A single-end precise ranging method for an extra-high voltage direct current transmission system

Abstract

The present application relates to the technical field of fault location of UHVDC transmission, in particular to a single-ended accurate fault location method for UHVDC transmission system, when single-pole grounding fault occurs in the line, positive and negative voltage and current signals at the installation position of the protection are collected, line mode and zero mode voltage reverse waves are obtained through Kalman-Bell transformation decoupling, the first wave head is positioned by difference and effective time domain data is intercepted, S transform is carried out for time-frequency mapping by using adaptive window width, time-frequency energy redistribution is realized by iterative optimization group delay fixed point, time direction high convergence time-frequency distribution is obtained, double-mode wave arrival time is extracted frequency by frequency and modulus time difference is calculated, initial fault distance sample is obtained by combining frequency variable propagation speed, the probability density peak value is taken as the final fault location result through non-parametric kernel density estimation, the present application does not need double-ended communication and synchronization, and greatly improves the wave arrival time extraction accuracy, anti-interference ability and fault location robustness.

Description

Technical Field

[0001] This invention relates to the field of fault location technology for ultra-high voltage direct current (UHVDC) transmission systems, and more specifically, to a single-end precise fault location method for UHVDC transmission systems. Background Technology

[0002] Fault location in ultra-high voltage direct current (UHVDC) transmission lines is an important technology, specifically applied to the single-end location of single-pole grounding faults in UHVDC transmission lines. High-resolution time-frequency analysis improves the accuracy of fault traveling wave arrival time extraction and the reliability of location measurement. UHVDC fault traveling waves exhibit dispersion attenuation and frequency-varying propagation characteristics. Single-end location requires precise extraction of the arrival times of each frequency component of the line-mode and zero-mode traveling waves. However, conventional time-frequency analysis methods employ fixed window width control strategies and exhibit divergent time-frequency energy distributions, making it impossible to accurately pinpoint the true arrival times of each frequency traveling wave. This leads to deviations in the calculation of the modulus time difference between the line-mode and zero-mode traveling waves, resulting in large errors in single-end fault location results and insufficient anti-interference capability and robustness. To address this technical problem, we provide a precise single-end location method for UHVDC transmission systems. Summary of the Invention

[0003] The purpose of this invention is to provide a single-end accurate ranging method for ultra-high voltage direct current transmission systems to solve the problems mentioned in the background art.

[0004] To achieve the above objectives, one of the objectives of this invention is to provide a single-end accurate ranging method for ultra-high voltage direct current transmission systems, comprising the following steps: S1. When a single-pole grounding fault occurs in a DC transmission line, the positive and negative voltage and current signals at the protection installation point are collected. The positive and negative voltage and current signals are decoupled using Kelvin-Bell transform to obtain the line-mode component and the zero-mode component. The voltage back-traveling wave signal of the line-mode component and the zero-mode component is calculated. S2. Calculate the differential sequences of the voltage back-traveling wave signals of the line-mode component and the zero-mode component respectively, and locate the time corresponding to the point of maximum absolute value of the difference in the differential sequence. Take this time as the center time of the first wave head of the corresponding mode. Based on the center time, extract data of predetermined lengths before and after to obtain the line-mode time sequence array and the zero-mode time sequence array respectively, and record the center time of extraction of both. S3. Construct an S-transform with adaptively adjustable window function standard deviation, wherein the window function is a Gaussian window function. Use the improved adaptive S-transform to process the linear mode time series array and the zero mode time series array respectively to obtain the corresponding two-dimensional complex time-frequency coefficient matrix. S4. Perform energy redistribution and compression on the two-dimensional complex time-frequency coefficient matrix, calculate the first generation group delay operator of the two-dimensional complex time-frequency coefficient matrix, perform iterative operation on the first generation group delay operator to find its fixed point, stop the iteration when the difference of the continuous iteration results is less than a set threshold, obtain the converged time coordinate estimate, project the magnitude of the original time-frequency coefficient matrix along the time axis and accumulate it onto the converged time coordinate to obtain the time-frequency distribution of energy concentrated in the time direction; S5. For time-frequency distribution, for each frequency in the preset frequency band, extract the time point when the time-frequency amplitude of the linear mode and the zero mode is the largest at that frequency, and take it as the arrival time of that frequency. Combined with the intercepted center time, calculate the modulus arrival time difference at each frequency to obtain the modulus time difference vector. S6. Based on the transmission line parameters, calculate the line mode wave velocity and zero mode wave velocity corresponding to each frequency in the preset frequency band, calculate a set of initial fault distance samples using the single-end ranging formula, process the initial fault distance samples using the non-parametric kernel density estimation method to obtain the probability density distribution of the fault distance, and take the distance corresponding to the peak value of the probability density distribution as the final fault ranging result.

[0005] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention employs a high-resolution time-frequency analysis scheme that combines adaptive window width optimization, time energy redistribution, and robust statistical estimation. This effectively solves the problems of insufficient accuracy in extracting the arrival time of fault traveling waves and large ranging errors caused by fixed window widths and time-frequency energy divergence in conventional methods. It can accurately extract the true arrival time of each frequency component of the fault traveling wave in UHVDC transmission lines, significantly reduce the calculation deviation of the time difference between the line mode and the zero mode traveling wave modulus, and significantly improve the accuracy, anti-interference ability, and robustness of single-end fault ranging. It can perfectly meet the long-distance, high-precision, and high-reliability fault ranging requirements of UHVDC transmission lines. Attached Figure Description

[0006] Figure 1 This is a diagram illustrating time redistribution. Figure 2 The waveforms show the frequency response characteristics of the linear mode and the zero mode. Figure 3 This is a schematic diagram of the transmission of a traveling wave during a fault. Figure 4 Here is a flowchart of the fault location algorithm; Figure 5 This is a topology diagram of the ±800kV system; Figure 6 The time-domain signal diagrams of the inverse traveling waves of the line-mode and zero-mode voltages are shown. Figure 7 The initial time-frequency energy distribution diagram of the standard S-transform; Figure 8To improve the time-frequency energy distribution map of STMSST; Figure 9 This is a graph showing the time of arrival (TOA) curve for modulus waves. Figure 10 This is a probability density distribution map of fault distance based on kernel density estimation. Detailed Implementation

[0007] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all 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.

