Seismic performance analysis method for ultra-high voltage transmission line towers in high-intensity earthquake zones

Abstract

The present invention discloses a method for analyzing the seismic performance of ultra-high voltage transmission line towers in high-intensity earthquake zones. The method includes establishing a finite element model of the transmission tower system and extracting an equivalent single-tower-mass analysis model taking into account the spatial effects of earthquakes. Based on different earthquake intensities and regions, the single-tower-mass analysis model is subjected to response spectrum analysis to obtain a single-tower design response spectrum. Seismic motion time history analysis is performed on the finite element model of the transmission tower system, taking into account the spatial effects of earthquake motion, as well as the coherence and traveling wave effects of earthquake motion. Simultaneously, an IDA analysis is performed on the single-tower-mass analysis model to obtain IDA curves at different intensities. The seismic performance of the towers is then analyzed based on the single-tower design response spectrum and the IDA curves. The present invention can provide a scientific and systematic seismic performance evaluation tool for the design of ultra-high voltage transmission line towers in high-seismic risk areas, thereby guiding engineering practice and ensuring the safe and stable operation of power systems.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic design of iron towers, and more particularly to a method for analyzing the seismic performance of an ultra-high voltage transmission line iron tower in a high-intensity earthquake zone. Background Art

[0002] With China's rapid economic development, the demand for electricity is growing. To efficiently address the uneven geographical distribution of energy resources and demand and the interconnection of regional power grids, China has vigorously developed ultra-high voltage (UHV) transmission technology. This technology not only provides a stable and reliable power supply for China's sustainable economic and social development, but also plays a key role in supporting the large-scale development and utilization of clean energy, demonstrating significant economies of scale.

[0003] Ultra-high voltage (UHV) transmission tower and line systems are critical infrastructure for long-distance, cross-regional power transmission. However, China is a country prone to frequent and severe earthquakes, particularly in the northwest and southwest regions, where seismic activity is frequent and high-intensity. For example, the Ningxia-Hunan ±800 kV UHV transmission line project traverses an area with active seismic fault zones and has experienced strong earthquakes such as the 8.5 magnitude Haiyuan earthquake in 1920. With a basic seismic intensity of up to 9 degrees in these areas, ensuring that UHV transmission towers have sufficient seismic resistance under these conditions is crucial to prevent power outages and socioeconomic losses.

[0004] Currently, few of the UHVDC transmission lines in operation or under construction pass through earthquake zones with a magnitude of 9, and research on the seismic design of tower structures has yet to be fully conducted. Furthermore, while the relevant Chinese power industry standard, the "Technical Regulations for the Structural Design of Overhead Transmission Line Towers," requires verification calculations for towers in areas with seismic fortification of magnitude 9 or higher, it lacks specific verification methods. This leads to a certain degree of blindness in design work, making it difficult to accurately determine whether tower structures can withstand the effects of earthquakes in specific areas.

[0005] Research following the Wenchuan earthquake revealed that, in addition to the secondary disasters caused by the earthquake, the earthquake itself also had adverse effects on tower structures, particularly those with long crossarms. Consequently, existing technologies lack targeted seismic performance assessment methods, making it difficult to effectively predict and improve tower performance in extreme earthquake environments. Summary of the Invention

[0006] In view of the above problems, the present invention provides a method for analyzing the seismic performance of ultra-high voltage transmission line towers in high-intensity earthquake zones in order to fill the gaps in the prior art.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] A method for analyzing the seismic performance of ultra-high voltage transmission line towers in high-intensity earthquake zones, comprising:

[0009] Establish a finite element model of the transmission tower and line system, and extract an equivalent single tower-mass point analysis model considering the spatial effects of earthquakes;

[0010] Based on different earthquake intensities and regions, a response spectrum analysis is performed on the single tower-particle analysis model to obtain a single tower design response spectrum;

[0011] Taking into account the spatial effect of earthquake motion, as well as the coherence effect and traveling wave effect of earthquake motion, the earthquake time history analysis is carried out on the finite element model of the transmission tower line system. At the same time, the IDA analysis is carried out on the single tower-particle analysis model to obtain the IDA curves under different intensities.

