, finally realizes split conductor using finite element method by calculation method
The solution of aeolian vibration provides reference so that it is determined that bundle conductor breeze vibration is horizontal for the Anti-vibration Design of route.
Summary of the invention:
The object of the present invention is to provide a kind of bundle conductor breeze vibrations for considering conductor spacer damping parameter to determine method, institute
The method of stating can make up for it the deficiency that bundle conductor breeze vibration is solved based on traditional discount coefficient method.
To achieve the above object, the invention adopts the following technical scheme: a kind of division for considering conductor spacer damping parameter is led
Line aeolian vibration determines method, comprising the following steps:
(1) the wire clamp damping parameter of conductor spacer is determined；
(2) average span of conductor spacer is determined；
(3) conductor spacer number and installation site are determined；
(4) bundle conductor breeze vibration FEM calculation is carried out.
A kind of bundle conductor breeze vibration considering conductor spacer damping parameter provided by the invention determines method, the step
(1) the wire clamp damping parameter of the conductor spacer in determines the logarithmic decrement δ of the wire clamp collet of conductor spacer by testing, so that it is determined that
Damping parameter.
A kind of bundle conductor breeze vibration considering conductor spacer damping parameter provided by the invention determines method, the test
The following steps are included:
The ontology of tested conductor spacer is rigidly fixed on test bracket, applies counterweight at the wire clamp of conductor spacer；?
Acceleration transducer is set on the wire clamp, and bent by the change in displacement that data collection system records wire clamp free vibration attenuation
Line；Direction along the wire clamp turning circumference of conductor spacer applies tangential force, so that wire clamp turns to extreme position, stops one point
Clock discharges, suddenly so that wire clamp free vibration.
Another preferred a kind of bundle conductor breeze vibration determination side for considering conductor spacer damping parameter provided by the invention
Method, the bracket are linked together conductor spacer with ground；The counterweight applied must make the natural frequency of vibration of wire clamp of conductor spacer be 1
~2Hz.
Another preferred a kind of bundle conductor breeze vibration determination side for considering conductor spacer damping parameter provided by the invention
Method, the logarithmic decrement δ are determined by following formula:
Wherein, Y1: first peak value of the displacement changing curve of wire clamp free vibration attenuation；
Y2: first valley of the displacement changing curve of wire clamp free vibration attenuation；
Y3: second peak value of the displacement changing curve of wire clamp free vibration attenuation；
Y4: second valley of the displacement changing curve of wire clamp free vibration attenuation；
The damping parameter ζ is determined by following formula:
Another preferred a kind of bundle conductor breeze vibration determination side for considering conductor spacer damping parameter provided by the invention
Method, average span in the step (2) are determined by 1.1-1.2 times of maximum span.
Another preferred a kind of bundle conductor breeze vibration determination side for considering conductor spacer damping parameter provided by the invention
Method, the maximum span are determined by following formula:
Wherein, 2X0: secondary span vibration amplitude, unit are rice；L: conductor spacer interval, unit are rice；V: wind speed, unit are
Meter per second；A: sub-conductor spacing, unit are rice；D: sub-conductor outer diameter, unit are rice；T: sub-conductor tension, unit are kilogram,
W: sub-conductor weight, unit are kg/m；E: the amplitude damping factor in signal period takes 0.05-0.1.
Another preferred a kind of bundle conductor breeze vibration determination side for considering conductor spacer damping parameter provided by the invention
Method, the conductor spacer number in the step (3) pass through following formula and determine:
In formula, M is conductor spacer number, and L is span length, and S is average span；
Centered on span midpoint calculated, conductor spacer is symmetrically arranged on split conductor by the right and left, adjacent
Distance between conductor spacer is average span.
Another preferred a kind of bundle conductor breeze vibration determination side for considering conductor spacer damping parameter provided by the invention
Method, determination process in the step (4) the following steps are included:
Determine finite element discretization and unit；
Solve the equation of motion；
Analyze rumble spectrum.