[0008] This embodiment provides a single-end accurate ranging method for an ultra-high voltage direct current transmission system, including the following steps: S1. When a single-pole grounding fault occurs in a DC transmission line, the positive and negative voltage and current signals at the protection installation point are collected. The positive and negative voltage and current signals are decoupled using the Kelvin-Bell transform to obtain the line-mode component and the zero-mode component. The voltage back-traveling wave signals of the line-mode component and the zero-mode component are calculated. S2. Calculate the differential sequences of the voltage back-traveling wave signals of the line-mode component and the zero-mode component respectively, and locate the time corresponding to the point of maximum absolute value of the difference in the differential sequence. Take this time as the center time of the first wave head of the corresponding mode. Based on the center time, extract data of predetermined lengths before and after to obtain the line-mode time sequence array and the zero-mode time sequence array respectively, and record the center time of extraction for both. S3. Construct an S-transform with adaptively adjustable window function standard deviation, with Gaussian window function as the window function. Use the improved adaptive S-transform to process the linear mode time series array and the zero mode time series array respectively to obtain the corresponding two-dimensional complex time-frequency coefficient matrix. S4. Perform energy redistribution and compression on the two-dimensional complex time-frequency coefficient matrix, calculate the first generation group delay operator of the two-dimensional complex time-frequency coefficient matrix, perform iterative operation on the first generation group delay operator to find its fixed point, stop the iteration when the difference of the continuous iteration results is less than the set threshold, obtain the converged time coordinate estimate, project the magnitude of the original time-frequency coefficient matrix along the time axis and accumulate it onto the converged time coordinate to obtain the time-frequency distribution of energy concentrated in the time direction; S5. For time-frequency distribution, for each frequency in the preset frequency band, extract the time point when the time-frequency amplitude of the linear mode and the zero mode is the largest at that frequency, and take it as the arrival time of that frequency. Combined with the intercepted center time, calculate the modulus arrival time difference at each frequency to obtain the modulus time difference vector. S6. Based on the transmission line parameters, calculate the line mode wave velocity and zero mode wave velocity corresponding to each frequency in the preset frequency band. Use the single-end ranging formula to calculate a set of initial fault distance samples. Use the non-parametric kernel density estimation method to process the initial fault distance samples to obtain the probability density distribution of the fault distance. Use the distance corresponding to the peak value of the probability density distribution as the final fault ranging result.

[0009] It should be further explained that this invention relates to the field of fault location technology for ultra-high voltage direct current (UHVDC) transmission systems, specifically a single-end precise location method for UHVDC transmission systems based on improved high time-frequency resolution analysis. This method effectively solves the problems of insufficient time-frequency resolution, inadequate consideration of wave velocity frequency variation characteristics, and weak resistance to noise and outlier interference in traditional single-end location methods by integrating improved adaptive S-transform, time redistribution multi-synchronization compression technology, and kernel density estimation method. It can achieve high-precision and high-robust single-end location of single-pole grounding faults in UHVDC transmission lines, which has important engineering application value for ensuring the safe and stable operation of UHVDC transmission systems, shortening fault investigation time, and reducing power outage losses.

[0010] When a single-pole ground fault occurs in a DC transmission line, the positive and negative voltage and current signals at the protection installation point are collected. The Kelvin transform is used to decouple the positive and negative voltage and current signals, obtaining the line-mode and zero-mode components. The voltage back-traveling wave signals of the line-mode and zero-mode components are then calculated. UHVDC transmission lines operate in bipolar mode. When a single-pole ground fault occurs, the traveling wave signal generated by the fault exhibits mode coupling during transmission, meaning the line-mode and zero-mode components intertwine. Directly analyzing the original voltage and current signals makes it difficult to accurately extract fault characteristics. Therefore, mode decoupling technology is needed to decompose the coupled signal into independent line-mode and zero-mode components to study their propagation characteristics separately. The Kelvin transform, a widely used mode decoupling method in power system traveling wave analysis, has the advantages of simple calculation and clear physical meaning. Its decoupling formula is as follows: in, , , , These represent the positive and negative voltage and current at the measurement point, respectively. , , , Let represent line-mode and zero-mode voltage and current, respectively. Through the above Kelenberger transform, the original positive and negative voltage and current signals can be decoupled into independent line-mode and zero-mode components. The line-mode components are mainly determined by the voltage and current difference between the lines, and have the characteristics of small attenuation, weak dispersion, and fast propagation speed. Their time-domain envelope is steep and contains rich high-frequency components. The zero-mode components are mainly determined by the voltage and current between the lines and ground, and have the characteristics of severe high-frequency attenuation and large differences in the propagation speed of each frequency component. Their time-domain envelope is steep and has a tail, and low-frequency components dominate.

[0011] After completing mode decoupling, it is necessary to further calculate the voltage back-traveling wave signals of the line mode component and the zero mode component. This is because the back-traveling wave signal only contains the initial traveling wave information of the fault propagating from the fault point to the protection installation point, and is not affected by the reflected wave from the opposite converter station. This can effectively avoid the interference of the reflected wave from the opposite end on the identification of the first wave head, thereby improving the accuracy of single-end ranging. The calculation formula for the voltage back-traveling wave is as follows: in, and These are the calculated line-mode voltage inverse traveling wave and zero-mode voltage inverse traveling wave, respectively. and These are the zero-mode impedance and the line-mode impedance, respectively. The formula for calculating the impedance is: L and C represent the inductance and capacitance per unit length, respectively. The line-mode and zero-mode voltage reverse traveling wave signals calculated using the above formula contain complete information about the first wavehead of the fault traveling wave, providing a reliable input signal for subsequent time-frequency analysis and wave arrival time extraction. The Kelvin transform achieves mode decoupling of the fault traveling wave, eliminating coupling interference between the line mode and the zero mode, allowing for targeted analysis based on the different propagation characteristics of the two modes. At the same time, by extracting the voltage reverse traveling wave signal, the influence of the reflected wave at the opposite end is effectively filtered out, significantly improving the accuracy and reliability of the first wavehead identification, laying a solid foundation for the accuracy of the entire ranging algorithm.