[0012] The seismic performance of the tower is analyzed based on the single tower design response spectrum and IDA curve.

[0013] Preferably, establishing a finite element model of a transmission tower line system includes:

[0014] Based on the natural frequency and mode of a single tower and the stress distribution of key parts under the action of earthquake motion, a finite element model of the UHV straight tower and tension tower beam was established;

[0015] Based on the finite element model of UHV straight tower and tension tower beam, considering the influence of conductor tension and conductor quality on the frequency and mode of single tower, the corresponding finite element model of transmission tower line system is established.

[0016] Preferably, an equivalent single-tower-mass point analysis model is extracted considering the spatial effect of earthquakes, and the steps include: simplifying the multi-tower and multi-span transmission tower line system into a single-tower two-line model with one tower and two spans; and simplifying the mass distribution of the conductor and the ground wire into a mass point attached to the single-tower two-line model.

[0017] Preferably, when simplifying the multi-tower and multi-span transmission tower line system into a single tower and two-line model with one tower and two spans,

[0018] For the UHV straight tower beam finite element model, the conductor is connected to the straight tower through a V-shaped insulator. The insulator is fixed in vertical displacement and is vertically constrained by the tower crossarm. The horizontal direction is constrained by the tension of the conductor on the other side and the insulator. The lateral stiffness is provided by the insulator. The ground wire is directly connected to the transmission tower and is constrained by the transmission tower.

[0019] For the finite element model of the UHV tension tower beam, the conductor is directly connected to the transmission tower through the insulator, and the ground wire is directly connected to the transmission tower.

[0020] Preferably, modal analysis is performed on the finite element model of the UHV straight tower and tension tower beam, the finite element model of the transmission tower line system, and the single tower-mass analysis model to adjust the mass space distribution of the ground wire and verify the reliability of the single tower-mass analysis model.

[0021] Preferably, the seismic waves used in the analysis are selected from the engineering site, and the artificial waves are generated and then obtained through filtering, baseline correction, and amplitude modulation processing;

[0022] The amplitude modulation process includes adjusting the peak acceleration of the earthquake.

[0023] Preferably, the single tower-mass point analysis model is subjected to IDA analysis, including:

[0024] Perform elastic-plastic time history analysis on the single tower-mass analysis model;

[0025] Extract the displacement of the top of the transmission tower;

[0026] Output the maximum characteristic displacement;

[0027] Gradually increase the peak acceleration of the earthquake and draw the IDA curve.

[0028] Preferably, the seismic performance of the tower is analyzed based on the single tower design response spectrum and IDA curve, including:

[0029] Determine the weak points of the single tower structure based on the design response spectrum, determine the seismic force and foundation force according to the IDA curve under the earthquake intensity corresponding to the design response spectrum, and

[0030] The performance of weak parts of the single tower structure is evaluated based on the seismic force and foundation force.

[0031] Preferably, the method further includes optimizing the control position and structural design of the tower under different earthquake intensities according to the evaluation results.

[0032] It can be seen from the above technical solutions that the present invention discloses a method for analyzing the seismic performance of ultra-high voltage transmission line towers in high-intensity earthquake zones. Compared with the existing technology, the present invention not only fills the gap in the existing technology, but also provides a scientific and systematic seismic performance evaluation tool for the design of ultra-high voltage transmission line towers in high earthquake risk areas, thereby guiding engineering practice, ensuring the safe and stable operation of the power system, and reducing the impact of possible earthquake disasters. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0034] Figure 1 A framework diagram of the seismic performance analysis method for ultra-high voltage transmission line towers in high-intensity earthquake zones provided by the present invention;

[0035] Figure 2 Schematic diagram of a typical straight tower and tension tower provided by the present invention;

[0036] Figure 3 Schematic diagram of the four-tower five-speed tower-line coupling system provided by the present invention;

[0037] Figure 4 A schematic diagram of a simplified single-tower-mass point model provided by the present invention;

[0038] Figure 5 This is the transmission tower IDA analysis flow chart provided by the present invention. DETAILED DESCRIPTION