Another preferred a kind of bundle conductor breeze vibration determination side for considering conductor spacer damping parameter provided by the invention
The matrix ODE of method, FEM calculation is as follows:
Wherein: mass matrix M=∫VNTρNdV；Damping matrix C=∫VNTμNdV；Stiffness matrix K=∫VBTDBdV；External force to
Amount A is respectively the vector acceleration, velocity vector, motion vector of node；N is single
First form function matrix；NTFor the transposed matrix of unit form function matrix；ρ is unit material density；μ is damped coefficient；BTFor strain
The transposed matrix of matrix；D is elastic matrix, indicates stress-strain relation；B strain matrix indicates strain-displacement relation；fiFor list
The body force acted in member；For the distributed force acted in boundary inside unit；V is entire computational domain；SσFor the power of entire computational domain
Act on boundary；
In Cable Power Computation, mass matrix uses concentrated quality method, improves calculating speed；Traverse calculation uses beam element,
It is for linear beam element mass matrix
For unit damping matrix, using Rayleigh damping, i.e.,
Ce=α Me+βKe (7)
Assume that damping is the linear combination of stiffness matrix and mass matrix；In transmission line of electricity aeolian vibration calculating, adopt
Damping results are equivalent to viscous damping with test measurement method；；M is the quality of unit；α, β are Rayleigh damping coefficient；
The general stiffness matrix of the linear beam element of conducting wire is
E is elasticity modulus；L is element length；A is unit sectional area；IzFor unit cross sectional moment of inertia；
Another preferred a kind of bundle conductor breeze vibration determination side for considering conductor spacer damping parameter provided by the invention
Method, it includes immediate integration and mode superposition method that the equation of motion, which solves,；
The immediate integration is directly to equation Integration Solving；Newmark immediate integration is selected, for doing transient state point
Analysis；
The mode superposition method decouples equation group using the natural mode of vibration of linear structural system, solves separate equation respectively,
Superposition obtains last solution.
Another preferred a kind of bundle conductor breeze vibration determination side for considering conductor spacer damping parameter provided by the invention
Method, the analysis rumble spectrum are under the simple harmonic oscillation load excitation of the intrinsic frequency of given power, when calculating steady-state vibration
The amplitude and phase of each measuring point, eventually for the calculating of the equalization point vibration parameters of transmission line of electricity system；Entire spectrum analysis
Process occurs in frequency domain；The spectrum analysis is also referred to as modal frequency response calculating；
The equation of motion of conducting wire aeolian vibration is
It calculates and is carried out in frequency domain, if physical responsesWherein { ξ (ω) } is modal coordinate, is solved
Decouple equation:
Diagonal matrix is all turned to after mass matrix, stiffness matrix and damping matrix transformation, therefore:
I.e.
Wherein, whereinVector acceleration, velocity vector, the motion vector of x simple harmonic motion；{ ξ (ω) } is mode
Coordinate vector；It is characterized vector matrix；[M], [C], [K], { P } are respectively mass matrix, damping matrix, stiffness matrix, lotus
Carry vector；ω,ωiRespectively external load frequency, i-th of modal frequency；mi、ci、ki、piIt is for i-th equation after decoupling
Number；ξi(ω) is i-th of equation modal coordinate vector；I is i-th of equation；
The quality and damping for considering conductor spacer simultaneously, take the actual measurement of a wire clamp of conductor spacer to damp, are applied to division and lead
On the link node of line；The quality of equispaced stick is attached on the corresponding link node of each root conducting wire simultaneously；
Formula (11) back substitution is entered into the displacement parameter that physical responses formula obtains aeolian vibration.
Compared with the nearest prior art, the technical scheme provide by that invention has the following excellent effect
1, method of the invention improves the accuracy of bundle conductor breeze vibration calculating；
2, method of the invention provides reference for the Anti-vibration Design of route；
3, method of the invention can make up for it the deficiency that bundle conductor breeze vibration is solved based on traditional discount coefficient method；
4, method of the invention effectively prevents that the major accidents such as broken string occur, and guarantees the safe operation of transmission line of electricity；
5, method of the invention provides high-quality, reliable power supply for national economy and social development.
Detailed description of the invention
Fig. 1 is the wire clamp of conductor spacer free vibration attenuation displacement changing curve figure of the method for the present invention；
Fig. 2 is the method for the present invention flow chart.
Specific embodiment
Below with reference to embodiment, the invention will be described in further detail.
Embodiment 1:
As shown in Figs. 1-2, it is true to provide a kind of bundle conductor breeze vibration for considering conductor spacer damping parameter for the invention of this example
Determine method, comprising the following steps:
1. wire clamp of conductor spacer damping parameter determines
The damping parameter of wire clamp of conductor spacer can determine that test method is as follows by test.
The ontology of tested conductor spacer is rigidly fixed on test bracket, applies certain match at wire clamp of conductor spacer
Weight.Apply tangential force along the direction of wire clamp of conductor spacer turning circumference, so that wire clamp turns to extreme position, stop one minute,
Then release suddenly, so that wire clamp free vibration.Acceleration transducer is installed on wire clamp, passes through data collection system call wire
The displacement changing curve of free vibration attenuation is pressed from both sides, example is as shown in Figure 1.The bracket is common shelf for fixing.
