Transmission line high-resolution fault positioning method based on Gaussian kernel function nonlinear correlation estimation

Abstract

The invention discloses a transmission line high-resolution fault positioning method based on Gaussian kernel function nonlinear correlation estimation, and the method comprises the steps: collecting the topological structure and parameter information of a power transmission line, and building a simulation model of the line; on the basis of the simulation model, traversing simulation is carried out by setting different fault positions, and a simulation database of fault voltage or current signals is constructed; the method comprises the following steps: when a fault occurs in a line actually, acquiring a high-frequency transient voltage or current traveling wave signal, performing spectral analysis, and screening out a target frequency band range highly related to a fault distance; calculating correlation coefficients of Gaussian kernel functions of the real fault signal and the reference fault signal in the target frequency band range at different fault positions along the line, and drawing a correlation coefficient curve of the Gaussian kernel functions; acquiring upper and lower bounds of the scaling parameter, and adjusting the correlation coefficient curve according to the upper and lower bounds of the scaling parameter; and obtaining a fault position according to the maximum value of the adjusted correlation coefficient curve.

Description

Technical Field

[0001] This invention belongs to the field of fault location technology, and particularly relates to a high-resolution fault location method for transmission lines based on Gaussian kernel function nonlinear correlation estimation. Background Technology

[0002] With the development of power systems towards higher voltage, longer transmission distances, and more complex network structures, transmission lines face higher requirements for fault location accuracy during operation. Traditional fault location methods mainly include traveling wave methods, impedance methods, and correlation-based full-wave matching methods. Among these, full-wave matching methods based on linear correlation metrics have received widespread attention in recent years due to their ability to achieve high location accuracy under single-ended conditions. These methods typically involve pre-constructing a standard fault waveform database, comparing transient signals measured during a fault with simulated signals at various locations in the database, and determining the fault point based on the location corresponding to the maximum correlation coefficient. Although this type of method is more robust than the traditional impedance method, it still has the following technical limitations:

[0003] 1) Strong frequency band dependence: Linear correlation measures (such as the Pearson correlation coefficient) have significantly different resolutions across different frequency bands. Especially in full-band analysis containing a large number of low-frequency components, the low-frequency-dominated insensitive components can mask the distance-related information contained in the high frequencies, causing the correlation curve to become flat and lose its resolution.

[0004] 2) High-frequency dependence but loss-limited: To obtain higher resolution, high-frequency resonant components are usually required. However, in long-distance overhead lines or underground cables and other high-loss lines, high-frequency components often attenuate severely during propagation, resulting in a decrease in signal-to-noise ratio and the generation of multiple sidelobes in the correlation curve, which seriously affects the reliability of positioning.

[0005] 3) Inability to adjust resolution and robustness: The linear criterion cannot flexibly adjust the sensitivity according to the circuit structure or signal characteristics, making it difficult to balance accuracy and stability under complex working conditions or strong interference.

[0006] In recent years, kernel methods have demonstrated excellent nonlinear feature extraction and pattern discrimination capabilities in fields such as image recognition, signal processing, and modal analysis. In particular, kernel functions, represented by the Gaussian radial basis function (RBF) kernel, possess good local sensitivity and adjustable scaling characteristics. Introducing them into the similarity assessment process of power system fault waveforms is expected to overcome the resolution bottleneck of traditional linear correlation methods, achieving high-precision localization in the low-frequency band, while also improving the applicability of the method in long-distance, high-loss power transmission line scenarios. Summary of the Invention

[0007] To solve the above technical problems, the application provides a transmission line high-resolution fault location method based on Gaussian kernel function nonlinear correlation estimation.

[0008] To achieve the above object, the application provides a transmission line high-resolution fault location method based on Gaussian kernel function nonlinear correlation estimation, which comprises the following steps.

[0009] Collecting the topological structure and parameter information of the power transmission line and establishing a simulation model of the transmission line;

[0010] Based on the simulation model of the transmission line, different fault positions are set along the line, simulation is performed at different fault positions, the simulation current waveform or voltage waveform at different fault positions is obtained, and a simulation current fault database or voltage fault database, i.e., a reference fault signal, is established;

[0011] When a fault occurs in the line, a current sensor or a voltage sensor is used to collect the high-frequency transient voltage traveling wave signal or current traveling wave signal of the fault, and a real fault signal is obtained;

[0012] The real fault signal is subjected to Fourier transform to obtain the frequency spectrum of the fault signal, the frequency spectrum is subjected to screening analysis, and a target frequency band range related to the fault distance is obtained;

[0013] The correlation coefficients of the real fault signal and the reference fault signal in the target frequency band range at different fault positions along the line are calculated, and a Gaussian kernel function correlation coefficient curve is drawn;

[0014] The upper and lower bounds of the scaling scale parameter are obtained, and the correlation coefficient curve is adjusted according to the upper and lower bounds of the scaling scale parameter;

[0015] The fault position is obtained according to the maximum value of the adjusted correlation coefficient curve.

