Line sag measurement method and device based on traveling wave and temperature frequency wave velocity coupling, medium and product

Abstract

The invention discloses a line sag measurement method and device based on traveling wave and temperature frequency wave velocity coupling, a medium and a product, and relates to the technical field of power transmission lines, and the method comprises the steps: calculating a modular domain wave velocity according to a traveling wave current signal in combination with a temperature frequency wave velocity coupling change function; based on the mode domain wave velocity, integration is carried out in combination with geometric characteristics of an oblique parabola, and a conductor oblique projectile traveling wave coupling coefficient is obtained; and establishing and deriving a sag expression of any point of the overhead conductor, and measuring to obtain the maximum sag of the overhead conductor in combination with the coupling coefficient. The invention provides a line sag measurement method and device based on traveling wave and temperature frequency wave velocity coupling, a medium and a product, the maximum sag position is locked through sag expression derivation, and calculation is completed in combination with the span, so that the maximum sag is obtained. The method can solve the problem of inaccurate sag calculation caused by the fact that an existing overhead conductor maximum sag calculation method does not consider the coupling influence of the temperature and the frequency on the traveling wave mode domain wave velocity and does not fully combine the geometrical characteristics of a conductor oblique parabola.

Description

Technical Field

[0001] This invention relates to the field of power transmission line technology, and in particular to a method, device, medium, and product for measuring line sag based on traveling wave and temperature-frequency wave velocity coupling. Background Technology

[0002] Calculating the maximum sag of overhead conductors is a key technology for ensuring the safe and stable operation of transmission lines. This technology can effectively prevent serious faults such as short circuits and line breaks caused by discharges or mechanical collisions between conductors and ground facilities or surrounding obstacles due to excessive sag. Simultaneously, it provides accurate scientific basis for transmission line design optimization, operation and maintenance inspection plan formulation, and dynamic capacity expansion strategy implementation, which is of great significance for reducing transmission line safety hazards, reducing operation and maintenance costs, and improving the stability and reliability of power grid supply. Existing methods for calculating the maximum sag of overhead conductors are diverse, mainly including manual inspection methods such as the equal-length method and the unequal-length method; mathematical model methods that simplify calculations and ensure accuracy based on parabolic and catenary models; sensor parameter detection methods that construct models by measuring conductor temperature, stress, and other data; and sag prediction methods that combine dynamic capacity expansion models of transmission lines with artificial intelligence algorithms.

[0003] However, existing methods for calculating the maximum sag of overhead conductors fail to consider the coupled effects of temperature and frequency on the wave velocity in the mode domain of traveling waves, and also do not fully incorporate the geometric characteristics of the conductor's oblique parabola, thus limiting the accuracy of the calculations. Specifically, manual inspection methods cannot perform real-time live monitoring and have significant errors; mathematical models do not incorporate actual operating conditions, resulting in low prediction accuracy; sensor parameter detection methods are complex to operate, pose risks during live installation, and have high monitoring costs; and intelligent algorithm prediction methods lack mechanistic model support, do not fit the specific operating conditions of the lines, and have weak generalization ability. Summary of the Invention

[0004] This invention provides a method, device, medium, and product for measuring line sag based on traveling wave and temperature-frequency wave velocity coupling, in order to solve the problem that existing methods for calculating the maximum sag of overhead conductors do not consider the coupling effect of temperature and frequency on the wave velocity of the traveling wave mode domain, and do not fully incorporate the geometric characteristics of the conductor's oblique parabola, resulting in inaccurate sag calculations.

[0005] To achieve the above objectives, this application provides a method for measuring line sag based on traveling wave and temperature-frequency wave velocity coupling, comprising: Traveling wave current signals are collected at the suspension points at both ends of the overhead conductor; Based on the traveling wave current signal, the mode domain wave velocity is calculated using the temperature-frequency wave velocity coupling change function; wherein, the temperature-frequency wave velocity coupling change function is established by converting the series impedance and parallel admittance of the transmission line in the frequency domain state into the mode domain state, and then combining the converted mode domain electrical parameters. Based on the time difference between the mode domain wave velocity and the time difference between the arrival of the traveling wave current signal at the two suspension points, and combined with the geometric characteristics of the oblique parabola, the coupling coefficient of the oblique parabola traveling wave of the conductor is calculated by curve integration. The sag expression for any point on the overhead conductor is established and differentiated. Combined with the span of the two suspension points and the coupling coefficient of the ballistic wave of the conductor, the maximum sag of the overhead conductor is measured.

[0006] This invention first collects traveling wave current signals at the suspension points at both ends of an overhead conductor, providing accurate raw data support for subsequent calculations and avoiding errors at the signal source. Addressing the issue of neglecting the coupling effect of temperature and frequency on the traveling wave velocity in the mode domain, this invention converts the series impedance and parallel admittance of the transmission line in the frequency domain into the mode domain state. Based on the converted mode domain electrical parameters, a temperature-frequency wave velocity coupling variation function is constructed. This ensures that the mode domain wave velocity calculation no longer considers a single factor in isolation, but fully integrates the interaction between temperature and frequency, accurately characterizing the dynamic impact of their coupling on the wave velocity. This solves the sag measurement deviation caused by wave velocity calculation distortion in traditional methods. Simultaneously, addressing the problem of insufficient integration of the conductor's parabolic geometry, this invention, based on the accurately acquired mode domain wave velocity and the time difference of the traveling wave arriving at both ends, solves for the conductor's parabolic traveling wave coupling coefficient through line integration combined with the parabolic geometry. This closely matches the actual suspension geometry of the conductor, avoiding the fragmentation of geometric characteristics in traditional simplified models. Finally, by establishing and differentiating the expression for the sag at any point on the overhead conductor, the location of the maximum sag can be accurately pinpointed. By combining the span between the two suspension points with the accurately calculated coupling coefficient of the ballistic wave of the conductor, the precise conversion from the sag distribution pattern to the specific maximum sag value can be achieved. This avoids the simplification bias of traditional methods throughout the process, systematically corrects errors from the source to the result, and effectively solves the problem of inaccurate calculations by existing methods.

[0007] Compared to existing technologies, this invention accurately calculates the mode domain wave velocity by constructing a temperature-frequency wave velocity coupling change function, thus overcoming the shortcomings of existing methods that ignore the influence of temperature and frequency on the coupling of mode domain wave velocity. At the same time, it combines the geometric characteristics of the oblique parabola with the traveling wave parameters to calculate the coupling coefficient, and uses the derivative of the sag expression to lock the position of the maximum sag and completes the calculation in combination with the span. By incorporating the actual geometry of the conductor, it corrects the measurement deviation and achieves an accurate solution for the maximum sag. Therefore, it can solve the problems of inaccurate sag calculation caused by existing methods for calculating the maximum sag of overhead conductors not considering the coupling influence of temperature and frequency on the mode domain wave velocity of traveling waves and not fully combining the geometric characteristics of the oblique parabola of the conductor.

[0008] As a preferred embodiment, the mode domain wave velocity is calculated based on the traveling wave current signal and the temperature-frequency wave velocity coupling change function, specifically: The traveling wave current signal is decomposed to obtain several modal components; The optimal modal component is extracted from the several modal components by calculating the envelope entropy; The energy spectrum of the optimal mode component is calculated based on the symmetric differential energy operator, the arrival time of the traveling wave is calibrated, and the effective signal segment is extracted. The center frequency is extracted from the effective signal segment, and the center frequency, the ambient temperature of the overhead conductor, and the conductor temperature are substituted into the temperature-frequency wave velocity coupling change function to calculate the mode domain wave velocity.

