A method for real-time determination of galloping risk of power transmission line under ice and wind coupled load conditions

Abstract

This invention belongs to the field of transmission line safety monitoring and operation and maintenance technology, specifically involving a real-time method for determining the galloping risk of transmission lines under ice and wind coupled load conditions. The method includes the following steps: S1: Collecting real-time conductor ice thickness and real-time wind speed time-series data of the transmission line, and simultaneously obtaining the basic parameters of the transmission line; S2: Based on the basic parameters and real-time conductor ice thickness time-series data, calculating the conductor shape and initial tension of bare conductors, iced conductors, and iced conductors under wind load, respectively, and establishing a static balance mathematical model of the transmission line; S3: Based on the static balance mathematical model, combined with real-time wind speed time-series data, considering the effect of ice and wind dynamic loads, establishing a three-degree-of-freedom motion equation for the iced conductors; S4: Calculating the real-time gap between conductors and ground wires during the galloping process of the transmission line; S5: Determining the galloping risk of the transmission line; This method solves the problems of delayed judgment and complex models in the prior art regarding transmission line galloping risk.

Description

Technical Field

[0001] This invention belongs to the field of transmission line safety monitoring and operation and maintenance technology, specifically relating to a method for real-time determination of transmission line galloping risk under ice and wind coupled load conditions. Background Technology

[0002] With the continuous growth of electricity demand, high-voltage transmission networks have been widely developed. Overhead transmission lines, as crucial channels for power transmission, operate in complex and ever-changing natural environments, bearing the effects of their own weight, wind loads, icing, and other factors. Under certain meteorological conditions, iced conductors can experience low-frequency, high-amplitude vibrations, known as galloping, which can cause phase-to-phase short circuits, damage to insulators and other components, and even serious accidents such as line breaks and tower collapses. This poses a significant threat to the safe operation of the power system and results in substantial economic losses.

[0003] Currently, research on transmission line galloping mainly focuses on galloping model establishment and galloping mechanism analysis. Existing technologies largely rely on offline, static data on icing thickness and wind speed to assess the risk of transmission line galloping, failing to fully consider the impact of dynamic, real-time changes in icing thickness and wind speed on the risk. This results in low accuracy and timeliness in risk assessment, leading to delays. Furthermore, existing solutions generally lack lightweight computational design, either relying on complex models that result in low computational efficiency or ignoring dynamic load coupling effects, leading to biased assessments and difficulty in achieving real-time on-site response. In terms of de-icing decisions, there is often a lack of scientific basis; indiscriminate de-icing may lead to icing detachment and galloping accidents, further exacerbating the safety risks of transmission lines.

[0004] Patent CN119646671A (publication date: March 18, 2025) proposes a method for icing status perception and risk assessment combined with satellite internet. This method collects icing data from icing monitoring probes, satellite equipment, and ground and satellite remote sensing meteorological data. First, an initial prediction result is obtained using an icing prediction model. Then, an LSTM model is used to construct a prediction correction model to optimize the result. Finally, a line fault probability model is constructed based on the target icing data, and a risk assessment is completed by combining indicators such as load shedding and voltage exceedance. However, this assessment method has a cumbersome calculation process, requiring multiple steps including meteorological data fusion, initial prediction, model correction, and fault probability modeling. It suffers from a lag in risk assessment and cannot meet the needs of real-time assessment.

[0005] Patent CN120467209B (publication date: September 12, 2025) is based on the time synchronization of a tension sensor and an image sensing device. It captures the time point when a conductor swings back to its original position using a tension change curve, filters target detection images, extracts the ice layer contour through edge recognition, and compares it with an ice-free image to determine the maximum ice thickness, thus outputting a warning message. This patent only focuses on the static measurement and warning of ice thickness, and does not address the analysis of the galloping response after ice removal, nor does it consider the real-time dynamic load of ice and wind.

[0006] Yun Liang et al. proposed a PSO-CGAN-based method for predicting galloping of icy transmission lines in their paper, "PSO-CGAN-Based Iced Transmission Line Galloping Prediction Method." This method constructs a finite element model of the icy transmission line using APDL, simulates the galloping response under different parameters using Fluent software to generate a dataset, and then optimizes the weight parameters of the CGAN loss function using PSO. Initial wind angle of attack, wind speed, and span distance are then input to achieve galloping prediction. However, this method suffers from high model complexity, requiring steps such as generating massive datasets through finite element simulation and algorithm training and optimization. It is computationally time-consuming, lacks lightweight characteristics, and is difficult to adapt to real-time on-site decision-making. Furthermore, it does not consider the real-time dynamic load abrupt changes during the de-icing process and only predicts icy galloping.

[0007] In their paper, "Analysis of the Dynamic Tension and Parameter Influence of Transmission Conductors Considering Ice-Wind Coupling," Lou Wenjuan et al. obtained the aerodynamic coefficients of crescent-shaped iced conductors with different thicknesses through wind tunnel tests. They then used finite element method (FEM) software to conduct simulation analysis of the dynamic response of transmission lines during de-icing, studying the influence of parameters such as wind angle of attack, wind speed, and ice thickness on the maximum dynamic tension of the conductors during de-icing. This study reveals to some extent the influence of ice-wind coupling on de-icing galloping and dynamic tension. However, it employs a research method combining numerical simulation and wind tunnel tests based on specific working conditions. This requires pre-setting a large number of parameter combinations for calculation, making it impossible to import real-time ice-wind data for dynamic response analysis and hindering real-time risk assessment in the field.

[0008] Therefore, there is an urgent need for a method that can import dynamic data on icing thickness and wind speed, accurately capture the real-time dynamic load coupling effect of ice and wind through lightweight calculations, and make real-time judgments on the galloping risk of transmission lines after icing and de-icing, so as to provide a scientific basis for de-icing decisions. Summary of the Invention

[0009] The purpose of this invention is to provide a real-time method for determining the galloping risk of transmission lines under ice and wind coupled load conditions, so as to solve the problems of lagging determination of transmission line galloping risk and complex models in the prior art.