[0016] Optionally, the establishment of the simulation current fault database or voltage fault database comprises the following steps.

[0017] A fault is set at a distance of L / 2 from the line end, the fault resistance is R, the simulation model outputs the fault voltage V or the fault current I, and different positions n are traversed from the line end to the line end L to establish the simulation current fault database or voltage fault database.

[0018] ​​​​​Optionally, when a line fault occurs, a current sensor or a voltage sensor is used to collect a high-frequency transient voltage traveling wave signal or a current traveling wave signal of the fault, and the real fault signal is obtained by:

[0019] By using a distributed online fault current sensor or a voltage sensor, a high-frequency transient voltage traveling wave signal or a current traveling wave signal of the fault is captured when the fault occurs , and the real fault signal is obtained, wherein the analog bandwidth of the current sensor or the voltage sensor should be not less than 1 MHz, and the sampling frequency should be not less than 10 MSps.

[0020] Optionally, the real fault signal is subjected to Fourier transform, including:

[0021] ;

[0022] wherein, is the kth frequency domain component of the output, is the value of the nth time domain sampling point, n is the index of the time domain sample, N is the total number of sample points subjected to the FFT operation, and j is an imaginary unit.

[0023] Optionally, the spectrum is subjected to screening analysis to obtain a target frequency band range related to the fault distance, including:

[0024] ;

[0025] determining the calculated frequency range , adopting the principle that the frequency band is as narrow as possible but needs to contain at least three main resonance frequencies, so that is slightly less than the first-order resonance frequency, i.e. , and is slightly greater than the third-order resonance frequency, i.e. .

[0026] Optionally, the correlation coefficient of the Gaussian kernel function of the real fault signal and the reference fault signal in the target frequency band range under different guessed fault positions along the line is calculated, including:

[0027] ;

[0028] wherein, is the value of the Gaussian radial basis function correlation coefficient, is the measured real position of the fault signal, is the simulated fault signal at the guessed fault position , and is a scaling scale factor of the RBF kernel function.

[0029] ​Optionally, the upper bound of the scaling factor comprises:

[0030] According to the fault waveform, an attenuation oscillation wave is obtained;

[0031] According to the attenuation oscillation wave, an attenuation constant is obtained;

[0032] According to the attenuation constant, an upper bound of the scaling factor is obtained:

[0033] ;

[0034] wherein, H is the upper bound of the scaling factor.

[0035] Optionally, the lower bound of the scaling factor comprises:

[0036] and The energy residual is defined as:

[0037] ;

[0038] is the maximum value of the RBF correlation coefficient , the lower bound of the value of is:

[0039] ;

[0040] wherein, L is the lower bound of the scaling factor.

[0041] Optionally, the distance resolution is adjusted to the desired degree by adjusting the scaling scale parameter in combination with the correlation coefficient curve, comprising:

[0042] ;

[0043] wherein, represents an average function, is an adjustable parameter, and by adjusting a suitable , an ideal positioning distance resolution is obtained.

[0044] Optionally, the fault position is obtained according to the maximum value of the RBF correlation coefficient, comprising:

[0045] ;

[0046] wherein, is the measured voltage of the fault, is the simulated reference voltage, To measure the correlation coefficient between the voltage and the simulation voltage.

[0047] Compared with the prior art, the present application has the following advantages and technical effects:

[0048] 1. The nonlinear correlation positioning method based on the kernel function can realize adaptive control of resolution by adjusting the scaling parameter of the kernel function without depending on the assumption of wave velocity and high-frequency resonance conditions, and has the "super-resolution" feature. Even in the case of limited signal frequency band or serious high-frequency attenuation, the feature information strongly related to the fault distance can still be extracted in the medium and low frequency range, and high-precision positioning can be realized.