[0012] After calculating the voltage reverse traveling wave signal, since the effective characteristic information of the fault traveling wave is mainly concentrated in a very short time near the first wave head, performing time-frequency analysis on the entire time-domain signal after the fault would not only significantly increase the computational load and reduce the real-time performance of the algorithm, but also introduce a large amount of noise and subsequent reflected wave interference, affecting the accuracy of the analysis results. Therefore, it is necessary to first roughly locate the first wave head and extract the effective data window containing the first wave head for subsequent analysis. To this end, step S2 is executed. S2 calculates the difference sequences of the voltage reverse traveling wave signals of the linear mode component and the zero mode component, respectively, and locates the time corresponding to the point where the absolute value of the difference in the difference sequence is the maximum. This time is taken as the center time of the first wave head of the corresponding mode. Based on the center time, data of predetermined lengths are extracted before and after, respectively, to obtain the linear mode time series array. and zero modulus time series array And record the center moment of both intercepts. and Differential sequences can effectively reflect the rate of change of a signal. The voltage signal at the first wavehead of a fault traveling wave undergoes a drastic change, reaching its maximum rate of change. Therefore, the location of the first wavehead can be roughly determined by finding the point with the maximum absolute value of the difference in the differential sequence. The formula for calculating the differential sequence is as follows: in, Indicates the discrete sampling point number. Indicates the first The reverse traveling wave voltage value at each sampling point Represents the reverse traveling wave voltage sequence, the first... The difference value of each sampling point The maximum difference moment is indicated by inputting the calculated line-mode voltage reverse traveling wave and zero-mode reverse traveling wave into the above differential calculation formula, respectively. This yields the differential sequences of the line-mode and zero-mode reverse traveling wave signals. Then, the moment corresponding to the point with the largest absolute value in each differential sequence is found. This moment is taken as the center time of the first wave head of the corresponding mode, and recorded as the center time of the linear mode. and the center moment of the zero model After determining the center time of the first wavehead, data of predetermined lengths need to be extracted before and after this time as the input signal for time-frequency analysis. In this invention, the predetermined length is set to 1ms. This is because a time length of 1ms can completely contain all the effective information of the first wavehead of the fault traveling wave without introducing too much subsequent reflected waves and noise interference. At the same time, at the commonly used sampling rate of 1MHz, 1ms corresponds to 1000 sampling points, which is a moderate amount of computation and can ensure the real-time performance of the algorithm. The formula for calculating the number of discrete sampling points is: in, The sampling rate is set to 1MHz in this embodiment, so 1000 data points need to be taken before and after the sampling. The resulting time series array can be expressed as: The obtained linear mode and zero-mode signals are as follows: Figure 6 As shown, the input for this step is the positive and negative voltage and current signals collected at the measurement point after the fault, and the output is a line-mode time series array. and zero-modulus time series array Simultaneously record the center moment of both captures. and These two center moments will serve as the benchmark for subsequent calculation of modulus time of arrival, unifying the time of arrival of the linear mode and zero mode. The differential maximum method enables rapid and coarse localization of the first wavehead of the fault traveling wave, significantly narrowing the scope of time-frequency analysis, effectively reducing computational complexity, and significantly improving the real-time performance of the algorithm. At the same time, by extracting a 1ms data window containing the first wavehead, the integrity of the effective information is ensured, while noise and interference from subsequent reflected waves are filtered out to the maximum extent, providing a high-quality input signal for subsequent high-precision time-frequency analysis. In addition, recording the center moments of the two modes provides the necessary prerequisites for unifying the time benchmark and accurately calculating the modulus time of arrival.

[0013] After obtaining the time series arrays of the linear mode and the zero mode, time-frequency analysis is required to extract the times of arrival at different frequencies. Traditional time-frequency analysis methods, such as the short-time Fourier transform, use a fixed window length, which cannot simultaneously consider the time resolution of the high-frequency band and the frequency resolution of the low-frequency band. Although the continuous wavelet transform has multi-resolution characteristics, it does not retain the absolute phase information of the signal and has the problem of difficulty in selecting the wavelet basis. The standard S-transform combines the advantages of the short-time Fourier transform and the continuous wavelet transform, retaining the absolute phase information of the signal and possessing frequency-dependent multi-resolution characteristics. However, its single window width control strategy, which is inversely proportional to the frequency, is difficult to adapt to the different signal morphologies of the linear mode and the zero mode, and cannot obtain accurate time-frequency information from the fault traveling wave signal. In order to solve the above problems, this invention improves the standard S-transform and constructs an S-transform with an adaptively adjustable window function standard deviation. For this purpose, step S3 is executed as follows: Construct an S-transform with adaptively adjustable window function standard deviation, where the window function is a Gaussian window function and the standard deviation of the Gaussian window is... Defined as: in, ,in, For the baseline window width parameter, Modulate the window width amplitude. To modulate the attenuation coefficient and control the exponential decay rate, the physical meaning of this model lies in dynamically adjusting the morphology of time-frequency atoms. Through this improvement, different window width adjustment strategies can be implemented by adjusting parameters during signal analysis to achieve ideal time-frequency analysis results. For example, when it is necessary to obtain low-frequency time-frequency information of the analyzed signal and high time resolution is required, f is relatively small. Approaching + It can be appropriately increased To reduce window width and increase temporal resolution; when entering the high-frequency band, Approaching This can be reasonably reduced. To ensure sufficient window width for signal analysis, the obtained linear mode time series array Uwin1 and zero mode time series array Uwin0 are used as inputs, and the output is a two-dimensional complex time-frequency coefficient matrix. as well as The S-transform (ST), proposed by R.G. Stockwell et al. in 1996, is a time-frequency analysis method that combines the advantages of the Short-Time Fourier Transform (STFT) and the Continuous Wavelet Transform (CWT). It preserves the absolute phase information of the signal while possessing frequency-dependent multi-resolution characteristics. The standard definition of the S-transform is: in, Let g(·) be the time point where the center of the observation window is located, and let g(·) be the Gaussian window function, whose expression is as follows: In the standard S-transform, As can be seen, the window width in the standard S-transform gradually decreases with increasing frequency, making it more suitable for analyzing broadband signals compared to the STFT. However, when analyzing fault traveling wave signals, different modes of the signal have different shapes. For example, the linear mode has a steep time-domain envelope due to its small attenuation and weak dispersion, containing rich high-frequency components. For the zero-mode component, the high-frequency attenuation is severe and the propagation speed of each frequency component differs greatly, resulting in a steep time-domain envelope with a tail, and low-frequency components dominate. Faced with signals of different shapes, the single window width control strategy in the standard S-transform, which is inversely proportional to the frequency, is often difficult to adapt. Therefore, it cannot obtain accurate information from fault traveling wave signals. According to the Heisenberg uncertainty principle, time resolution and frequency resolution cannot be optimal at the same time. When analyzing different signals, a more flexible strategy is needed to reasonably allocate time and frequency resolution resources. In order to accurately analyze the time and frequency information contained in fault traveling waves of different shapes, this invention constructs an exponential adaptive adjustment window by introducing a nonlinear adjustment factor in the definition of standard deviation, as shown below: in, For the baseline window width parameter, Modulate the window width amplitude. To modulate the attenuation coefficient and control the exponential decay rate, the physical meaning of this model lies in dynamically adjusting the morphology of time-frequency atoms. Through this improvement, different window width adjustment strategies can be implemented by adjusting parameters during signal analysis to achieve ideal time-frequency analysis results. For example, when it is necessary to obtain low-frequency time-frequency information of the analyzed signal and high time resolution is required, this... Smaller Approaching β can be appropriately increased to reduce the window width and increase the time resolution; when entering the high-frequency band, Approaching This can be reasonably reduced. To ensure sufficient window width for signal analysis, the improved S-transform is defined as follows: Using the improved adaptive S-transform described above, the linear time series arrays obtained in step S2 are respectively processed... and zero modulus time series array After processing, a two-dimensional complex time-frequency coefficient matrix can be output. as well as By introducing an exponential nonlinear adjustment factor, adaptive adjustment of the S-transform window width is achieved. This allows for dynamic adjustment of the time-frequency resolution based on the signal's frequency characteristics and the signal morphology of different modes. Higher time resolution is achieved in the low-frequency band, while sufficient frequency resolution is maintained in the high-frequency band. This effectively solves the problem that the standard S-transform's single window width control strategy cannot adapt to different signal morphologies of linear and zero modes, significantly improving the accuracy and adaptability of time-frequency analysis. Simultaneously, the improved S-transform retains the absolute phase information and multi-resolution characteristics of the standard S-transform, providing a reliable foundation for subsequent group delay calculations and energy redistribution. Although the improved adaptive S-transform... While the improved S-transform already provides better time-frequency resolution than the standard S-transform, for strongly time-varying fault traveling wave signals, the time-frequency energy still exhibits some divergence. That is, energy at the same moment is distributed across multiple frequency points, and energy at the same frequency is distributed across multiple time points. This energy divergence increases the error in wave arrival time extraction, failing to meet the high-precision ranging requirements of ultra-high voltage direct current transmission systems. To further improve the concentration of time-frequency energy and eliminate energy divergence in the time direction, this invention introduces a time redistribution multi-synchronization compression technique. The improved adaptive S-transform is used to post-process the time-frequency coefficient matrix obtained. Step S4 is executed for this purpose, as follows: For two-dimensional complex time-frequency coefficient matrix as well as Energy redistribution and compression specifically include: Received as well as It can be written in polar coordinates: Taking the logarithm of the expression and then taking the partial derivative with respect to frequency: After simplifying the left side of the above equation and taking the imaginary parts of both sides, substituting the expression back into the equation and simplifying, we get: As can be seen from the above formula, the key to obtaining GD lies in... Take the partial derivative with respect to frequency f: Decompose it into a linear combination of two integrals: The derivative of the first term in the above equation mainly affects the real part of the calculation result, while the influence of the imaginary part mainly comes from the second term. From the equation, we can see that the calculation of GD is obtained by taking the imaginary part. Therefore, after taking the imaginary part of the equation, the following approximate calculation is performed: To quantify the deviation of the signal energy relative to the current observation time t, a variable substitution technique is introduced to decompose the integral kernel τ, as shown below: Substituting the equation into the equation, we get: Further simplification yields: As can be seen from the above equation, the frequency partial derivative of the S-transform can be decomposed into a linear combination of two integrals. To simplify the right side of the equation, the following definition is made: in, Defined as a time-deviation weighted S-transform, this transform uses linear weights (t-) to calculate the first-order time moment of the signal relative to the window center t within a local time-frequency window. Therefore, the equation can be simplified to: Substituting the above equation into the formula, we get: Further simplification yields: For any complex number The imaginary part is calculated as follows: Therefore, the expression can be simplified as follows: Finally, simplifying both sides of the equation, we get: As can be seen from the above equation, the group delay can be obtained by subtracting the deviation calculated from the transformation ratio from the current time. Where... as well as All of these are calculated using the improved exponential adaptive Gaussian window. On the other hand, from the perspective of signal energy distribution, based on the Cohen-class representation of the S-transform, the group delay operator is defined as the local time centroid of the signal Wigner-Ville distribution under adaptive Gaussian kernel weighting, which can also be obtained through analytical simplification.