Enabling the corresponding shift value in the midpoint Fig. 11,2,3,4 is respectively Y1, Y2, Y3, Y4, then the logarithmic decrement of conductor spacer collet
Rate δ can be calculated by formula (1).
Damping parameter ζ can have formula (2) calculating.
2. the calculating of average span of conductor spacer
According to engineering operation experience, maximum span is about 1.1-1.2 times of average span.Therefore, it acquires maximum time
Span you can get it average span.
The main requirement for considering sub-conductor amplitude restrictive condition of the calculating of maximum span.Son is led when subspan oscillation occurs
The amplitude of line generally requires the half less than sub-conductor spacing, collides when to avoid sub-conductor oscillation.Sub-conductor vibration
Maximum time span under width restrictive condition is determined by formula (3).
Wherein, 2X0: secondary span vibration amplitude (m), l: conductor spacer interval (m) V: wind speed (m/s), a: sub-conductor spacing
(m), D: sub-conductor outer diameter (m), T: sub-conductor tension (kgf), W: sub-conductor weight (kg/m), E: the amplitude in signal period declines
Lapse rate takes 0.05-0.1.
3. the determination of conductor spacer number and installation site
Conductor spacer number is determined by averagely secondary span.The half or so of generally only intermediate time span of time span is held, therefore
End time span is calculated half span, other secondary spans calculate one span.If a length of L of span, average time span is S,
Every stick number be N, relationship are as follows:
In formula, N is conductor spacer number, and L is span length, and S is average span.
For the calculating convenient for split conductor vibration characteristics, the conductor spacer number that can be calculated by above formula, to calculate span midpoint
Centered on, conductor spacer is symmetrically arranged on split conductor by the right and left.
4. bundle conductor breeze vibration FEM calculation
(1) finite element discretization and unit calculate
The basic thought of Finite Element is to go to approach one continuously infinitely with a discrete finite degrees of freedom space
Freedom degree space.Non-individual body is specifically divided into the junior unit that limited freedom degree is connected, using in each unit
Approximate function carrys out Approximation and solves unknown field function on domain entirely.
The matrix ODE of FEM calculation is as follows.
Wherein:
Mass matrix M=∫VNTρNdV
Damping matrix C=∫VNTμNdV
Stiffness matrix K=∫VBTDBdV
Outer force vector
In Cable Power Computation, mass matrix generallys use lumped mass method, improves calculating speed.Traverse calculation can be used
Beam element is for linear beam element mass matrix
For unit damping matrix, since in practical projects, damping effect is relatively complicated, Rayleigh resistance is generallyd use
Buddhist nun, i.e.,
Ce=α Me+βKe (7)
Namely assume that damping is certain linear combination of stiffness matrix and mass matrix.It is calculated in transmission line of electricity aeolian vibration
In, damping results can also be equivalent to viscous damping using test measurement method by us.
The general stiffness matrix of the linear beam element of conducting wire is
(2) solution of the equation of motion
The equation of motion is second order ordinary differential equation group, and method for solving is generally divided into direct integral in finite Element Dynamic Analysis
Method and mode superposition method two major classes.
Immediate integration does not need to do the equation of motion special transformation, directly to equation Integration Solving, but it is general
The limitation of having time step-length, current implementation method selects Newmark immediate integration, for doing transient analysis.
Mode superposition method needs the natural mode of vibration decoupling equation group using system, then solves separate equation respectively, then
Substituted back into equationObtain last solution.
(3) vibration frequency specturm analysis
The equation of motion of conducting wire aeolian vibration is
The purpose of the analysis is under the simple harmonic oscillation load excitation of certain intrinsic frequency of given power, to calculate stable state vibration
The amplitude and phase of each measuring point when dynamic, eventually for the calculating of the equalization point vibration parameters of transmission line of electricity system.Entire frequency spectrum
Analytical calculation process occurs in frequency domain.Spectrum analysis herein is alternatively referred to as modal frequency response calculating.
It calculates and is carried out in frequency domain, if physical responsesWherein { ξ (ω) } is modal coordinate, can be with
Solve decoupling equation:
In general, diagonal matrix can be turned to after mass matrix, stiffness matrix and damping matrix transformation.So having
I.e.
