Power distribution network cable early arc fault recognition method based on convolution cross-spectrum coherence

Abstract

This invention discloses a method for identifying early arc faults in distribution network cables based on convolutional cross-spectral coherence. The method includes: acquiring zero-sequence current and grounding current signals at the cable's head end; constructing a coupled detection sequence and a source reference sequence through full convolution operations; determining the fault activity zone based on envelope analysis and relative thresholds; calculating the convolutional cross-spectral coherence within an extended calculation interval; generating adaptive thresholds for low-frequency and high-frequency band coherence using robust statistical methods based on data from the normal period before triggering; comparing the average coherence of the low-frequency and high-frequency bands with their respective thresholds using a dual-band consistency criterion to identify whether a fault has occurred; calculating the effective fault duration through convolutional effect compensation; and classifying early arc faults into half-cycle, multi-cycle, and severe faults. This invention can effectively distinguish between early arc faults, severe faults, and common disturbances such as load switching, with high identification accuracy. Furthermore, the required current signals are readily available, making it highly practical and adaptable for engineering applications.

Description

Technical Field

[0001] This invention belongs to the field of power distribution network fault detection and condition monitoring technology, specifically referring to a method for identifying early arc faults in power distribution network cables based on convolutional cross-spectral coherence. Background Technology

[0002] With the acceleration of urbanization and the continuous increase in the cable coverage of power distribution networks, accurate detection and identification of early cable faults has become a key technical challenge to ensure the safe and stable operation of power distribution networks. Early arc faults, as typical precursors to cable insulation defects, are characterized by complex development processes, weak electrical characteristics, strong nonlinearity, intermittent occurrence, short duration, and susceptibility to background interference. Because their current amplitude is small, they are often masked by normal load fluctuations, making it difficult for traditional overcurrent-based protection devices to effectively identify them. This leads to the inability to promptly isolate the fault, which may eventually evolve into a permanent fault, causing widespread power outages and significant economic losses.

[0003] Currently, detection methods for early arc faults still face many challenges. First, analysis methods based on single-ended current or voltage signals are easily affected by common disturbances such as load switching and electromagnetic interference, resulting in a high false alarm rate. Second, discrimination mechanisms using fixed thresholds are difficult to adapt to the complex and variable noise environments of different sites, making it difficult to balance sensitivity and reliability. Furthermore, existing methods have limitations in feature extraction, lacking the ability to characterize the weak and nonlinear features of early faults. While the traveling wave method performs well in detecting obvious faults, it is slow to respond to the weak transient features of early arcs and relies on high-frequency sampling equipment, leading to high implementation costs and low engineering practicality. The impedance method is greatly affected by transition resistance, limiting its ability to detect early arcs. Traditional frequency domain analysis methods often focus on a single frequency band, failing to fully utilize the coupling characteristics of early arc faults across multiple frequency bands, making it difficult to effectively distinguish true early arc faults from various disturbances.

[0004] Of particular note is that the characteristics of early arc faults and normal operational disturbances highly overlap in both the time and frequency domains, resulting in significant deficiencies in the reliability of existing detection methods. Although zero-sequence current and grounding current contain crucial information reflecting fault coupling, single-signal analysis is susceptible to interference from the complex electromagnetic environment on-site, and effective dual-channel collaborative analysis and feature enhancement techniques are still lacking. Summary of the Invention

[0005] The purpose of this invention is to provide a method for identifying early arc faults in power distribution cables based on convolutional cross-spectral coherence. This method can effectively distinguish between early arc faults, severe faults, and common disturbances such as load switching. It has a high identification accuracy and the required current signal is easy to obtain, thus having high engineering practicality and adaptability.

[0006] To achieve the above objectives, the present invention provides a method for early arc fault identification in distribution network cables based on convolutional cross-spectral coherence, comprising the following steps:

[0007] Step 1) Use the measuring devices installed at the beginning of each cable section of the distribution network to collect zero-sequence current signal and grounding wire current signal in real time. When the monitored quantity meets the preset trigger criteria, extract the normal period data for the two power frequency cycles before the trigger time and the fault period data for the five power frequency cycles after the trigger time.

