JP6536253B2 - Transmission line behavior analysis device, transmission line behavior analysis method, transmission line behavior analysis program and transmission line system - Google Patents

Description

  The present invention relates to a transmission line behavior analysis device, a transmission line behavior analysis method, a transmission line behavior analysis program, and a transmission line system, and more particularly to a dynamic behavior analysis technique.

  Conventionally, a method of analyzing the behavior of a transmission line by the finite element method has been proposed (see, for example, Non-Patent Document 1). In this behavior analysis method, static balance analysis is performed on the transmission line model in the state where gravity is applied to the transmission line first, and then dynamic behavior analysis is performed in the balance state under gravity. Do.

  In the design of a transmission line system including steel towers and transmission lines, it is important to prevent a ground fault or the like of the transmission line. Therefore, conventionally, behavior analysis of a transmission line in a state where an external force is applied to the transmission line by the finite element method has been performed (see, for example, Non-Patent Document 1). The behavior analysis of the transmission line described in Non-Patent Document 1 includes static balance analysis and dynamic behavior analysis. In static balance analysis, static balance analysis is performed on the transmission line model in the state where gravity is applied to the transmission line first, and the stiffness parameter of the transmission line in the state where gravity acts on the transmission line is calculated Do. And in dynamic balance analysis, dynamic behavior analysis of the power transmission line in the state where gravity and fluctuating external force acted is performed based on Newmark beta method using the stiffness parameter computed by static balance analysis.

Mikio Shimizu, Masato Mamoru, Jun-ichi Sato, "Geometrical Nonlinear Analysis of Galloping on Transmission Lines", Proceedings of Structural Engineering, The Japan Society of Civil Engineers, March 1998, Vol. 44A, p. 951-960

However, in the technique described in Non-Patent Document 1, when the time when gravity and fluctuating external force act simultaneously at the time of dynamic behavior analysis, depending on the characteristics of fluctuating external force, an accurate analysis result may not be obtained. There is.
Specifically, for example, it is assumed that the fluctuating external force has a relatively large amplitude and a short fluctuation period, such as a seismic wave transmitted from the steel tower to the transmission line. And, if it is assumed that gravity acts on the transmission line with a constant magnitude in a unit step in a unit step from the analysis target time 0, the behavior analysis result becomes something that can not be realized in the actual transmission line.

  Then, an object of this invention is to aim at the precision improvement of the behavior analysis of a transmission line.

The present disclosure includes the following inventions. However, the present invention is defined by the scope of claims.
A transmission line behavior analysis device according to the present disclosure is an analysis device that analyzes the dynamic behavior of a transmission line by a finite element method, and has a function of constructing a transmission line as a collection of a plurality of elements, and a first external force A function of calculating time histories of the elements in the second period in which the second external force other than the first external force and the first external force acts after calculating the time histories of the elements constituting the power transmission line in the first period; It has a function of asymptotically approaching the first external force to the prescribed external force corresponding to gravity in the first period, and maintaining the first external force as the prescribed external force in the second period.

A transmission line behavior analysis method according to the present disclosure according to another aspect of the present invention is an analysis method for analyzing the dynamic behavior of a transmission line by a finite element method, comprising the steps of constructing the transmission line as a collection of plural elements. Calculating the time history of each element constituting the power transmission line in the first period in which the first external force acts, and the time of each element in the second period in which the second external force other than the first external force and the first external force acts Calculating a history, wherein the first external force is asymptotically approached to the prescribed external force corresponding to the gravity in the first period, and maintained at the prescribed external force in the second period.

The transmission line behavior analysis program according to the present disclosure as viewed from another point of view is a transmission line behavior analysis program that causes a computer to realize an analysis process for analyzing the dynamic behavior of a transmission line by the finite element method. The steps of constructing the transmission line as a group of a plurality of elements, calculating the time history of each of the plurality of elements in the first period in which only the first external force acts, and the second external force other than the first external force and the first external force Calculating time histories of each of the plurality of elements in the second period in which the external force acts, wherein the first external force is asymptotically approached to the prescribed external force corresponding to gravity in the first period, and the prescribed external force in the second period maintain.

A transmission line system according to the present disclosure as viewed from another point of view includes a steel tower having arm gold parts, and a plurality of first power transmission lines connected to one arm gold metal part that constitutes a part of the steel tower via insulators. And a second transmission line connecting two of the plurality of first transmission lines, wherein the second transmission line is based on the results of the dynamic behavior analysis of the first and second transmission lines and the insulator device. Thus, the shortest distance between the second power transmission line and the arm portion is set to be larger than the distance threshold.

The present disclosure can be realized not only as such a characteristic analysis device or analysis method, but also as a system including such an analysis device. In addition, the present invention can be realized as a semiconductor integrated circuit that realizes part or all of the analysis device. Furthermore, the program can be stored in a storage medium such as a CD-ROM.

  According to the present invention, it is possible to improve the accuracy of behavior analysis of a transmission line.