[0010] This invention is achieved using the following technical solution:

[0011] A method for real-time assessment of transmission line galloping risk under ice and wind coupled load conditions includes the following steps:

[0012] S1: Collect real-time conductor ice thickness and real-time wind speed time series data of the transmission line, and at the same time obtain the basic parameters of the transmission line, including conductor unit length mass, cross-sectional area, comprehensive elastic modulus, torsional stiffness, span, height difference, conductor and ground wire installation position parameters, conductor breaking force and voltage level;

[0013] S2: Based on the obtained basic parameters and real-time conductor icing thickness time series data, the conductor shape and initial tension of bare conductors, iced conductors and iced conductors under wind load are calculated respectively, and a static balance mathematical model of the transmission line is established.

[0014] S3: Based on the static equilibrium mathematical model, combined with real-time wind speed time series data, considering the effect of ice wind dynamic load, establish and solve the three-degree-of-freedom motion equation of the ice-covered conductor to obtain the galloping response and real-time total tension of the transmission line under real-time ice wind dynamic load.

[0015] S4: Calculate the real-time gap between the conductors and ground wires during the galloping process of the transmission line based on the galloping response and the installation position parameters of the conductors and ground wires;

[0016] S5: Based on the real-time gap and real-time total tension, combined with the safety gap standard corresponding to the voltage level and the conductor breaking force, the galloping risk of the transmission line is determined.

[0017] Further, in step S1, the acquisition of the real-time conductor icing thickness time-series data includes:

[0018] High-definition industrial cameras are installed on the towers at both ends of the tension section of the transmission line to collect images of the conductor. A calibration plate is fixedly installed within the camera's field of view to calibrate the mapping relationship between image pixels and actual physical dimensions in real time.

[0019] For the circular icing structure formed on the conductor under wind load, the image recognition method is used to preprocess the acquired conductor image, extract the conductor contour, and segment the icing area. Based on the pixel-physical size mapping coefficient determined by the calibration plate, the icing thickness of the measuring point is calculated, and the icing thickness value of the circular icing on the conductor is output.

[0020] The continuously collected ice thickness data is filtered to generate time-series data of ice thickness that are continuous in time.

[0021] Further, in step S1, the acquisition of the real-time wind speed time series data includes:

[0022] An anemometer is installed on each of the towers at both ends of the tension section of the transmission line, at the same height as the conductor suspension point; the anemometer synchronously records wind speed and wind direction data.

[0023] The wind speed data of the two towers are fused in real time to obtain the real-time wind speed time series data of the tension section, ensuring the continuity of the time series data.

[0024] Furthermore, in step S2, establishing the static balance mathematical model of the transmission line specifically includes:

[0025] S2.1: Analyze the force conditions of the conductor, including axial tension, vertical load, concentrated load and aerodynamic force, wherein the aerodynamic force includes aerodynamic drag, aerodynamic lift and torque;

[0026] S2.2: Establish the static equilibrium control differential equation for the conductor. The key parameters in the equation include the tensile stiffness of the conductor, the static tension of each arc segment, the mass per unit length, and the concentrated load.

[0027] S2.3: Combining the corresponding boundary conditions, the static equilibrium control differential equation is solved by integration to obtain the static equilibrium configuration analytical equation and tension analytical equation for bare conductors, iced conductors, and iced conductors under wind load.

[0028] Furthermore, in step S3, establishing and solving the three-degree-of-freedom equations of motion for the icing conductor specifically includes:

[0029] S3.1: Construct the kinetic energy equation and potential energy equation for the conductor, wherein the potential energy equation includes gravitational potential energy, torsional potential energy and elastic potential energy;

[0030] S3.2: Establish the three-degree-of-freedom motion equations for the icing conductor, including the crosswind motion equation, the downwind motion equation, and the torsional motion equation;

[0031] S3.3: Based on real-time conductor icing thickness time series data and real-time wind speed time series data, aerodynamic forces are calculated using quasi-steady theory, including aerodynamic drag, aerodynamic lift and torque. The aerodynamic coefficients change dynamically with the wind angle of attack, which is determined by the conductor torsion angle, crosswind vibration velocity, torsional vibration velocity and real-time wind speed.

[0032] S3.4: The equations of motion are reduced in order to a set of first-order differential equations. The simulation time and time step are determined. The fourth-order Runge-Kutta iterative method is used for numerical solution to obtain the time history of the generalized displacement, that is, the galloping displacement response of the transmission line under real-time ice wind dynamic load.

[0033] Further, in step S3.3, the wind attack angle is dynamically calculated according to the following expression:

[0034] ;

[0035] in, The real-time wind angle of attack is given, and R is the conductor radius including the icing thickness. For the twist angle, The crosswind vibration velocity, For the torsional angular velocity, For real-time wind speed, t represents the spatial coordinates along the length of the conductor, and t represents the time coordinate.

[0036] Furthermore, in step S4, the real-time gap includes the static icing gap and the de-icing process gap, and its calculation includes the following sub-steps:

[0037] S4.1: The static gap calculation under icing conditions is determined by the spacing between the conductor suspension points and the arc sag difference after icing, thus obtaining the icing static gap;

[0038] S4.2: Calculation of gaps during the de-icing process under windless conditions, taking into account the vertical ice jump height, to obtain the time series of de-icing gaps under windless conditions;

[0039] S4.3: Calculation of gaps during de-icing under windy conditions, taking into account the vertical ice jump height and lateral swing amplitude, to obtain the time series of de-icing gaps under windy conditions;

[0040] S4.4: Traverse the time series of ice removal gaps in windless conditions obtained in S4.2 and the time series of ice removal gaps in windy conditions obtained in S4.3, and take the minimum value of each time gap as the minimum real-time gap of the ice removal process.