[0008] Step 2) Perform a full convolution operation on the zero-sequence current and the ground wire current to obtain a coupling detection sequence characterizing the dual-loop coupling features. The zero-sequence current is then subjected to a self-convolution operation to obtain the source reference sequence. ,in It is the zero-sequence current. This is the grounding current;

[0009] Step 3) During the fault period, based on the envelope of the coupled detection sequence, the fault activity area is determined using the relative threshold method and the debounce retention mechanism;

[0010] Step 4) Based on the fault activity region, expand the calculation interval and use short-time Fourier transform to calculate the instantaneous cross-power spectral density and self-power spectral density of the coupled detection sequence and the source reference sequence, and then calculate the convolutional cross-spectral coherence. ;

[0011] Step 5) The cross-spectral coherence of the convolution Within the preset low-frequency and high-frequency bands, in-band averaging is performed and then averaged over time to obtain the average convolutional cross-spectral coherence of the low-frequency band and the average convolutional cross-spectral coherence of the high-frequency band. and ;

[0012] Step 6) On the data from the normal time period, construct a convolutional sequence using the same method and calculate the cross-spectral coherence of the convolution. Based on the statistical characteristics of the average coherence within the normal time period band, generate a low-frequency band adaptive coherence threshold. and high-frequency band adaptive coherence threshold ;

[0013] Step 7) Using the dual-band consistency criterion, the average convolutional cross-spectral coherence of the low-frequency band and the average convolutional cross-spectral coherence of the high-frequency band in the fault activity area are compared with the corresponding adaptive thresholds. When the average coherence of both frequency bands is not lower than their adaptive thresholds, a fault is determined to have occurred; otherwise, it is determined to be a disturbance.

[0014] Step 8) Within the fault activity area, the effective fault duration is calculated based on the envelope of the coupled detection sequence and the time broadening effect of the convolution operation. The fault is then classified into half-cycle, multi-cycle early arc fault, and severe fault types with the power frequency cycle as a reference.

[0015] As a further aspect of the present invention: In step 2), the full convolution operation adopts full mode, and the convolution sequence length is 2N-1, where N is the length of the input signal. The convolution operation enhances the coupling characteristics between the zero-sequence current and the ground wire current, while suppressing single-ended independent noise.

[0016] The coupling detection sequence is the result of the full convolution of the zero-sequence current and the ground wire current: This is used to enhance fault coupling characteristics;

[0017] The source reference sequence is the fully convolutional result of zero-sequence current and zero-sequence current: It is used to provide a reference in the calculation of cross-spectral coherence.

[0018] As a further aspect of the present invention: in step 3), the determination of the fault activity area includes:

[0019] (a) Perform Hilbert transform on the coupled detection sequence to obtain its analytic signal and calculate the envelope curve;

[0020] (b) After the triggering time, the peak value of the envelope curve is obtained, and a relative threshold is determined according to a preset ratio of the peak value, wherein the ratio is preferably 3%-8%;

[0021] (c) Search backward from the position corresponding to the triggering time. When the envelope is lower than the relative threshold for the first time and is held continuously for a period of not less than the preset holding time, the time corresponding to the starting point is determined as the end point of the fault activity area. The holding time is preferably set to 0.2 power frequency cycles.

[0022] (d) When the total duration of the fault activity area is less than the preset minimum duration threshold, the triggering event is directly determined to be a disturbance. The preset minimum duration threshold is 0.008 seconds.

[0023] As a further aspect of the present invention: in step 4), the calculation of convolutional cross-spectral coherence includes:

[0024] (a) The extended calculation interval is set as the time interval of one power frequency cycle extended backward based on the fault activity area to cover the transient process of the arc decay stage and avoid the impact of truncation on the stability of time-frequency estimation.

[0025] (b) Perform short-time Fourier transforms on the coupled detection sequence and the source reference sequence respectively within the extended computation interval to obtain the corresponding complex spectra. correspond , correspond ;

[0026] (c) Calculate the cross-power spectral density and the auto-power spectral density of the two convolutional sequences based on the complex spectrum:

[0027] Signal With signal Cross-power spectral density:

[0028] Signal Self-power spectral density:

[0029] Signal Self-power spectral density:

[0030] (d) Calculate the cross-spectral coherence of the convolution: .