The transmission line system which concerns on embodiment is shown, (a) is a schematic perspective view, (b) is a principal part enlarged view. It is a schematic block diagram of the analysis system concerning an embodiment. It is a flowchart which shows operation | movement of the analyzer which concerns on embodiment. It is a flowchart which shows operation | movement of the analyzer which concerns on embodiment. An example of the model of the power transmission line system which concerns on embodiment is shown, (a) is a schematic diagram of a power transmission line system, (b) is a conceptual diagram of a model. It is a figure showing an external force function concerning an embodiment, and (a) is an external force function showing an external force corresponding to gravity, (b) is an external force function showing an external force caused by an earthquake. It is a figure which shows the result of behavior analysis of the transmission line system in a certain time, (a) is an analysis result by an analysis device concerning comparative example 1, (b) is an analysis result by an analysis device concerning comparative example 2, (c) These show the analysis result by the analyzer which concerns on embodiment. It is a figure which shows the external force function showing the external force corresponding to the gravity which the analyzer which concerns on the comparative example 2 uses. It is a figure which shows the result of the behavior analysis of a transmission line system, (a) is a figure which shows the behavior of the jumper wire at a certain time, (b) is between the beam element which comprises a jumper wire, and an arm metal part It is a figure which shows the time history of distance. It is a flowchart which shows operation | movement of the analyzer which concerns on a modification.

[1. Summary of the Embodiment]
As described above, the present invention has been made for the purpose of improving the accuracy of behavior analysis of power transmission lines, and the gist thereof includes at least the configurations shown in (1) to (11) below.

  (1) The analysis apparatus according to the embodiment is an analysis apparatus that analyzes the dynamic behavior of the transmission line by the finite element method, and has a function of constructing the transmission line as an assembly of a plurality of elements, and a first external force acts Calculating a time history of each of the plurality of elements in the first period, and calculating the time history of each of the plurality of elements in the second period in which the second external force other than the first external force and the first external force acts; The first external force is approximated to a defined external force corresponding to gravity from 0 in the first period, and is maintained at the defined external force in the second period.

  According to this configuration, after calculating the time histories of each of the plurality of elements in the first period in which the first external force acts, the plurality of elements in the second period in which the second external force other than the first external force and the first external force acts Calculate the time history of each element. Then, the first external force gradually approaches from 0 to the defined external force corresponding to the gravity in the first period, and is maintained by the defined external force in the second period. Thereby, the unit time of the external force acting on the transmission line is compared with the case where the time history of each of the plurality of elements is calculated as the first external force and the second external force simultaneously act on the transmission line at a certain time within the analysis target time. The maximum value of the change amount of the hit is reduced. Therefore, when calculating the time history of each of the plurality of elements using a numerical integration method (for example, the Newmark β method or the like), the accuracy of the calculated time history can be improved.

(2) Further, for example, in the analysis device of (1), the first external force becomes a constant value at the end time of the first period, and becomes the prescribed external force.
In this case, the amount of change in the first external force when switching from the first period to the second period is zero. Thus, in the second period, the amount of change in the external force corresponds to only the amount of change in the second external force. Therefore, when calculating the time histories of each of the plurality of elements using the numerical integration method, Since the divergence can be suppressed, the accuracy of the calculated time history can be improved.

(3) Further, for example, in the analysis device of (2), the first external force is represented by a time function which smoothly increases with the prescribed external force as a maximum value.
In this case, the amount of change of the first external force monotonically decreases to 0 in the first period. Thereby, when calculating the time history of each of a plurality of elements using a numerical integration method, it is possible to improve the accuracy of the time history at the time near the end time of the first period.

(4) Further, for example, in the analysis device of (3), the mass of each of the plurality of elements is m, the gravitational acceleration is g, and the prescribed external force is mg.
In this case, it is possible to analyze the behavior of the transmission line in the case where the second external force further acts in a state where the gravity acts on the transmission line.

(5) The analysis apparatus according to the embodiment may calculate time histories of each of the plurality of elements by linear acceleration.
According to this configuration, for example, the calculation error can be made smaller than the time history calculated by the average acceleration method.

(6) The analysis device according to the embodiment calculates the stiffness element corresponding to each of the plurality of elements when the first external force acts on the transmission line by static balance analysis, and is based on the calculated stiffness element Alternatively, a stiffness matrix may be generated, and the generated stiffness matrix may be used to calculate a time history of each of the plurality of elements.
According to this configuration, it is possible to analyze the behavior of the transmission line in consideration of the influence of the tension generated in the transmission line due to the first external force on the rigidity of the transmission line, so the accuracy of the time history can be improved. Can be

(7) In the analysis apparatus according to the embodiment, each of the plurality of elements may be configured of a one-dimensional beam element.
According to this configuration, the number of elements can be reduced compared to, for example, the case where the transmission line is formed of a three-dimensional solid element. Therefore, the amount of calculation performed in the behavior analysis of the transmission line can be reduced. Thus, the processing load can be reduced.

(8) The analysis method according to the embodiment viewed from another viewpoint is an analysis method for analyzing the dynamic behavior of the transmission line by the finite element method, and the step of constructing the transmission line as a collection of a plurality of elements Calculating a time history of each of the plurality of elements in the first period in which the first external force acts, and a time history of each of the plurality of elements in the second period in which the second external force other than the first external force and the first external force acts Calculating the first external force asymptotically to the defined external force corresponding to the gravity in the first period, and may be maintained in the defined external force in the second period.
According to this configuration, after calculating the time histories of each of the plurality of elements in the first period in which the first external force acts, the plurality of elements in the second period in which the second external force other than the first external force and the first external force acts Calculate the time history of each element. Then, the first external force gradually approaches from 0 to the defined external force corresponding to the gravity in the first period, and is maintained by the defined external force in the second period. Thereby, the unit time of the external force acting on the transmission line is compared with the case where the time history of each of the plurality of elements is calculated as the first external force and the second external force simultaneously act on the transmission line at a certain time within the analysis target time. The maximum value of the change amount of the hit is reduced. Therefore, when calculating the time history of each of the plurality of elements using a numerical integration method (for example, the Newmark β method or the like), the accuracy of the calculated time history can be improved.