[0014] Under complex multi-component signals, energy rearrangement using the group delay operator obtained from a single calculation is difficult to achieve ideal results. To further improve the energy concentration, an iterative strategy for finding the group delay fixed point is proposed. The initial group delay operator obtained from the calculation is denoted as... To correct for estimation bias, the update formula for the Nth iteration is: To ensure energy focusing performance while avoiding computational redundancy caused by excessive iterations, it is necessary to establish an iteration termination condition. This paper sets the following termination condition: Where λ is the iteration termination threshold. When the above condition is met, iteration stops, and the convergence time coordinate is obtained. Then, a multi-synchronous compression operation is performed. The amplitude of the original S-transform is then... Projected along the time axis and accumulated to the corrected coordinate position, as shown below: Where τ is the redistributed time variable, and δ(·) is the Dirac function. In practical digital signal processing, the above integration process is transformed into a discrete summation operation. The final discrete form of the time-frequency distribution can be expressed as: Where n and m are the time sampling index and frequency index of the original signal, respectively, u is the time index after redistribution, L is the signal length, and round(·) represents the rounding function. For processing strongly time-varying signals, the TMSST algorithm was first proposed in existing technologies. This method, based on the Short Time Fourier Transform (STFT), effectively solves the time-frequency ambiguity problem of strongly time-varying signals by introducing an iterative operator to find the fixed point of the group delay. However, since the STFT uses a fixed window length, it cannot simultaneously consider the time resolution of the high-frequency band and the frequency resolution of the low-frequency band, resulting in limitations in processing broadband impulse signals. To overcome this deficiency, some studies have extended the time redistribution technique to continuous wavelet transform, proposing a time rearrangement synchronous compression transform based on wavelet transform. Utilizing the multi-resolution characteristics of wavelet transform, this method can effectively handle transient signals... While exhibiting excellent performance in signal analysis, the preprocessing method based on wavelet transform still exhibits low-frequency oscillations after compression in the time domain by TMSST. Machine learning correction is required when extracting the time of arrival, increasing the algorithm's complexity and computational load. Other research combines the absolute phase advantage of STFT with the multi-resolution characteristics of CWT, proposing a TMSST algorithm based on S-transform, which has been successfully applied to bearing fault diagnosis. However, this algorithm uses the standard S-transform as preprocessing and still suffers from the problem of unadaptive window width adjustment, resulting in limited accuracy in time-frequency analysis. This invention, based on the aforementioned improvements to the time-frequency window and combined with time redistribution multi-synchronization compression technology, can obtain a highly concentrated time-frequency representation, effectively solving the shortcomings of the existing technologies. To perform energy redistribution, the group delay of the signal must first be calculated. As can be seen from the above equation, the group delay can be obtained by subtracting the deviation calculated from the transform ratio from the current time. This expression has a clear physical meaning, is simple to calculate, and fully utilizes the high-precision time-frequency analysis results of the improved adaptive S-transform. Under complex multi-component signals, it is difficult to achieve ideal results by rearranging the energy using the group delay operator obtained from a single calculation, because a single group delay calculation is affected by the interference of adjacent components, resulting in a certain degree of divergence after energy rearrangement. To further improve the energy concentration, this invention adopts an iterative strategy to find the group delay fixed point, and the initial group delay operator obtained from the equation is denoted as... To correct for estimation bias, the update formula for the Nth iteration is: To ensure energy focusing effectiveness while avoiding computational redundancy caused by excessive iteration, an iteration termination condition needs to be established. This invention sets the termination condition as follows: Where λ is the iteration termination threshold. When the above condition is met, iteration stops, and the convergence time coordinate is obtained. Then, a multi-synchronous compression operation is performed. The amplitude of the original S-transform is then... Projected along the time axis and accumulated to the corrected coordinate position, as shown below: Where τ is the redistributed time variable, and δ(·) is the Dirac function. In practical digital signal processing, the above integration process is transformed into a discrete summation operation. The final discrete form of the time-frequency distribution can be expressed as: Where n and m are the time sampling index and frequency index of the original signal, respectively, u is the redistributed time index, L is the signal length, and round(·) represents the floor function. Through the above steps, the two-dimensional complex time-frequency coefficient matrix is ​​processed. and By redistributing and compressing energy, a time-frequency distribution in which energy is highly concentrated in the time direction can be obtained. and By employing a time redistribution multi-synchronization compression technique based on an improved adaptive S-transform, the originally divergent energy on the time-frequency plane is redistributed to the true time trajectory, generating a time-frequency representation with highly concentrated energy in the time direction. This effectively eliminates time-frequency ambiguity and significantly improves the accuracy of wave arrival time extraction. Simultaneously, by iteratively searching for the group delay fixed point, the degree of energy concentration is further improved, solving the problem of poor energy rearrangement effect under complex multi-component signals. Furthermore, the TMSST algorithm of this invention uses the improved adaptive S-transform as preprocessing, combining the absolute phase advantage and multi-resolution characteristics of the S-transform, avoiding the defects of TMSST algorithms based on STFT and wavelet transform. It does not require machine learning correction, reducing the complexity and computational load of the algorithm, and improving its practicality and real-time performance.