[0039] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0040] The embodiment of the present invention discloses a method for analyzing the seismic performance of an ultra-high voltage transmission line tower in a high-intensity earthquake zone, comprising the following steps:

[0041] S1. Establish a finite element model of the transmission tower line system and extract an equivalent single tower-mass point analysis model considering the spatial effect of earthquakes;

[0042] S2. Based on different earthquake intensities and regions, performing response spectrum analysis on the single tower-particle analysis model to obtain a single tower design response spectrum;

[0043] S3. Considering the spatial effect of earthquake motion, as well as the coherence effect and traveling wave effect of earthquake motion, the finite element model of the transmission tower line system is analyzed for earthquake motion time history. At the same time, the IDA analysis is performed on the single tower-mass analysis model to obtain the IDA curves under different intensities.

[0044] S4. Analyze the seismic performance of the tower based on the single tower design response spectrum and IDA curve.

[0045] This paper analyzes and rationally simplifies the complex tower-line coupling model into a relatively simple single-tower model, and provides a reasonable calculation method for the internal force of the tower under earthquake action, thereby guiding the design of UHVDC transmission towers in the nine-degree earthquake zone. Figure 1 shown, specifically,

[0046] In step S1, establishing a finite element model of a transmission tower line system includes:

[0047] This application establishes finite element analysis models for typical ±800kV UHV straight-line towers and tension towers, as well as corresponding typical four-tower, five-stage tower-line coupled systems. By establishing a hybrid finite element model of ±800kV UHV straight-line towers and tension tower beams, the natural frequencies and modes of straight-line and tension towers, as well as the stress distribution in key areas under earthquake motion, are examined. At the same time, considering the effects of conductor tension and conductor quality on the frequencies and modes of a single tower, a corresponding finite element model of a typical four-tower, five-stage tower-line coupled system is established. The differences between transmission towers in single-tower and tower-line systems are compared.

[0048] In the prior art, when analyzing the seismic performance of a transmission tower-line system, an analysis model with four towers and five lines or more is usually adopted. However, this model requires a large amount of calculation and has low analysis efficiency.

[0049] In order to improve the analysis efficiency, the tower-line system is gradually simplified, and a hybrid finite element model of ±800kV UHV typical straight tower and tension tower beam is established (such as Figure 2 ), and establish the corresponding typical four-tower five-speed tower-line coupling system as an accurate finite element model (such as Figure 3 ), and use this as a benchmark to simplify and verify the model.

[0050] Considering the spatial effect of earthquakes, an equivalent single-tower-mass point analysis model is extracted. The steps include:

[0051] First, the multi-tower, multi-span transmission tower-line system is simplified into a single-tower, two-line model with one tower and two spans.

[0052] The difference between the one-tower, two-line model and the multi-tower, multi-line model lies primarily in the boundary conditions for the conductor (or ground wire) across the middle tower. When using finite element software to calculate the dynamic response of the combined tower-line system, the connection between the conductor (or ground wire) and the tower can be simulated by defining a connection relationship. The conductor is connected to the insulator string, and the ground wire is directly constrained by the tower.

[0053] The conductor boundary conditions of typical straight towers and tension towers of ±800kV UHV transmission lines need to be considered separately.

[0054] For straight towers, the conductors are connected to the towers via V-shaped insulators. These insulators can be considered rigid rods and vertically constrained by the tower's crossarms. Vertical displacement can be considered fixed. Horizontal constraints are provided by the tension of the conductor on the other side and the insulator. Lateral stiffness is provided by the insulator. These two constraints can be determined by appropriate derivation and combined with finite element analysis. The ground wire is directly connected to the tower and constrained by the tower. Since the tower's mass is much greater than the conductor, it can be initially considered a fixed connection.

[0055] For tension towers, the conductors are directly connected to the transmission towers through insulators, and the ground wires are directly connected to the transmission towers, both of which are initially considered to be fixed.

[0056] Modal analysis and dynamic response analysis were performed on the simplified model, and the low-order modal vibration shapes and frequencies in each direction and the tower top displacement time history curve under dynamic analysis were compared to verify the reliability of the simplified single-tower two-line model.