[0049] 2. Compared with the positioning method based on the linear correlation degree or the natural frequency method, the present application has stronger robustness to the sidelobe interference formed by the resonance frequency. The kernel mapping mechanism can significantly amplify the weak differences between different fault positions, while suppressing low-frequency interference and false correlation peaks, effectively avoiding multi-solution, misjudgment and other problems, and is suitable for long-distance, strong loss, high-coupling and other transmission line medium scenes. BRIEF DESCRIPTION OF DRAWINGS

[0050] The accompanying drawings, which form a part of this application, are included to provide a further understanding of the application and are incorporated in and constitute a part of this application. The embodiments of this application and their description are used to explain the application and are not intended to limit the application. In the drawings:

[0051] Figure 1 is a kernel function projection schematic diagram of the embodiment of the present application;

[0052] Figure 2 is a schematic diagram of the equivalent circuit of the line ground fault of the embodiment of the present application;

[0053] Figure 3 is a flowchart of a transmission line high-resolution fault positioning method based on nonlinear correlation estimation of a Gaussian kernel function of the embodiment of the present application;

[0054] Figure 4 is a comparison diagram of the linear correlation coefficient curve and the Gaussian kernel function correlation coefficient curve with different values of the embodiment of the present application;

[0055] Figure 5 is a schematic diagram of the linear correlation coefficient curve under different fault distances of the embodiment of the present application;

[0056] Figure 6 is a schematic diagram of the Gaussian kernel function correlation coefficient curve when the fault distance is 44km of the embodiment of the present application;

[0057] Figure 7 is a schematic diagram of the linear correlation coefficient curve of the fault with different grounding resistances of the embodiment of the present application; ​

[0058] Figure 8 is the Gaussian kernel function correlation coefficient curve of the high resistance fault condition (ground resistance is 1000

[0059] Figure 9 is the 10kV tower structure and the field photo when the fault occurs of the embodiment of the application;

[0060] Figure 10 is the 10kV real fault power distribution line topology graph of the embodiment of the application;

[0061] Figure 11 is the linear and Gaussian kernel function correlation coefficient curve comparison graph based on real fault data of the embodiment of the application. DETAILED DESCRIPTION

[0062] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0063] It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a group of computer executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described herein can be executed in a different order.

[0064] The embodiment proposes a transmission line high-resolution fault location method based on Gaussian kernel function nonlinear correlation estimation, as shown in Figure 3 , specifically comprising the following steps:

[0065] Collect the topology structure and parameter information of the power transmission line, and establish a simulation model of the transmission line;

[0066] Based on the simulation model of the transmission line, different fault positions are set along the line, and simulation is performed at different fault positions to obtain simulation current waveforms or voltage waveforms at different fault positions, and a simulation current fault database or voltage fault database, i.e. a reference fault signal, is established;

[0067] When a fault occurs on the line, a current sensor or a voltage sensor is used to collect the high-frequency transient voltage traveling wave signal or current traveling wave signal of the fault, and a real fault signal is obtained;

[0068] The real fault signal is subjected to Fourier transform to obtain the frequency spectrum of the fault signal, the frequency spectrum is analyzed by screening, and a target frequency band range related to the fault distance is obtained;

[0069] ​Correlation coefficients of the Gaussian kernel function of the real fault signal and the reference fault signal in the target frequency band range are calculated at different fault positions along the line, and a Gaussian kernel function correlation coefficient curve is drawn;

[0070] Upper and lower bounds of the scaling scale parameter are obtained, and the correlation coefficient curve is adjusted according to the upper and lower bounds of the scaling scale parameter;

[0071] The fault position is obtained according to the maximum value of the adjusted correlation coefficient curve.

[0072] Specifically, step one: collect the topological structure and parameter information of the power transmission line, and establish a simulation model.

[0073] Step two: when a fault occurs on the line, the high-frequency transient voltage traveling wave signal of the fault is collected by using a voltage sensor, and the preliminary estimated fault position is calculated by using the traveling wave method.

[0074] Step three: in the vicinity of the estimated fault position, the power transmission line in the simulation model is divided into shorter segments, and multiple reference positions are set. The same type of fault simulation as the real fault is performed at each reference position to obtain multiple reference fault signals.

[0075] Step four: Fourier transform is performed on the real fault signal and the reference fault signal to convert all time-domain voltage signals into frequency-domain signals.

[0076] Step five: a specific frequency band is selected, and the Gaussian kernel function correlation coefficient of the real fault signal and the reference fault signal in the frequency domain is calculated. The reference signal position corresponding to the maximum value of the correlation coefficient is the positioning result.