The quality and damping for considering conductor spacer simultaneously, take the actual measurement of a wire clamp of conductor spacer to damp, are applied to division and lead
On the link node of line.The quality of equispaced stick simultaneously, is attached on the corresponding link node of each root conducting wire.
Finally (11) back substitution is entered physical responses formula you can get it the displacement parameter of aeolian vibration.
FEM calculation basic procedure:
Input data: node, equation number, load working condition, solves requirement at unit
Assessment processing: according to discrete scale, assessment calculates the memory headroom needed and resource, calculates adjacency matrix
Computing unit: mass matrix, damping matrix, stiffness matrix, unit vector
Unit assembling: all cell matrix and vector are assembled according to adjacency matrix
BORDER PROCESSING: apply displacement constraint and edge load
Integrated solution: global matrix is solved according to type is solved, obtains fundamental unknown variables or feature pair
Back substitution process: processing the solution of global matrix, calculates derived physical quantities or does special transformation
Output result: calculative physical quantity is output to file and is saved
Finally it should be noted that: the above embodiments are merely illustrative of the technical scheme of the present invention and are not intended to be limiting thereof, institute
The those of ordinary skill in category field is although should be understood with reference to the above embodiments: still can be to a specific embodiment of the invention
It is modified or replaced equivalently, these are without departing from any modification of spirit and scope of the invention or equivalent replacement, in Shen
Within claims of the invention that please be pending.
Claims (10)
1. a kind of bundle conductor breeze vibration for considering conductor spacer damping parameter determines method, it is characterised in that: including following step
It is rapid:
(1) the wire clamp damping parameter of conductor spacer is determined；
(2) average span of conductor spacer is determined；
(3) conductor spacer number and installation site are determined；
(4) bundle conductor breeze vibration FEM calculation is carried out；
Determination process in the step (4) the following steps are included:
Determine finite element discretization and unit；
Solve the equation of motion；
Analyze rumble spectrum；
The matrix ODE of FEM calculation is as follows:
Wherein: mass matrix M=∫VNTρNdV；Damping matrix C=∫VNTμNdV；Stiffness matrix K=∫VBTDBdV；Outer force vector A is respectively the vector acceleration, velocity vector, motion vector of node；N is unit
Form function matrix；NTFor the transposed matrix of unit form function matrix；ρ is unit material density；μ is damped coefficient；BTTo answer bending moment
The transposed matrix of battle array；D is elastic matrix, indicates stress-strain relation；B strain matrix indicates strain-displacement relation；fiFor unit
The body force of upper effect；For the distributed force acted in boundary inside unit；V is entire computational domain；SσFor the masterpiece of entire computational domain
Use boundary；
In Cable Power Computation, mass matrix uses concentrated quality method, improves calculating speed；Traverse calculation uses beam element, for
Linearly beam element mass matrix is
For unit damping matrix, using Rayleigh damping, i.e.,
Ce=α Me+βKe (7)
Assume that damping is the linear combination of stiffness matrix and mass matrix；In transmission line of electricity aeolian vibration calculating, using examination
It tests measurement method and damping results is equivalent to viscous damping；M is the quality of unit；α, β are Rayleigh damping coefficient；
The general stiffness matrix of the linear beam element of conducting wire is
E is elasticity modulus；L is element length；A is unit sectional area；IzFor unit cross sectional moment of inertia.
2. a kind of bundle conductor breeze vibration for considering conductor spacer damping parameter as described in claim 1 determines method, special
Sign is: the wire clamp damping parameter of the conductor spacer in the step (1) determines the logarithm of the wire clamp collet of conductor spacer by testing
Attenuation rate δ, so that it is determined that damping parameter.
3. a kind of bundle conductor breeze vibration for considering conductor spacer damping parameter as claimed in claim 2 determines method, special
Sign is: it is described test the following steps are included:
The ontology of tested conductor spacer is rigidly fixed on test bracket, applies counterweight at the wire clamp of conductor spacer；Described
Acceleration transducer is set on wire clamp, and records the displacement changing curve of wire clamp free vibration attenuation by data collection system；
Direction along the wire clamp turning circumference of conductor spacer applies tangential force, so that wire clamp turns to extreme position, stops one minute, dashes forward
So release, so that wire clamp free vibration.
4. a kind of bundle conductor breeze vibration for considering conductor spacer damping parameter as claimed in claim 3 determines method, special
Sign is: the bracket is linked together conductor spacer with ground；The counterweight applied must make the self-vibration frequency of wire clamp of conductor spacer
Rate is 1~2Hz.