(9) The transmission line behavior analysis program according to the embodiment viewed from another viewpoint is a transmission line behavior analysis program that causes a computer to realize an analysis process for analyzing the dynamic behavior of the transmission line by the finite element method. The process comprises the steps of constructing the transmission line as a group of a plurality of elements, calculating the time history of each of the plurality of elements in the first period in which only the first external force acts, and other than the first external force and the first external force Calculating a time history of each of the plurality of elements in the second period in which the second external force acts, wherein the first external force is approximated to the prescribed external force corresponding to gravity in the first period, and in the second period Maintain specified external force.
According to this configuration, after calculating the time histories of each of the plurality of elements in the first period in which the first external force acts, the plurality of elements in the second period in which the second external force other than the first external force and the first external force acts Calculate the time history of each element. Then, the first external force gradually approaches from 0 to the defined external force corresponding to the gravity in the first period, and is maintained by the defined external force in the second period. Thereby, the unit time of the external force acting on the transmission line is compared with the case where the time history of each of the plurality of elements is calculated as the first external force and the second external force simultaneously act on the transmission line at a certain time within the analysis target time. The maximum value of the change amount of the hit is reduced. Therefore, when calculating the time history of each of the plurality of elements using a numerical integration method (for example, the Newmark β method or the like), the accuracy of the calculated time history can be improved.

(10) A transmission line system according to an embodiment viewed from another viewpoint comprises a plurality of steel towers having arm bars and a plurality of first steel bars connected to the arm bars constituting a part of the steel tower through a ladder device. According to the dynamic behavior analysis of the first and second transmission lines and the ladder device, the second transmission line includes: one transmission line; and a second transmission line connecting two of the plurality of first transmission lines. The shortest distance between the obtained second power transmission line and the arm portion is set to be larger than the distance threshold.
According to this configuration, the shortest distance between the second transmission line and the arm metal part obtained by the dynamic behavior analysis of the first and second transmission lines and the insulator device is set to be larger than the distance threshold value. There is. Thus, the shortest distance between the second transmission line and the arm portion is calculated in advance by dynamic behavior analysis of the first and second transmission lines and the insulator device, and the distance threshold is set between the transmission line and the arm portion The ground fault can be prevented by setting the distance longer than the distance at which the dielectric breakdown occurs.

(11) Further, in the transmission line system according to the embodiment, in the dynamic behavior analysis, each of the first and second transmission lines and the insulator device is constructed as an assembly of a plurality of elements, and the first external force acts Calculating a time history of each of the plurality of elements constituting the second transmission line in the first period, and then the second transmission line in the second period in which the first external force and the second external force other than the first external force act Calculating a time history of each of a plurality of elements constituting the first element, the first external force asymptotically approaches the prescribed external force corresponding to gravity from 0 in the first period, and is maintained by the prescribed external force in the second period It may be
According to this configuration, in the dynamic behavior analysis, since the behaviors of the first and second power transmission lines and the insulator device can be accurately captured, it is possible to determine the presence or absence of a ground fault and to take measures.

[2. Details of the embodiment]
Hereinafter, details of the embodiment will be described with reference to the drawings. Note that at least a part of the embodiments described below may be combined arbitrarily.

<1> Configuration <1-1> Regarding Analysis Target First, the configuration of a transmission line system that is an analysis target according to the present embodiment will be described.
FIG. 1 shows a power transmission line system according to the present embodiment, where (a) is a schematic perspective view and (b) is an enlarged view of the main part.
The transmission line system includes a plurality of (three in FIG. 1 (a)) steel towers 1, an anchor wire 3 connected to the adjacent steel tower 1 via a ladder device 2, and a jumper for connecting the anchor wires 3 to each other. And a line 4. Here, the ladder device 2 is connected to the arm metal part 11 of each steel tower 1. Further, both ends of the jumper wire 4 are connected to the interference wire 3 on the side opposite to the side connected to the arm gold portion 11 in the insulator device 2. A transmission line is composed of the insulator device 2, the wire 3 and the jumper wire 4.

<1-2> Analysis System Next, the configuration of the analysis system 50 according to the present embodiment will be described.
FIG. 2 is a schematic configuration diagram of an analysis system 50 according to the present embodiment.
The analysis system 50 includes an analysis device 51, an input device 52, and a display device 53.
The analysis device 51 includes, for example, a general-purpose computer. The analysis device 51 includes an arithmetic processing unit 511 and a storage unit 512. Here, the arithmetic processing unit 511 includes, for example, a processor. In addition, the storage unit 512 is configured of a memory.

The storage unit 512 stores an analysis computer program. The computer program for analysis corresponds to, for example, finite element analysis using the Newmark β method. Examples of the computer program for analysis include "Nastran" manufactured by MSC. The details of the “Newmark β method” will be described in detail in <2>. The storage unit 512 can further store various parameters required by the analysis computer program in a dedicated storage area.
The arithmetic processing unit 511 reads the computer program for analysis and various parameters from the storage unit 512, and executes the computer program for analysis to perform analysis processing.

The input device 52 includes, for example, a keyboard. When the user operates the input device 52, various parameters are set in the storage unit 512 of the analysis device 51.
The display device 53 includes, for example, a display. The display device 53 displays the result analyzed by the analysis device 51 to the user.