[0077] In this embodiment, Gaussian radial basis function (RBF) kernel is introduced to map the transient fault waveform to high-dimensional Hilbert space, realize nonlinear amplification of the weak difference between signals, and significantly improve the spatial resolution. On this basis, an adjustable kernel correlation coefficient (Kernel Correlation Coefficient, KCC) is constructed to measure the nonlinear similarity between the measured signal and the preset simulation signal, and the position corresponding to the maximum KCC value is taken as the fault point to realize super-resolution positioning of the fault position in long-distance overhead lines, underground cables and complex distribution networks.

[0078] Further, the kernel method based on the kernel function is to convert the data that is difficult to be linearly separated in the low-dimensional space to the Hilbert high-dimensional feature space by means of the support vector machine nonlinear mapping technology, so that it becomes linearly separable in the high-dimensional space, thereby effectively amplifying the difference between the data, as shown in Figure 1 Suppose there is a fault voltage signal at the position With a fault voltage signal occurring at a traditional linear correlation index expressed as equation (1):

[0079]

[0080] By mapping function , two sets of data are projected into high-dimensional space, and the similarity between them is calculated using kernel functions as shown in equation (2). Unlike simple distance indicators such as Euclidean distance, which are:

[0081]

[0082] Equation (2) can represent the correlation coefficient of two sets of data in high-dimensional feature space, which is called kernel-based correlation coefficient. Where and satisfy non-negativity and symmetry.

[0083] The advantage of kernel method is that it does not need to explicitly define high-dimensional feature space H and mapping function to calculate the inner product after mapping. Common kernel functions include linear kernel , polynomial kernel , and Gaussian kernel (Radial Basis Function, RBF):

[0084]

[0085] where are two sets of fault signal data. For linear kernel, its essence is still to calculate the linear correlation of data, which cannot achieve the goal of amplifying signal difference; for polynomial kernel, especially high-order polynomial kernel, it may be affected by complex decision boundary of distant points (including noise or outliers), leading to overfitting of data, and distant noise points will bring uncontrollable influence on the selection of parameters, resulting in poor generalization ability.

[0086] For Gaussian kernel, its kernel value decreases exponentially with distance, which means it focuses on nearby points and ignores distant points. Taking the derivative of its expression with respect to :

[0087]

[0088] Smaller will make the derivative of Gaussian kernel steeper, i.e. small differences in will cause rapid changes in Therefore, according to the characteristics of the data used, can be adjustedThe value of the Gaussian kernel function correlation coefficient between the reference data of the non-fault position and the noise point and the real fault data decreases rapidly, only the reference data of the fault position and the real fault data are kept, and the high spatial resolution positioning research purpose is achieved.

[0089] In formula (3) is a scaling factor of the Gaussian kernel function, which controls the kernel value of the two groups of fault signal data , and further affects the decay rate of the similarity between the non-fault position and the real fault position, which will directly affect the spatial resolution of the positioning result. The value range of the Gaussian kernel function correlation coefficient changes with the characteristics of each group of signal data, such as signal strength and propagation loss, so a fixed value of the Gaussian kernel function correlation coefficient cannot adapt to each group of data with different characteristics, but should be dynamically valued based on the statistical characteristics of the Gaussian kernel function correlation coefficient , such as formula (5).

[0090]

[0091] In the formula, represents the average function, is an adjustable parameter, and the ideal positioning result bandwidth is obtained by adjusting the appropriate .

[0092] In summary, the Gaussian kernel function correlation coefficient is used as the positioning criterion of the embodiment “a transmission line high-resolution fault location method based on Gaussian kernel function nonlinear correlation estimation”, and the specific implementation scheme of step five is as follows. For a power transmission line with a length of L as shown in Figure 2 , a ground fault occurs at a distance of L from the left end, the ground resistance is , the voltage signal generated at the fault is , the impedances at the first and last ends of the line are respectively , and the unit length impedance of the line is . The fault traveling wave propagates on the line and reflects at the impedance discontinuity, and finally the fault voltage traveling wave measured at the left end of the line is . According to this model, a group of fault voltage traveling wave reference signals is generated by simulation analysis, numerical simulation, etc. The above signals are converted to the frequency domain, respectively , , and the Gaussian kernel function correlation coefficient is:

[0093]

[0094] When the Gaussian kernel function correlation coefficient takes the maximum value, the similarity between the reference signal and the real signal is the largest, and the reference position corresponding to this reference signal is the positioning result i.e.

[0095]

[0096] Further, the establishment of the simulation current fault database or the voltage fault database comprises:

[0097] Setting a fault at a distance of , combining the simulation model to output the fault voltage or the current , traversing different positions from the line head to the line end L, and establishing the simulation current fault database or the voltage fault database.