[0015] After obtaining the highly concentrated time-frequency distribution of energy, it is necessary to extract the arrival times of the fault traveling wave head at different frequencies in order to calculate the modulus time difference. The overhead line parameters of UHVDC transmission lines are affected by dispersion, and the wave velocity exhibits obvious frequency-varying characteristics, that is, the propagation speed of the traveling wave components at different frequencies in the transmission line is different. If a single average wave velocity is used for ranging, it will introduce a large ranging error. Therefore, it is necessary to consider the frequency-varying characteristics of the wave velocity, extract the arrival times at different frequencies, and use multi-frequency information for comprehensive ranging. To this end, step S5 is executed, as follows: For time-frequency distribution For each frequency within the preset frequency band The time points at which the linear mode and zero mode have the largest time-frequency amplitudes at that frequency are extracted respectively, and these are taken as the arrival times at that frequency. This is combined with the center time of interception. and Calculate the modulus time of arrival at each frequency. Obtain the modulus time difference vector ,in, and These are the zero-mode and linear-mode wave arrival time points set. To obtain a value, firstly, it is necessary to calculate the frequency-varying wave velocity of the UHVDC transmission line. According to traveling wave propagation theory, for any mode... Its propagation coefficient Defined as: This refers to the angular frequency of the corresponding frequency component. , , , Modes at a given frequency Resistance, inductance, conductance, and capacitance per unit length. and These are the attenuation constant and the phase constant, respectively, where the attenuation constant... The phase constant determines the attenuation of the traveling wave signal during transmission. The phase change rate of the traveling wave signal is determined, and the propagation coefficient is extracted. imaginary part Subsequently, the propagation speed of the fault traveling wave is determined by the phase constant, for a given frequency. Linear mode wave speed and zero-mode wave speed They can be calculated using the following formulas: Based on the above formula, the relationship between the wave velocity of the linear mode and the zero mode and the frequency can be obtained. The frequency-dependent characteristic curves of the wave velocity of the linear mode and the zero mode are shown below. Figure 2 As shown, the linear mode wave velocity varies little with frequency and remains relatively stable over a wide frequency range, while the zero-mode wave velocity varies significantly with frequency, and the attenuation constant of its high-frequency components is much greater than that of the linear mode. This results in the high-frequency components of the zero mode having extremely weak energy after long-distance transmission, making it difficult to accurately extract their time of arrival. To extract the precise time of arrival of the first wavefront of different mode fault traveling waves at different frequencies, a TMSST based on an improved S-transform is used to process the first wavefront. The traveling wave signal generated by the fault is mapped to a two-dimensional time-frequency matrix. As shown below: The time-frequency distribution is in discrete form, where For time indexing, Using frequency indexing, for the first wavefront, its arrival time at different frequencies corresponds to the moment when the energy is strongest at that frequency. Because the energy of the fault traveling wave's first wavefront reaches its maximum at its arrival time, therefore the... The arrival time of each frequency should be: It is the magnitude of the time-frequency coefficient. For the first Based on the frequency index corresponding to each frequency, and according to the above formula, extract the arrival time of the line mode and zero mode at each frequency within the preset frequency band, as follows: Figure 1 As shown, the preset frequency band in this invention is 1kHz to 350kHz. This is because the effective energy of the traveling wave from the UHVDC transmission fault is mainly concentrated in this frequency band. Components below 1kHz are greatly affected by the steady-state components of the system, while components above 350kHz suffer severe attenuation, resulting in a low signal-to-noise ratio and making it difficult to accurately extract the arrival time. The arrival time sets for both modes are thus extracted. and Next, the modulus time difference vector needs to be calculated, due to the intercept center time of the linear mode and the zero mode. and They may differ, therefore it is necessary to unify the arrival times of the two modes to the same time base. For the first mode... The arrival time of each frequency, combined with the center time marked in step S2. and The calculation yielded: in, and These are the zero-mode and linear-mode wave arrival time points set. By calculating the modulus time difference for frequencies from 1kHz to 350kHz using the above formula, the modulus time difference vector can be obtained. This method fully considers the frequency-varying characteristics of wave velocity in UHVDC transmission lines. By extracting the arrival times at different frequencies, it utilizes the broadband information of the fault traveling wave for distance measurement, avoiding the distance measurement error caused by a single wave velocity. Simultaneously, by unifying the time references for the line mode and zero mode, the accuracy of modulus time difference calculation is ensured. Furthermore, selecting an effective frequency band from 1kHz to 350kHz ensures sufficient effective information is obtained while avoiding interference from low-frequency steady-state components and high-frequency noise, thus improving the reliability of wave arrival time extraction. After obtaining the modulus time difference vector and the corresponding frequency-varying wave velocity, a set of initial fault distance samples can be calculated. However, this is affected by signal noise interference and dispersion. Due to the influence of effect fitting residuals and the Heisenberg uncertainty principle, these initial fault distance samples will contain random errors and may include outliers caused by algorithm limitations. Traditional statistical methods, such as directly calculating the average or taking the median, are very sensitive to outliers and are prone to producing large ranging deviations, which cannot meet the high-precision ranging requirements of UHVDC transmission systems. In order to extract the true fault location from the initial fault distance samples containing random errors and outliers, this invention introduces a nonparametric kernel density estimation method. By fitting the probability density distribution of the samples, the region with the most concentrated samples is found, thereby determining the final fault distance. For this purpose, step S6 is executed, as follows: Calculate the line mode wave velocity corresponding to each frequency within the preset frequency band based on the transmission line parameters. and zero-mode wave speed A set of initial fault distance samples was obtained by using the single-end ranging formula. The initial fault distance samples are processed using a nonparametric kernel density estimation method. The probability density distribution of the fault distance is obtained. The kernel density estimation uses a Gaussian kernel function with a bandwidth of [missing information]. According to the sample The median absolute deviation is adaptively determined, and finally, the distance corresponding to the peak value of the probability density distribution is taken as the final fault location result. First, the basic principle of single-ended ranging is introduced. When a single-phase ground fault occurs in section AB of the line, the initial traveling wave of the fault transmitted through the line can be regarded as a step signal. The fault point These represent the times when the linear mode and the zero mode arrive at points A and B, respectively. and These represent the time differences between the arrival times of the two moduli at points A and B. Taking point A as an example, given the absolute times when the first wave of the linear modulus and the first wave of the zero modulus arrive at point A, the distance from the fault point F to the protection installation location can be calculated using the modulus time difference and the wave velocities of the two moduli. in, and These are the linear mode wave velocity and the zero mode wave velocity, respectively. Based on the single-end ranging formula described above, and combined with the modulus time difference vector obtained in step S5, the following parameters are considered: and the linear mode wave velocity corresponding to each frequency calculated in step S6 and zero-mode wave speed A set of initial fault distance samples can be calculated. ,in Given a preset number of frequency points within a frequency band, due to signal noise interference, dispersion effects, fitting residuals, and the Heisenberg uncertainty principle, directly averaging or taking the median of this sample often fails to obtain accurate fault locations. If outliers exist in the sample due to algorithmic limitations, traditional statistical methods are prone to significant bias. To extract the true fault location from distance samples containing random errors, this invention introduces nonparametric kernel density estimation. Unlike parametric estimation, nonparametric kernel density estimation does not require prior assumptions that the data follows a specific distribution. Instead, it directly uses the information of the sample itself to fit the probability density function of the data, highlighting the most concentrated area of ​​the sample, thereby determining the fault distance. The core idea of ​​nonparametric kernel density estimation is to transform each discrete sample into a continuous probability distribution and superimpose them. Its mathematical expression is: For the sample size, For bandwidth, The choice of kernel function is crucial for determining the final fault distance. The kernel function assigns different weights to points surrounding each sample point; points closer to the sample point have higher weights, and points farther away have lower weights. Considering that the Gaussian kernel function assigns higher weights to the data surrounding the sample point, and that the weights decay exponentially with distance, and that the Gaussian kernel function smooths the data and effectively suppresses noise, this invention chooses the Gaussian kernel function, whose expression is: On the other hand, bandwidth The bandwidth is also a key parameter affecting the performance of nonparametric kernel density estimation. If the bandwidth is too small, the probability density distribution may have spurious peaks, leading to overfitting; while if the bandwidth is too large, it will mask the detailed features of the distribution, leading to underfitting. To ensure the adaptability and rationality of the bandwidth selection, this invention uses the Silverman rule of thumb for calculation. Considering that the traditional sample standard deviation may be amplified by outliers, leading to an overestimated bandwidth estimate, thus making the probability density distribution too smooth and unable to accurately reflect the concentration area of ​​the sample, this invention uses the median absolute deviation instead of the standard deviation for bandwidth estimation. The median absolute deviation has stronger robustness to outliers and can effectively avoid the influence of outliers on bandwidth estimation. The bandwidth calculation formula is shown below: The probability density distribution is calculated using the above formula. Finally, the coordinates corresponding to the peak value are taken as the fault distance: By introducing a nonparametric kernel density estimation method, it is not necessary to pre-assume the distribution type of the initial fault distance samples. It can directly fit the probability density distribution using the information of the samples themselves, which has strong adaptability. At the same time, the bandwidth is determined by using the median absolute deviation, which is robust to outliers, effectively suppressing the influence of outliers and noise, and improving the robustness of ranging. In addition, by taking the peak value of the probability density distribution as the final fault distance, the region where the samples are most concentrated, i.e. the location of the real fault, can be accurately found, which significantly improves the accuracy and reliability of ranging.