[0009] This optimized scheme solves the problems of susceptibility to interference and difficulty in extracting effective information from traveling wave current signals through closed-loop processing involving modal decomposition, optimal mode extraction, energy spectrum analysis, and center frequency substitution. Modal decomposition enables signal layering, and envelope entropy filtering accurately locates the optimal mode component containing core traveling wave information, eliminating interference from redundant noise modes and improving signal purity. The symmetric differential energy operator quantifies the intensity of signal changes, accurately calibrates the arrival time of the traveling wave, and extracts effective signal segments, avoiding the influence of invalid signals on subsequent calculations. By substituting the center frequency and temperature parameters into the coupling function, the modal domain wave velocity calculation is adapted to both frequency characteristics and temperature changes, overcoming the limitation of traditional wave velocity calculations that ignore multi-factor coupling. This provides high-precision basic data for subsequent sag calculations, improving the overall method's anti-interference capability and computational reliability.

[0010] As a preferred embodiment, the traveling wave current signal is decomposed to obtain several modal components, specifically: The noisy residual is iteratively updated according to the preset Gaussian white noise until the residual signal of the corresponding order shows a single trend or the number of extreme points is less than the preset value, and then the several modal components are output. In each iteration, empirical mode decomposition is performed on the Gaussian white noise, and noise components are extracted according to the decomposition order corresponding to the previous order. The noise components are added to the noisy residual of the previous order to obtain the noisy residual of the current order. In the first iteration, the noisy residual of the first order is calculated by taking the set mean of the first order intrinsic mode functions as the first order mode component and calculating it based on the traveling wave current signal and the first order mode component. The first order intrinsic mode functions are obtained by superimposing the Gaussian white noise on the traveling wave current signal and performing empirical mode decomposition on the generated noisy signal.

[0011] This preferred scheme achieves mode decomposition by iteratively updating the noisy residuals using Gaussian white noise. This effectively overcomes the technical shortcomings of traditional empirical mode decomposition, which is prone to mode aliasing, ensuring the independence and integrity of the modal components. The precise extraction and superposition of noise components during the iteration process gradually optimizes the residual signal morphology, making the output modal components more closely resemble the true characteristics of the traveling wave signal. In the first iteration, the initial residual is constructed based on the mean of the intrinsic mode function set, ensuring the initial accuracy of mode decomposition and avoiding the accumulation of initial errors. Through a dual criterion of the number of extreme points and their changing trends, it can flexibly adapt to traveling wave signals with different interference intensities, achieving adaptive adjustment of the decomposition process. This provides a high-quality data source for subsequent optimal mode extraction, further solidifying the signal processing foundation of the entire computational method.

[0012] As a preferred embodiment, the optimal modal component is extracted from the plurality of modal components by calculating the envelope entropy, specifically as follows: Calculate the envelope entropy of each of the modal components, and define the modal component with the maximum envelope entropy as the optimal modal component.

[0013] This preferred scheme uses envelope entropy as the criterion for selecting optimal modal components, achieving quantitative determination of mode selection and replacing traditional subjective experience-based selection methods, thus improving the objectivity and consistency of the selection results. Envelope entropy can accurately characterize the information complexity of modal components; the modal component corresponding to the maximum envelope entropy can retain the core features of the traveling wave signal to the maximum extent, while suppressing background noise and irrelevant interference information. This method is simple to operate and computationally efficient, requiring no complex feature matching algorithms, and can quickly lock the target mode from multiple sets of modal components, shortening the signal processing cycle. By accurately selecting the optimal mode, the interference of invalid modes on subsequent energy spectrum analysis and time calibration is reduced, ensuring the accuracy of traveling wave feature extraction and providing accurate input for mode domain wave velocity calculation.

[0014] As a preferred embodiment, the energy spectrum of the optimal mode component is calculated based on the symmetric differential energy operator, the arrival time of the traveling wave is calibrated, and the effective signal segment is extracted, specifically as follows: Based on the symmetric differential energy operator, the signal energy of the optimal mode component is quantified by capturing the signal change intensity of adjacent sampling points in the discrete signal, and several energy values ​​are obtained. Establish the mapping relationship between the aforementioned energy values ​​and the corresponding sampling times, and generate the energy spectrum of the symmetric differential energy operator for the optimal modal components; The first energy mutation peak is extracted from the energy spectrum of the symmetric differential energy operator, and the sampling time corresponding to the first energy mutation peak is marked as the location time when the fault traveling wave first arrives at the monitoring terminal; In the discrete signal sequence of the optimal mode components, the traveling wave signal pulse interval corresponding to the positioning time is extracted to obtain the effective signal segment.

[0015] This preferred scheme, based on the energy spectrum analysis method of symmetric differential energy operators, can keenly capture the intensity of local changes in discrete signals and accurately quantify the energy distribution of optimal mode components, solving the problems of ambiguous arrival time calibration and inaccurate effective signal segment extraction in traditional traveling wave methods. The precise mapping between the first energy mutation peak and the arrival time of the traveling wave enables millisecond-level calibration of the first arrival time, improving the measurement accuracy of time parameters. Targeted truncation of the traveling wave signal pulse interval can eliminate interference from the leading and trailing edges, retaining the core effective signal and reducing errors in subsequent center frequency extraction. This method eliminates the need for complex filtering, improving processing efficiency while ensuring signal integrity, providing accurate frequency and time parameters for mode domain wave velocity calculation, and indirectly improving the overall accuracy of sag calculation.

[0016] As a preferred embodiment, the temperature-frequency wave velocity coupling change function is established by converting the series impedance and parallel admittance of the transmission line in the frequency domain state into the mode domain state, and then combining the converted mode domain electrical parameters, specifically: By using the Karenbauer transform, the series impedance and parallel admittance of the overhead conductor in the frequency domain state of the transmission line are converted into the modal domain state to obtain the modal domain electrical parameters; The traveling wave attenuation constant and phase constant are calculated based on the electrical parameters of the mode domain, and the curve equations of frequency and wave velocity are established based on the traveling wave attenuation constant and the phase constant. Substituting the electrical parameters of the overhead conductor's transmission line distribution into the frequency and wave velocity curve equations, the temperature-frequency-wave velocity coupling variation function is obtained.

[0017] This preferred scheme converts frequency-domain electrical parameters into mode-domain states using the Karenbauer transform, effectively eliminating coupling interference between different modes and making the electrical parameters more closely match the actual propagation characteristics of traveling waves, thus improving the accuracy of parameter characterization. Based on the attenuation constant and phase constant, a curve equation for frequency and wave velocity is established, accurately depicting the influence of frequency changes on the propagation speed of traveling waves, overcoming the limitation of traditional wave velocity calculations using fixed values. By substituting the distributed electrical parameters of the transmission line into a coupling function, a quantitative characterization of the relationship between temperature, frequency, and wave velocity is achieved. The calculated wave velocity value can be dynamically adjusted according to actual operating conditions, adapting to line scenarios under different temperature and frequency conditions. This function construction method is logically rigorous and physically meaningful, providing theoretical support for the accurate calculation of mode-domain wave velocity and improving the method's adaptability to complex operating conditions.