[0041] Furthermore, in step S5, the determination of the dancing risk includes:

[0042] S5.1: Gap Risk Assessment: The static icing gap is compared with the operational safety gap standard for the corresponding voltage level, the minimum real-time gap during the de-icing process is compared with the power frequency safety gap standard for the corresponding voltage level, and a comprehensive assessment is made in conjunction with the discharge risk coefficient.

[0043] S5.2: Tension Risk Assessment: The real-time total tension is compared with the preset ratio of the conductor breaking force to make a assessment;

[0044] S5.3: Comprehensive risk assessment: If gap risk or tension risk exists, the transmission line is determined to have galloping risk.

[0045] Furthermore, in step S5.1, the discharge risk coefficient is calculated and determined based on the highest operating voltage between conductors, the voltage value corresponding to a 50% discharge probability, and the icing environment effect coefficient.

[0046] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the method described in this invention.

[0047] This invention provides a method for real-time determination of transmission line galloping risk under ice and wind coupled load conditions, which has the following advantages compared with the prior art:

[0048] 1. This invention dynamically calculates aerodynamic forces based on quasi-steady theory by real-time acquisition of ice thickness and wind speed time-series data, and incorporates real-time response parameters such as crosswind vibration velocity and torsional angular velocity into the wind angle of attack calculation formula, thus achieving dynamic tracking of the ice-wind coupling effect. Compared with existing finite element simulation methods that rely on offline static data or preset operating parameters, this invention can accurately capture the dynamic response caused by sudden load changes and wind speed fluctuations at the moment of ice shedding, resulting in more real-time and accurate judgment results.

[0049] 2. This invention establishes a static equilibrium mathematical model and three-degree-of-freedom motion equations for the conductor, and uses the fourth-order Runge-Kutta method for numerical solution, avoiding the complex mesh generation, multi-component coupled modeling, and implicit integration iteration process of traditional finite element methods. A single risk assessment takes only a few minutes, more than ten times the efficiency of existing simulation calculations that take several hours, meeting the needs of real-time on-site monitoring and rapid decision-making.

[0050] 3. This invention calculates the static gap of icing, the gap during windless de-icing, and the gap during windy de-icing, and extracts the minimum real-time gap as the judgment criterion by traversing the entire time history. It also incorporates a discharge risk coefficient for quantitative assessment. Regarding tension risk, the real-time total tension is compared with a preset ratio of the conductor breaking force, forming a comprehensive judgment system of "gap + tension," providing a scientific basis for de-icing decisions and effectively avoiding secondary accidents caused by blind de-icing. Attached Figure Description

[0051] Figure 1 This is a technical roadmap for the transmission line galloping risk assessment method in this invention.

[0052] Figure 2 This is a schematic diagram of the static equilibrium state of the ground wire under ice and wind load in this invention.

[0053] Figure 3 This is a schematic diagram of the initial and post-icing equilibrium states of the conductor ground wire in this invention.

[0054] Figure 4 This is a schematic diagram illustrating the gap calculation of a transmission line during the de-icing process under windless conditions in this invention.

[0055] Figure 5 This is a schematic diagram illustrating the calculation of the minimum gap between conductors and ground wires during the ice shedding process in windless conditions, as described in this invention.

[0056] Figure 6 This is a schematic diagram of the icing and de-icing states of the conductor under wind conditions according to the present invention.

[0057] Figure 7 This is a schematic diagram of the icing and de-icing states of the conductor ground wire in this invention. Detailed Implementation

[0058] A method for real-time assessment of transmission line galloping risk under ice-wind coupled load conditions, such as Figure 1 As shown, it includes the following steps:

[0059] S1: Data Acquisition and Parameter Acquisition

[0060] Real-time conductor icing thickness and real-time wind speed data of transmission lines are collected, and basic parameters of the transmission lines are also obtained.

[0061] The acquisition of real-time conductor icing thickness time-series data includes: such as Figure 2 As shown, a high-definition industrial camera is installed on each of the towers at both ends of the tension section of the transmission line to capture images of the conductor. The camera lens adopts a long-focal-length image-stabilized design and is equipped with an infrared supplementary light to ensure image clarity in nighttime and low-light environments. The camera is installed at a perpendicular angle to the conductor to avoid interference from background clutter. A calibration plate is fixedly installed within the camera's field of view for real-time calibration of the mapping relationship between image pixels and actual physical dimensions.

[0062] Transmission lines in naturally icing environments undergo a gradual process of dynamic equilibrium of torque between the ice layer and the conductor, accumulating through repeated torsion. This process mainly involves three key stages: "wing-shaped ice formation—periodic torsion—circular ice formation," ultimately resulting in a circular icing structure. The primary icing type is rime ice (ice density taken as 900 kg / m³). 3 The acquired conductor images were processed using image recognition methods to identify the thickness of the circular ice accretion on the conductor. First, grayscale conversion, adaptive threshold segmentation, and noise reduction were performed to separate the conductor, ice-covered area, and background environment. Then, the Canny edge detection algorithm was used to extract the outer contour of the conductor, and the Hough circle transform was used to fit the baseline contour of the conductor's bare diameter (calibrated based on the conductor's bare diameter parameters calibrated from historical ice-free images). Next, the ice-covered area was segmented based on color and morphological features, eliminating interference areas such as reflections and condensation on the conductor's metal surface. Finally, the ice thickness at each measurement point was calculated based on the pixel-physical size mapping coefficient determined by the calibration plate. The ice thickness refers to the radial thickness of the ice layer covering the conductor surface, i.e., the vertical distance from the outer surface of the conductor's bare diameter to the outer surface of the ice layer. Three measurement points (60° intervals) were evenly selected along the conductor's circumference, and the ice thickness at each point was calculated. The average of the three measurements was taken as the output value of the ice thickness at that moment.