[0098] Further, when a fault occurs in the line, the real fault signal is acquired by using a current sensor or a voltage sensor to collect the high-frequency transient voltage traveling wave signal or the current traveling wave signal of the fault, comprising:

[0099] The real fault signal is acquired by using a distributed online fault current sensor or a voltage sensor to capture the high-frequency transient voltage traveling wave signal or the current traveling wave signal of the fault when the fault occurs, wherein the analog bandwidth of the current sensor or the voltage sensor should be not less than 1 MHz, and the sampling frequency should be not less than 10 MSps.

[0100] Further, the Fourier transform of the real fault signal comprises:

[0101] ; (8)

[0102] wherein is the kth frequency domain component of the output, is the value of the nth time domain sampling point, n is the index of the time domain sample, N is the total number of sample points for the FFT operation, and j is the imaginary unit.

[0103] Further, the target frequency band range related to the fault distance is obtained by screening and analyzing the spectrum, comprising:

[0104] ; (9)

[0105] The calculated frequency range is determined, the principle of as narrow a frequency band as possible but at least containing 3 orders of main resonance frequencies is adopted, let be slightly less than the first order resonance frequency, i.e. , and let be slightly greater than the third order resonance frequency, i.e. .

[0106] ​Further, the correlation coefficient of the Gaussian kernel function of the real fault signal and the reference fault signal in the target frequency band range under different guessed fault positions along the line includes:

[0107] (9)

[0108] wherein, is the Gaussian radial basis function correlation coefficient value, is the measured real position fault signal, is the simulated fault signal at the guessed fault position is the scaling scale factor of the RBF kernel function.

[0109] Further, the upper bound of the scaling scale factor includes:

[0110] According to the fault waveform, an attenuation oscillation wave is obtained;

[0111] According to the attenuation oscillation wave, an attenuation constant is obtained;

[0112] According to the attenuation constant, the upper bound of the scaling scale factor is obtained:

[0113] (10)

[0114] wherein, H is the upper bound of the scaling scale factor.

[0115] Further, the lower bound of the scaling scale factor includes:

[0116] and The energy residual is defined as:

[0117] (11)

[0118] is the maximum value of the RBF correlation coefficient , then The lower bound of the value of

[0119] (12)

[0120] wherein, L is the lower bound of the scaling scale factor.

[0121] Specifically, adjusting the scaling scale parameter in combination with the correlation coefficient curve adjusts the distance resolution to the desired degree, including:

[0122] ​(14)

[0123] wherein, represents the average function, is an adjustable parameter, by adjusting the appropriate get the ideal positioning distance resolution.

[0124] According to the RBF correlation coefficient curve resolution (half width) adjustment to the expected value. When smaller, the corresponding distance resolution smaller (better), but the anti-noise ability is worse; when greater, the corresponding distance resolution greater (worse), but the anti-noise ability is stronger.

[0125] Further, according to the maximum value of the RBF correlation coefficient, the fault location including:

[0126] (15)

[0127] wherein, is the measured voltage of the fault, is the simulation reference voltage, is the correlation coefficient between the measured voltage and the simulation voltage.

[0128] Specifically, whether the calculated correlation coefficient curve satisfy the condition: extreme value characteristics are obvious, in range of 100 meters, a rapid downward trend, range of 100 meters, and the maximum value . If satisfied, according to the maximum value of the Gaussian kernel function correlation coefficient, the positioning result is obtained; if not satisfied, the target frequency band is reselected, the Gaussian kernel function correlation coefficient is recalculated according to the reselected target frequency band, and the positioning result is obtained according to the recalculated Gaussian kernel function correlation coefficient.

[0129] Further, in the case of close-range fault (low fault traveling wave propagation loss) and low fault impedance, the simulation comparison analysis of the Gaussian kernel function correlation coefficient and the linear correlation coefficient is carried out, and the influence of the selection of different scaling factors on the spatial resolution of the positioning result is studied. A single-phase AC line with a length of 50 km is built by using PSCAD software, the voltage level is 10 kV, the power supply is located at the leftmost of the model, the voltage sensor is located at the left side of the line, and the sampling rate is 50 MHz. The fault type is set to ground fault, the fault location is set to 6 km from the left side of the line, and the grounding resistance is set to 20 , the low ground fault resistance. Both ends of the line are connected to a 100k resistance to simulate the high resistance module of the transformer, load and other in the real line, so that the traveling wave signal has a larger reflection coefficient at the discontinuity of the line. In the line 5km before and after the fault location, multiple reference positions are set, and the same ground fault simulation is performed. The fault voltage signal is collected as a set of reference signal database, and the simulation fault signal at 6km is used as the real fault signal in step five.