<2> Operation Next, the operation of the analysis device 51 according to the present embodiment will be described.
The analysis device 51 first performs static balance analysis in a state where gravity acts on each of the plurality of beam elements constituting the ladder device 2, the wire 3, and the jumper wire 4, and then the dynamic balance analysis I do.
3 and 4 are flowcharts showing the operation of the analysis device 51 according to the present embodiment. Here, the overall operation of the analysis device 51 and the operation in time history calculation included in the overall operation will be separately described.

<2-1> Overall Operation First, the analysis device 51 creates a model to be analyzed (step S1). Here, the analysis device 51 creates a model including the ladder device 2, the bar 3 and the jumper 4. Then, the analysis device 51 creates a model based on various parameters stored in the storage unit 512 by the user operating the input device 52.

FIG. 5: shows an example of the model of the transmission line system which concerns on this embodiment, (a) is a schematic diagram of a transmission line system, (b) is a conceptual diagram of a model.
In the model, each of the ladder device 2, the wire 3 and the jumper wire 4 is constructed as a set of a plurality of beam elements. Here, the "beam element" corresponds to an element that transmits a load of tension, bending, and torsion.

Here, the forceps device 2 is constructed of “B2” beam elements, the wire 3 is constructed of “B3” beam elements, and the jumper wire 4 is constructed of “B4” beam elements. Then, the numbers B2, B3 and B4 of beam elements are set to 10, 170 and 100, for example.
The wire diameter, the Young's modulus, the Poisson's ratio, and the density of the beam elements of the ladder device 2, the wire 3, and the jumper wire 4 are set as follows, for example.

  And the arm metal part 11 to which the insulator apparatus 2 was connected vibrates resulting from an earthquake. At this time, an external force caused by an earthquake is applied to the ladder wire 3 and the jumper wire 4 from the arm metal part 11 through the insulator device 2 to the ladder device 2, the wire 3 and the jumper wire 4.

  As described above, the ladder device 2, the wire 3 and the jumper 4 are composed of one-dimensional beam elements. As a result, for example, the number of elements can be reduced compared to the case where the forceps device 2, the wire 3 and the jumper wire 4 are composed of three-dimensional solid elements. The amount of calculation performed in the behavior analysis of 3 and the jumper wire 4 can be reduced, and the processing load can be reduced.

  Returning to FIG. 3, after the process of step S1, the analysis device 51 performs static balance analysis on the model (step S2). Thereby, the analysis device 51 calculates rigid elements corresponding to a plurality of elements constituting each of the forceps device 2, the wire 3, and the jumper wire 4. Then, the analysis device 51 generates a stiffness matrix M used for time history calculation performed in steps S6 and S10 described later based on the calculated stiffness element.

Next, an external force function P [i] indicating the external force applied to the forceps device 2, the anchor wire 3 and the jumper wire 4 is set to an external force function Pg [i] indicating the external force (first external force) corresponding to the gravity Step S3). Here, i is a parameter reflecting time, and is an integer of 0 or more that increases with the passage of time.
FIG. 6 is a view showing external force functions Pg [i] and Ps [i] according to the present embodiment, where (a) is an external force function Pg [i] representing an external force corresponding to gravity, and (b) is an earthquake. It is an external force function Ps [i] that represents the resulting external force.
Here, an external force function Pg [i] representing an external force corresponding to gravity satisfies the relational expression of the following expression (1).

Here, t: time, Pg [t]: external force (first external force) corresponding to gravity, T1 (= N1): end time of the first period.
Expression (1) indicates that the first external force becomes a constant value at the end time of the first period and becomes the defined external force (gravity).

More specifically, the external force function Pg [i] satisfies the relational expression of the following expression (2).
Here, t: time, Pg [t]: external force (first external force) corresponding to gravity, T1: length of first period.
The first external force represented by the external force function Pg [i] is represented by a time function that increases smoothly with a sin curve with the defined external force (Pg0) as the maximum value. The first external force gradually approaches the defined external force Pg0 corresponding to the gravity from 0 in the first period T1 (time 0 to time N1), and is maintained at the defined external force Pg0 in the second period T2 (after time N1). In addition, it is also possible to use smooth curves other than sin curve.

Further, the first external force further satisfies a relational expression of the following expression (3).
However, m: mass of each of a plurality of elements, g: gravitational acceleration.

  As shown in Formula (1), when switching from the first period T1 to the second period T2, the amount of change in the external force corresponding to the gravity becomes zero. Thus, in the second period T2, the amount of change in the external force corresponds to only the amount of change in the external force caused by the earthquake. Therefore, when calculating the time histories of each of the plurality of beam elements constituting the ladder device 2, the anchor wire 3 and the jumper wire 4 using the numerical integration method, since the divergence of the calculated value can be suppressed, the calculated time history Accuracy can be improved.

  Further, as shown in the equation (2), the amount of change in the external force corresponding to the gravity in the first period T1 monotonously decreases to zero. Thereby, when calculating the time history of each of the plurality of beam elements constituting the ladder device 2, the anchor wire 3 and the jumper wire 4 using the numerical integration method, the calculated value at the time near the end of the first period T1. Can be suppressed, so that the accuracy of the time history near the end of the first period T1 can be improved.

  Furthermore, as shown in the equation (3), the prescribed external force Pg0 is set to a value corresponding to the gravity applied to each of the plurality of beam elements. Thereby, the behavior analysis of the insulator device 2, the anchor wire 3 and the jumper wire 4 in the case where the external force caused by the earthquake further acts in a state where the gravity is acting on the insulator device 2, the anchor wire 3 and the jumper wire 4. It can be performed.