[0063] Image acquisition frequency was set to once every 3 minutes, and the image recognition algorithm processed a single frame image in ≤3 seconds to ensure that one valid ice thickness data point was output every 3 minutes. A 5G industrial module was used to transmit the acquired images and recognition results in real time, and H.265 encoding was used for image compression. Moving average filtering was applied to the continuously acquired ice thickness data to remove outliers caused by sudden interference, generating continuous time-series ice thickness data δ. ice (t).

[0064] The acquisition of the real-time wind speed time series data includes: such as Figure 2 As shown, a three-dimensional ultrasonic anemometer is installed on each of the towers at both ends of the tension section of the transmission line, at the same height as the conductor suspension point. The anemometer has a measurement range of 0-60 m / s, an accuracy of ±0.1 m / s, and a wind direction measurement range of 0-360°. It can simultaneously output wind speed components in the alongwind, crosswind, and vertical directions, and synchronously record wind speed and direction data. The sampling frequency is set to once every 3 minutes.

[0065] The wind speed data of the two towers are fused in real time, and the real-time wind speed time series data U(t) of the tension section is calculated by weighted average method (0.5 for each tower). An effective wind speed data point is generated every 3 minutes to ensure the continuity of the time series data and cover the dynamic change cycle of ice wind load.

[0066] The basic parameters include the conductor's mass per unit length, cross-sectional area, comprehensive elastic modulus, torsional stiffness, span, height difference, conductor and ground wire installation position parameters, conductor breaking force, and the voltage level corresponding to the transmission line. The conductor's mass per unit length ranges from 1-50 kg / m, and the cross-sectional area ranges from 100-400 mm². 2 The comprehensive elastic modulus ranges from 1×10. 10 -1×10 11 N / m 2 Torsional stiffness ranges from 10 to 500 Nm 2 / rad, span range is 100-700m, height difference range is 0-100m, conductor and ground wire installation position parameters include vertical spacing (1-10m) and horizontal spacing (1-20m), conductor breaking force range is 10-1000kN, voltage level includes common levels such as 110kV, 220kV, 500kV, and 1000kV.

[0067] S2: Establish a static equilibrium mathematical model

[0068] Based on the acquired basic parameters and real-time conductor icing thickness time-series data, the conductor shape and initial tension of bare conductors, iced conductors, and iced conductors under wind load are calculated respectively, establishing a static balance mathematical model for the transmission line. Specifically, this includes:

[0069] S2.1: Analyze the stress conditions on the conductor, including axial tension T, vertical load (the conductor's own weight ρgδs, the weight of icing ρgδs), and other stresses. ice gδs), concentrated load (spacers, etc.) and aerodynamic forces (aerodynamic drag) Aerodynamic lift and torque Where ρ is the mass per unit length of the conductor; g is the acceleration due to gravity; δs is the arc length of the infinitesimal segment; ρ ice Mass per unit length of icing; Let be the i-th concentrated load.

[0070] S2.2: Establish the static equilibrium governing differential equations for the conductor, which include the tensile stiffness EA of the conductor and the static tension T in each arc segment. Mass per unit length ρ, concentrated load Key parameters, etc. Among them, These are the spatial coordinates (arc length coordinates) along the length of the conductor.

[0071] S2.3: For different types of conductors, and in conjunction with the corresponding boundary conditions, the static equilibrium control differential equations are solved by integration to obtain the analytical expressions for the static equilibrium configuration and tension of the conductors:

[0072] Bare conductor: Taking the lowest point of the line as the coordinate origin of the span, and setting corresponding boundary conditions, the conductor configuration and tension are calculated through integration. The bare conductor configuration is described by the catenary equation: , ;in, Let be the horizontal coordinate with the lowest point of the conductor as the origin, y be the vertical coordinate, H be the tension at the lowest horizontal point, ρ be the mass per unit length of the conductor, and g be the acceleration due to gravity. The tension at any point on the conductor is: The tension range at the lowest horizontal point is 10-100kN.

[0073] For conductors with concentrated loads: After setting the boundary conditions of the span, determine the relevant parameters based on the static balance relationship, and calculate the configuration and tension by segment integration and recursion according to the installation position of the concentrated load to ensure that the tension is continuous in the concentrated load range, and the concentrated load size range is 10-100N.

[0074] Icing conductor: The total mass per unit length is the sum of the mass per unit length of the conductor and the mass per unit length of the icing. The mass per unit length of the icing is calculated based on the ice thickness and ice density. The configuration and tension analytical formulas replace the mass parameters with the bare conductor form, while also considering the torque caused by icing eccentricity. ,in, GI is the external torque per unit length. p For the torsional stiffness of the conductor, For the conductor twist angle, This represents the torsion angle gradient.

[0075] Icing conductor under wind load: The conductor deviates from the vertical plane under wind load. The corresponding control differential equation is established and the three-dimensional configuration is obtained by solving the boundary conditions. The aerodynamic drag, lift and torque are calculated according to the corresponding coefficients and operating parameters.

[0076] Through the above steps, the static equilibrium configuration and tension analysis formulas of bare conductors, iced conductors, and iced conductors under wind load are obtained.

[0077] S3: Establish and solve the three-degree-of-freedom motion equations.

[0078] Based on the aforementioned static equilibrium mathematical model, combined with real-time wind speed time-series data, and considering the effect of icing wind dynamic loads, a three-degree-of-freedom motion equation for the iced conductor is established and solved to obtain the galloping response and real-time total tension of the transmission line under real-time icing wind dynamic loads. Specifically, this includes:

[0079] S3.1: Construct the kinetic energy equation for the conductor under wind load and de-icing conditions: ,in, Represents the translational kinetic energy of the conductor. The value represents the torsional kinetic energy, L is the total length of the conductor, and m is the mass per unit length. Crosswind speed, Downwind speed, Let J be the torsional angular velocity and J be the moment of inertia per unit length.

[0080] Based on the galloping characteristics of the conductor, the potential energy equations for its gravity, torsion, and elastic potential energy are constructed as follows: Among them, tensile strain Torsional strain Where y is the vertical displacement, m is the mass per unit length, and g is the acceleration due to gravity.