[0018] As a preferred embodiment, the distributed electrical parameters of the transmission line include distributed impedance, distributed conductance, and distributed inductance.

[0019] This preferred scheme clearly defines the specific composition of the distributed electrical parameters of the transmission line, providing a clear parameter input basis for establishing the temperature-frequency-wave velocity coupling variation function and avoiding function derivation errors caused by ambiguity in parameter ranges. Distributed impedance, conductance, and inductance are core parameters affecting the traveling wave propagation characteristics; their accurate substitution ensures that the coupling function accurately reflects the relationship between the line's electrical characteristics and wave velocity. This limitation makes the parameter measurement and substitution process more operable, facilitating the accurate acquisition of required parameters in practical engineering applications and reducing the difficulty of function construction.

[0020] As a preferred embodiment, based on the time difference between the mode domain wave velocity and the arrival time of the traveling wave current signal at the two suspension points, and combined with the geometric characteristics of the oblique parabola, the coupling coefficient of the oblique parabolic traveling wave of the conductor is calculated by curve integration, specifically: A coordinate system is constructed with the lowest point of the overhead conductor as the origin. The equation of the oblique parabola of the conductor is established based on the force balance relationship of the conductor segment, combined with the angle between the line connecting the two suspension points and the horizontal direction. Based on the propagation path shape of the overhead conductor, the time difference between the mode domain wave velocity and the traveling wave current signal reaching the two suspension points is calculated by curve integration, and the equation of the conductor's oblique parabola is established to establish the adaptive calculation relationship between the coordinates of the two suspension points, thus obtaining the comprehensive calculation formula. Substituting the span between the two suspension points, the modal wave velocity, and the time difference between the arrival of the traveling wave current signal at the two suspension points into the comprehensive calculation formula, the coupling coefficient of the oblique projectile traveling wave of the conductor is calculated.

[0021] This preferred scheme constructs a coordinate system with the lowest point of the conductor as the origin, and establishes equations based on the geometric characteristics of the oblique parabola. This accurately matches the actual suspension shape of the overhead conductor, overcoming geometric model errors caused by traditional straight-line approximations or horizontal parabolic assumptions. By using line integrals to organically combine the modal domain wave velocity, time difference, and conductor geometry, it achieves coupled calculation of electrical and geometric parameters, breaking through the limitation of traditional sag calculations that separate these two types of parameters. The adaptive calculation relationship established by the simultaneous equations fully considers actual working conditions such as the angle between the two suspension points and the span, making the calculation of the conductor's oblique parabolic wave coupling coefficient more closely aligned with engineering practice. This method improves the calculation accuracy of the coupling coefficient, providing crucial support for the accurate solution of maximum sag, and is particularly suitable for complex line scenarios with non-horizontal suspension, expanding the application scope of the method.

[0022] This application also provides a line sag measurement device based on traveling wave and temperature frequency wave velocity coupling, including a signal module, a wave velocity module, a coefficient module and a sag module; The signal module is used to collect traveling wave current signals at the suspension points at both ends of the overhead conductor. The wave velocity module is used to calculate the mode domain wave velocity based on the traveling wave current signal and the temperature-frequency wave velocity coupling change function; wherein, the temperature-frequency wave velocity coupling change function is established by converting the series impedance and parallel admittance of the transmission line in the frequency domain state into the mode domain state and combining the converted mode domain electrical parameters. The coefficient module is used to calculate the conductor's oblique parabolic traveling wave coupling coefficient by performing curve integration based on the mode domain wave velocity and the time difference between the arrival of the traveling wave current signal at the two suspension points, combined with the geometric characteristics of the oblique parabola. The sag module is used to establish the sag expression for any point on the overhead conductor and perform differentiation. Combined with the span of the two suspension points and the coupling coefficient of the ballistic wave of the conductor, the maximum sag of the overhead conductor is measured.

[0023] This application also provides a storage medium storing a computer program, which is called and executed by a computer to implement the line sag measurement method based on traveling wave and temperature frequency wave velocity coupling as described above.

[0024] This application also provides a computer program product, including a computer program or instructions, which, when executed by a communication device, implements the line sag measurement method based on traveling wave and temperature-frequency wave velocity coupling as described above. Attached Figure Description

[0025] Figure 1 This is a schematic flowchart of a line sag measurement method based on traveling wave and temperature-frequency wave velocity coupling provided in an embodiment of this application; Figure 2 This is a schematic diagram of the CEEMDAN operating principle provided in the embodiments of this application; Figure 3 This application provides a traveling wave current signal and its mode function diagram after decomposition using the CEEMDAN algorithm. Figure 4 This is the SDEO energy spectrum of the mode function IMF1 provided in the embodiments of this application; Figure 5 This is an example of the spectrum of the optimal modal component IMF1 obtained by envelope entropy filtering according to the embodiments of this application; Figure 6 This is a schematic diagram of a parabolic guide rail model when the suspension points are at different heights, provided in an embodiment of this application. Figure 7 This is the overall flowchart provided in the embodiments of this application; Figure 8 This is a schematic diagram of a line sag measurement device based on traveling wave and temperature-frequency wave velocity coupling provided in an embodiment of this application. Detailed Implementation

[0026] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0027] In the description of this application, unless otherwise stated, "a number" means two or more.

[0028] The present application provides a method for measuring line sag based on the coupling of traveling wave and temperature frequency wave velocity. This method aims to solve the defects of traditional methods in the existing overhead conductor sag monitoring and calculation, such as poor real-time performance, low accuracy, complex operation, high cost, or weak generalization ability. At the same time, it overcomes the technical problems of relying on manual experience to determine the traveling wave velocity, which is not accurate enough, and the traditional sag calculation parameters being complicated and having low accuracy.

[0029] Example 1: Please see Figure 1 The embodiments of this application provide a method for measuring line sag based on traveling wave and temperature-frequency wave velocity coupling, including S1~S4, and the specific implementation steps are as follows: S1. Collect traveling wave current signals at the suspension points at both ends of the overhead conductor.

[0030] Step S1 in this embodiment of the application is specifically as follows: At the suspension points at both ends of the overhead conductor, the traveling wave current signal of the line is collected in real time through detection terminals. x ( t Simultaneously, the ambient temperature of the line and the temperature of the conductor itself are collected. Among them, "overhead conductor" refers to the core carrier of the overhead transmission line used for power transmission and requiring sag monitoring, and is also the main transmission medium for traveling wave current signals; "suspension points at both ends" refers to the suspension positions of the towers at both ends of the overhead conductor used for support and fixation (corresponding to points A and B in the subsequent conductor inclined parabolic model), and is also the key location for installing detection terminals to accurately collect traveling wave current signals.

[0031] S2. The mode domain wave velocity is calculated based on the traveling wave current signal and the temperature-frequency wave velocity coupling change function. The temperature-frequency wave velocity coupling change function is established by converting the series impedance and parallel admittance of the transmission line in the frequency domain state into the mode domain state and then combining the converted mode domain electrical parameters.