  Returning to FIG. 3, after the process of step S2, the analyzer 51 sets the initial value i0 of the time parameter i to "0" (step S4), and sets the end value N of the time parameter i to "N1". It sets (step S5). Thereby, the first period T1 is set to a period from time "0" to time "N1".

  Next, time history calculation is performed with the initial value i0 and the end value N set in steps S3 and S4 as arguments (step S6). Details of the process in this time history calculation will be described in detail in <2-2>. The analysis apparatus 51 acquires the time history of each beam element in the first period T1 (time “0” to time N1) by performing the process of step S5.

Subsequently, the analysis device 51 calculates an external force function P [i] as an external force function Pg [i] representing an external force corresponding to gravity and an external force function Ps [i] representing an external force (second external force) caused by an earthquake. The function is set to a function corresponding to the sum of (step S7). Here, as shown in FIG. 6B, the external force function Ps [i] has three components Psx [that oscillate in the directions of three axes (X axis, Y axis, Z axis) orthogonal to each other as time i elapses. i], Psy [i], Psz [i]. Further, in FIG. 6 (b), the three axes are set so that, for example, the extension direction of each of the insulator device 2, the wire 3 and the jumper wire 4 is the X axis and the vertical direction is the Z axis.
As described above, the external force caused by the earthquake is transmitted from the arm portion 11 of the steel tower 1 to each of the beam elements constituting the insulator device 2, the wire 3 and the jumper wire 4.

  Thereafter, the analyzer 51 sets the initial value i0 of the time parameter i to "N1 + 1" (step S8), and sets the end value N of the time parameter i to "N2" (step S9). Thus, the second period T1 is set to a period from time "N1 + 1" to time "N2". And the analysis object period by the analysis apparatus 51 is corresponded between time "0"-time "N2".

  Next, the analysis device 51 performs time history calculation with the initial value i0 and the end value N set in steps S7 and S8 as arguments (step S10). The analysis device 51 acquires the data indicating the behavior of each beam element from time N1 + 1 to time N2 by performing the process of step S9.

  As described above, in the analysis device 51 according to the present embodiment, first, each of the plurality of beam elements in the case where an external force (first external force) corresponding to gravity acts on the insulator device 2, the anchoring wire 3 and the jumper wire 4 The rigid element corresponding to is calculated by static balance analysis. Next, the analysis device 51 generates a stiffness matrix M based on the calculated stiffness elements, and uses the generated stiffness matrix M to calculate time histories of each of the plurality of beam elements.

  Thus, in consideration of the influence of the tension generated due to the external force corresponding to the gravity acting on the insulator device 2, the anchor wire 3 and the jumper wire 4, the behavior of the insulator device 2, the anchor wire 3 and the jumper wire 4 Analysis can be performed. Therefore, it is possible to improve the accuracy of the time history of each beam element constituting each of the ladder device 2, the wire 3, and the jumper wire 4.

<2-2> Operation in Time History Calculation Next, an operation in the time history calculation of the analysis device 51 will be described.
First, the analysis device 51 sets the time parameter i to the initial value i0 (step S11). Here, in the case of time history calculation in step S6, i0 is set to “0”, and in the case of time history calculation in step S10, i0 is set to “N1 + 1”.

  Next, the analysis device 51 uses the relational expression of the following equation (4) to determine the time parameter i + 1 from the displacement u [i], the displacement velocity v [i], and the displacement acceleration a [i] corresponding to the time parameter i. The displacement acceleration a [i + 1] corresponding to is calculated (step S12). Here, Δt is a value reflecting the difference time between the time corresponding to the time parameter i and the time corresponding to the time parameter i + 1.

  Here, the displacement u [i], the displacement velocity v [i], and the displacement acceleration a [i] are represented by vectors as shown in the following equation (5).

  That is, displacement u [i], displacement velocity v [i], and displacement acceleration a [i] are displacements in the three axial directions of each of a plurality of beam elements constituting each of the forceps device 2, the wire 3 and the jumper wire 4 , Displacement velocity, and displacement acceleration are represented by vectors.

Further, M represents a mass matrix, C represents a damping matrix, and K represents a stiffness matrix. Further, P [i] is represented by a matrix having elements corresponding to the three axial directions of each beam element constituting each of the ladder device 2, the wire 3, and the jumper wire 4.
Here, the stiffness matrix K is generated by the static balance analysis in step S2 described above.

  Subsequently, the analysis device 51 uses the relational expression of the following equation (6) to determine the displacement velocity v [i] corresponding to the time parameter i, the displacement acceleration a [i], and the displacement acceleration a [i] corresponding to the time parameter i + 1. The displacement velocity v [i + 1] corresponding to the time parameter i + 1 is calculated from i + 1] (step S13).

  After that, the analysis device 51 uses the relational expression of the following equation (7) to cope with the displacement u [i], the displacement velocity v [i], the displacement acceleration a [i], and the time parameter i + 1 corresponding to the time parameter i. The displacement u [i + 1] corresponding to the time parameter i + 1 is calculated from the displacement acceleration a [i + 1] (step S14).

  The displacement acceleration a [i + 1], the displacement velocity v [i + 1], and the displacement u [i + 1] are calculated by using, for example, the Newton-Raphson method.

  Next, the analysis device 51 increments the time parameter i by “1” (step S15).

