An overhead line-cable hybrid line single-phase ground fault locating method and system

Abstract

This invention discloses a method and system for locating single-phase grounding faults in overhead-cable hybrid lines. Signal detection points are deployed at key nodes of the hybrid line to collect three-phase current data before and after the fault, perform phase-mode conversion, and separate the zero-mode component and line-mode component. The Pearson correlation coefficient of the zero-mode component is used to determine the fault range. Based on the Artificial Lemming Algorithm (ALA), the variational mode decomposition (VMD) parameters are optimized, and an adaptive mode decomposition (AMD) model is constructed to decompose the line-mode component. After extracting the IMF4 component, the arrival time of the traveling wave front is captured. The fault distance is calculated using a corresponding dual-end location formula based on the characteristics of the fault range. Simultaneously, multidimensional scaling analysis and the local anomaly factor method are introduced to process abnormal data and remove interfering measurements. This invention can effectively adapt to the structural characteristics of hybrid lines in distribution networks of different voltage levels (110kV and 35kV) and different fault location scenarios, improving the reliability and accuracy of fault location under complex operating conditions, and providing technical support for efficient operation and maintenance of distribution networks.

Description

Technical Field

[0001] This invention relates to a method and system for locating single-phase grounding faults in overhead line-cable hybrid lines based on adaptive mode decomposition optimized by the artificial lemming algorithm, belonging to the field of power system distribution network fault detection technology. Background Technology

[0002] Overhead-cable hybrid lines, as an important component of the distribution network, serve as a crucial channel connecting the core urban power supply area with remote load centers. Their operational stability directly determines the reliability of the distribution network's power supply and has always been a key focus of power system operation and maintenance. One of the main threats to the safe operation of hybrid lines comes from single-phase grounding faults. Line outages caused by such faults not only disrupt industrial production and limit residential power supply but can also lead to regional power outages due to the escalation of the fault, resulting in significant economic losses and social impacts.

[0003] Due to the significant differences in physical structure between overhead lines and cables, diagnosing single-phase grounding faults in mixed lines is far more difficult than in single lines. The open structure of overhead lines makes them susceptible to natural factors such as lightning strikes and icing, resulting in faults that are often transient but exhibit frequent traveling wave reflections. While the enclosed structure of cables can avoid external environmental interference, this often leads to permanent faults with concealed locations. Furthermore, the presence of cable insulation significantly reduces the traveling wave velocity, creating a significant velocity mismatch with overhead lines. These characteristics not only cause conventional traveling wave location methods to produce errors of hundreds of meters due to difficulties in wavefront identification, but also make it difficult for relay protection systems to accurately determine the fault zone, even leading to false tripping or failure to trip. Therefore, developing a technical method that can adapt to the structural characteristics of mixed lines and achieve high-precision fault location has significant engineering application value for improving the efficiency of distribution network fault handling and reducing accident losses. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method and system for locating single-phase grounding faults in overhead line-cable hybrid lines. This method effectively adapts to the structural characteristics of hybrid lines in distribution networks with different voltage levels (110kV and 35kV) and different fault location scenarios, improving the reliability and accuracy of fault location under complex operating conditions and providing technical support for efficient operation and maintenance of distribution networks.

[0005] This invention is implemented according to the following technical solution:

[0006] In a first aspect, the present invention provides a method for locating a single-phase grounding fault in an overhead line-cable hybrid line, comprising the following steps:

[0007] S1: Deploy signal detection points at key nodes of overhead line-cable hybrid lines to collect three-phase current data before and after line faults;

[0008] S2: Perform phase-mode conversion on the collected three-phase current data to separate the zero-mode component and the line-mode component;

[0009] S3: Use the Pearson correlation coefficient of the zero-mode component to determine the fault range;

[0010] S4: Based on the Artificial Lemming Algorithm (ALA), optimize the variational mode decomposition (VMD) parameters, construct an adaptive mode decomposition (AMD) model to perform mode decomposition on the linear mode components, and extract the decomposed IMF4 components;

[0011] S5: Calculate the instantaneous energy of the IMF4 component and capture the time when the traveling wavefront arrives at each signal detection point based on the energy change characteristics;

[0012] S6: Calculate the fault distance by selecting the corresponding dual-end positioning formula based on the characteristics of the fault zone;

[0013] S7: Construct a fault offset matrix, use multidimensional scaling analysis to reduce the dimensionality of the high-dimensional offset matrix, combine the local anomaly factor method to detect and remove abnormal data, and recalculate the fault distance to correct the location results.