[0032] Step S2 in this embodiment includes S2.1 to S2.5; wherein, S2.1 is the process of generating several modal components based on the traveling wave current signal, S2.2 is the process of determining the optimal modal component from the several modal components, S2.3 is the process of obtaining the effective signal segment based on the optimal modal component, S2.4 is the process of establishing the temperature-frequency wave velocity coupling change function, and S2.5 is the process of generating the mode domain wave velocity based on the effective signal segment and the temperature-frequency wave velocity coupling change function, specifically as follows: S2.1. Iteratively update the noisy residuals according to the preset Gaussian white noise until the residual signal of the corresponding order shows a single trend or the number of extreme points is less than the preset value, and output several modal components; wherein, in each iteration, empirical mode decomposition is performed on the Gaussian white noise, and the noise component is extracted according to the decomposition order corresponding to the previous order. The noise component is added to the noisy residual of the previous order to obtain the noisy residual of the current order; in the first iteration, the noisy residual of the first order is obtained by taking the set mean of the first order intrinsic mode functions as the first order modal component, and calculating it according to the traveling wave current signal and the first order modal component. The first order intrinsic mode function is obtained by superimposing Gaussian white noise on the traveling wave current signal and performing empirical mode decomposition on the generated noisy signal.

[0033] The specific iterative process is as follows: Step 1: Extract the first IMF component (IMF1). First, set the ensemble average number m and the Gaussian white noise required for the corresponding m trials. n m ( t ), to the original traveling wave current signal x ( t The Gaussian white noise is repeatedly superimposed on the signal, with the number of superpositions equal to the ensemble average number m, thus generating m groups of noisy signals. Empirical Mode Decomposition (EMD) is performed on each group of noisy signals to extract the first-order eigenmode functions obtained from each decomposition. These m first-order eigenmode functions are then... The result of ensemble averaging is the first-order modal component of the algorithm. IMF 1( t This refers to the first modal component; simultaneously, it is based on the traveling wave current signal. x ( t ) and first-order modal components IMF 1( t The first-order residual was calculated. r 1( t ), ; k-th order: Extract the k-th order IMF component (IMF) k (k≥2). Entering the recursive extraction stage, to obtain the k-th modal component, it is necessary to first obtain the previous order residual. r k-1 ( tInjecting specially modulated adaptive noise into the Gaussian white noise—this noise is achieved by modulating Gaussian white noise. n m ( t The process involves performing EMD decomposition and extracting the (k-1)th order IMF component to achieve precise matching between the noise frequency band and the current order residual frequency band characteristics. This adaptive noise process is then repeated multiple times, with each generated noisy residual undergoing EMD decomposition and first-order IMF extraction. The average of all extracted first-order IMFs is then calculated to finally obtain the k-th order modal component. IMF k ( t Simultaneously update the residuals to... ; Repeat the above recursive extraction process until the obtained residuals show a monotonically changing trend or the number of extreme points is insufficient, then stop the modal component extraction; finally, extract all the extracted IMFn modal components (IMF1, IMF2, ..., IMFn). k (where k is the total order at which iteration stops) constitutes several modal components.

[0034] For examples of this application, please refer to [link / reference]. Figure 2 , 3 , Figure 2 This is a schematic diagram of the CEEMDAN operating principle provided in the embodiment of this application, which shows the entire process logic of obtaining several modal components by setting the set average degree and Gaussian white noise, adding noise to the original signal and performing EMD decomposition, recursively extracting IMF components of each order, updating the residuals until the residuals are monotonic or there are insufficient extreme points. Figure 3 This application provides a terminal-measured traveling wave current signal and a mode function graph after decomposition by the CEEMDAN algorithm. It shows the waveform of the original traveling wave current signal collected by the detection terminal at a sampling rate of 1MHz (single sampling point time is 1μs), and the waveform comparison of multiple independent mode components (IMFn) obtained after decomposition by the CEEMDAN algorithm. It intuitively presents the decomposition effect of the algorithm on the traveling wave current signal.

[0035] In this embodiment, S2.1, mode decomposition is achieved by iteratively updating the noisy residual using Gaussian white noise. This effectively overcomes the technical defect of traditional empirical mode decomposition, which is prone to mode aliasing, ensuring the independence and integrity of the mode components. The precise extraction and superposition of noise components during the iteration process gradually optimizes the residual signal morphology, making the output mode components more closely resemble the true characteristics of the traveling wave signal. In the first iteration, the initial residual is constructed based on the mean of the intrinsic mode function set, ensuring the initial accuracy of mode decomposition and avoiding the accumulation of initial errors. Through the dual criteria of the number of extreme points and their changing trends, it can flexibly adapt to traveling wave signals with different interference intensities, achieving adaptive adjustment of the decomposition process. This provides a high-quality data source for subsequent optimal mode extraction, further solidifying the signal processing foundation of the entire calculation method.

[0036] S2.2 Calculate the envelope entropy of all modal components in several modal components respectively, and define the modal component corresponding to the maximum envelope entropy as the optimal modal component.

[0037] To apply the embodiments of this application, please refer to Table 1. Table 1 is a table comparing the envelope entropy of each modal component function provided in the embodiments of this application, clearly showing the specific envelope entropy values ​​corresponding to core modal components such as IMF1, IMF2, and IMF3. Thus, it can be clearly identified that IMF1, with the largest envelope entropy, is the optimal modal component. This example verifies the feasibility of selecting the optimal modal component through envelope entropy. Furthermore, the selected IMF1 can provide crucial data support for the subsequent accurate calibration of the arrival time of the fault traveling wave using the symmetric differential energy operator, fully demonstrating the practicality and effectiveness of this technical solution.

[0038] Table 1. Envelope Entropy Comparison Table for Each Modal Component Function In this embodiment, S2.2 uses envelope entropy as the criterion for selecting the optimal modal component, realizing a quantitative determination of modal selection, replacing the traditional subjective experience-based selection method, and improving the objectivity and consistency of the selection results. Envelope entropy can accurately characterize the information complexity of modal components. The modal component corresponding to the maximum envelope entropy can retain the core features of the traveling wave signal to the maximum extent, while suppressing background noise and irrelevant interference information. This method is simple to operate and has high computational efficiency. It does not require complex feature matching algorithms and can quickly lock the target mode from multiple sets of modal components, shortening the signal processing cycle. By accurately selecting the optimal mode, the interference of invalid modes on subsequent energy spectrum analysis and time calibration is reduced, ensuring the accuracy of traveling wave feature extraction and providing accurate input for mode domain wave velocity calculation.

[0039] S2.3. The calculation formula based on the Symmetric Differential Energy Operator (SDEO) is used to capture the signal change intensity of adjacent sampling points in the discrete signal and quantify the signal energy of the optimal mode component. Because the arrival of the fault traveling wave will cause a sudden change in the signal, the difference between the signal values ​​of adjacent sampling points will increase significantly. Based on this characteristic, the operator can quantize the signal change amplitude into a specific energy value and finally output several energy values ​​that correspond one-to-one with each sampling time. A mapping relationship between several energy values ​​and their corresponding sampling times is established. Through the correlation matching of "energy value - sampling time," the symmetric differential energy operator (SDEO) energy spectrum of the optimal modal components is generated, such as... Figure 4 As shown; The first energy mutation peak is extracted from the energy spectrum of the symmetric differential energy operator. This peak is a direct manifestation of the signal mutation caused by the fault traveling wave. Therefore, the sampling time corresponding to the first energy mutation peak is marked as the location time when the fault traveling wave first arrives at the monitoring terminal. In the discrete signal sequence of the optimal mode components, the traveling wave signal pulse interval corresponding to the above positioning time is located and extracted. Irrelevant noise interference is filtered out to obtain the effective signal segment.