[0130] All the time domain signals mentioned above are imported into MATLAB, converted to the frequency domain, and a wide frequency band of 10Hz~500kHz is selected. The Gaussian kernel function correlation coefficient of the real fault signal and the reference fault signal is calculated, and the Gaussian kernel function correlation coefficient curve about the fault distance is drawn, named as the correlation coefficient curve, as shown in Figure 4 , where "RBF" in the legend represents the Gaussian kernel function correlation coefficient. The spatial resolution is defined as the bandwidth corresponding to the correlation coefficient of 0.8 in the correlation coefficient curve. Then, according to the correlation coefficient curve, in the case of close distance fault and low fault impedance, the spatial resolution of the linear correlation coefficient positioning result is 2000m, while the spatial resolution of the Gaussian kernel function correlation coefficient positioning result is 600m ( =1), and the spatial resolution is significantly improved. And with the decrease of , the Gaussian kernel function correlation coefficient at non-fault positions decreases more obviously, and better spatial resolution can be achieved. When =0.1, the spatial resolution is 100m, which is 20 times higher than the linear correlation coefficient algorithm.

[0131] In the case of long distance fault (high traveling wave propagation loss) and low fault impedance, the high frequency components of the fault information are greatly attenuated; and when there is high propagation loss, due to the mutual superposition of line correlation resonance, discharge voltage spectrum of fault point and low frequency noise introduced by stray parameters, the spatial resolution of the linear correlation coefficient positioning result is deteriorated. In the simulation line, the fault distance is set at 6km, 20km and 44km respectively, and the linear correlation coefficient curve is shown in Figure 5 . When the fault distance is 44km, due to the influence of traveling wave propagation loss, the correlation coefficient at the distance of 5km before and after the fault position will reach more than 0.8, and the spatial resolution is poor. When the fault position is 44km, the Gaussian kernel function correlation coefficient is used for fault positioning, and the correlation coefficient curve is shown in Figure 6 . When =0.1, the spatial resolution is 400m, which is significantly improved compared with the linear correlation coefficient.

[0132] In the case of close fault (low loss of fault traveling wave propagation) and high fault impedance, the reflection loss of fault traveling wave at the fault point is large, the traveling wave is refracted to the other side of the fault, complex reflection and superposition of reflected traveling wave occur, the signal measured by the sensor at the left end of the line is the traveling wave after serious attenuation and complex superposition, which leads to the deterioration of the spatial resolution of the linear correlation coefficient positioning result. In the simulation line, the grounding resistance is set to 20 , 100 , 500 , 1000 , and the linear correlation coefficient curve is shown in Figure 7 . Due to the influence of the reflection loss at the fault, when the grounding resistance is 100 , 500 , 1000 , the correlation coefficient at the distance of 5km before and after the fault position will reach above 0.8, and the spatial resolution is poor. When the fault position is 1000 , the Gaussian kernel function correlation coefficient is used for fault positioning, and the correlation coefficient curve is shown in Figure 8 . When =0.1, the spatial resolution is 100m, which is significantly improved compared with the linear correlation coefficient.

[0133] In summary, in the case of high line propagation loss and high fault impedance, the spatial resolution of the linear correlation coefficient fault positioning result deteriorates seriously, which leads to the failure to achieve accurate and effective positioning. The fault positioning method based on the Gaussian kernel function correlation coefficient still has high spatial resolution, and can achieve super-resolution by adjusting the scaling factor to meet the positioning accuracy requirement.

[0134] A set of real fault data of power transmission line is available, which is used to verify the proposed fault positioning method. The three-phase AC line voltage level is 10kV, the main line is 9334.8m long, and there are four main branches. The fault occurs on one of the branches. The branch is 2727m long, and the B-phase grounding fault occurs at a distance of 1515m from the branch head. The current sensor is located at the 25th tower at a distance of 2525m from the branch head. The tower structure information and the grounding fault discharge diagram are shown in Figure 9 . The three-phase power frequency and high-frequency traveling wave signals of the fault are measured, the power frequency sampling rate is 20kHz, the traveling wave sampling rate is 20MHz, and the traveling wave sampling time is 1ms. Combined with the above information and the line diagram, the complete line topology diagram can be obtained as shown in Figure 10 .