[0014] In some embodiments, the deployment rules for signal detection points in step S1 are as follows:

[0015] Overhead lines are divided into at least two sections of equal length, with one signal detection point at each end of the section; cables have one signal detection point at each end, and the signal detection point at the beginning of the cable coincides with the signal detection point at the end of the overhead line at the overhead line-cable connection point.

[0016] In some embodiments, the specific process of step S4 is as follows:

[0017] A1: Initialize the population position of the Artificial Lemming Algorithm (ALA), with the decision variable being the penalty factor of Variational Mode Decomposition (VMD);

[0018] A2: Calculate the fitness of each individual in the population. The fitness function is the sum of the sample entropy of each modal component after variational mode decomposition (VMD).

[0019] A3: Calculate the energy coefficient ,when When performing exploration behavior: migration probability 30%, digging probability 70%, when During development, the following behaviors are executed: 50% probability of foraging and 50% probability of avoidance.

[0020] A4: Iteratively update the population position until the maximum number of iterations is reached or the fitness converges, and output the optimal penalty factor;

[0021] A5: Construct an adaptive mode decomposition (AMD) model based on the optimal penalty factor, calculate the sample entropy of the mode components after variational mode decomposition (VMD), and stop the decomposition and output the IMF4 component when the decreasing trend of sample entropy slows down and the rate of change is less than 0.01 for three consecutive iterations.

[0022] In some embodiments, in step S5, the instantaneous energy of the IMF4 component is calculated using the Teager energy operator (TEO). The Teager energy operator (TEO) is calculated as follows:

[0023] For discrete IMF4 component signals Its instantaneous energy is , where n is the discrete time series index; when When a peak occurs, the corresponding time is determined to be the arrival time of the traveling wave front.

[0024] In some embodiments, in step S6, the corresponding double-end positioning formula is selected according to the fault range determined in step S3, and the fault distance is calculated in combination with the wavefront time obtained in step S5; if the fault is located in the first half or the second half of the overhead line, the double-end positioning formula based on the length of the overhead line is used; if the fault is located in the first half or the second half of the cable, the double-end positioning formula based on the superposition of the cable length and the length of the overhead line is used.

[0025] In some embodiments, the dual-end positioning formula includes:

[0026] When the fault is located in the first half of the overhead line, the fault distance is... ,in This refers to the total length of the overhead power line. , The time to the primary and secondary wavefronts at the detection point at the beginning of the overhead line. , The wavefront time is the time it takes for the detectors at the middle and end points of the overhead line to reach the detection points.

[0027] When the fault is located in the latter half of the overhead line, the fault distance... ,in The time to reach the secondary wavefront at the overhead end detection point;

[0028] When the fault is located at the cable tip, the fault distance is... ,in This is the total length of the cable. The wavefront time to the detection point at the rear end of the cable;

[0029] When the fault is located at the end of the cable, the fault distance is... ,in The time for the secondary wavefront to reach the detection point at the rear end of the cable.

[0030] In some embodiments, the fault location detection process is as follows: the fault is determined to occur in the front section, the rear section, or the cable section of the overhead line by comparing the Pearson correlation; when the fault occurs in the cable section, the fault is determined to occur in the front section or the rear section of the cable section by comparing the time it takes for the wavefront to reach the signal detection points on both sides of the cable.

[0031] In some embodiments, the abnormal data processing procedure in step S7 is as follows:

[0032] B1: Calculate the fault offset value of each signal detection point and construct... Fault offset matrix;

[0033] B2: Perform a bi-centering transformation on the fault offset matrix, calculate the inner product matrix, and extract the first two eigenvectors to obtain the dimensionality-reduced low-dimensional matrix;

[0034] B3: Calculate the k-distance neighborhood of each element in the low-dimensional matrix, and calculate the local reachability density based on the reachability distance of the elements in the neighborhood;

[0035] B4: When the Local Occurrence Factor (LOF) of an element is less than 1, the element is determined to be abnormal data. After removing the abnormal signal segment of the corresponding detection point, steps S5-S6 are executed again.