[0040] The formula for calculating the symmetric difference energy operator is as follows: (Equation 1); in, x ( n ) represents the corresponding discrete sampled signal; n +1、 n , n -1 represents the current sampling point. n The next point, the current point, and the previous point form a three-point symmetrical window; ϕ [·] represents the energy operator; To x ( n The estimated value is obtained by applying the energy operator and then performing symmetric difference smoothing.

[0041] For examples of this application, please refer to [link / reference]. Figure 4 , Figure 4 The SDEO energy spectrum of the modal function IMF1 provided in this application embodiment shows the corresponding distribution relationship between the energy value and the sampling time after the optimal modal component IMF1 is processed by the symmetric differential energy operator. It clearly shows the trend of energy change over time, highlighting the first energy mutation peak and the corresponding horizontal axis sampling time, which intuitively reflects the key time node when the fault traveling wave first arrives at the monitoring terminal.

[0042] This embodiment, S2.3, utilizes an energy spectrum analysis method based on a symmetric differential energy operator. This method can keenly capture the intensity of local changes in discrete signals and accurately quantify the energy distribution of optimal mode components, solving the problems of ambiguous arrival time calibration and inaccurate extraction of effective signal segments in traditional traveling wave methods. The precise mapping between the first energy mutation peak and the arrival time of the traveling wave enables millisecond-level calibration of the first arrival time, improving the measurement accuracy of time parameters. Targeted extraction of the traveling wave signal pulse interval can eliminate interference from the leading and trailing edges, retaining the core effective signal and reducing errors in subsequent center frequency extraction. This method eliminates the need for complex filtering, improving processing efficiency while ensuring signal integrity. It provides accurate frequency and time parameters for mode domain wave velocity calculation, indirectly improving the overall accuracy of sag calculation.

[0043] S2.4. By using the Karenbauer transformation, the series impedance and parallel admittance of the overhead conductor in the frequency domain state of the transmission line are converted into the modal domain state to obtain the modal domain electrical parameters. The traveling wave attenuation constant and phase constant are calculated based on the electrical parameters of the mode domain, and the curve equations of frequency and wave velocity are established based on the traveling wave attenuation constant and phase constant. Substituting the distributed electrical parameters of overhead transmission lines into the frequency and wave velocity curve equations yields the temperature-frequency-wave velocity coupling variation function. The distributed electrical parameters of the transmission lines include conductor distributed impedance, conductor distributed conductance, conductor distributed inductance, and conductor distributed capacitance.

[0044] The specific process for establishing the temperature-frequency wave velocity coupling change function is as follows: (1) Establishment of electrical parameters of transmission line distribution: The four major distribution parameters of transmission line are calculated accurately, and temperature-related influencing factors are included in each parameter.

[0045] ① Distributed impedance of conductors: (Equation 2); in, α 20 The temperature coefficient of the conductor material is expressed as 20℃, with 0.00403℃ for aluminum wire. -1 The steel wire temperature is 0.0011℃. -1 ; t c For conductor temperature; skin effect coefficient k The value is 0.0025. R 20 This is the DC resistance per unit length of the conductor at a standard reference temperature of 20°C.

[0046] ② Conductivity distribution in the conductor: (Equation 3); in, U Represented as transmission line voltage; δ =(3.92+ b ) / (273+ T ) represents the relative density of air. b , T These are atmospheric pressure and ambient temperature, respectively. r The radius of the conductor; D eq For the geometric distance of the conductors; for the surface smoothness coefficient of the conductors. m 1. The value ranges from 0.87 to 0.83; meteorological coefficient. m 2 is set to 1, and for severe conditions, the value is 0.8; Δ S g This represents the total power of the corona loss per unit length of a three-phase transmission line as measured in practice.

[0047] ③ Distributed inductance of the conductor: For an overhead lossless single conductor, assuming the ground is an ideal conductor, the distributed inductance of the conductor is: (Equation 4); in, h c Expressed as the average height of the conductor above the ground; free permeability μ 0 = 4π × 10 -7 H / m; relative permeability μ r = μ r0 (1+ α Δ T ), α The temperature coefficient of relative permeability is 1×10⁻⁶. -5 ℃ -1 , μ r0 denoted as the initial relative permeability.

[0048] ④ Distributed capacitance of conductors: For an overhead lossless single conductor, assuming the ground is an ideal conductor, the conductor's distributed capacitance is: (Equation 5); Among them, the vacuum permittivity ε 0 = 1 / (4π × 9 × 10) 9 F / m; relative permittivity ε r =1+ Ap t / T + ρ ω tB + ρ ω C / T ,p t Atmospheric pressure, ρ ω The absolute humidity of the air. A =1.552×10 -6 km 2 / N, B =3.456×10 -3 km 3 / kg, C =-76.57×10 -6 m 3 / kg.

[0049] (2) Modal domain transformation and parameter derivation: ① By using the Karrenbauer transformation (Equation 6, the core of which is the transformation form of decoupling the frequency domain parameters of the three-phase system to the mode domain), the series impedance matrix and parallel admittance matrix of the overhead conductor in the frequency domain state of the transmission line are converted into three independent mode domain states (corresponding to three moduli m=0, 1, 2); each modulus corresponds to the mode domain impedance Z. m (ω) and admittance Y m (ω), i.e., Z m and Y m Further disassembly yields the modulus resistance R per unit length. m (ω), Inductance L m (ω), conductivity G m (ω), capacitance C m (ω) constitutes the mode domain parameters; where m=0 corresponds to the zero-mode impedance Z0(ω) and zero-mode admittance Y0(ω), and m=1 and m=2 correspond to the impedances Z1(ω) and Z2(ω) and admittances Y1(ω) and Y2(ω) of the two line modes, respectively. Equation 6 is as follows: ; (Formula 6); Where m = 0, 1, 2; R m ( ω ), L m ( ω ), G m ( ω )and C m ( ω The values ​​of modulus resistance, inductance, conductance, and capacitance per unit length of the transmission line are all functions of frequency. Z 1( ω ), Z 2( ω )and Y 1( ω ), Y 2( ω ) represent the line-mode impedance and admittance, respectively. Z 0( ω )and Y 0( ω ) represent zero-mode impedance and admittance, respectively; Z is the series impedance matrix per unit length of the three-phase line in the frequency domain, Y is the parallel admittance matrix per unit length of the three-phase line in the frequency domain, S is the Karrenbauer transform matrix, and Q is the inverse Karrenbauer transform matrix.

[0050] ② Considering the traveling wave dispersion effect, for the three independent moduli (m=0,1,2) obtained after the Karrenbauer transformation, based on the unit length electrical parameters of the modulus corresponding to each modulus in the modulus domain parameters ( R m ( ω ), L m ( ω ), G m ( ω )and C m ( ω The mode domain impedance corresponding to each modulus is calculated using Equation 7. Z cm and traveling wave transmission coefficient γ m Equation 7 is: ; (Equation 7); in, α m ( ω )and β m ( ω These are the traveling wave attenuation constant and traveling wave phase constant in the mode domain, respectively. β m ( ω As shown in Equation 8: (Equation 8); ③Therefore, based on the angular frequency of the traveling wave signal ω and traveling wave phase constant β m ( ω The frequency-wave speed curve equation (the curve equation of frequency and wave speed) is derived, as shown in Equation 9: (Equation 9); (3) Construction of curve equation and coupling function: Substitute the expressions of the four major distributed parameters of the transmission line (Equation 2-5) into the frequency-wave velocity curve equation (Equation 9) to finally construct the temperature-frequency-wave velocity coupling change relationship function, that is, the temperature-frequency-wave velocity coupling change function.