[0057] To improve efficiency, a single-tower two-line simplified model can be used instead of a multi-tower multi-line model for verification in subsequent studies on the single-tower-mass simplified model and high-intensity seismic design method.

[0058] Considering that the single tower two-line model is still too complex for actual engineering design, in order to meet the needs of engineering design, the single tower two-line model is further simplified to a single tower-mass point model (such as Figure 4 ), considering the mass distribution of the conductor ground wire, simplify it into a mass point attached to the single tower model,

[0059] Modal analysis and dynamic response analysis were performed on the simplified model, the mass space distribution of the ground wire was adjusted, and the low-order modal vibration shapes and frequencies in each direction and the tower top displacement time history curves under dynamic analysis were compared to verify the reliability of the simplified single-tower-mass point model.

[0060] To further optimize the above technical solution, modal analysis was performed on the finite element models of the UHV straight tower and tension tower beam, the finite element model of the transmission tower line system, and the single tower-mass analysis model, respectively, to adjust the mass space distribution of the ground wire and verify the reliability of the single tower-mass analysis model.

[0061] Finite element software was used to model a single transmission tower and a typical tower-line coupled system. Based on the mass and stiffness distribution of the transmission tower structure, the frequency, damping, and modal vibration shape of the single transmission tower were determined. Finite element modal analysis was also used to determine the distribution of measurement points and the location of reference points during the test. In later stages, the test modal results can be used to calibrate the finite element modal structure and improve model accuracy. Modal testing involves exciting multiple points on the transmission tower structure or measuring the responses at multiple points. The project team will use EMA or OMA modal testing methods to conduct modal testing studies on the corresponding transmission tower models.

[0062] Due to conductor tension and inertia, the vibration characteristics, frequencies, and modes of a single transmission tower differ significantly from those of a tower in a tower-line system. Modal analysis is the foundation for analyzing the dynamic response of transmission tower structures. Therefore, experimental research on the vibration characteristics, frequencies, and modes of transmission towers is crucial.

[0063] In step S2, a seismic response spectrum analysis is performed on a single-base iron tower under different earthquake intensity and regional combination conditions;

[0064] Different earthquake intensities and locations in earthquake records result in significant differences in the calculated earthquake response spectra. To perform earthquake response spectrum analysis on transmission towers, the design response spectrum of a single transmission tower is derived based on the different locations and earthquake intensities.

[0065] Based on the current transmission line corridor and my country's earthquake intensity distribution map, a preliminary selection of ground motions was conducted. On this basis, a ground motion response spectrum analysis of a single transmission tower was conducted.

[0066] The study focused on the impact of earthquake intensity and site conditions on the design parameters of an equivalent simplified single-tower model. Through parameter analysis, the influence of each factor on the reliability of the single-tower-mass model was established. Based on this, the single-tower-mass model was modified to obtain the design response spectra of single transmission towers for different sites and earthquake intensities.

[0067] In step S3, considering the spatial effect of seismic motion, as well as the coherence effect and traveling wave effect of seismic motion, the finite element model of the transmission tower line system is subjected to seismic motion time history analysis. At the same time, the IDA analysis is performed on the single tower-particle analysis model to obtain IDA curves under different intensities; that is, the weak parts of the single tower structure are determined based on the design response spectrum, the seismic force and foundation force are determined according to the IDA curve under the earthquake intensity corresponding to the design response spectrum, and the performance of the weak parts of the single tower structure is evaluated based on the seismic force and foundation force.

[0068] S31. Considering the spatial correlation and traveling wave effect of earthquake acceleration time history, finite element numerical simulation of the seismic response of a single-base iron tower is performed;

[0069] Considering the spatial effects of seismic motion, a seismic time history analysis was conducted on a typical tower-line coupled system, examining the failure paths and weak points of towers under different earthquake intensities and locations. Based on this, a finite element analysis was conducted on the acceleration response, displacement response, torsional response, and strain response of a single tower, resulting in a method for calculating seismic forces under different earthquake intensities.