[0036] In some embodiments, step S3 specifically involves: calculating the Pearson correlation coefficient between the zero-mode components of each signal detection point, determining the fault location interval based on the difference in correlation coefficients, wherein the absolute value of the Pearson correlation coefficient of the zero-mode components of the detection points on both sides of the fault interval is close to 1, and the absolute value of the Pearson correlation coefficient of the zero-mode components of the detection points on both sides of the non-fault interval is close to 0.

[0037] Secondly, the present invention provides a single-phase grounding fault location system for overhead line-cable hybrid lines, comprising:

[0038] The signal acquisition module is configured to deploy signal detection points at key nodes of overhead-cable hybrid lines to collect three-phase current data before and after line faults.

[0039] The phase-mode conversion module is configured to perform phase-mode conversion on the collected three-phase current data to separate the zero-mode component and the line-mode component;

[0040] The fault zone determination module is configured to calculate the Pearson correlation coefficient between the zero-mode components of each signal detection point and determine the fault zone based on the difference in the correlation coefficient.

[0041] The adaptive mode decomposition module is configured to optimize variational mode decomposition (VMD) parameters based on the artificial lemming algorithm (ALA), construct an adaptive mode decomposition (AMD) model to perform mode decomposition on the linear mode components, and extract the decomposed IMF4 components;

[0042] The wavefront detection module is configured to calculate the instantaneous energy of the IMF4 component and capture the time when the traveling wavefront arrives at each signal detection point based on the energy change characteristics.

[0043] The fault distance calculation module is configured to select the corresponding double-end positioning formula based on the determined fault interval and calculate the fault distance in combination with the obtained wavefront time.

[0044] The abnormal data correction module is configured to construct a fault offset matrix, use multidimensional scaling analysis to reduce the dimensionality of the high-dimensional offset matrix, combine the local anomaly factor method to detect and remove abnormal data, and recalculate the fault distance to correct the location results.

[0045] Beneficial effects of this invention:

[0046] The method and system for locating single-phase grounding faults in overhead-cable hybrid lines provided by this invention have a location error of no more than 100m and a calculation accuracy better than 0.9% in distribution network overhead-cable hybrid lines with voltage levels of 35kV-110kV and total line lengths of 40km-100km. Attached Figure Description

[0047] The accompanying drawings, as part of this invention, are provided to further illustrate the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention, but do not constitute an undue limitation thereof. Clearly, the drawings described below are merely some embodiments, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0048] In the attached diagram:

[0049] Figure 1 This is a flowchart of a single-phase grounding fault location method for an overhead line-cable hybrid line according to the present invention;

[0050] Figure 2 This is a schematic diagram of the signal detection point in an embodiment of the present invention;

[0051] Figure 3 This is a flowchart of the ALA-AMD algorithm according to an embodiment of the present invention;

[0052] Figure 4 This is a schematic diagram of a traveling wave during a fault in the front section of an overhead line, according to an embodiment of the present invention.

[0053] Figure 5 This is a schematic diagram of a fault traveling wave in the latter part of an overhead line according to an embodiment of the present invention;

[0054] Figure 6 This is a schematic diagram of a traveling wave in the cable front section fault according to an embodiment of the present invention;

[0055] Figure 7 This is a schematic diagram of a traveling wave in a cable segment fault according to an embodiment of the present invention;

[0056] Figure 8 This is a PSCAD model for an embodiment of the present invention;

[0057] Figure 9 This refers to the phase-mode current in Embodiment 1 of the present invention;

[0058] Figure 10 The IMF4 obtained by AMD calculation in Embodiment 1 of this invention;

[0059] Figure 11 The TEO calculation results and wavefront time are from Embodiment 1 of the present invention;

[0060] Figure 12 This refers to the phase-mode current in Embodiment 2 of the present invention;

[0061] Figure 13 The IMF4 obtained by AMD calculation in Embodiment 2 of this invention;

[0062] Figure 14 The TEO calculation results and wavefront time are for Embodiment 2 of the present invention.