[0051] In this embodiment, S2.4 converts frequency-domain electrical parameters into mode-domain states using the Karenbauer transform, effectively eliminating coupling interference between different modes and making the electrical parameters more closely match the actual propagation characteristics of traveling waves, thus improving the accuracy of parameter characterization. A frequency-wave velocity curve equation is established based on the attenuation constant and phase constant, accurately depicting the influence of frequency changes on the propagation speed of traveling waves, overcoming the limitation of traditional wave velocity calculations using fixed values. By substituting the distributed electrical parameters of the transmission line into a coupling function, a quantitative characterization of the relationship between temperature, frequency, and wave velocity is achieved. The calculated wave velocity value can be dynamically adjusted according to actual operating conditions, adapting to line scenarios under different temperature and frequency conditions. This function construction method is logically rigorous and has clear physical meaning, providing theoretical support for the accurate calculation of mode-domain wave velocity and improving the method's adaptability to complex operating conditions. Furthermore, clarifying the specific composition of the distributed electrical parameters of transmission lines provides a clear parameter input basis for establishing the temperature-frequency-wave velocity coupling variation function, avoiding function derivation errors caused by ambiguity in parameter ranges. Distributed impedance, conductance, and inductance are core parameters affecting the propagation characteristics of traveling waves; their accurate substitution ensures that the coupling function accurately reflects the relationship between the line's electrical characteristics and wave velocity. This limitation makes the parameter measurement and substitution process more operable, facilitating the accurate acquisition of required parameters in practical engineering applications and reducing the difficulty of function construction.

[0052] S2.5 Extract the center frequency from the effective signal segment, and substitute the center frequency, ambient temperature of the overhead conductor, and conductor temperature into the temperature-frequency wave velocity coupling variation function to calculate the mode domain wave velocity. v .

[0053] For examples of this application, please refer to [link / reference]. Figure 5 , Figure 5 This is an example spectrum diagram of the optimal mode component IMF1 obtained by envelope entropy filtering according to an embodiment of this application. The diagram is drawn based on the measured data of the effective signal segment extracted above, and clearly presents the frequency distribution law of the effective signal segment of the optimal mode component in the form of an example, intuitively marking the example value of the core center frequency of the signal segment.

[0054] This embodiment S2 solves the problems of traveling wave current signals being susceptible to interference and difficult to extract effective information through closed-loop processing of mode decomposition, optimal mode extraction, energy spectrum analysis, and center frequency substitution. Mode decomposition enables signal layering, and envelope entropy screening can accurately locate the optimal mode component containing core traveling wave information, eliminate interference from redundant noise modes, and improve signal purity. The symmetric differential energy operator can quantify the intensity of signal changes, accurately calibrate the arrival time of the traveling wave, and extract the effective signal segment, avoiding the influence of invalid signals on subsequent calculations. Substituting the center frequency and temperature parameters into the coupling function allows the mode domain wave velocity calculation to simultaneously adapt to frequency characteristics and temperature changes, breaking through the limitation of traditional wave velocity calculation ignoring multi-factor coupling, providing high-precision basic data for subsequent sag calculations, and improving the overall method's anti-interference capability and computational reliability.

[0055] S3. Based on the time difference between the mode domain wave velocity and the time difference between the arrival of the traveling wave current signal at both suspension points, and combined with the geometric characteristics of the oblique parabola, the coupling coefficient of the oblique parabolic traveling wave of the conductor is calculated by curve integration.

[0056] Step S3 in this embodiment includes S3.1 to S3.2; wherein, S3.1 is the process of establishing the equation of the traverse parabola, and S3.2 is the process of generating the coupling coefficient of the traverse parabolic traveling wave based on the mode domain wave velocity and the equation of the traverse parabola, specifically as follows: S3.1 For the application of the embodiments of this application, please refer to Figure 6 , Figure 6 This is a schematic diagram of a parabolic traverse model of a conductor when the suspension points are at different heights, as provided in the embodiments of this application. The following is in conjunction with... Figure 6 The method for establishing the equation of the oblique parabola of a traverse is explained in detail: A coordinate system is constructed with the lowest point of the overhead conductor as the origin. The equation of the oblique parabola of the conductor is established based on the force balance relationship of the conductor segment, combined with the angle between the line connecting the two suspension points and the horizontal direction. Construct a dedicated coordinate system with the lowest point C of the overhead conductor as the origin: In this coordinate system, points A and B correspond to the left and right suspension points of the conductor, and the span between the two suspension points is... l The height difference is h The angle formed by the line connecting them and the horizontal direction is φ Combining the angle between the line connecting the two suspension points and the horizontal direction, and based on the force balance relationship of the conductor segment under actual working conditions, the corresponding equation for the inclined parabola of the conductor is derived through integral calculation, as shown in Equation 10: (Equation 10); in, σ 0 represents the stress per unit area at the origin. g This refers to the conductor load per unit area.

[0057] S3.2. Based on the propagation path morphology of overhead conductors, the mode domain wave velocity is...v The time difference Δ between the traveling wave current signal and the two suspension points t Line integral calculations are performed, and the equations of the traverse parabola are simultaneously established to create a suitable calculation relationship between the coordinates of the two corresponding points at the two suspension points, resulting in a comprehensive calculation formula. The span and mode domain wave velocity at the two suspension points are then considered. v The time difference Δ between the traveling wave current signal and the two suspension points. t Substituting into the comprehensive calculation formula, the coupling coefficient of the duct oblique projectile traveling wave is calculated. k .

[0058] Among them, the coupling coefficient of the oblique projectile wave of the conductor k The specific calculation method is as follows: Based on the parabolic propagation path of the overhead conductor, and using the traveling wave current signal corresponding to the line interference signal collected by the suspension points at both ends A and B as a basis, the mode domain wave velocity is accurately obtained through the aforementioned "traveling wave establishment" process. v and the time difference Δ between the traveling wave and points A and B t ; A line integral is performed along the propagation path of the traveling wave. Simultaneously, the equations for the oblique parabola of the traverse are established to construct a calculation relationship suitable for the coordinates of the suspension points at points A and B. Finally, a comprehensive calculation formula is derived. The specific process is as follows: ① Based on the above information v Given Δt, by performing line integral operations and simultaneously solving the equation of the oblique parabola of the conductor, the oblique parabola-traveling wave relationship function is established, as shown in Equation 11: (Equation 11); in, x A Here are the horizontal coordinates of the left suspension point A of the conductor. x B Here are the horizontal coordinates of the right suspension point B of the conductor. y For overhead conductors at any horizontal coordinate x The vertical coordinate value at that location.

[0059] ② To simplify the calculation, let k Equal to the target representation (Equation 12), combined with the coordinate correspondence between points A and B in the traverse parabola model (Equation 13), and substituted into Equation 11, we obtain the comprehensive calculation formula for the coupling coefficient k (Equation 14); the calculation formulas are shown below: (Equation 12); (Equation 13); (Equation 14); Finally, the known spans of the suspension points at both ends A and B are... l Height difference hAnd the measured arrival time difference Δ of the traveling wave t Calculated mode domain wave velocity v By substituting into the comprehensive calculation formula, the coupling coefficient of the oblique projectile wave of the conductor can be accurately solved. k .