[0016] To verify the effectiveness and accuracy of the method proposed in this invention, a bipolar DC transmission model was built using the Yunnan-Guangdong ±800kV high-voltage direct current transmission project as a prototype. The system topology is as follows: Figure 5As shown, this model adopts a frequency-dependent phase model, which can accurately simulate the frequency-dependent parameter characteristics of transmission lines. The line is a six-split conductor, and the total length of the line is set to 1438km in the simulation. The specific parameters of the line model conform to the actual engineering parameters. In the simulation experiment, a single-phase ground fault with a 0Ω transition resistance occurs 800km away from the rectifier side of the positive line as an example. The sampling rate is set to 1MHz and the fault time is set to 0.4s. First, step S1 is executed to collect the positive and negative voltage and current signals of the DC line on the rectifier side. The collected time-domain signals are decoupled using Kelvin transform to obtain the line mode component and zero-current component. The modal components are analyzed, and then the zero-mode wave impedance Z0 and the line-mode wave impedance Z1 are calculated according to the wave impedance calculation formula. Then, the line-mode voltage reverse traveling wave and the zero-mode voltage reverse traveling wave are calculated according to the voltage reverse traveling wave calculation formula. The obtained reverse traveling wave signals of the two modes include the steady-state information before the fault and the time-domain information after the fault. This invention only needs to analyze the arrival times of each frequency in the first wavehead of the line-mode voltage reverse traveling wave and the zero-mode voltage reverse traveling wave. Next, step S2 is executed to calculate the difference sequences of the voltage reverse traveling wave signals of the line-mode component and the zero-mode component, respectively. The time corresponding to the point of maximum absolute value of the difference in the difference sequence is located and taken as the center time of the first wavehead of the corresponding mode, and recorded as the center time of the line mode. and the center moment of the zero model Then, using this central time as a reference, 1ms of data are extracted before and after it, i.e., 1000 sampling points are extracted in each direction, resulting in linear model time series arrays. and zero modulus time series array The obtained time-domain signals of the inverse traveling wave of the linear mode and zero mode voltages are as follows: Figure 6 As shown, then step S3 is executed, using the improved adaptive S-transform to process the linear time series arrays respectively. and zero modulus time series array To process this, the parameters in the improved S-transform are first adjusted to a=1 and b=0. At this point, the improved S-transform degenerates into the standard S-transform, and the resulting initial time-frequency energy distribution diagram is shown below. Figure 7 As shown, where Figure 7 (a) is the time-frequency diagram of the standard S-transform of the linear model. Figure 7 (b) is the time-frequency diagram of the zero-mode standard S-transform, from Figure 7It can be seen that the energy distribution obtained from the initial time-frequency energy distribution map is relatively blurry, making it difficult to extract the arrival times of each frequency component. This also verifies the limitations of the standard S-transform in processing fault traveling wave signals. Next, step S4 is executed to redistribute and compress the energy of the two-dimensional complex time-frequency coefficient matrix obtained by the standard S-transform, calculate the initial group delay operator, and then perform iterative calculations to find the group delay fixed point. When the difference between the results of consecutive iterations is less than a set threshold of 1 μs, the iteration stops, and a converged time coordinate estimate is obtained. Then, the amplitude of the original time-frequency coefficient matrix is ​​projected along the time axis and accumulated onto the converged time coordinate to obtain a time-frequency distribution with energy concentrated in the time direction. The parameters of the improved S-transform are adjusted based on the obtained time-frequency compacted image. , and To obtain a clearer time-frequency energy distribution map, the final time-frequency energy distribution map of the improved STMSST is as follows: Figure 8 As shown, where Figure 8 (a) is the compacted time-frequency image of the line model. Figure 8 (b) is the zero-mode compacted time-frequency image, compared with Figure 7 and Figure 8 It is evident that after the improved adaptive S-transform and time redistribution multi-synchronization compression processing, the concentration of time-frequency energy is greatly enhanced, and the time-frequency image is clearer, providing a reliable foundation for subsequent time-of-arrival extraction. Then, step S5 is executed: for the obtained time-frequency distribution, for each frequency f in the 1kHz to 350kHz frequency band, the time points with the largest time-frequency amplitudes of the linear mode and zero mode at that frequency are extracted as the time of arrival at that frequency, thus obtaining the set of time-of-arrival points for the linear mode and zero mode. and Then, combined with the extraction of the center moment and Calculate the modulus time of arrival at each frequency. Obtain the modulus time difference vector The obtained modulus wave time-of-arrival curve is as follows: Figure 9 As shown, observe Figure 9 As shown in the modulus time difference curve, in the low-frequency band (below 20kHz), the arrival time difference between the line mode and the zero mode is relatively stable with frequency, exhibiting good regularity. However, when the frequency exceeds 20kHz, the time difference curve shows obvious fluctuations and tortuosities. This is because the zero mode attenuates severely, and the high-frequency signal has extremely low energy after transmission over 800km, resulting in a large deviation in the extracted time of arrival. Therefore, to ensure ranging accuracy, this invention selects the effective frequency band below 20kHz for subsequent fault distance calculation. Finally, step S6 is executed to calculate the line mode wave velocity corresponding to each frequency below 20kHz based on the transmission line parameters. and zero-mode wave speed A set of initial fault distance samples was obtained by using the single-end ranging formula. Then, a nonparametric kernel density estimation method is used to process the initial fault distance sample. First, calculate the sample The median absolute deviation (MAD) is then calculated using the bandwidth formula. Adaptive bandwidth determination Then, the probability density distribution of the fault distance is calculated using a Gaussian kernel function. The resulting fault distance probability density distribution map based on kernel density estimation is shown below. Figure 10 As shown, finally, the distance corresponding to the peak value of the probability density distribution is taken as the final fault location result. The calculated final fault distance was 799.8524 km, with an absolute error of only -147.6 m and a relative error of less than 0.02% compared to the actual fault distance of 800 km. This result fully verifies the high precision and effectiveness of the proposed method. In summary, the single-end accurate ranging method for UHVDC transmission systems based on improved high time-frequency resolution analysis proposed in this invention achieves dynamic adjustment of time-frequency resolution through improved adaptive S-transform, solving the problem that the standard S-transform cannot adapt to different modal signal morphologies. The time redistribution multi-synchronization compression technology further improves the concentration of time-frequency energy, eliminates time-frequency ambiguity, and significantly improves the accuracy of wave arrival time extraction. By considering the frequency-varying characteristics of wave velocity, wave arrival times at multiple frequencies are extracted, and wideband information is used for ranging, avoiding errors caused by a single wave velocity. By introducing a kernel density estimation method based on median absolute deviation, the influence of noise and outliers is effectively suppressed, improving the robustness and accuracy of ranging. Simulation results show that the method of this invention can effectively measure single-pole grounding faults in UHVDC transmission lines. This invention achieves high-precision single-end ranging with an absolute error of less than 150m and a relative error of less than 0.02%, demonstrating significant engineering application value and promising prospects. This method is not only applicable to ±800kV UHVDC transmission systems but can also be extended to other voltage-level DC transmission systems, playing a crucial role in ensuring the safe and stable operation of power systems. Furthermore, the improved adaptive S-transform and the TMSST algorithm based on the improved S-transform proposed in this invention can be applied not only to power system fault ranging but also to other fields requiring high-precision time-frequency analysis, such as mechanical fault diagnosis, seismic signal processing, and biomedical signal processing, showing broad application prospects. In addition, this invention only requires single-end voltage and current signals, eliminating the need for two-end communication and synchronization, thus reducing system construction costs and maintenance difficulty, and improving the reliability and practicality of the ranging system. It provides crucial support for the intelligent operation and maintenance and rapid fault handling of UHVDC transmission systems, effectively reducing outage time, minimizing outage losses, and improving the power supply reliability and economic efficiency of the power system.