[0031] As a further aspect of the present invention: in step 5), a low-frequency band and a high-frequency band are preset in the frequency direction, and the convolutional cross-spectral coherence is measured within each frequency band. Averaging along the frequency axis yields the in-band instantaneous average coherence curve, followed by time averaging to obtain the low-frequency band average convolutional cross-spectral coherence. Coherence with average convolutional cross spectrum in high-frequency band .

[0032] As a further aspect of the present invention: in step 6), the low-frequency band adaptive coherence threshold... and high-frequency band adaptive coherence threshold The generation methods include:

[0033] (a) On the data during the normal time period, calculate the convolutional cross-spectral coherence under the normal time period in the manner described in steps 2) to 4);

[0034] (b) Intra-band averaging of the convolutional cross-spectral coherence during normal time periods is performed in both the low-frequency and high-frequency bands to obtain the intra-band instantaneous average coherence curves for the low-frequency and high-frequency bands. and ;

[0035] (c) Calculate the median and median absolute deviation for the intra-band average coherence time series of each frequency band, and obtain the low-frequency band adaptive threshold and high-frequency band adaptive threshold by weighting the median by the median absolute deviation:

[0036] Low-frequency adaptive threshold:

[0037] High-frequency adaptive threshold: .

[0038] As a further aspect of the present invention: in step 7), the dual-band consistency criterion is:

[0039] Low-frequency band average coherence And the average coherence in the high-frequency band If the condition is met, a fault is determined to have occurred; otherwise, it is considered a disturbance.

[0040] As a further aspect of the present invention: in step 8), the calculation of the effective fault duration and the classification of fault types include:

[0041] (a) Within the fault activity region, the duration for which the envelope of the statistically coupled detection sequence exceeds the relative threshold. , to obtain the duration after convolution;

[0042] (b) Considering the broadening effect caused by convolution operations, the convolutional duration is compressed to obtain the effective fault duration. ;

[0043] (c) Using the power frequency period T as the time scale, the effective fault duration is divided into intervals:

[0044] Half-cycle arc fault:

[0045] Multi-cycle arc fault:

[0046] Critical fault: .

[0047] The above method is implemented using an early arc fault identification device for power distribution network cables. This device includes: a sampling module, a storage module, a communication module, a power supply module, and a main control module; wherein:

[0048] The sampling module is used to synchronously acquire zero-sequence current and grounding current signals at the beginning of each cable section, and to complete analog conditioning and analog-to-digital conversion.

[0049] The storage module is used to store current waveform data, calculation results, and fault records;

[0050] The communication module supports wired or wireless communication protocols and is used for data interaction and remote configuration between the early fault identification device and the master station.

[0051] The power module provides a stable power supply for the early fault identification device and supports AC / DC adaptation and backup power switching.

[0052] The main control module is the core processing unit, configured with a high-performance processor, used to execute the steps of the method described in any one of claims 1 to 8, and to realize real-time fault identification and analysis.

[0053] The aforementioned early arc fault identification device for distribution network cables belongs to the early arc fault identification system for distribution network cables. The system also includes measuring equipment and a master station system. The measuring equipment is used to realize the synchronous measurement of zero-sequence current and grounding current at the beginning of each cable section, providing dual-channel raw current signals for fault identification.

[0054] Early arc fault identification devices for distribution network cables are deployed at the beginning of each cable section of the distribution network to achieve local fault identification.

[0055] The main station system is used to centrally monitor multiple early fault identification devices and perform data storage, alarm management, operation analysis, and human-machine interaction functions.

[0056] Compared with existing technologies, the beneficial effects of this invention are as follows: It enhances the coupling characteristics of early arc faults through convolution operations, improving the signal-to-noise ratio and effectively distinguishing common disturbances such as early arc faults, severe faults, and load switching, achieving high identification accuracy; the dual-band consistency criterion effectively distinguishes arc faults from single-ended disturbances, reducing false alarm rates; the threshold generation method based on normal time period data automatically adapts to different noise environments, improving adaptability; and it requires no special high-frequency sampling equipment, making it suitable for upgrading existing distribution network automation systems and possessing high engineering practicality. Attached Figure Description

[0057] Figure 1 This is a flowchart of the method of the present invention.

[0058] Figure 2 This is a schematic diagram of the power distribution network simulation model in an embodiment of the present invention. Detailed Implementation

[0059] The invention will now be further described with reference to the accompanying drawings.