[0070] Due to the large spans of transmission tower-line systems, ground properties vary from tower to tower, potentially leading to variations in seismic waves. Therefore, it is essential to consider the spatiotemporal variations in the vicinity of the earthquake source caused by changes in distance from the source. Furthermore, the impact of angular and directional variations in ground motion at the same source location on the spatial correlation of ground motion is investigated. Furthermore, the effects of focal depth and propagation path on the response of individual transmission towers are considered to construct an envelope diagram of the seismic response of individual transmission towers.

[0071] S32. Considering the coherence effect and traveling wave effect of earthquake motion, conduct earthquake motion time history analysis on the typical tower-line coupling system of the line, study the control position and design reinforcement scheme of the tower under different earthquake intensities, and derive the calculation method of the foundation force under different earthquake intensities. Based on the calculation results, evaluate the seismic resistance of the UHVDC transmission tower.

[0072] To further optimize the above technical solution, the seismic waves used in the analysis were selected from the engineering site, and artificial waves were generated and obtained through filtering, baseline correction, and amplitude modulation processing;

[0073] The amplitude modulation process includes adjusting the peak acceleration of the earthquake.

[0074] In order to further optimize the above technical solution, IDA analysis was performed on the single tower-mass analysis model, such as Figure 5 Shown, including:

[0075] Perform elastic-plastic time history analysis on the single tower-mass analysis model;

[0076] Extract the displacement of the top of the transmission tower;

[0077] Output the maximum characteristic displacement;

[0078] Gradually increase the peak acceleration of the earthquake and draw the IDA curve.

[0079] The IDA curve can intuitively reveal the elastic-plastic state of the transmission tower under different earthquake intensities, so as to facilitate the evaluation of the seismic resistance of UHVDC transmission towers.

[0080] To further optimize the above technical solution, it also includes: optimizing the control parts and structural design of the tower under different earthquake intensities based on the evaluation results.

[0081] By analyzing the internal force distribution characteristics of UHVDC transmission line towers in high-intensity seismic zones under earthquake action, this invention identifies the locations where internal forces are dominant, allowing targeted reinforcement design of key areas to achieve maximum seismic safety at minimal cost. This ensures the safe and stable operation of UHV transmission towers in areas with a magnitude of nine. Furthermore, this invention proposes a structural seismic design verification method for UHV transmission line towers in high-intensity seismic zones, addressing a gap in the existing technology.

[0082] To further illustrate the implementation process of the present invention, the relevant theoretical basis is given below:

[0083] 1. Time-history analysis method of transmission tower structure under earthquake motion

[0084] The time-history analysis method is a dynamic analysis method and a commonly used numerical integration method for solving differential motion. It integrates from the structure's initial state until the end of the entire ground motion. This method can determine the response of each node and unit within the structure during the entire process of the structure's transition from static to vibrating and then back to static under ground motion, and further, the internal force response history of each component.

[0085] The linear motion differential equation of the tower structure under the action of ground motion can be expressed as:

[0086]

[0087] Where: M is the mass matrix of the structure, C is the damping matrix of the structure, and K is the elastic stiffness matrix of the structure; is the acceleration vector of the structural system, is the velocity vector of the structural system, u is the displacement vector of the structural system; is the horizontal acceleration vector of ground motion; Ku is the elastic restoring force when the deformation of the structural system is u; R is the seismic influence coefficient matrix.

[0088] As the tower structure enters the nonlinear deformation stage, the structural restoring force is considered to be related to the time history, that is, u is expressed as u(t). Therefore, the nonlinear motion differential equation at any time t is expressed as follows:

[0089]

[0090] Where: are the relative acceleration vector, relative velocity vector, relative displacement vector and horizontal acceleration vector of the ground motion of each node of the tower at any time t. Equation (2) also holds true at time t+Δt, that is:

[0091]

[0092] Where: Δt is the time increment.