Subsequently, the analysis device 51 determines whether the time parameter i is larger than the end value N (step S16).
If it is determined in step S16 that the time parameter i is larger than the end value N (step S16: Yes), the analysis apparatus 51 ends the process.
On the other hand, if it is determined in step S16 that the time parameter i is less than or equal to the end value N (step S16: No), the analysis apparatus 51 performs the process of step S12 again.
Then, the analysis device 51 performs a series of processes in steps S1 to S16 to calculate time histories of a plurality of beam elements constituting each of the ladder device 2, the anchor wire 3 and the jumper wire 4. Then, the analysis device 51 causes the display device 53 to display the time history (analysis result) for a plurality of beam elements constituting each of the ladder device 2, the anchoring wire 3 and the jumper wire 4.

  By the way, in this embodiment, the linear acceleration method is adopted in which the displacement acceleration changes linearly from a [j] to a [j + 1] within the minute time Δt. That is, β was set to 1/6.

  Thereby, for example, the calculation error can be made smaller than the time history calculated by the average acceleration method.

<3> Analysis Result Next, an analysis result of the analysis device 51 according to the present embodiment will be described.
FIG. 7 is a diagram showing the result of behavior analysis of the transmission line system at a certain time, where (a) is an analysis result by the analysis apparatus according to comparative example 1, and (b) is an analysis result by the analysis apparatus according to comparative example 2. And (c) show the analysis result by the analysis device 51 according to the present embodiment. Here, the analysis device according to the first comparative example performs analysis ignoring the influence of gravity. Moreover, the analysis apparatus which concerns on the comparative example 2 uses the external force function Pg2 [i] different from the external force function Pg [i] which concerns on this embodiment as an external force function which represents a gravity component.

FIG. 8 is a view showing an external force function Pg2 [i] representing an external force corresponding to the gravity used by the analysis device according to the second comparative example.
The external force function Pg2 [i] is a unit step function which is maintained at "0" at a time before the time N11 at which the external force function Ps [i] representing the earthquake component rises, and becomes Pg0 at the time N11.
Also, in these behavior analysis, the minute time Δt was set to 0.01 sec. The attenuation matrix C is obtained by multiplying the unit matrix by the constant 0.997.

  In the analysis result by the analysis device according to Comparative Example 1, the shape of the interposing wire 3 is a wave in a short cycle. However, it is far from the actual behavior of the wire 3 at the time of the earthquake.

  Further, in the analysis result by the analysis device according to Comparative Example 2, the amplitude becomes large due to the addition of the gravity component and the addition of the earthquake component being started at the same time, and the actual interference wire at the time of earthquake 3 It is far from the behavior of

  On the other hand, in the analysis result by the analysis device according to the present embodiment, the wire 3 has a smooth wavy shape, which is relatively close to the behavior of the actual wire 3.

  FIG. 9 is a diagram showing the result of behavior analysis of the transmission line system, where (a) is a diagram showing the behavior of the jumper wire 4 at a certain time, and (b) is a beam element Po1 composing the jumper wire 4 It is a figure which shows the time history of distance Wd between arms 11. In FIG. 9B, “Wd1” corresponds to the distance between the beam element Po1 and the arm 11 in the case where the jumper wire 4 maintains a balanced state under gravity.

  As shown in FIG. 9A, the jumper wire 4 vibrates in a unique vibration mode determined by its Young's modulus, Poisson's ratio, and the like. The shortest distance Wd2 between the beam element Po1 and the arm gold portion 11 is the shortest among the shortest distances between the beam elements constituting the jumper wire 4 and the arm gold portion 11.

  Further, as shown in FIG. 9B, when both of the gravity and the external force caused by the earthquake are applied to the jumper wire 4, the distance Wd between the beam element Po1 and the arm gold portion 11 is the shortest. It vibrates between the distance Wd2 and the longest distance Wd3.

Here, jumper wire 4 and arm metal portion 11 are obtained by analyzing dynamic behavior of ladder device 2, transmission wire 3 (first transmission wire) and jumper wire 4. Is set to be larger than the distance threshold (for example, Wd2). Here, the “distance threshold” is set to be longer than the distance at which the dielectric breakdown occurs between the jumper wire 4 and the arm portion 11.
Thus, if the shortest distance (for example, Wd2) between the jumper wire 4 and the arm metal portion 11 is calculated in advance by dynamic behavior analysis of the insulator device 2, the anchoring wire 3 and the jumper wire 4, the presence or absence of a ground fault can be obtained. It can be judged and measures can be taken.

  Then, in the above-mentioned dynamic behavior analysis, as described above, the external force corresponding to the gravity gradually approaches 0 to the defined external force Pg0 corresponding to the gravity in the first period T1 and is maintained at the defined external force Pg0 in the second period T2. Ru. As a result, in the above-mentioned dynamic behavior analysis, the behaviors of the insulator device 2, the anchoring wire 3 and the jumper wire 4 can be accurately captured, so that the presence or absence of a ground fault can be determined, and measures can be taken.

<4> Summary After all, first, the analysis device 51 according to the present embodiment includes the forceps device 2, the anchor wire 3, and the jumper wire 4 in the first period T1 (0 to N1) in which gravity (first external force) acts. The time history of each of a plurality of beam elements constituting Thereafter, time histories of each of the plurality of beam elements in a second period T2 (after N1) in which an external force (second external force) caused by gravity and an earthquake acts are calculated. Then, the gravity gradually approaches from 0 to the defined external force corresponding to the gravity in the first period T1, and is maintained by the defined external force in the second period T2. Thus, for example, the gravity and the seismic force simultaneously act on jumper wire 4 etc. at time “0”, compared with the case where the time histories of each of the plurality of beam elements are calculated, the external force acting on jumper wire 4 etc. The maximum value of the variation per unit time is reduced. Therefore, when the time histories of each of the plurality of beam elements are calculated using a numerical integration method (for example, the Newmark β method or the like), the accuracy of the calculated time history can be improved.