[0060] like Figure 1 As shown, the method for identifying early arc faults in distribution network cables based on convolutional cross-spectral coherence includes the following steps:

[0061] Step 1) Use the measuring devices installed at the beginning of each cable section of the distribution network to collect zero-sequence current signal and grounding wire current signal in real time. When the monitored quantity meets the preset trigger criteria, extract the normal period data for the two power frequency cycles before the trigger time and the fault period data for the five power frequency cycles after the trigger time.

[0062] Step 2) Perform a full convolution operation on the zero-sequence current and the ground wire current to obtain a coupling detection sequence characterizing the dual-loop coupling features. The zero-sequence current is then subjected to a self-convolution operation to obtain the source reference sequence. .in It is the zero-sequence current. This is the grounding current.

[0063] The full convolution operation uses full mode, with a convolution sequence length of 2N-1, where N is the input signal length. The convolution operation enhances the coupling characteristics between zero-sequence current and ground wire current while suppressing single-ended independent noise. Specifically:

[0064] The coupling detection sequence is the result of the full convolution of the zero-sequence current and the ground wire current: This is used to enhance fault coupling characteristics;

[0065] The source reference sequence is the fully convolutional result of the zero-sequence current and the zero-sequence current: It is used to provide a reference in the calculation of cross-spectral coherence.

[0066] Step 3) During the fault period, based on the envelope of the coupled detection sequence, the fault activity area is determined by the relative threshold method and the maintenance debouncing mechanism.

[0067] Determining the faulty activity area includes the following steps:

[0068] (a) Perform Hilbert transform on the coupled detection sequence to obtain its analytic signal and calculate the envelope curve;

[0069] (b) After the triggering time, obtain the peak value of the envelope curve, and determine the relative threshold according to the preset proportion of the peak value, preferably 3%-8%;

[0070] (c) Search backward from the position corresponding to the triggering time. When the envelope is lower than the relative threshold for the first time and is held continuously for a period of not less than the preset holding time, the time corresponding to the starting point is determined as the end point of the fault activity area. The holding time is preferably set to 0.2 power frequency cycles.

[0071] (d) When the total duration of the fault activity area is less than the preset minimum duration threshold, the triggering event is directly determined to be a disturbance. The preset minimum duration threshold is 0.008 seconds.

[0072] Step 4) Based on the fault activity region in Step 3), expand the calculation range. Within the expanded calculation range, use short-time Fourier transform to calculate the instantaneous cross-power spectral density and self-power spectral density of the coupled detection sequence and the source reference sequence, and then calculate the convolutional cross-spectral coherence. .

[0073] The calculation of convolutional cross-spectral coherence includes the following steps:

[0074] (a) The extended calculation interval is set as the time interval of one power frequency cycle extended backward based on the fault activity area to cover the transient process of the arc decay stage and avoid the impact of truncation on the stability of time-frequency estimation.

[0075] (b) Perform short-time Fourier transforms on the coupled detection sequence and the source reference sequence within the extended computation interval to obtain the corresponding complex spectra. correspond , correspond , , These are time-domain representations;

[0076] (c) Calculate the cross-power spectral density and the auto-power spectral density of the two convolutional sequences based on the complex spectrum:

[0077] Signal With signal Cross-power spectral density:

[0078] Signal Self-power spectral density:

[0079] Signal Self-power spectral density: ;

[0080] (d) Calculate the cross-spectral coherence of the convolution: .

[0081] Step 5) In the convolutional cross-spectral coherence Within the preset low-frequency and high-frequency bands, in-band averaging is performed and then averaged over time to obtain the average convolutional cross-spectral coherence of the low-frequency band and the average convolutional cross-spectral coherence of the high-frequency band, respectively. and ;

[0082] Specifically, low-frequency and high-frequency bands are preset in the frequency direction, and the cross-spectral coherence of the convolution is measured within each frequency band. Averaging along the frequency axis yields the in-band instantaneous average coherence curve, followed by time averaging to obtain the low-frequency band average convolutional cross-spectral coherence. Coherence with average convolutional cross spectrum in high-frequency band .