[0081] S3.2: Establish the three-degree-of-freedom equations of motion for the icing conductor, including the equations of motion in the crosswind direction, the alongwind direction, and the torsional direction:

[0082] Crosswind motion equation: ;

[0083] Equation of motion with the wind: ;

[0084] Equation of motion in the direction of twisting: ;

[0085] Where m is the mass per unit length, L is the span (conductor length), and V is the generalized displacement in the crosswind direction. This is the crosswind damping coefficient. Crosswind generalized force, W is downwind generalized displacement. The downwind damping coefficient. Downwind generalized force The moment of inertia per unit length, To reverse the generalized displacement, The torsional damping coefficient is... Reversal of general forces.

[0086] S3.3: Based on real-time conductor icing thickness time-series data and real-time wind speed time-series data, aerodynamic forces, including aerodynamic drag, aerodynamic lift, and torque, are calculated using quasi-steady theory.

[0087] Aerodynamic drag: ;

[0088] Aerodynamic lift: ;

[0089] Aerodynamic torque: ;

[0090] in, Let U(t) be the air density, U(t) be the real-time wind speed data, and D be the diameter of the conductor including the icing thickness. , , These are the drag coefficient, lift coefficient, and torque coefficient, respectively, and each coefficient is dynamically determined based on the real-time wind attack angle α(t).

[0091] The wind attack angle α(t) is determined by the conductor's twist angle, crosswind vibration velocity, torsional vibration velocity, and real-time wind speed, and is dynamically calculated according to the following expression:

[0092] ;

[0093] in, The real-time wind angle of attack is given, and R is the conductor radius including the icing thickness. For the twist angle, The crosswind vibration velocity, For the torsional angular velocity, For real-time wind speed, t represents the spatial coordinates along the length of the conductor, and t represents the time coordinate.

[0094] S3.4: Numerical solution of the equations of motion. First, the equations of motion are reduced in order. Let... , , , , , The equations are transformed into a system of first-order differential equations. Then, the simulation time and time step (0.01-0.1s) are determined. Finally, the fourth-order Runge-Kutta iterative method is used for numerical solution to obtain the time history of the generalized displacement, that is, the galloping displacement response of the transmission line under real-time ice wind dynamic load (including crosswind amplitude, downwind amplitude, and torsional angle amplitude). At the same time, the real-time total tension (the sum of static tension and galloping dynamic tension increment) can be calculated from the solution of the equations of motion.

[0095] S4: Calculate the real-time gap

[0096] Based on the galloping response and conductor / ground wire installation position parameters, the real-time gap between the conductors and ground wires during the galloping process of the transmission line is calculated. The real-time gap includes the static gap due to icing and the gap during the de-icing process, and its calculation includes the following sub-steps:

[0097] S4.1: Static gap calculation under icing conditions. The static gap of the conductor and ground wire after icing is determined by the spacing between the conductor and ground wire suspension points and the sag difference after icing, such as... Figure 3 As shown, the calculation formula is:

[0098] ;

[0099] in, , The vertical spacing of the conductor suspension points. The horizontal spacing between the conductor suspension points. The sag of the conductor after icing. This represents the sag of the ground line after icing. The sag is calculated using the catenary formula.

[0100] S4.2: Gap calculation only during the de-icing process under windless conditions. For example... Figure 4 As shown, when a transmission line is not subjected to wind load, the conductor will only undergo vertical displacement response during ice removal. Therefore, considering the vertical ice jump height, the time series of the ice removal interval in windless conditions is obtained:

[0101] Minimum gap between conductors ;

[0102] in, The vertical spacing between adjacent conductors. The maximum ice jump height of the de-icing phase conductor is obtained from the galloping response calculated in step S3.

[0103] like Figure 5 As shown, the minimum gap between conductors and ground wires .

[0104] S4.3: Gap Calculation During De-icing under Windy Conditions. When transmission lines are subjected to wind loads, de-icing generates vertical vibrations and lateral swaying. The real-time ice jump height and lateral sway amplitude need to be considered to obtain the time series of gaps during windy de-icing:

[0105] like Figure 6 As shown, the minimum gap between the conductors is:

[0106] ;

[0107] ;

[0108] in, The horizontal spacing between the suspension points of adjacent circuit conductors. The height of an ice jump at a certain moment. The horizontal swing amplitude at a certain moment.

[0109] like Figure 7 As shown, the minimum gap between conductors and ground wires: ;

[0110] S4.4: Traverse the time series of ice removal gaps in windless conditions obtained in S4.2 and the time series of ice removal gaps in windy conditions obtained in S4.3, and take the minimum value of each time gap as the minimum real-time gap of the ice removal process.

[0111] S5: Dancing Risk Assessment

[0112] Based on the real-time gap and real-time total tension, combined with the safety gap standard corresponding to the voltage level and the conductor breaking force, the galloping risk of the transmission line is determined. Specifically, this includes:

[0113] S5.1: Gap Risk Assessment. The static icing gap calculated in step S4 is compared with the operational safety gap standard for the corresponding voltage level. The minimum real-time gap during the de-icing process is compared with the power frequency safety gap standard for the corresponding voltage level. A comprehensive assessment is then made, taking into account the discharge risk coefficient.

[0114] Safety clearance comparison and judgment: The static clearance for icing must be greater than the operating safety clearance for the corresponding voltage level; otherwise, it is judged as a static clearance risk for icing. The minimum clearance during the de-icing process must be greater than the power frequency safety clearance for the corresponding voltage level; otherwise, it is judged as a dynamic clearance risk for de-icing.

[0115] Discharge risk factor determination: Introducing a discharge risk factor Among them, the highest operating voltage between conductors (U represents the rated voltage); conductor breakdown voltage ( =0.8 is the icing environmental effect coefficient. (This refers to the voltage value corresponding to a 50% discharge probability). If... ≥1 indicates an extremely high risk of gap discharge, and is directly classified as a gap risk; if 0.8≤ <1, a comprehensive judgment is made based on the gap comparison results; if <0.8, no risk of discharge.