[3. Modified example]
(1) In the embodiment, an example is described in which the linear acceleration method (β: 1/6) is assumed to assume that the displacement acceleration changes linearly within the minute time Δt, but the change of the displacement acceleration within the minute time Δt Is not limited linearly. For example, an average acceleration method (β: 1/4) may be adopted, which assumes that the displacement acceleration in the minute time Δt is maintained at the average value of the first value and the last value in the minute time Δt. .
According to this configuration, the values of displacement, displacement velocity, and displacement acceleration that are calculated are more stable than linear acceleration.

In addition, even if the stepwise acceleration method (β: 1/8) is adopted, it is assumed that the displacement acceleration in the minute time Δt changes stepwise from the first value to the last value at an intermediate time point in the minute time Δt. Good. Furthermore, the value of β may be set to 1/12.
According to this configuration, it is possible to improve the accuracy of the displacement, displacement velocity and displacement acceleration which are calculated, as compared with the linear acceleration method.

(2) In the embodiment, the Newmark β method calculates the time history of the next time i + 1 (time parameter i + 1), the displacement speed, and the displacement acceleration from the displacement, the displacement speed, and the displacement acceleration of time i (time parameter i) An example was described. However, for example, assuming that the acceleration at time i (time parameter i) corresponds to the average value of the acceleration at time i-3 to time i-1, the time history of displacement, displacement speed and displacement acceleration at time i is calculated You may do it.

FIG. 10 is a flowchart showing an operation in time history calculation of the analysis apparatus according to the present modification.
First, the analysis apparatus calculates displacement u [i0], displacement velocity v [i0] and displacement acceleration a [i0] at time i0 by the same calculation method as that of the embodiment (step S21), and then at time i0 + 1. The displacement u [i0 + 1], the displacement velocity v [i0 + 1], and the displacement acceleration a [i0 + 1] are calculated (step S22).
Next, the analysis device sets the time parameter i to the initial value i0 + 2 (step S23).

  Subsequently, the analysis apparatus uses the relational expression of the following equation (8) to determine the displacement u [i] corresponding to the time parameter i, the displacement velocity v [i], and the displacement acceleration corresponding to the time parameters i-2 to i. The displacement acceleration a [i + 1] corresponding to the time parameter i + 1 is calculated from a [i-2] to a [i] (step S24). Here, Δt is a value reflecting the difference time as in the embodiment.

  Here, the displacement u [i], the displacement velocity v [i], and the displacement acceleration a [i] are represented by vectors as shown in the above equation (5), as in the embodiment.

  Also, as in the embodiment, M represents a mass matrix, C represents an attenuation matrix, and K represents a stiffness matrix. Further, P [i] is a vector having elements corresponding to the three axial directions of each beam element constituting each of the ladder device 2, the wire 3, and the jumper wire 4.

  Subsequently, the analysis device 51 uses the relational expression of the following equation (9) to determine the displacement velocity v [i] corresponding to the time parameter i and the displacement acceleration a [i corresponding to the time parameters (i-2) to i. From -2] to a [i], the displacement velocity v [i + 1] corresponding to the time parameter i + 1 is calculated (step S25).

  After that, the analysis apparatus uses the relational expression of the following equation (7), and the displacement u [i] corresponding to the time parameter i, the displacement velocity v [i], and the displacement corresponding to the time parameters (i-2) to i The displacement u [i + 1] corresponding to the time parameter i + 1 is calculated from the acceleration a [i] (step S26).

  Next, the analysis device increments the time parameter i by "1" (step S27), and subsequently determines whether the time parameter i is larger than the end value N (step S28).

  According to this configuration, when the displacement u [i + 1], the displacement velocity v [i + 1], and the displacement acceleration a [i + 1] corresponding to the time parameter i + 1 are calculated, three times (i−) before time (i + 1) are calculated. 2) Use the average value of displacement acceleration in i. As a result, even when the displacement acceleration changes rapidly and significantly, it is possible to suppress the divergence of the calculated displacement, displacement speed and displacement acceleration, so that the calculated displacement, displacement speed and displacement acceleration are stable in time. It is possible to improve the quality.

(3) In the embodiment, the example of calculating the displacement acceleration, the displacement velocity and the displacement using the Newmark β method has been described, but the calculation method is not limited thereto. For example, the Wilson θ method or Runge-Kutta method is adopted. May be

(4) In the embodiment, an example has been described in which gravity applied to each of the forceps device 2, the wire 3 and the jumper wire 4 is reflected as the first external force. However, if the type of the first external force reflects the force continuously applied with a constant magnitude in a constant direction to each of the ladder device 2, the anchor wire 3 and the jumper wire 4, the gravity is reflected. It is not limited to things. For example, it is assumed that any one of the ladder device 2, the wire 3 and the jumper wire 4 is fixed to another fixed structure by an insulating member which can ignore elastic characteristics and the like. In this case, as the first external force, in addition to gravity, a force pulled by the insulating member may be reflected as the first external force.