[0083] Step 6) On the data from the normal time period, construct the convolutional sequence using the same method and calculate the convolutional cross-spectral coherence. Based on the statistical characteristics of the average coherence within the normal time period band, generate a low-frequency band adaptive coherence threshold. and high-frequency band adaptive coherence threshold ;

[0084] Low-frequency band adaptive coherence threshold and high-frequency band adaptive coherence threshold The generation methods include:

[0085] (a) On the data during the normal time period, calculate the convolutional cross-spectral coherence under the normal time period in the manner described in steps 2) to 4);

[0086] (b) In both the low-frequency and high-frequency bands, the convolutional cross-spectral coherence under normal time periods is averaged within the band and averaged over time to obtain the intra-band instantaneous average coherence curves for the low-frequency and high-frequency bands. and ;

[0087] (c) Calculate the median and median absolute deviation for the intra-band average coherence time series of each frequency band, and obtain the low-frequency band adaptive threshold and high-frequency band adaptive threshold by weighting the median by the median absolute deviation:

[0088] Low-frequency adaptive threshold:

[0089] High-frequency adaptive threshold: .

[0090] Step 7) Using the dual-band consistency criterion, the average convolutional cross-spectral coherence of the low-frequency band and the average convolutional cross-spectral coherence of the high-frequency band in the fault activity area are compared with the corresponding adaptive thresholds. When the average coherence of both frequency bands is not lower than their adaptive thresholds, a fault is determined to have occurred; otherwise, it is determined to be a disturbance.

[0091] The dual-band consistency criterion is:

[0092] Low-frequency band average coherence And the average coherence in the high-frequency band If the condition is met, a fault is determined to have occurred; otherwise, it is considered a disturbance.

[0093] Step 8) Calculate the effective fault duration within the fault activity area based on the envelope of the coupled detection sequence and the time broadening effect of convolution operation. Classify the fault into half-cycle, multi-cycle early arc fault and severe fault types with the power frequency cycle as a reference.

[0094] Effective fault duration calculation and fault type classification include:

[0095] (a) Within the fault activity region, the duration for which the envelope of the statistically coupled detection sequence exceeds a relative threshold. , to obtain the duration after convolution;

[0096] (b) Considering the broadening effect caused by convolution operations, the duration after convolution is compressed to obtain the effective fault duration. ;

[0097] (c) Using the power frequency period T as the time scale, the effective fault duration is divided into intervals:

[0098] Half-cycle arc fault:

[0099] Multi-cycle arc fault:

[0100] Critical fault: .

[0101] To verify the reliability and effectiveness of this invention, a system was built in PSCAD / EMTDC as follows. Figure 2 The power distribution network simulation model shown has a system power frequency of 50Hz, a current sampling frequency of 200kHz, and uses cable laying for the lines, with feeder lengths ranging from 1 to 5km. Zero-sequence current and grounding current measurement points are configured at the beginning of each cable section to collect the single-end current required by the method of this invention.

[0102] Early cable faults were simulated using the Cassie arc model, simulating multi-cycle arcs, half-cycle arcs, and severe faults, with faults set at different locations. For each operating condition, normal time data for the two power frequency cycles before the triggering time and fault time data for the five power frequency cycles after the triggering time were extracted. Based on the zero-sequence current at the beginning of each section and the grounding current, convolutional detection sequences and convolutional reference sequences were constructed. The cross-spectral coherence of the convolution was calculated, and adaptive threshold criteria were introduced in the low-frequency and high-frequency bands to distinguish faults from common disturbances. Furthermore, based on the effective duration of the detection sequence envelope, faults were further classified into half-cycle, multi-cycle early arc faults, and severe faults. Some results under typical simulation conditions are shown in Table 1.

[0103] Table 1. Segment location results under different fault conditions

[0104]

[0105] As can be seen from Table 1, under different fault types, fault durations, and fault locations, the early arc fault identification method for distribution network cables based on convolutional cross-spectral coherence proposed in this invention can ensure that the average coherence of the low-frequency band and high-frequency band under fault conditions is higher than their respective normal time thresholds, while the coherence remains below the threshold under disturbance conditions. The fault and disturbance discrimination results, as well as the classification of half-cycle early arc faults, multi-cycle early arc faults, and severe fault types, are all correct.

[0106] The invention has been described and verified above with reference to typical simulation conditions, demonstrating its basic principles, main features, and beneficial effects. This invention is not limited to the specific embodiments described above. Any equivalent substitutions or modifications made to the system topology, parameter values, frequency band range, and threshold setting methods without departing from the spirit and scope of this invention shall fall within the scope of protection defined by the claims.