[0116] Comprehensive gap risk assessment: A gap risk is determined to exist if any of the following conditions are met: Icing static gap < operational safe gap; De-icing dynamic minimum gap < power frequency safe gap; Discharge risk coefficient. ≥1.

[0117] S5.2: Tension Risk Assessment. The real-time total tension (the sum of static tension and dynamic tension increments during galloping) is compared with the preset ratio (80%-90%) of the conductor breaking force. If the real-time total tension is greater than or equal to the preset ratio of the conductor breaking force, then a tension risk is assessed.

[0118] S5.3: Comprehensive Risk Assessment. If gap risk or tension risk exists, the transmission line is determined to have galloping risk; if neither gap risk nor tension risk exists, the transmission line is determined to have no galloping risk.

[0119] The present invention will be further explained and illustrated below with reference to embodiments. Obviously, the described embodiments are only a part of the embodiments, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0120] Example

[0121] Taking a typical tension section of a 1000kV ultra-high voltage transmission line as an example, the method of the present invention will be described in detail.

[0122] S1: Data Acquisition and Parameter Acquisition

[0123] Conductor parameters: Model JL / G2A-1000 / 85, mass per unit length ρ=42.79kg / m, cross-sectional area A=1081.5mm² 2 The overall elastic modulus E = 6.58 × 10¹⁰ N / m 2 The tensile stiffness EA = E × A = 7.12 × 10 7 N, torsional stiffness GI p =139Nm 2 / rad, conductor breaking force F break =600kN.

[0124] Line geometric parameters: span l AB =500m, l BC =600m, l CD =550m, height difference hAB =30m, h BC =25m, h CD =35m.

[0125] Conductor and ground wire installation parameters: Vertical distance ΔH between the suspension point of phase A conductor and ground wire CG =6m, horizontal spacing ΔL CG =5.46m, vertical spacing ΔH between adjacent phase conductor suspension points CC =4m, horizontal spacing ΔL between adjacent circuit conductors CC =8m.

[0126] Voltage level: 1000kV, corresponding safety clearance standard values ​​are taken from Table 1.

[0127] Table 1 Safety clearance standards for different voltage levels

[0128]

[0129] Load data: Real-time time-series data of conductor icing thickness is acquired, and the data is recorded as δ. ice (t); Obtain real-time wind speed time series data and record it as U(t), and record wind direction information synchronously for a period of not less than 1 hour to ensure coverage of the dynamic change cycle of ice thickness and wind speed.

[0130] S2: Establish a static equilibrium mathematical model

[0131] Based on the conditions of force equilibrium and geometric compatibility, establish the governing differential equations. Mass per unit length of icing. The wire diameter D = 42.8 mm, and the ice density is... =900kg / m 3 Take the ice thickness δ at a certain moment ice =20mm, ρi is calculated ce =2.86kg / m, total mass per unit length ρ total =ρ+ρ ice =45.65kg / m.

[0132] Boundary conditions: The origin of the cross-gap (BC gap) is taken as the lowest point of the line, x(0)=0, y(0)=0, and the tension at the lowest horizontal point is H=70kN.

[0133] Configuration and Calculation:

[0134] .

[0135]

[0136] ;

[0137] Calculation of sag after icing: using the catenary formula , of which horizontal stress The span is l = 600m, and the elevation difference angle is β = arctan(h). BC / l BC ) = arctan(25 / 600) ≈ 2.39°, and f is calculated. C =28.5m; Sag of ground wire after icing f G =16.2m.

[0138] Static balance calculations were performed on the icing conductor based on real-time wind speed data, and the mass per unit length of icing was calculated. The conductor diameter (including icing) D = 42.8 + 2 × 20 = 82.8 mm = 0.0828 m, and the wind angle of attack α = 15°, obtained from FLUENT simulation. C D =0.72, C L =0.45, , .

[0139] In the initial state x(0)=y(0)=z(0)=0, the final displacement in the z direction under the action of aerodynamic force at the midpoint of BC is z=0.86m.

[0140] S3: Establish and solve the three-degree-of-freedom motion equations.

[0141] The galloping process of the transmission line at the BC section is analyzed and calculated.

[0142] Kinetic energy calculation: ,in, Polar moment of inertia per unit length ,therefore, .

[0143] Potential energy calculation: .

[0144] Calculation of generalized aerodynamic forces: Integral yields , , .

[0145] Calculation of generalized damping force: Damping ratio , natural frequency rad / s, calculated N·s / m, N·s·m / rad.

[0146] Based on the above calculations, the three-degree-of-freedom nonlinear motion equations of the conductor are obtained:

[0147] ;

[0148] ;

[0149] .

[0150] Calculation of dynamic loads from ice winds: Real-time wind angle of attack , where R=D / 2=0.0414m.

[0151] Numerical solution of the equations of motion: (1) Let , , , , , , which is transformed into a system of first-order differential equations; (2) Parameter settings: simulation time t=180s, time step is 0.05s; (3) Iteratively solve the equations to obtain the galloping response: maximum crosswind amplitude V max =1.8m, maximum amplitude W in the downwind direction max =0.12m, maximum torsional amplitude Θ max =10°, ice jump height H at a certain moment J (t) = 1.5m, lateral swing L H (t) = 0.9m.

[0152] S4: Calculate the real-time gap

[0153] Calculation of static gap after icing: ,in =18.3m, =5.46m, therefore, =19.12m.

[0154] Calculation of gaps during de-icing of transmission lines under no-wind load: (1) Minimum gap between conductors: (2) Minimum gap between conductors and ground wires: .

[0155] Calculation of gaps during de-icing of transmission lines under wind load: (1) Minimum gap between conductors: , Take the minimum value (2) Minimum gap between conductors and ground wires: .