[0060] In this embodiment, S3.2, a coordinate system is constructed with the lowest point of the conductor as the origin. Equations are established based on the geometric characteristics of the parabolic curve, accurately reflecting the actual suspension shape of the overhead conductor and overcoming geometric model errors caused by traditional straight-line approximations or horizontal parabolic assumptions. By using line integrals to organically combine the modal wave velocity, time difference, and conductor geometry, coupled calculations of electrical and geometric parameters are achieved, overcoming the limitation of traditional sag calculations that separate these two types of parameters. The adaptive calculation relationship established by the simultaneous equations fully considers actual working conditions such as the angle between the two suspension points and the span, making the calculation of the conductor's parabolic traveling wave coupling coefficient more closely aligned with engineering practice. This method improves the accuracy of the coupling coefficient calculation, providing crucial support for the accurate solution of the maximum sag, and is particularly suitable for complex line scenarios with non-horizontal suspension, expanding the application scope of the method.

[0061] S4. Establish the sag expression for any point on the overhead conductor and differentiate it. Combine the span of the suspension points at both ends and the coupling coefficient of the ballistic wave of the conductor to measure the maximum sag of the overhead conductor.

[0062] Step S4 in this embodiment of the application is specifically as follows: based on Figure 6 The parabolic model of the conductor shown first establishes the sag relationship expression at any point on the overhead conductor (Equation 15). To accurately obtain the maximum sag of the line, the derivative expression of the sag relationship is derived to obtain the derivative expression (Equation 16). By analyzing the derivative results of Equation 16, it can be seen that when x = h / (2 kl When the sag reaches its maximum value, the coupling coefficient of the oblique projectile wave calculated above is applied. k Substituting the known span *l* between the two suspension points into the extreme condition, and combining it with Equation 17, the maximum sag of the overhead conductor can be accurately calculated. f xmax .

[0063] The calculation formulas are shown below: (Equation 15); (Equation 16); (Equation 17); Overall, this embodiment has the following beneficial effects: This invention first collects traveling wave current signals at the suspension points at both ends of an overhead conductor, providing accurate raw data support for subsequent calculations and avoiding errors at the signal source. Addressing the issue of neglecting the coupling effect of temperature and frequency on the traveling wave velocity in the mode domain, this invention converts the series impedance and parallel admittance of the transmission line in the frequency domain into the mode domain state. Based on the converted mode domain electrical parameters, a temperature-frequency wave velocity coupling variation function is constructed. This ensures that the mode domain wave velocity calculation no longer considers a single factor in isolation, but fully integrates the interaction between temperature and frequency, accurately characterizing the dynamic impact of their coupling on the wave velocity. This solves the sag measurement deviation caused by wave velocity calculation distortion in traditional methods. Simultaneously, addressing the problem of insufficient integration of the conductor's parabolic geometry, this invention, based on the accurately acquired mode domain wave velocity and the time difference of the traveling wave arriving at both ends, solves for the conductor's parabolic traveling wave coupling coefficient through line integration combined with the parabolic geometry. This closely matches the actual suspension geometry of the conductor, avoiding the fragmentation of geometric characteristics in traditional simplified models. Finally, by establishing and differentiating the expression for the sag at any point on the overhead conductor, the location of the maximum sag can be accurately determined. By combining the span of the suspension points at both ends with the accurately solved coupling coefficient of the oblique projectile wave of the conductor, the accurate transformation from the sag distribution law to the specific maximum sag value can be achieved. This avoids the simplification bias of traditional methods throughout the process, systematically corrects errors from the source to the result, and effectively solves the problem of inaccurate calculations by existing methods. In summary, the calculation parameters of this invention are simplified, and the model construction is concise and easy to understand, thus lowering the threshold for practical application. The introduced traveling wave detection technology has high accuracy, is less affected by environmental factors, and is basically unaffected by transition resistance and neutral grounding method, effectively reducing the sources of error in sag calculation. It can significantly improve the accuracy of overhead conductor sag solution and provide reliable support for real-time monitoring of transmission line sag.

[0064] For examples of this application, please refer to [link / reference]. Figure 7 , Figure 7 This is the overall flowchart provided in the embodiments of this application, which shows the core process of real-time monitoring of line sag of the present invention. With "traveling wave establishment" and "model construction" as the two key modules, it clearly shows the complete technical path from the acquisition, processing and accurate acquisition of traveling wave current signals, to the construction of a model by combining the characteristics of oblique parabolic curves, and finally solving for the maximum sag.

[0065] Example 2: Please see Figure 8 The embodiments of this application provide a line sag measurement device based on traveling wave and temperature frequency wave velocity coupling, including a signal module 10, a wave velocity module 20, a coefficient module 30 and a sag module 40. Among them, the signal module 10 is used to collect traveling wave current signals at the suspension points at both ends of the overhead conductor; Wave velocity module 20 is used to calculate the mode domain wave velocity based on the traveling wave current signal and the temperature-frequency wave velocity coupling change function. The temperature-frequency wave velocity coupling change function is established by converting the series impedance and parallel admittance of the transmission line in the frequency domain state into the mode domain state and combining the converted mode domain electrical parameters. Coefficient module 30 is used to calculate the coupling coefficient of the inclined parabolic traveling wave of the conductor by performing curve integration based on the mode domain wave velocity and the time difference between the arrival of the traveling wave current signal at the two suspension points, combined with the geometric characteristics of the inclined parabola. The sag module 40 is used to establish the sag expression at any point on the overhead conductor and perform differentiation. Combined with the span of the suspension points at both ends and the coupling coefficient of the oblique projectile wave of the conductor, the maximum sag of the overhead conductor is measured.

[0066] It should be noted that the technical concept of this second embodiment is completely consistent with that of the first embodiment. The two maintain a high degree of synergy at the technical logic level. The specific technical details can be referred to the relevant description of the first embodiment, which will not be repeated here.

[0067] Example 3: This application provides a computer-readable storage medium, which includes a stored computer program, wherein the computer program, when running, controls the device where the computer-readable storage medium is located to execute the described method for measuring line sag based on traveling wave and temperature-frequency wave velocity coupling. The method for measuring line sag based on traveling wave and temperature-frequency wave velocity coupling, when implemented as a software functional unit and used as an independent product, can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc.

[0068] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer programs or instructions. When the computer program or instructions are loaded and executed on a computer, the processes or functions described in the embodiments of this application are performed entirely or partially. The computer can be a general-purpose computer, a special-purpose computer, a computer network, a network device, a user equipment, or other programmable device. The computer program or instructions can be stored in a computer-readable storage medium or transferred from one computer-readable storage medium to another. For example, the computer program or instructions can be transferred from one website, computer, server, or data center to another website, computer, server, or data center via wired or wireless means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium, such as a floppy disk, hard disk, or magnetic tape; it can also be an optical medium, such as a digital video optical disc; or it can be a semiconductor medium, such as a solid-state drive. The computer-readable storage medium may be a volatile or non-volatile storage medium, or may include both types of storage media.