[0063] It should be noted that these accompanying drawings and textual descriptions are not intended to limit the scope of the invention in any way, but rather to illustrate the concept of the invention to those skilled in the art by referring to specific embodiments. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments will be clearly and completely described below with reference to the accompanying drawings. The following embodiments are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0065] like Figure 1 As shown, this invention provides an algorithm for locating single-phase grounding faults in overhead line-cable hybrid lines, comprising the following steps:

[0066] S1: Deploy signal detection points at the overhead line segment nodes, the connection points between the overhead line and the cable, and both ends of the cable in the overhead line-cable hybrid line to collect three-phase current data before and after the line fault;

[0067] S2: The collected three-phase current data is converted using Karrenbauer phase-mode conversion to separate the zero-mode component and two line-mode components;

[0068] S3: Calculate the Pearson correlation coefficient between the zero-mode components of each signal detection point, and determine the fault location based on the difference in correlation coefficient. The absolute value of the Pearson correlation coefficient of the zero-mode components of the detection points on both sides of the fault interval is close to 1, while the absolute value of the Pearson correlation coefficient of the zero-mode components of the detection points on both sides of the non-fault interval is close to 0.

[0069] S4: Construct an adaptive mode decomposition (AMD) model based on the Artificial Lemming Algorithm (ALA), using sample entropy stability as the decomposition termination criterion, perform mode decomposition on the linear mode components, and extract the decomposed IMF4 components; The ALA optimization process includes simulating four behaviors of lemmings: migration, digging, foraging, and hiding, and dynamically switching between the exploration and development stages through energy coefficients to optimize the penalty factor of variational mode decomposition (VMD);

[0070] S5: The instantaneous energy of the IMF4 component is calculated using the Teager energy operator (TEO), and the arrival time of the traveling wavefront at each signal detection point is captured based on the energy change characteristics.

[0071] S6: Based on the fault range determined in step S3, select the corresponding double-end positioning formula and calculate the fault distance by combining the wavefront time obtained in step S5; if the fault is located in the first or second half of the overhead line, use the double-end positioning formula based on the length of the overhead line; if the fault is located in the first or second half of the cable, use the double-end positioning formula based on the superposition of the cable length and the length of the overhead line.

[0072] S7: Construct a fault offset matrix, use multidimensional scaling analysis to reduce the dimensionality of the high-dimensional offset matrix, combine the local anomaly factor method to detect and remove abnormal data, and recalculate the fault distance to correct the location results.

[0073] Further options, such as Figure 2 As shown, in step S1, the deployment rules for signal detection points are as follows: the overhead line is divided into at least two sections of equal length, and one signal detection point is set at the end of each section; the cable is set with one signal detection point at each end, and the signal detection point at the beginning of the cable coincides with the signal detection point at the end of the overhead line at the connection point between the overhead line and the cable.

[0074] Further options, such as Figure 3 As shown, the specific process of ALA optimizing VMD parameters is as follows:

[0075] A1: Initialize the ALA population position, with the decision variable being the penalty factor for VMD;

[0076] A2: Calculate the fitness of each individual in the population. The fitness function is the sum of the sample entropy of each modal component after VMD decomposition.

[0077] A3: Calculate the energy coefficient ,when When the exploration behavior is executed (migration probability 30%, digging probability 70%), When performing development behavior (50% probability of foraging, 50% probability of avoidance);

[0078] A4: Iteratively update the population position until the maximum number of iterations is reached or the fitness converges, and output the optimal penalty factor;

[0079] A5: Construct an AMD model based on the optimal penalty factor, calculate the sample entropy for the modal components after VMD decomposition, and stop the decomposition and output the IMF4 component when the decreasing trend of sample entropy slows down and the rate of change is less than 0.01 for three consecutive iterations.

[0080] In a further embodiment, in step S5, the Teager energy operator is calculated as follows: for discrete IMF4 component signals... Its instantaneous energy is , where n is the discrete time series index; when When a peak occurs, the corresponding time is determined to be the arrival time of the traveling wave front.

[0081] A further solution, in step S6, when the fault is located in the first half of the overhead line, such as... Figure 4 As shown, fault distance ,in This refers to the total length of the overhead power line. , The time to the primary and secondary wavefronts at the detection point at the beginning of the overhead line. , The wavefront time is the time it takes for the fault to reach the detection points at the middle and end of the overhead line; when the fault is located in the latter half of the overhead line, such as Figure 5 As shown, fault distance ,in This refers to the second wavefront time reaching the detection point at the end of the overhead cable; when the fault is located at the cable's front end, such as... Figure 6 As shown, fault distance ,in This is the total length of the cable. This refers to the wavefront time reaching the detection point at the rear end of the cable; when the fault is located at the rear end of the cable, such as... Figure 7 As shown, fault distance ,in The time for the secondary wavefront to reach the detection point at the rear end of the cable.