[0156] By traversing the entire time process, the minimum gap D during the de-icing process is obtained. min =2.2m.

[0157] S5: Dancing Risk Assessment

[0158] Gap risk assessment: (1) Safety gap comparison: As shown in Table 1, the safe gap between phases at the 1000kV voltage level is 5.0m, and the minimum gap during the de-icing process is 2.2m < 5.0m, indicating a dynamic gap risk during de-icing; the static gap during icing is 19.12m > 7.5m (safe gap for conductor and ground wire operation), indicating no static gap risk during icing; (2) Discharge risk coefficient: kV, kV (the voltage value corresponding to a 50% discharge probability at the 1000kV level is 1800). (3) The gap risk assessment result is There is an extremely high risk of discharge.

[0159] Tension risk assessment: (1) Real-time total tension: Static tension T static =73.25kN, dynamic tension increment ΔT=4.8kN, total tension T total =73.25+4.8=78.05kN; (2) Risk threshold: The preset ratio of conductor breaking force is 85%, and the threshold F threshold =600×85%=510kN; (3) Judgment result: 78.05kN<510kN, no tension risk.

[0160] Overall Risk and De-icing Decision: Given the presence of gap risk and the absence of tension risk, the transmission line is deemed to be at risk of galloping, and immediate de-icing is not recommended.

[0161] Comparative Example

[0162] Comparative approach: The method of transmission line galloping response and risk assessment based on finite element analysis is adopted. This method requires the establishment of a coupled finite element model of conductor-insulator string-tower using Abaqus, importing preset ice and wind load parameters, using implicit integration algorithm to solve the dynamic response, and finally combining simulation results to complete the risk assessment.

[0163] The present invention employs a lightweight mathematical modeling approach, constructing a static balance mathematical model of the transmission line during galloping and the three-degree-of-freedom motion equations of the conductors, and combining real-time ice and wind load data for calculation and analysis to complete risk assessment.

[0164] Taking a tension section of a 220kV transmission line as the test object, the line foundation parameters and the range of dynamic ice and wind loads are as follows:

[0165] Conductor parameters: Model JL / G1A-300 / 40, mass per unit length ρ=1.13kg / m, cross-sectional area A=338.9mm² 2 The overall elastic modulus E = 6.3 × 10⁻⁶ 10 N / m 2 The tensile stiffness EA = E × A = 2.13 × 10 7N, torsional stiffness GI p =35Nm 2 / rad, conductor breaking force F break =185kN;

[0166] Line geometric parameters: span l AB =300m, l BC =320m, l CD =280m, height difference h AB =15m, h BC =12m, h CD =18m;

[0167] Conductor and ground wire installation parameters: Vertical distance ΔH between the suspension point of phase A conductor and ground wire CG =4m, horizontal spacing ΔL CG =3.5m, vertical spacing ΔH between adjacent phase conductor suspension points CC =3m, horizontal spacing ΔL between adjacent circuit conductors CC =5m;

[0168] Ice thickness time series data: The data collection period is 1 hour, and ice thickness data is collected every 3 minutes.

[0169] Wind speed time series data: The data collection period is 1 hour, with data collected every 3 minutes, including wind speed and wind direction data.

[0170] The comparison results are shown in Table 2.

[0171] Table 2 Comparison results between the comparative scheme and the present invention.

[0172]

[0173] This invention analyzes and calculates the galloping response and risk assessment of transmission lines under ice-wind coupled load conditions by constructing a mathematical model of the transmission line and the three-degree-of-freedom motion equations of the conductors. This eliminates the need for cumbersome steps such as finite element model mesh generation, multi-component coupled modeling, and setting complex boundary conditions. Furthermore, this invention can use real-time collected ice thickness and wind speed time-series data to calculate the ice-wind dynamic load in real time using quasi-steady theory, dynamically tracking the ice-wind coupling effect and updating the galloping response calculation results in real time. This allows for a more accurate response to dynamic load changes in real-world scenarios such as sudden changes in ice thickness and wind speed fluctuations. In contrast, the comparative scheme can only perform offline static load simulations based on preset operating parameters, which has significant limitations when dealing with real-time load changes in the field. Moreover, this invention obtains the galloping displacement response of the transmission line by constructing a dynamic model and performing iterative solutions. The entire calculation process is simple and efficient, with a single risk assessment taking only a few minutes, meeting the needs of real-time on-site monitoring and rapid decision-making. The comparative scheme, however, relies on implicit integration algorithms for complex finite element simulations, often requiring several hours for a single solution, resulting in significant computational delays and lagging risk assessment.

[0174] Therefore, this invention is significantly superior to existing mainstream risk assessment schemes (such as finite element method) in terms of lightweight, efficiency and real-time performance. It can realize real-time assessment of galloping risk under dynamic ice and wind loads, providing scientific and efficient decision support for the operation and maintenance of transmission lines.

[0175] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for real-time determination of transmission line galloping risk under ice and wind coupled load conditions, characterized in that: Includes the following steps: S1: Collect real-time conductor ice thickness and real-time wind speed time series data of the transmission line, and at the same time obtain the basic parameters of the transmission line, including conductor unit length mass, cross-sectional area, comprehensive elastic modulus, torsional stiffness, span, height difference, conductor and ground wire installation position parameters, conductor breaking force and voltage level; S2: Based on the obtained basic parameters and real-time conductor icing thickness time series data, the conductor shape and initial tension of bare conductors, iced conductors and iced conductors under wind load are calculated respectively, and a static balance mathematical model of the transmission line is established. S3: Based on the static equilibrium mathematical model, combined with real-time wind speed time series data, considering the effect of ice wind dynamic load, establish and solve the three-degree-of-freedom motion equation of the ice-covered conductor to obtain the galloping response and real-time total tension of the transmission line under real-time ice wind dynamic load. S4: Calculate the real-time gap between the conductors and ground wires during the galloping process of the transmission line based on the galloping response and the installation position parameters of the conductors and ground wires; S5: Based on the real-time gap and real-time total tension, combined with the safety gap standard corresponding to the voltage level and the conductor breaking force, the galloping risk of the transmission line is determined.