5. a kind of bundle conductor breeze vibration for considering conductor spacer damping parameter as claimed in claim 2 determines method, special
Sign is: the logarithmic decrement δ is determined by following formula:
Wherein, Y1: first peak value of the displacement changing curve of wire clamp free vibration attenuation；
Y2: first valley of the displacement changing curve of wire clamp free vibration attenuation；
Y3: second peak value of the displacement changing curve of wire clamp free vibration attenuation；
Y4: second valley of the displacement changing curve of wire clamp free vibration attenuation；
The damping parameter ζ is determined by following formula:
6. a kind of bundle conductor breeze vibration for considering conductor spacer damping parameter as described in claim 1 determines method, special
Sign is: average span in the step (2) is determined by 1.1-1.2 times of maximum span.
7. a kind of bundle conductor breeze vibration for considering conductor spacer damping parameter as claimed in claim 6 determines method, special
Sign is: the maximum span is determined by following formula:
Wherein, 2X0: secondary span vibration amplitude, unit are rice；L: conductor spacer interval, unit are rice；V: wind speed, unit are meter per second；
A: sub-conductor spacing, unit are rice；D: sub-conductor outer diameter, unit are rice；T: sub-conductor tension, unit are kilogram, and W: son is led
Line weight, unit are kg/m；E: the amplitude damping factor in signal period takes 0.05-0.1.
8. a kind of bundle conductor breeze vibration for considering conductor spacer damping parameter as claimed in claim 7 determines method, special
Sign is: the conductor spacer number in the step (3) is determined by following formula:
In formula, M is conductor spacer number, and L is span length, and S is average span；
Centered on span midpoint calculated, conductor spacer is symmetrically arranged on split conductor by the right and left, adjacent spaces
Distance between stick is average span.
9. a kind of bundle conductor breeze vibration for considering conductor spacer damping parameter as claimed in claim 8 determines method, special
Sign is: it includes immediate integration and mode superposition method that the equation of motion, which solves,；
The immediate integration is directly to equation Integration Solving；Newmark immediate integration is selected, for doing transient analysis；
The mode superposition method decouples equation group using the natural mode of vibration of linear structural system, solves separate equation respectively, is superimposed
Obtain last solution.
10. a kind of bundle conductor breeze vibration for considering conductor spacer damping parameter as claimed in claim 9 determines method, special
Sign is: the analysis rumble spectrum is to calculate stable state vibration under the simple harmonic oscillation load excitation of the intrinsic frequency of given power
The amplitude and phase of each measuring point when dynamic, eventually for the calculating of the equalization point vibration parameters of transmission line of electricity system；Entire frequency spectrum
Analytic process occurs in frequency domain；The spectrum analysis is also referred to as modal frequency response calculating；
The equation of motion of conducting wire aeolian vibration is
It calculates and is carried out in frequency domain, if physical responsesSolve decoupling equation:
Diagonal matrix is all turned to after mass matrix, stiffness matrix and damping matrix transformation, therefore:
I.e.
Wherein,Vector acceleration, velocity vector, the motion vector of x simple harmonic motion；{ ξ (ω) } is modal coordinate vector；It is characterized vector matrix；[M], [C], [K], { P } are respectively mass matrix, damping matrix, stiffness matrix, load vector；
ω、ωiRespectively external load frequency, i-th of modal frequency；mi、ci、ki、piFor the coefficient of i-th of equation after decoupling；ξi
(ω) is i-th of equation modal coordinate vector；I is i-th of equation；
The quality and damping for considering conductor spacer simultaneously, take the actual measurement of a wire clamp of conductor spacer to damp, are applied to split conductor
On link node；The quality of equispaced stick is attached on the corresponding link node of each root conducting wire simultaneously；
Formula (11) back substitution is entered into the displacement parameter that physical responses formula obtains aeolian vibration.
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| CN102436546A (en) * | 2011-10-17 | 2012-05-02 | 西安交通大学 | Computing method for torsional rigidity of split conductor of overhead power transmission line |
| CN102564715A (en) * | 2011-01-24 | 2012-07-11 | 东北电力大学 | 500kV compact power transmission line three phase bundle conductor breeze vibration simulation test platform |
| CN104156511A (en) * | 2014-07-25 | 2014-11-19 | 国家电网公司 | Spacer subspan setting optimizing method |
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| KR101119672B1 (en) * | 2009-09-18 | 2012-03-16 | 한국전기연구원 | Boltless type spacer damper for 6 bundled conductors |
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