[0093] Subtracting (2) from (3) yields:

[0094]

[0095] Where: According to the following algorithm, subtracting (2) from (3) can directly obtain Δf = KΔu

[0096] Δf=f(u(t+Δt))-f(u(t)) (5)

[0097]

[0098]

[0099]

[0100] When Δt is small, the displacement of the structure changes:

[0101] Δu=u(t+Δt)-u(t) (9)

[0102] If Δf is not large, then Δf can be approximately calculated by the tangent stiffness matrix K(t) of the tower structure at the corresponding time t, that is:

[0103] Δf=K(t)Δu(t) (10)

[0104] Substituting equation (10) into equation (4), we obtain the incremental form of the nonlinear motion differential equation of the damped tower structure system:

[0105]

[0106] In the motion equation of the tower structure system, it is considered that the mass matrix and stiffness matrix have an impact on the damping matrix, so the Rayleigh damping matrix is ​​adopted:

[0107] C=αM+βK (12)

[0108] Where: α and β are constants related to the frequency and damping ratio of the structure;

[0109] When calculating α and β, the natural frequency and damping ratio obtained from the modal analysis of the tower structure can be used, namely:

[0110]

[0111] Where, ω i 、ω j are the frequencies of the i-th and j-th order vibration modes, ξ i ,ξ j is the corresponding damping ratio. In the analysis, the damping ratio of the first two vibration modes is generally taken. For the steel structure tower in this article, according to the seismic code, ξ i =ξ j =0.02.

[0112] Among all the numerical solutions to the motion equations, the commonly used step-by-step integration method is selected. This method usually has the following forms to choose from: linear acceleration method, Wilson-θ method, midpoint acceleration method, Newmark-β method and Runge-Kutta method, etc. In this paper, the Newmark-β method is used to solve the differential equations of motion.

[0113] The Newmark-β method assumes that the displacement increment Δu and velocity increment of the structure in equation (11) are The following relations are satisfied:

[0114]

[0115] Substituting (14) into (11), we get:

[0116]

[0117] Where:

[0118]

[0119] Δu(t+Δt)=u(t+Δt)-u(t) (18)

[0120] At this time, the equation group obtained by formula (15) is very similar in form to the nonlinear equation group obtained in static analysis, and can be solved by giving the convergence condition and selecting the Newton-Raphson iteration method.

[0121] 2. Explicit dynamic analysis of transmission tower structures under earthquake motion

[0122] There are many methods available for complex nonlinear problems in power transmission. Among them, the explicit central difference method is the main method used by dynamic software such as LS-DYNA, and the implicit Newmark method is the main method used in the dynamic response calculation part of ANSYS. The implicit algorithm is suitable for solving static and quasi-static problems, while the explicit algorithm is suitable for solving quasi-static and dynamic problems.

[0123] The explicit central difference method solves the solution for the tn+1 time step when the solutions for the 0, ..., tn time steps are known. Therefore, the state at the end of the incremental step depends only on the displacement, velocity, and acceleration at the beginning of the incremental step. However, the explicit central difference method is not always stable and has restrictions on the time step. Therefore, the variable step increment method is used in the calculation. The time step at each moment is controlled by the stability condition of the current configuration.

[0124] 3. Modal analysis of transmission towers under earthquake motion

[0125] When studying a transmission tower's ability to withstand seismic and other dynamic loads, it's important to first understand the tower's dynamic characteristics, as the tower's dynamic response is solely related to its inherent characteristics. These include factors such as the tower's structural period, frequency, damping ratio, and mode shape, as well as the structure's type, mass, stiffness, material properties, and connections. These characteristics reflect the tower's inherent dynamic performance. Resonance can occur when the structure is subjected to loads close to its own frequency, so it's important to rationally adjust the stiffness and mass of the structure to prevent resonance under external excitation.

[0126] At the same time, analyzing the dynamic characteristics of transmission tower structures can help determine whether the stiffness and mass of the structure are reasonable, thereby avoiding low stiffness or periodicity similar to buildings. Therefore, analyzing the natural vibration characteristics of the transmission tower-line system under external forces is of great significance.

[0127] Dynamic characteristics analysis (also known as modal analysis) can determine the natural vibration characteristics of a structure and is the basis for structural dynamic time-history analysis, vibration analysis, and frequency-domain analysis. The basic dynamic characteristics of transmission towers primarily include the structure's natural frequencies and modes, which are related to the composition of the structural system. The basic dynamic characteristics of transmission towers primarily include the structure's natural frequencies and modes, which are related to the composition of the structural system, material properties, and conductor layout. The essence of modal analysis is to calculate the structure's eigenvalues.