[0017] The overall fault location algorithm flowchart of this invention is as follows: Figure 4 As shown in the diagram, the fault traveling wave propagation is illustrated below. Figure 3 As shown above, the basic principles, main features, and advantages of the present invention have been illustrated and described. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples of the present invention and are not intended to limit the invention. Various changes and modifications can be made to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A single-end precise ranging method for an ultra-high voltage direct current transmission system, characterized in that: Includes the following steps: S1. When a single-pole grounding fault occurs in a DC transmission line, the positive and negative voltage and current signals at the protection installation point are collected. The positive and negative voltage and current signals are decoupled using Kelvin-Bell transform to obtain the line-mode component and the zero-mode component. The voltage back-traveling wave signal of the line-mode component and the zero-mode component is calculated. S2. Calculate the differential sequences of the voltage back-traveling wave signals of the line-mode component and the zero-mode component respectively, and locate the time corresponding to the point of maximum absolute value of the difference in the differential sequence. Take this time as the center time of the first wave head of the corresponding mode. Based on the center time, extract data of predetermined lengths before and after to obtain the line-mode time sequence array and the zero-mode time sequence array respectively, and record the center time of extraction of both. S3. Construct an S-transform with adaptively adjustable window function standard deviation, wherein the window function is a Gaussian window function. Use the improved adaptive S-transform to process the linear mode time series array and the zero mode time series array respectively to obtain the corresponding two-dimensional complex time-frequency coefficient matrix. S4. Perform energy redistribution and compression on the two-dimensional complex time-frequency coefficient matrix, calculate the first generation group delay operator of the two-dimensional complex time-frequency coefficient matrix, perform iterative operation on the first generation group delay operator to find its fixed point, stop the iteration when the difference of the continuous iteration results is less than a set threshold, obtain the converged time coordinate estimate, project the magnitude of the original time-frequency coefficient matrix along the time axis and accumulate it onto the converged time coordinate to obtain the time-frequency distribution of energy concentrated in the time direction; S5. For time-frequency distribution, for each frequency in the preset frequency band, extract the time point when the time-frequency amplitude of the linear mode and the zero mode is the largest at that frequency, and take it as the arrival time of that frequency. Combined with the intercepted center time, calculate the modulus arrival time difference at each frequency to obtain the modulus time difference vector. S6. Based on the transmission line parameters, calculate the line mode wave velocity and zero mode wave velocity corresponding to each frequency in the preset frequency band, calculate a set of initial fault distance samples using the single-end ranging formula, process the initial fault distance samples using the non-parametric kernel density estimation method to obtain the probability density distribution of the fault distance, and take the distance corresponding to the peak value of the probability density distribution as the final fault ranging result.