Claims

1. A method for identifying early arc faults in distribution network cables based on convolutional cross-spectral coherence, characterized in that, Includes the following steps: Step 1) Use the measuring devices installed at the beginning of each cable section of the distribution network to collect zero-sequence current signal and grounding wire current signal in real time. When the monitored quantity meets the preset trigger criteria, extract the normal period data for the two power frequency cycles before the trigger time and the fault period data for the five power frequency cycles after the trigger time. Step 2) Perform a full convolution operation on the zero-sequence current and the ground wire current to obtain a coupling detection sequence characterizing the dual-loop coupling features. The zero-sequence current is then subjected to a self-convolution operation to obtain the source reference sequence. ,in It is the zero-sequence current. This is the grounding current; Step 3) During the fault period, based on the envelope of the coupled detection sequence, the fault activity area is determined using the relative threshold method and the debounce retention mechanism; Step 4) Based on the fault activity region, expand the calculation interval and use short-time Fourier transform to calculate the instantaneous cross-power spectral density and self-power spectral density of the coupled detection sequence and the source reference sequence, and then calculate the convolutional cross-spectral coherence. ; Step 5) The cross-spectral coherence of the convolution Within the preset low-frequency and high-frequency bands, in-band averaging is performed and then averaged over time to obtain the average convolutional cross-spectral coherence of the low-frequency band and the average convolutional cross-spectral coherence of the high-frequency band. and ; Step 6) On the data from the normal time period, construct a convolutional sequence using the same method and calculate the cross-spectral coherence of the convolution. Based on the statistical characteristics of the average coherence within the normal time period band, generate a low-frequency band adaptive coherence threshold. and high-frequency band adaptive coherence threshold ; Step 7) Using the dual-band consistency criterion, the average convolutional cross-spectral coherence of the low-frequency band and the average convolutional cross-spectral coherence of the high-frequency band in the fault activity area are compared with the corresponding adaptive thresholds. When the average coherence of both frequency bands is not lower than their adaptive thresholds, a fault is determined to have occurred; otherwise, it is determined to be a disturbance. Step 8) Within the fault activity area, the effective fault duration is calculated based on the envelope of the coupled detection sequence and the time broadening effect of the convolution operation. The fault is then classified into half-cycle, multi-cycle early arc fault, and severe fault types with the power frequency cycle as a reference.

2. The method for early arc fault identification of distribution network cables based on convolutional cross-spectral coherence as described in claim 1, characterized in that, In step 2), the full convolution operation is performed in full mode, with a convolution sequence length of 2N-1, where N is the input signal length. The convolution operation enhances the coupling characteristics between the zero-sequence current and the grounding current while suppressing single-ended independent noise. The coupling detection sequence is the result of the full convolution of the zero-sequence current and the ground wire current: This is used to enhance fault coupling characteristics; The source reference sequence is the fully convolutional result of zero-sequence current and zero-sequence current: It is used to provide a reference in the calculation of cross-spectral coherence.

3. The method for early arc fault identification of distribution network cables based on convolutional cross-spectral coherence as described in claim 1, characterized in that, In step 3), the determination of the fault activity area includes: (a) Perform Hilbert transform on the coupled detection sequence to obtain its analytic signal and calculate the envelope curve; (b) After the triggering time, the peak value of the envelope curve is obtained, and a relative threshold is determined according to a preset ratio of the peak value, wherein the ratio is preferably 3%-8%; (c) Search backward from the position corresponding to the triggering time. When the envelope is lower than the relative threshold for the first time and is held continuously for a period of not less than the preset holding time, the time corresponding to the starting point is determined as the end point of the fault activity area. The holding time is preferably set to 0.2 power frequency cycles. (d) When the total duration of the fault activity area is less than the preset minimum duration threshold, the triggering event is directly determined to be a disturbance. The preset minimum duration threshold is 0.008 seconds.