[0128] Transmission towers are typically symmetrical truss structures with spatial regularity. The free vibration equation for these structures describes the free vibration state of the structure in the absence of external interference and ignores any form of energy loss, that is, does not consider damping. By solving the eigenvalues ​​and eigenvectors of the free vibration equation, the natural frequency and mode shape of the structure can be obtained, providing a basis for dynamic response analysis of the structure. The free vibration equation is expressed as:

[0129]

[0130] Where M is the mass matrix; K is the stiffness matrix; x is the node displacement; is the node acceleration and its characteristic equation is

[0131] ([K]-ω 2 [M]){Φ}=0

[0132] Where ω is the natural frequency and {Φ} is the eigenvector.

[0133] The generalized eigenvalue of the tower structure can be obtained by applying the subspace iteration method according to the formula:

[0134]

[0135] Where, [Λ] = diag(λi ), i=1,2,...,p is the eigenvalue; p is the number of eigenvalues ​​or eigenvectors Φ

[0136] 4. Transmission Tower Seismic Response Spectrum Analysis Method

[0137] The earthquake response spectrum is the functional relationship between the maximum response of a single-degree-of-freedom elastic system to a specific earthquake acceleration and the system's natural vibration characteristics. This maximum response can be velocity or displacement, while the natural vibration characteristics refer to the natural period or frequency and damping ratio.

[0138] In a single degree of freedom system, there is mass m, damping c, and stiffness k. The seismic vibration motion equation under earthquake action can be described as:

[0139]

[0140] Or written as

[0141]

[0142] in, is the circular frequency of the single-degree-of-freedom system in the absence of damping;

[0143] ζ=c / 2mω is the damping ratio;

[0144] is the ground acceleration time history value;

[0145] In general, the initial displacement and initial velocity before the earthquake are both zero, so the solution of the above equation is:

[0146]

[0147] in is the circular frequency of the natural vibration of the single degree of freedom system under damping;

[0148] By integrating the above formula once and twice respectively, we can get the velocity response and acceleration response of the earthquake:

[0149]

[0150] Let S d =|x(t) max is the maximum absolute value of the relative displacement response; is the maximum absolute value of the relative velocity; is the maximum value of the absolute value of the absolute acceleration;

[0151]

[0152] For a certain earthquake, if the ground acceleration, natural frequency and damping ratio are known, they can be substituted into the formula to obtain the maximum displacement response Sd, maximum velocity response Sv and maximum acceleration response Sa of the structure under the earthquake.

[0153] By using different natural vibration periods (T) or different circular frequencies as the abscissa and Sd, Sv, and Sa as the ordinates, we can obtain curves showing how Sd, Sv, and Sa vary with natural vibration period and frequency. This gives us the displacement response spectrum, velocity response spectrum, and acceleration response spectrum. Collectively, these curves are referred to as the earthquake response spectrum.

[0154] A response spectrum can be calculated for every seismic motion record. However, due to variations in seismic intensity and location, the resulting response spectra can vary significantly. To standardize response spectra for ease of use, the concept of design response spectra was developed.

[0155] Therefore, the design response spectrum has a certain universality and generality. According to the different sites and earthquake intensities, the corresponding design response spectrum can be found.

[0156] The design response spectrum in the "Code for Seismic Design of Power Facilities" is given in the form of horizontal seismic influence coefficients. The figure shows the horizontal seismic influence coefficient curve.