[0082] The fault location detection is achieved by comparing Pearson correlation data to determine whether the fault occurs in the preceding or following section of the overhead line, or in the cable section. When the fault occurs in the cable section, the timing of the wavefront arrival at signal detection points on both sides of the cable is compared to determine whether the fault occurs in the preceding or following section of the cable.

[0083] A further solution is that, in step S7, the abnormal data processing procedure is as follows:

[0084] B1: Calculate the fault offset value of each signal detection point and construct... Fault offset matrix;

[0085] B2: Perform a bi-centering transformation on the fault offset matrix, calculate the inner product matrix, and extract the first two eigenvectors to obtain the dimensionality-reduced low-dimensional matrix;

[0086] B3: Calculate the k-distance neighborhood of each element in the low-dimensional matrix, and calculate the local reachability density based on the reachability distance of the elements in the neighborhood;

[0087] B4: When the Local Occurrence Factor (LOF) of an element is less than 1, the element is determined to be abnormal data. After removing the abnormal signal segment of the corresponding detection point, steps S5-S6 are executed again.

[0088] It should be noted that, to ensure the effectiveness of this invention, simulation analysis was performed, and a model of an overhead line-cable hybrid line was built in PSCAD software, as shown below. Figure 8 As shown, simulations of single-phase grounding faults at different locations on 110kV, 100km and 35kV, 40km lines were performed.

[0089] Example 1:

[0090] In a model with a 100km line, where both overhead lines and cables are 50km long, the current phase-mode transition at a fault 28km from the first segment is as follows: Figure 9 As shown, the AMD calculation results are as follows: Figure 10 As shown, the TEO calculation results and wavefront time are as follows: Figure 11 As shown, the fault location result is:

[0091]

[0092] The error is 12m, and the calculation accuracy is 0.043%.

[0093] Example 2:

[0094] In a model with a 40km line, 30km of overhead line and 10km of cable, the current phase-mode transition at a fault 31km from the first segment is as follows: Figure 12 As shown, the AMD calculation results are as follows: Figure 13 As shown, the TEO calculation results and wavefront time are as follows: Figure 14 As shown, the fault location result is:

[0095]

[0096] The error is 43m, and the calculation accuracy is 0.14%.

[0097] This invention also provides a single-phase grounding fault location system for overhead line-cable hybrid lines, comprising:

[0098] The signal acquisition module is configured to deploy signal detection points at key nodes of overhead-cable hybrid lines to collect three-phase current data before and after line faults.

[0099] The phase-mode conversion module is configured to perform phase-mode conversion on the collected three-phase current data to separate the zero-mode component and the line-mode component;

[0100] The fault zone determination module is configured to calculate the Pearson correlation coefficient between the zero-mode components of each signal detection point and determine the fault zone based on the difference in the correlation coefficient.

[0101] The adaptive mode decomposition module is configured to optimize variational mode decomposition (VMD) parameters based on the artificial lemming algorithm (ALA), construct an adaptive mode decomposition (AMD) model to perform mode decomposition on the linear mode components, and extract the decomposed IMF4 components;

[0102] The wavefront detection module is configured to calculate the instantaneous energy of the IMF4 component and capture the time when the traveling wavefront arrives at each signal detection point based on the energy change characteristics.

[0103] The fault distance calculation module is configured to select the corresponding double-end positioning formula based on the determined fault interval and calculate the fault distance in combination with the obtained wavefront time.

[0104] The abnormal data correction module is configured to construct a fault offset matrix, use multidimensional scaling analysis to reduce the dimensionality of the high-dimensional offset matrix, combine the local anomaly factor method to detect and remove abnormal data, and recalculate the fault distance to correct the location results.