(5) As described in the embodiment, when the time history of each of displacement acceleration, displacement velocity and displacement is calculated using the Newmark β method, the accuracy of the calculated time history is calculated by using the forceps device 2, the interference wire 3 and It depends on the natural vibration characteristic of each jumper wire 4. Specifically, it depends on the magnitude relationship between the minimum natural period of each of the ladder device 2, the wire 3, and the jumper wire 4 and the minute time Δt used in the Newmark β method. The minute time Δt is about 1/5 to 1/6 of the minimum natural period of each of the ladder device 2, the wire 3, and the jumper wire 4.

Therefore, in the embodiment, the minute time Δt may be set based on the minimum natural period of each of the insulator device 2, the wire 3, and the jumper wire 4. In this case, the minimum natural period may be calculated by, for example, the subspace method.
According to this configuration, it is possible to improve the accuracy of the displacement acceleration, the displacement speed, and the time history of each of the displacements.

(6) In the embodiment, each of the ladder device 2, the wire 3 and the jumper wire 4 is composed of the beam element, but the present invention is not necessarily limited to the beam element. For example, all or part of the ladder device 2, the wire 3 and the jumper wire 4 may be composed of a shell element or a solid element.
For example, when each of the ladder device 2, the wire 3 and the jumper wire 4 is composed of a three-dimensional solid element, the behavior of each of the device 2, the wire 3 and the jumper wire 4 is analyzed in more detail be able to.

[4. Appendix]
The above embodiments and modifications should be considered as illustrative in all points and not restrictive. The scope of the present invention is defined by the terms of the claims, rather than the description above, and is intended to include any modifications within the scope and meaning equivalent to the terms of the claims.

REFERENCE SIGNS LIST 1 steel tower 2 ladder device 3 engagement wire 4 jumper wire 11 arm metal portion 50 analysis system 51 analysis device 52 input device 53 display device 511 calculation processing unit 512 storage unit

Claims (10)

A transmission line behavior analysis apparatus for analyzing the dynamic behavior of a transmission line by the finite element method,
A function of constructing the transmission line as a collection of a plurality of elements,
After calculating the time history of each of the plurality of elements in the first period in which the first external force acts, the time of each of the plurality of elements in the second period in which the first external force and the second external force other than the first external force act Function to calculate history, and
The transmission line behavior analysis device which has a function which makes said 1st external force asymptotically approach to prescribed external force corresponding to gravity from 0 in said 1st period, and to maintain said prescribed external force in said 2nd period.   The power transmission line behavior analysis device according to claim 1, wherein the first external force becomes a constant value at the end time of the first period and becomes the prescribed external force.   The transmission line behavior analysis device according to claim 2, wherein the first external force is represented by a time function that smoothly increases with the prescribed external force as a maximum value.   The transmission line behavior analysis device according to claim 3, wherein the prescribed external force is mg, where m is a mass of each of the plurality of elements and g is a gravitational acceleration.   The transmission line behavior analysis device according to any one of claims 1 to 4, wherein the time history of each of the plurality of elements is calculated by a linear acceleration method. The stiffness element corresponding to each of the plurality of elements when the first external force acts on the transmission line is calculated by static balance analysis, and a stiffness matrix is generated based on the calculated stiffness element,
The transmission line behavior analysis device according to claim 5, wherein the time history of each of the plurality of elements is calculated using the generated stiffness matrix. The transmission line behavior analysis device according to any one of claims 1 to 6, wherein each of the plurality of elements is configured of a one-dimensional beam element. An analysis method for analyzing the dynamic behavior of a transmission line by the finite element method,
Constructing the transmission line as an assembly of a plurality of elements;
Calculating time histories of each of the plurality of elements in a first period in which only the first external force acts;
Calculating time histories of each of the plurality of elements in a second period in which a first external force and a second external force other than the first external force act,
A transmission line behavior analysis method, wherein the first external force is asymptotically approached to a defined external force corresponding to gravity in the first period, and is maintained at the defined external force in the second period. A transmission line behavior analysis program that causes a computer to realize analysis processing that analyzes the dynamic behavior of a transmission line by the finite element method,
The analysis process is
Constructing the transmission line as an assembly of a plurality of elements;
Calculating time histories of each of the plurality of elements in a first period in which only the first external force acts;
Calculating time histories of each of the plurality of elements in a second period in which a first external force and a second external force other than the first external force act,
The transmission line behavior-analysis program which makes the said 1st external force asymptotically approach to the prescription | regulation external force corresponding to gravity in the said 1st period, and is maintained at the said prescription | regulation external force in the said 2nd period. A steel tower with arms,
A plurality of first power transmission lines connected via insulators to one arm metal part constituting a part of the steel tower;
A second power transmission line connecting two of the plurality of first power transmission lines;
In the second power transmission line, the shortest distance between the second power transmission line and the arm portion is greater than the distance threshold based on the results of dynamic behavior analysis of the first and second power transmission lines and the insulator device. Power transmission line system set to be large ,
In the dynamic behavior analysis,
Each of the first and second power transmission lines and the insulator device is constructed as an assembly of a plurality of elements,
After calculating the time histories of each of the plurality of elements constituting the second power transmission line in the first period in which the first external force acts, in the second period in which the first external force and the second external force other than the first external force act Calculating a time history of each of a plurality of elements constituting the second power transmission line;
The transmission line system which makes said 1st external force asymptotically approach to the prescription external force corresponding to gravity from 0 in said 1st period, and to maintain said prescription external force in said 2nd period .