2. The method for real-time determination of transmission line galloping risk under ice and wind coupled load conditions according to claim 1, characterized in that: In step S1, the acquisition of the real-time conductor icing thickness time-series data includes: High-definition industrial cameras are installed on the towers at both ends of the tension section of the transmission line to collect images of the conductor. A calibration plate is fixedly installed within the camera's field of view to calibrate the mapping relationship between image pixels and actual physical dimensions in real time. The image recognition method is used to preprocess the acquired conductor image, extract the conductor contour, and segment the icing area. Based on the pixel-physical size mapping coefficient determined by the calibration plate, the icing thickness of the measuring point is calculated, and the icing thickness value of the circular icing of the conductor is output. The continuously collected ice thickness data is filtered to generate time-series data of ice thickness that are continuous in time.

3. The method for real-time determination of transmission line galloping risk under ice and wind coupled load conditions according to claim 1, characterized in that: In step S1, the acquisition of the real-time wind speed time series data includes: An anemometer is installed on each of the towers at both ends of the tension section of the transmission line, at the same height as the conductor suspension point; the anemometer synchronously records wind speed and wind direction data. The wind speed data of the two towers are fused in real time to obtain the real-time wind speed time series data of the tension section, ensuring the continuity of the time series data.

4. The method for real-time determination of transmission line galloping risk under ice and wind coupled load conditions according to claim 1, characterized in that: In step S2, establishing the static balance mathematical model of the transmission line specifically includes: S2.1: Analyze the force conditions of the conductor, including axial tension, vertical load, concentrated load and aerodynamic force, wherein the aerodynamic force includes aerodynamic drag, aerodynamic lift and torque; S2.2: Establish the static equilibrium control differential equation for the conductor. The key parameters in the equation include the tensile stiffness of the conductor, the static tension of each arc segment, the mass per unit length, and the concentrated load. S2.3: Combining the corresponding boundary conditions, the static equilibrium control differential equation is solved by integration to obtain the static equilibrium configuration analytical equation and tension analytical equation for bare conductors, iced conductors, and iced conductors under wind load.

5. The method for real-time determination of transmission line galloping risk under ice and wind coupled load conditions as described in claim 1, characterized in that: In step S3, establishing and solving the three-degree-of-freedom equations of motion for the icing conductor specifically includes: S3.1: Construct the kinetic energy equation and potential energy equation for the conductor, wherein the potential energy equation includes gravitational potential energy, torsional potential energy and elastic potential energy; S3.2: Establish the three-degree-of-freedom motion equations for the icing conductor, including the crosswind motion equation, the downwind motion equation, and the torsional motion equation; S3.3: Based on real-time conductor icing thickness time series data and real-time wind speed time series data, aerodynamic forces are calculated using quasi-steady theory, including aerodynamic drag, aerodynamic lift and torque. The aerodynamic coefficients change dynamically with the wind angle of attack, which is determined by the conductor torsion angle, crosswind vibration velocity, torsional vibration velocity and real-time wind speed. S3.4: The equations of motion are reduced in order to a set of first-order differential equations. The simulation time and time step are determined. The fourth-order Runge-Kutta iterative method is used for numerical solution to obtain the time history of the generalized displacement, that is, the galloping displacement response of the transmission line under real-time ice wind dynamic load.

6. The method for real-time determination of transmission line galloping risk under ice and wind coupled load conditions according to claim 5, characterized in that: In step S3.3, the wind attack angle is dynamically calculated according to the following expression: ； in, The real-time wind angle of attack is given, and R is the conductor radius including the icing thickness. For the twist angle, The crosswind vibration velocity, For the torsional angular velocity, For real-time wind speed, t represents the spatial coordinates along the length of the conductor, and t represents the time coordinate.

7. The method for real-time determination of transmission line galloping risk under ice and wind coupled load conditions according to claim 1, characterized in that: In step S4, the real-time gap includes the static icing gap and the de-icing process gap, and its calculation includes the following sub-steps: S4.1: The static gap calculation under icing conditions is determined by the spacing between the conductor suspension points and the arc sag difference after icing, thus obtaining the icing static gap; S4.2: Calculation of gaps during the de-icing process under windless conditions, taking into account the vertical ice jump height, to obtain the time series of de-icing gaps under windless conditions; S4.3: Calculation of gaps during de-icing under windy conditions, taking into account the vertical ice jump height and lateral swing amplitude, to obtain the time series of de-icing gaps under windy conditions; S4.4: Traverse the time series of ice removal gaps in windless conditions obtained in S4.2 and the time series of ice removal gaps in windy conditions obtained in S4.3, and take the minimum value of each time gap as the minimum real-time gap of the ice removal process.

8. The method for real-time determination of transmission line galloping risk under ice and wind coupled load conditions according to claim 7, characterized in that: In step S5, the determination of the dancing risk includes: S5.1: Gap Risk Assessment: The static icing gap is compared with the operational safety gap standard for the corresponding voltage level, the minimum real-time gap during the de-icing process is compared with the power frequency safety gap standard for the corresponding voltage level, and a comprehensive assessment is made in conjunction with the discharge risk coefficient. S5.2: Tension Risk Assessment: The real-time total tension is compared with the preset ratio of the conductor breaking force to make a assessment; S5.3: Comprehensive risk assessment: If gap risk or tension risk exists, the transmission line is determined to have galloping risk.

9. The method for real-time determination of transmission line galloping risk under ice and wind coupled load conditions according to claim 8, characterized in that: In step S5.1, the discharge risk coefficient is calculated and determined based on the highest operating voltage between conductors, the voltage value corresponding to a 50% discharge probability, and the icing environment effect coefficient.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by the processor, it implements the method as described in any one of claims 1 to 9.

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