[0157] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0158] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for analyzing the seismic performance of ultra-high voltage transmission line towers in high-intensity earthquake zones, characterized in that: include: Establish a finite element model of the transmission tower and line system, and extract an equivalent single tower-mass point analysis model considering the spatial effects of earthquakes; Based on different earthquake intensities and regions, a response spectrum analysis is performed on the single tower-particle analysis model to obtain a single tower design response spectrum; including: Determine the seismic vibration motion equation of a single degree of freedom system under earthquake action, The initial displacement and initial velocity before the earthquake are both zero, and the solution to the equation is: The velocity response and acceleration response of the earthquake are obtained by integrating the solution of the equation once and twice respectively. According to the velocity response and acceleration response, the maximum displacement response Sd, the maximum velocity response Sv and the maximum acceleration response Sa are obtained. With different natural oscillation periods T as the horizontal coordinate or different circular frequencies as the horizontal coordinate, and Sd, Sv and Sa as the vertical coordinate, the curves of Sd, Sv and Sa changing with the natural oscillation period and the curves of Sd, Sv and Sa changing with the frequency are obtained; Taking into account the spatial effect of earthquake motion, as well as the coherence effect and traveling wave effect of earthquake motion, the earthquake time history analysis is carried out on the finite element model of the transmission tower line system. At the same time, the IDA analysis is carried out on the single tower-mass analysis model to obtain the IDA curves under different earthquake intensities, including: Perform elastic-plastic time history analysis on the single tower-mass analysis model; Extract the displacement of the top of the transmission tower; Output the maximum characteristic displacement; Gradually increase the peak acceleration of the earthquake motion and draw the IDA curve; The seismic performance of the tower is analyzed based on the single tower design response spectrum and IDA curve.

2. The method for analyzing the seismic performance of an iron tower according to claim 1, wherein: Establishing the finite element model of the transmission tower line system includes: Based on the natural frequency and mode of a single tower and the stress distribution of key parts under the action of earthquake motion, a finite element model of the UHV straight tower and tension tower beam was established; Based on the finite element model of UHV straight tower and tension tower beam, considering the influence of conductor tension and conductor quality on the frequency and mode of single tower, the corresponding finite element model of transmission tower line system is established.

3. The method for analyzing the seismic performance of an iron tower according to claim 2, wherein: Taking into account the spatial effects of earthquakes, an equivalent single-tower-mass point analysis model is extracted. The steps include: simplifying the multi-tower and multi-span transmission tower-line system into a single-tower, two-line model with one tower and two spans; and simplifying the mass distribution of the conductors and ground wires into mass points attached to the single-tower, two-line model.

4. The method for analyzing the seismic performance of an iron tower according to claim 3, wherein: When simplifying the multi-tower and multi-span transmission tower line system into a single tower and two-line model with one tower and two spans, For the UHV straight tower beam finite element model, the conductor is connected to the straight tower through a V-shaped insulator. The insulator is fixed in vertical displacement and is vertically constrained by the tower crossarm. The horizontal direction is constrained by the tension of the conductor on the other side and the insulator. The lateral stiffness is provided by the insulator. The ground wire is directly connected to the transmission tower and is constrained by the transmission tower. For the finite element model of the UHV tension tower beam, the conductor is directly connected to the transmission tower through the insulator, and the ground wire is directly connected to the transmission tower.

5. The method for analyzing the seismic performance of an iron tower according to claim 3, wherein: Modal analysis was performed on the finite element models of the UHV straight tower and tension tower beam, the finite element model of the transmission tower line system, and the single tower-mass analysis model to adjust the mass space distribution of the ground wire and verify the reliability of the single tower-mass analysis model.

6. The method for analyzing the seismic performance of an iron tower according to claim 1, wherein: The seismic waves used in the analysis were selected from the engineering site and artificial waves were generated and obtained through filtering, baseline correction, and amplitude modulation processing; The amplitude modulation process includes adjusting the peak acceleration of the earthquake.

7. The method for analyzing the seismic performance of an iron tower according to claim 1, wherein: According to the single tower design response spectrum and IDA curve, the seismic performance of the tower is analyzed, including: Determine the weak points of the single tower structure based on the design response spectrum, determine the seismic force and foundation force according to the IDA curve under the earthquake intensity corresponding to the design response spectrum, and The performance of weak points of a single tower structure is evaluated based on seismic forces and foundation forces.

8. The method for analyzing the seismic performance of an iron tower according to claim 7, wherein: Also includes: Based on the evaluation results, the control parts and structural design of the tower under different earthquake intensities are optimized.

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