[0105] In summary, this invention provides a method and system for locating single-phase grounding faults in overhead line-cable hybrid lines, achieving the following functions and effects:

[0106] This invention aims to solve the problem of low fault location accuracy in hybrid power lines caused by wave velocity mismatch, complex traveling wave reflections, and data anomaly interference. The method first deploys signal detection points at key nodes of the hybrid power line to collect three-phase current data before and after the fault. Through Karrenbauer phase-mode conversion, the zero-mode component and line-mode component are separated. The Pearson correlation coefficient of the zero-mode component is used to determine the fault interval. Based on the Artificial Lemming Algorithm (ALA), the variational mode decomposition (VMD) parameters are optimized, and an adaptive mode decomposition (AMD) model is constructed to decompose the line-mode component. After extracting the IMF4 component, the arrival time of the traveling wave front (TEO) is accurately captured using the Teager energy operator. The fault distance is calculated using a corresponding dual-end location formula selected based on the characteristics of the fault interval. Simultaneously, multidimensional scaling analysis and the local anomaly factor method are introduced to process abnormal data and remove interfering measurements. Simulation verification shows that this algorithm can effectively adapt to the structural characteristics of hybrid power lines in distribution networks of different voltage levels (110kV and 35kV) and different fault location scenarios, improving the reliability and accuracy of fault location under complex operating conditions, and providing technical support for efficient operation and maintenance of distribution networks.

[0107] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0108] Furthermore, those skilled in the art will understand that although some embodiments described herein include certain features found in other embodiments but not others, combinations of features from different embodiments are also within the scope of protection of this invention and form different embodiments. For example, in the embodiments described above, those skilled in the art can use them in combination based on known technical solutions and the technical problems to be solved by this application.

[0109] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-described technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for locating single-phase grounding faults in an overhead line-cable hybrid line, characterized in that, Includes the following steps: S1: Deploy signal detection points at key nodes of overhead line-cable hybrid lines to collect three-phase current data before and after line faults; S2: Perform phase-mode conversion on the collected three-phase current data to separate the zero-mode component and the line-mode component; S3: Use the Pearson correlation coefficient of the zero-mode component to determine the fault range; S4: Based on the Artificial Lemming Algorithm (ALA), optimize the variational mode decomposition (VMD) parameters, construct an adaptive mode decomposition (AMD) model to perform mode decomposition on the linear mode components, and extract the decomposed IMF4 components; S5: Calculate the instantaneous energy of the IMF4 component and capture the time when the traveling wavefront arrives at each signal detection point based on the energy change characteristics; S6: Calculate the fault distance by selecting the corresponding dual-end positioning formula based on the characteristics of the fault zone; S7: Construct a fault offset matrix, use multidimensional scaling analysis to reduce the dimensionality of the high-dimensional offset matrix, combine the local anomaly factor method to detect and remove abnormal data, and recalculate the fault distance to correct the location results.

2. The method for locating a single-phase grounding fault in an overhead line-cable hybrid line according to claim 1, characterized in that, In step S1, the deployment rules for signal detection points are as follows: Overhead lines are divided into at least two sections of equal length, with one signal detection point at each end of the section; cables have one signal detection point at each end, and the signal detection point at the beginning of the cable coincides with the signal detection point at the end of the overhead line at the overhead line-cable connection point.

3. The method for locating a single-phase grounding fault in an overhead line-cable hybrid line according to claim 1, characterized in that, The specific process of step S4 is as follows: A1: Initialize the population position of the Artificial Lemming Algorithm (ALA), with the decision variable being the penalty factor of Variational Mode Decomposition (VMD); A2: Calculate the fitness of each individual in the population. The fitness function is the sum of the sample entropy of each modal component after variational mode decomposition (VMD). A3: Calculate the energy coefficient ,when When performing exploration behavior: migration probability 30%, digging probability 70%, when During development, the following behaviors are executed: 50% probability of foraging and 50% probability of avoidance. A4: Iteratively update the population position until the maximum number of iterations is reached or the fitness converges, and output the optimal penalty factor; A5: Construct an adaptive mode decomposition (AMD) model based on the optimal penalty factor, calculate the sample entropy of the mode components after variational mode decomposition (VMD), and stop the decomposition and output the IMF4 component when the decreasing trend of sample entropy slows down and the rate of change is less than 0.01 for three consecutive iterations.

4. The method for locating a single-phase grounding fault in an overhead line-cable hybrid line according to claim 1, characterized in that, In step S5, the instantaneous energy of the IMF4 component is calculated using the Teager energy operator (TEO). The calculation method of the Teager energy operator (TEO) is as follows: For discrete IMF4 component signals Its instantaneous energy is , where n is the discrete time series index; when When a peak occurs, the corresponding time is determined to be the arrival time of the traveling wave front.