4. The method for early arc fault identification of distribution network cables based on convolutional cross-spectral coherence as described in claim 1, characterized in that, In step 4), the calculation of convolutional cross-spectral coherence includes: (a) The extended calculation interval is set as the time interval of one power frequency cycle extended backward based on the fault activity area to cover the transient process of the arc decay stage and avoid the impact of truncation on the stability of time-frequency estimation. (b) Perform short-time Fourier transforms on the coupled detection sequence and the source reference sequence respectively within the extended computation interval to obtain the corresponding complex spectra. correspond , correspond ; (c) Calculate the cross-power spectral density and the auto-power spectral density of the two convolutional sequences based on the complex spectrum: Signal With signal Cross-power spectral density: Signal Self-power spectral density: Signal Self-power spectral density: (d) Calculate the cross-spectral coherence of the convolution: .

5. The method for early arc fault identification of distribution network cables based on convolutional cross-spectral coherence as described in claim 1, characterized in that: In step 5), a low-frequency band and a high-frequency band are preset in the frequency direction, and the convolutional cross-spectral coherence is measured within each frequency band. Averaging along the frequency axis yields the in-band instantaneous average coherence curve, followed by time averaging to obtain the low-frequency band average convolutional cross-spectral coherence. Cross-spectral coherence with high-frequency band average convolution .

6. The method for early arc fault identification of distribution network cables based on convolutional cross-spectral coherence as described in claim 1, characterized in that: In step 6), the low-frequency band adaptive coherence threshold and high-frequency band adaptive coherence threshold The generation methods include: (a) On the data during the normal time period, calculate the convolutional cross-spectral coherence under the normal time period in the manner described in steps 2) to 4); (b) Intra-band averaging of the convolutional cross-spectral coherence during normal time periods is performed in both the low-frequency and high-frequency bands to obtain the intra-band instantaneous average coherence curves for the low-frequency and high-frequency bands. and ; (c) Calculate the median and median absolute deviation for the intra-band average coherence time series of each frequency band, and obtain the low-frequency band adaptive threshold and high-frequency band adaptive threshold by weighting the median by the median absolute deviation: Low-frequency adaptive threshold: High-frequency adaptive threshold: .

7. The method for early arc fault identification of distribution network cables based on convolutional cross-spectral coherence as described in claim 1, characterized in that: In step 7), the dual-band consistency criterion is: Low-frequency band average coherence And the average coherence in the high-frequency band If the condition is met, a fault is determined to have occurred; otherwise, it is considered a disturbance.

8. The method for early arc fault identification of distribution network cables based on convolutional cross-spectral coherence as described in claim 1, characterized in that: In step 8), the calculation of effective fault duration and the classification of fault types include: (a) Within the fault activity region, the duration for which the envelope of the statistically coupled detection sequence exceeds the relative threshold. , to obtain the duration after convolution; (b) Considering the broadening effect caused by convolution operations, the convolutional duration is compressed to obtain the effective fault duration. ; (c) Using the power frequency period T as the time scale, the effective fault duration is divided into intervals: Half-cycle arc fault: Multi-cycle arc fault: Critical fault: .

9. The method for early arc fault identification of distribution network cables based on convolutional cross-spectral coherence according to any one of claims 1 to 8, characterized in that, This method is implemented using an early arc fault identification device for power distribution network cables. This device includes: a sampling module, a storage module, a communication module, a power supply module, and a main control module; wherein: The sampling module is used to synchronously acquire zero-sequence current and grounding current signals at the beginning of each cable section, and to complete analog conditioning and analog-to-digital conversion. The storage module is used to store current waveform data, calculation results, and fault records; The communication module supports wired or wireless communication protocols and is used for data interaction and remote configuration between the early fault identification device and the master station. The power module provides a stable power supply for the early fault identification device and supports AC / DC adaptation and backup power switching. The main control module is the core processing unit, configured with a high-performance processor, used to execute the steps of the method described in any one of claims 1 to 8, and to realize real-time fault identification and analysis.

10. The method according to claim 9, characterized in that, This device belongs to the early arc fault identification system of power distribution network cables. The system also includes measuring equipment and a master station system. The measuring equipment is used to realize the synchronous measurement of zero-sequence current and grounding current at the beginning of each cable section, providing dual-channel raw current signals for fault identification. Early arc fault identification devices for distribution network cables are deployed at the beginning of each cable section of the distribution network to achieve local fault identification. The main station system is used to centrally monitor multiple early fault identification devices and perform data storage, alarm management, operation analysis, and human-machine interaction functions.

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