2. The single-end precise ranging method for an ultra-high voltage direct current transmission system according to claim 1, characterized in that: In S1, the process of decoupling the positive and negative voltage and current signals using the Kelvin transform to obtain the line-mode component and the zero-mode component is as follows: When a single-pole grounding fault occurs on an ultra-high voltage direct current (HVDC) transmission line, the positive and negative voltage and current signals of the DC line are collected at the protection installation point on the rectifier side. Then, the collected time-domain signals are decoupled using Kelvin transform to separate the independent line-mode and zero-mode components. The mathematical expression is as follows: Among them, among them, , , , U1m, I1m, U0m, and I0m represent the positive and negative voltages and currents at the measurement points, respectively; U1m, I1m, U0m, and I0m represent the line-mode and zero-mode voltages and currents, respectively. After obtaining the line-mode and zero-mode voltages and currents, the reverse traveling waves of the line-mode voltage and the zero-mode voltage are further calculated based on traveling wave theory for subsequent wavefront analysis. The calculation formulas are as follows: in, and These are the calculated zero-mode voltage inverse traveling wave and the line-mode voltage inverse traveling wave, respectively. and These are the zero-mode impedance and the line-mode impedance, calculated based on the inductance and capacitance per unit length of the line, respectively.

3. The single-end precise ranging method for an ultra-high voltage direct current transmission system according to claim 1, characterized in that: The calculated inverse traveling wave signals of the two modes and Including steady-state and transient time-domain information before and after the fault, the arrival times of each frequency component in the first wavefront are analyzed. First, the interval containing the first wavefront needs to be located from the entire signal. This is achieved by calculating the differential sequences of the line-mode and zero-mode voltage inverse traveling wave signals separately, and finding the point with the maximum absolute value of the difference. This point corresponds to the moment when the signal amplitude changes most drastically, i.e., the center of the first wavefront. The calculation formula is as follows: in, Indicates the discrete sampling point number. Indicates the first The reverse traveling wave voltage value at each sampling point Represents the inverse traveling wave voltage sequence. The difference value of each sampling point This indicates the maximum difference time, with that time taken as the center time of the first wavehead of the corresponding mode. and ; After locating the center time, a segment of data is extracted before and after that time as the target analysis signal. To ensure complete inclusion of the first wavefront information, the extraction time is set to 1 millisecond (ms). The formula for calculating the number of discrete sampling points N is as follows: ,in, Given the sampling rate, the extracted time series array is represented as follows: The output consists of a linear modulus time series array Uwin1 and a zero modulus time series array Uwin0.

4. The single-end precise ranging method for an ultra-high voltage direct current transmission system according to claim 1, characterized in that: In S3, the improved adaptive S-transform window function is a Gaussian window with adjustable standard deviation, whose standard deviation... and window width adjustment factor Defined as: in, For the baseline window width parameter, Modulate the window width amplitude. The modulation attenuation coefficient controls the exponential decay rate; The expression for the improved adaptive S-transform is: When performing step S3, first set the parameter to , This degenerates the improved adaptive S-transform into the standard S-transform, yielding the corresponding two-dimensional complex time-frequency coefficient matrix. and .

5. The single-end precise ranging method for an ultra-high voltage direct current transmission system according to claim 1, characterized in that: In S4, for the two-dimensional complex time-frequency coefficient matrix and Energy redistribution and compression specifically include: S4.1, Time-frequency coefficient matrix obtained based on S3 Calculate the group delay operator of the signal The specific calculation formula is as follows: in, The time-biased weighted S-transform is defined as follows: ； in, It is a Gaussian window function; S4.

2. Perform iterative operations on the group delay operator to find its fixed point. The update formula for the Nth iteration is: The iteration termination condition is: ,in This is the preset iteration termination threshold; S4.3 After the iteration terminates, the original time-frequency coefficient matrix is... amplitude Projected along the time axis and accumulated to the converged time coordinates The above yields the time-frequency distribution of energy concentrated in the time direction. Its discrete form is in, These are the time sampling index and frequency index of the original signal, respectively. Here is the time index after redistribution, and L is the signal length. Represents the floor function; S4.4 Observed time-frequency distribution and The energy focusing effect is restored, and the window width adjustment factor is returned to S3. Parameters in , , Repeat steps S3 and S4 until the time-frequency energy distribution map is obtained.

6. The single-end precise ranging method for an ultra-high voltage direct current transmission system according to claim 1, characterized in that: In S5, the preset frequency band is from 1kHz to 350kHz, and for each frequency within this band... Porta Time and The extraction formula is: in, It is the time-frequency coefficient The modulus value, the modulus time-of-arrival vector Each element in The calculation formula is: in, and These are the zero-mode and linear-mode wave arrival time points in the set of time points. A number.

7. The single-end precise ranging method for an ultra-high voltage direct current transmission system according to claim 1, characterized in that: In S6, the initial fault distance sample is calculated. When selecting the modulus time difference vector The effective frequency band with stable time difference variation is calculated, and the effective frequency band is the frequency band below 20kHz.

8. The single-end precise ranging method for an ultra-high voltage direct current transmission system according to claim 1, characterized in that: In S6, the process of using a nonparametric kernel density estimation method to process the initial fault distance sample X specifically involves: The probability density function of the kernel density estimation is: in, For the sample size, For bandwidth, For kernel functions; The kernel function is a Gaussian kernel function, and its expression is: The bandwidth h is adaptively determined based on the median absolute deviation of sample X, and the calculation formula is as follows: in, This indicates taking the median. This represents the standard deviation estimated based on the absolute deviation of the median.

9. A single-end precise ranging method for an ultra-high voltage direct current transmission system according to claim 7, characterized in that: In S6, the process of using a non-parametric kernel density estimation method to process the initial fault distance sample X to obtain the probability density distribution of the fault distance specifically includes the following steps: S6.1 Calculate the absolute deviation of the median σ^ of the sample X={xi}, using the following formula: S6.2, Based on the absolute deviation of the median calculated in step S6.1 An improved form of the Silverman rule is used to adaptively determine the bandwidth h required for kernel density estimation, calculated as follows: S6.3 Select the Gaussian kernel function Each initial fault distance sample X is transformed into a continuous probability distribution centered at that sample point and with a bandwidth h controlling the width. S6.

4. Superimpose the kernel functions corresponding to all sample points to form the fault distance. Nonparametric probability density estimation Its expression is: This step robustly fits the distribution area of ​​the fault location by performing a smooth probability density estimation on the initial distance samples containing noise and outliers.

10. A single-end precise ranging method for an ultra-high voltage direct current transmission system according to claim 1, characterized in that: In S6, the distance corresponding to the peak value of the probability density distribution is taken as the final fault location result. Specifically, it is calculated and determined using the following formula: in, Let the fault distance probability density function be... The operation represents the search for the probability density function of the fault distance. The independent variable that achieves the global maximum value .

Images