[0069] The above are preferred embodiments of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A method for measuring line sag based on traveling wave and temperature-frequency wave velocity coupling, characterized in that, include: Traveling wave current signals are collected at the suspension points at both ends of the overhead conductor; Based on the traveling wave current signal, the mode domain wave velocity is calculated using the temperature-frequency wave velocity coupling change function; wherein, the temperature-frequency wave velocity coupling change function is established by converting the series impedance and parallel admittance of the transmission line in the frequency domain state into the mode domain state, and then combining the converted mode domain electrical parameters. Based on the time difference between the mode domain wave velocity and the time difference between the arrival of the traveling wave current signal at the two suspension points, and combined with the geometric characteristics of the oblique parabola, the coupling coefficient of the oblique parabola traveling wave of the conductor is calculated by curve integration. The sag expression for any point on the overhead conductor is established and differentiated. Combined with the span of the two suspension points and the coupling coefficient of the ballistic wave of the conductor, the maximum sag of the overhead conductor is measured.

2. The method for measuring line sag based on traveling wave and temperature-frequency wave velocity coupling as described in claim 1, characterized in that, Based on the traveling wave current signal, the mode domain wave velocity is calculated using the temperature-frequency wave velocity coupling change function, specifically as follows: The traveling wave current signal is decomposed to obtain several modal components; The optimal modal component is extracted from the several modal components by calculating the envelope entropy; The energy spectrum of the optimal mode component is calculated based on the symmetric differential energy operator, the arrival time of the traveling wave is calibrated, and the effective signal segment is extracted. The center frequency is extracted from the effective signal segment, and the center frequency, the ambient temperature of the overhead conductor, and the conductor temperature are substituted into the temperature-frequency wave velocity coupling change function to calculate the mode domain wave velocity.

3. The method for measuring line sag based on traveling wave and temperature-frequency wave velocity coupling as described in claim 2, characterized in that, The traveling wave current signal is decomposed to obtain several modal components, specifically: The noisy residual is iteratively updated according to the preset Gaussian white noise until the residual signal of the corresponding order shows a single trend or the number of extreme points is less than the preset value, and then the several modal components are output. In each iteration, empirical mode decomposition is performed on the Gaussian white noise, and noise components are extracted according to the decomposition order corresponding to the previous order. The noise components are added to the noisy residual of the previous order to obtain the noisy residual of the current order. In the first iteration, the noisy residual of the first order is calculated by taking the set mean of the first order intrinsic mode functions as the first order mode component and calculating it based on the traveling wave current signal and the first order mode component. The first order intrinsic mode functions are obtained by superimposing the Gaussian white noise on the traveling wave current signal and performing empirical mode decomposition on the generated noisy signal.

4. The method for measuring line sag based on traveling wave and temperature-frequency wave velocity coupling as described in claim 2, characterized in that, The optimal mode component is extracted from the aforementioned modal components by calculating the envelope entropy, specifically as follows: Calculate the envelope entropy of each of the modal components, and define the modal component with the maximum envelope entropy as the optimal modal component.

5. The method for measuring line sag based on traveling wave and temperature-frequency wave velocity coupling as described in claim 2, characterized in that, The energy spectrum of the optimal mode component is calculated using the symmetric differential energy operator, the arrival time of the traveling wave is calibrated, and the effective signal segment is extracted, specifically as follows: Based on the symmetric differential energy operator, the signal energy of the optimal mode component is quantified by capturing the signal change intensity of adjacent sampling points in the discrete signal, and several energy values ​​are obtained. Establish the mapping relationship between the aforementioned energy values ​​and the corresponding sampling times, and generate the energy spectrum of the symmetric differential energy operator for the optimal modal components; The first energy mutation peak is extracted from the energy spectrum of the symmetric differential energy operator, and the sampling time corresponding to the first energy mutation peak is marked as the location time when the fault traveling wave first arrives at the monitoring terminal; In the discrete signal sequence of the optimal modal components, the traveling wave signal pulse interval corresponding to the positioning time is extracted to obtain the effective signal segment.

6. The method for measuring line sag based on traveling wave and temperature-frequency wave velocity coupling as described in claim 1, characterized in that, The temperature-frequency wave velocity coupling variation function is established by converting the series impedance and parallel admittance of the transmission line in the frequency domain into the mode domain, and then combining the converted mode domain electrical parameters. Specifically: By using the Karenbauer transform, the series impedance and parallel admittance of the overhead conductor in the frequency domain state of the transmission line are converted into the modal domain state to obtain the modal domain electrical parameters; The traveling wave attenuation constant and phase constant are calculated based on the electrical parameters of the mode domain, and the curve equations of frequency and wave velocity are established based on the traveling wave attenuation constant and the phase constant. Substituting the electrical parameters of the overhead conductor's transmission line distribution into the curve equations of frequency and wave velocity, the temperature-frequency-wave velocity coupling variation function is obtained.

7. The method for measuring line sag based on traveling wave and temperature-frequency wave velocity coupling as described in claim 6, characterized in that, The distributed electrical parameters of the transmission line include distributed impedance, distributed conductance, and distributed inductance.

8. The method for measuring line sag based on traveling wave and temperature-frequency wave velocity coupling as described in claim 1, characterized in that, Based on the time difference between the mode domain wave velocity and the arrival time of the traveling wave current signal at the two suspension points, and by performing curve integration using the geometric characteristics of the oblique parabola, the coupling coefficient of the oblique parabolic traveling wave of the conductor is calculated as follows: A coordinate system is constructed with the lowest point of the overhead conductor as the origin. The equation of the oblique parabola of the conductor is established based on the force balance relationship of the conductor segment, combined with the angle between the line connecting the two suspension points and the horizontal direction. Based on the propagation path shape of the overhead conductor, the time difference between the mode domain wave velocity and the traveling wave current signal reaching the two suspension points is calculated by curve integration, and the equation of the conductor's oblique parabola is established to establish the adaptive calculation relationship between the coordinates of the two suspension points, thus obtaining the comprehensive calculation formula. Substituting the span between the two suspension points, the modal wave velocity, and the time difference between the arrival of the traveling wave current signal at the two suspension points into the comprehensive calculation formula, the coupling coefficient of the oblique projectile traveling wave of the conductor is calculated.

9. A line sag measurement device based on traveling wave and temperature-frequency wave velocity coupling, characterized in that, Includes signal module, wave velocity module, coefficient module and sag module; The signal module is used to collect traveling wave current signals at the suspension points at both ends of the overhead conductor. The wave velocity module is used to calculate the mode domain wave velocity based on the traveling wave current signal and the temperature-frequency wave velocity coupling change function; wherein, the temperature-frequency wave velocity coupling change function is established by converting the series impedance and parallel admittance of the transmission line in the frequency domain state into the mode domain state and combining the converted mode domain electrical parameters. The coefficient module is used to calculate the conductor's oblique parabolic traveling wave coupling coefficient by performing curve integration based on the mode domain wave velocity and the time difference between the arrival of the traveling wave current signal at the two suspension points, combined with the geometric characteristics of the oblique parabola. The sag module is used to establish the sag expression for any point on the overhead conductor and perform differentiation. Combined with the span of the two suspension points and the coupling coefficient of the ballistic wave of the conductor, the maximum sag of the overhead conductor is measured.

10. A storage medium, characterized in that, The storage medium stores a computer program, which is called and executed by a computer to implement a line sag measurement method based on traveling wave and temperature-frequency wave velocity coupling as described in any one of claims 1 to 7.

11. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by the communication device, they implement a line sag measurement method based on traveling wave and temperature-frequency wave velocity coupling as described in any one of claims 1 to 8.

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