5. The method for locating a single-phase grounding fault in an overhead line-cable hybrid line according to claim 1, characterized in that, In step S6, based on the fault range determined in step S3, the corresponding double-end positioning formula is selected, and the fault distance is calculated in combination with the wavefront time obtained in step S5. If the fault is located in the first or second half of the overhead line, the double-end positioning formula based on the length of the overhead line is used. If the fault is located in the first or second half of the cable, the double-end positioning formula based on the superposition of the cable length and the length of the overhead line is used.

6. The method for locating a single-phase grounding fault in an overhead line-cable hybrid line according to claim 5, characterized in that, Dual-end positioning formula include: When the fault is located in the first half of the overhead line, the fault distance is... ,in This refers to the total length of the overhead power line. , The time to the primary and secondary wavefronts at the detection point at the beginning of the overhead line. , The wavefront time is the time it takes for the detectors at the middle and end points of the overhead line to reach the detection points. When the fault is located in the latter half of the overhead line, the fault distance... ,in The time to reach the secondary wavefront at the overhead end detection point; When the fault is located at the cable tip, the fault distance is... ,in This is the total length of the cable. The wavefront time to the detection point at the rear end of the cable; When the fault is located at the end of the cable, the fault distance is... ,in The time for the secondary wavefront to reach the detection point at the rear end of the cable.

7. The method for locating a single-phase grounding fault in an overhead line-cable hybrid line according to claim 6, characterized in that, The fault location detection process is as follows: the fault is determined to occur in the front section, rear section, or cable section of the overhead line by comparing the Pearson correlation; when the fault occurs in the cable section, the fault is determined to occur in the front section or rear section of the cable section by comparing the time it takes for the wavefront to reach the signal detection points on both sides of the cable.

8. The method for locating a single-phase grounding fault in an overhead line-cable hybrid line according to claim 1, characterized in that, In step S7, the abnormal data processing procedure is as follows: B1: Calculate the fault offset value of each signal detection point and construct... Fault offset matrix; B2: Perform a bi-centering transformation on the fault offset matrix, calculate the inner product matrix, and extract the first two eigenvectors to obtain the dimensionality-reduced low-dimensional matrix; B3: Calculate the k-distance neighborhood of each element in the low-dimensional matrix, and calculate the local reachability density based on the reachability distance of the elements in the neighborhood; B4: When the Local Occurrence Factor (LOF) of an element is less than 1, the element is determined to be abnormal data. After removing the abnormal signal segment of the corresponding detection point, steps S5-S6 are executed again.

9. A method for locating a single-phase grounding fault in an overhead line-cable hybrid line according to claim 1, characterized in that, The specific process of step S3 is as follows: calculate the Pearson correlation coefficient between the zero-mode components of each signal detection point, and determine the fault interval based on the difference in correlation coefficient. The absolute value of the Pearson correlation coefficient of the zero-mode components of the detection points on both sides of the fault interval is close to 1, and the absolute value of the Pearson correlation coefficient of the zero-mode components of the detection points on both sides of the non-fault interval is close to 0.

10. A single-phase grounding fault location system for an overhead line-cable hybrid line, characterized in that, include: The signal acquisition module is configured to deploy signal detection points at key nodes of overhead-cable hybrid lines to collect three-phase current data before and after line faults. The phase-mode conversion module is configured to perform phase-mode conversion on the collected three-phase current data to separate the zero-mode component and the line-mode component; The fault zone determination module is configured to calculate the Pearson correlation coefficient between the zero-mode components of each signal detection point and determine the fault zone based on the difference in the correlation coefficient. The adaptive mode decomposition module is configured to optimize variational mode decomposition (VMD) parameters based on the artificial lemming algorithm (ALA), construct an adaptive mode decomposition (AMD) model to perform mode decomposition on the linear mode components, and extract the decomposed IMF4 components; The wavefront detection module is configured to calculate the instantaneous energy of the IMF4 component and capture the time when the traveling wavefront arrives at each signal detection point based on the energy change characteristics. The fault distance calculation module is configured to select the corresponding double-end positioning formula based on the determined fault interval and calculate the fault distance in combination with the obtained wavefront time. The abnormal data correction module is configured to construct a fault offset matrix, use multidimensional scaling analysis to reduce the dimensionality of the high-dimensional offset matrix, combine the local anomaly factor method to detect and remove abnormal data, and recalculate the fault distance to correct the location results.

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