[0135] The single-ended traveling wave method is used, and the line wave speed is m / s, the preliminary fault location is estimated to be 1582 m away from the branch line head using the B-phase real fault traveling wave. In the vicinity of this location, the line is subdivided at 10 m intervals, and at a distance from this location, the line is subdivided at 20 m, 50 m, 100 m, etc. The line is subdivided from the No. 1 tower (101 m) to the No. 25 tower where the sensor is located. The B-phase ground fault is set at the 48 reference data points obtained by subdivision, and the ground resistance is 20 Thus, 48 reference fault signals are obtained. All reference fault signals and the real fault signal are converted to the frequency domain, and the linear correlation coefficient and the Gaussian kernel function correlation coefficient are calculated. The correlation coefficient curve is shown in Figure 11 .

[0136] The positioning results of the traveling wave method with different wave velocities, the method based on the linear correlation coefficient, and the method based on the Gaussian kernel function correlation coefficient are shown in Table 1. The traveling wave method based on wave head extraction and wave velocity has a maximum error of 9.6%, while the error of the positioning method based on similarity is only 13 m, i.e. 0.85%, and the positioning is more accurate. From the perspective of spatial resolution, the positioning result of the method based on the Gaussian kernel function correlation coefficient improves the spatial resolution to 60 m, and the spatial resolution of the method based on the linear correlation coefficient is 310 m, i.e. the spatial resolution of the method is improved by 5 times in this 10 kV real fault case. It is proved that in the real lossy line, the power transmission line fault location method based on the Gaussian kernel function similarity estimation can realize accurate positioning with high spatial resolution, and meets the engineering index requirements.

[0137] Table 1

[0138] Positioning method Positioning position / m Absolute error / m Relative error Spatial resolution / m Traveling wave method ) 1618 103 8.4% / Traveling wave method ) 1582 67 6.6% / Traveling wave method ) 1713 198 9.6% / Method based on linear correlation coefficient 1528 13 0.85% 310 Method based on Gaussian kernel function correlation coefficient 1528 13 0.85% 60

[0139] The above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any changes or replacements within the technical scope disclosed in the present application can be easily thought of by those skilled in the art, and should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A high-resolution fault location method for transmission lines based on nonlinear correlation estimation of Gaussian kernel functions, characterized in that, The method comprises the following steps: Collecting the topological structure and parameter information of a power transmission line and establishing a simulation model of the transmission line; Based on the simulation model of the transmission line, different fault positions are set along the line, simulation is performed at different fault positions, simulation current waveforms or voltage waveforms at different fault positions are obtained, and a simulation current fault database or a voltage fault database, i.e., a reference fault signal, is established; When a fault occurs in the line, a current sensor or a voltage sensor is used to collect a high-frequency transient voltage traveling wave signal or a current traveling wave signal of the fault, and a real fault signal is obtained; The real fault signal is subjected to Fourier transform to obtain a frequency spectrum of the fault signal, the frequency spectrum is subjected to screening analysis, and a target frequency band range related to the fault distance is obtained; The correlation coefficients of the Gaussian kernel functions of the real fault signal and the reference fault signal in the target frequency band range at different fault positions along the line are calculated, and a Gaussian kernel function correlation coefficient curve is drawn; The upper and lower bounds of the scaling scale parameter are obtained, and the correlation coefficient curve is adjusted according to the upper and lower bounds of the scaling scale parameter; The fault position is obtained according to the maximum value of the adjusted correlation coefficient curve.

2. The method of claim 1, wherein, Establishing the simulation current fault database or the voltage fault database comprises: In distance A fault is set at the location, and the fault resistance is... The simulation model outputs the fault voltage. or current Traverse different positions from the beginning of the line to the end of the line at point L. Establish a simulated current fault database or voltage fault database.

3. The method of claim 1, wherein the method is characterized by, When a fault occurs in the line, a current sensor or a voltage sensor is used to collect a high-frequency transient voltage traveling wave signal or a current traveling wave signal of the fault, and a real fault signal is obtained; By means of distributed online fault current sensors or voltage sensors, high-frequency transient voltage traveling wave signals of the fault are captured at the time of fault occurrence or current traveling wave signals , the real fault signal is obtained, wherein the analog bandwidth of the current sensor or voltage sensor should be not less than 1MHz, and the sampling frequency should be not less than 10MSps.

4. The method of claim 1, wherein the method is characterized by, The real fault signal is subjected to Fourier transform to obtain a frequency spectrum of the fault signal, the frequency spectrum is subjected to screening analysis, and a target frequency band range related to the fault distance is obtained; ； wherein is the kth frequency domain component output, is the value of the nth time domain sample, n is the index of the time domain sample, N is the total number of sample points for which the FFT operation is performed, and j is the imaginary unit.

5. The method of claim 1, wherein the method is characterized by, The correlation coefficients of the Gaussian kernel functions of the real fault signal and the reference fault signal in the target frequency band range at different fault positions along the line are calculated, and a Gaussian kernel function correlation coefficient curve is drawn; ； Determination of the frequency range of the calculation , adopting the principle of making the frequency band as narrow as possible but at least containing the 3rd order main resonance frequency, , making the 1st order resonance frequency slightly smaller, i.e. , making the 3rd order resonance frequency slightly larger, i.e. , and .

6. The method of claim 1, wherein, The upper and lower bounds of the scaling scale parameter are obtained, and the correlation coefficient curve is adjusted according to the upper and lower bounds of the scaling scale parameter; ； wherein is a Gaussian radial basis function correlation coefficient value, is a measured real position is a fault signal at the fault location, is a simulated fault signal at the guessed fault location is a simulated fault signal at the guessed fault location is a scaling factor of the RBF kernel function.

7. The method of claim 6, wherein the method is characterized by, The fault position is obtained according to the maximum value of the adjusted correlation coefficient curve. Establishing the simulation current fault database or the voltage fault database comprises: When a fault occurs in the line, a current sensor or a voltage sensor is used to collect a high-frequency transient voltage traveling wave signal or a current traveling wave signal of the fault, and a real fault signal is obtained; The real fault signal is subjected to Fourier transform to obtain a frequency spectrum of the fault signal, the frequency spectrum is subjected to screening analysis, and a target frequency band range related to the fault distance is obtained; ； wherein H is an upper bound for the scale factor.

8. The method of claim 1, wherein the method is characterized by, The correlation coefficients of the Gaussian kernel functions of the real fault signal and the reference fault signal in the target frequency band range at different fault positions along the line are calculated, and a Gaussian kernel function correlation coefficient curve is drawn; and The energy residual is defined as: ； is the RBF correlation coefficient is the maximum value of the lower bound of the value of is ； wherein L is the lower bound for the scale factor.

9. The method of claim 1, wherein the method is characterized by, The upper and lower bounds of the scaling scale parameter are obtained, and the correlation coefficient curve is adjusted according to the upper and lower bounds of the scaling scale parameter; The fault position is obtained according to the maximum value of the adjusted correlation coefficient curve. Establishing the simulation current fault database or the voltage fault database comprises: When a fault occurs in the line, a current sensor or a voltage sensor is used to collect a high-frequency transient voltage traveling wave signal or a current traveling wave signal of the fault, and a real fault signal is obtained; The real fault signal is subjected to Fourier transform to obtain a frequency spectrum of the fault signal, the frequency spectrum is subjected to screening analysis, and a target frequency band range related to the fault distance is obtained; The correlation coefficients of the Gaussian kernel functions of the real fault signal and the reference fault signal in the target frequency band range at different fault positions along the line are calculated, and a Gaussian kernel function correlation coefficient curve is drawn; The upper and lower bounds of the scaling scale parameter are obtained, and the correlation coefficient curve is adjusted according to the upper and lower bounds of the scaling scale parameter; The fault position is obtained according to the maximum value of the adjusted correlation coefficient curve. Establishing the simulation current fault database or the voltage fault database comprises: When a fault occurs in the line, a current sensor or a voltage sensor is used to collect a high-frequency transient voltage traveling wave signal or a current traveling wave signal of the fault, and a real fault signal is obtained; The real fault signal is subjected to Fourier transform to obtain a frequency spectrum of the fault signal, the frequency spectrum is subjected to screening analysis, and a target frequency band range related to the fault distance is obtained; The correlation coefficients of the Gaussian kernel functions of the real fault signal and the reference fault signal in the target frequency band range at different fault positions along the line are calculated, and a Gaussian kernel function correlation coefficient curve is drawn; The upper and lower bounds of the scaling scale parameter are obtained, and the correlation coefficient curve is adjusted according to the upper and lower bounds of the scaling scale parameter; The fault position is obtained according to the maximum value of the adjusted correlation coefficient curve. ； wherein, represents the average function, is an adjustable parameter, by adjusting the appropriate to obtain the desired positioning distance resolution.

10. The method of claim 1, wherein the method is characterized by, According to the maximum value of the RBF correlation coefficient, the fault position is derived Comprising: ； wherein, is the measured voltage at fault, is the simulated reference voltage, is the correlation coefficient between the measured voltage and the simulated voltage.

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