A cable network fault locating method based on feature modal impedance spectrum

Abstract

This application discloses a cable network fault location method based on characteristic modal impedance spectrum, belonging to the field of distribution network fault diagnosis technology. Addressing the industry pain points of existing cable fault location methods, such as weak anti-interference capability, low accuracy under high-impedance faults, and high requirements for sampling hardware, this solution first constructs a multi-conductor transmission line model and simultaneously collects multiple electrical signals from the cable head end. After preprocessing and mode decoupling, fault-sensitive characteristic modal components are obtained. After constructing a fault initiation criterion, the characteristic modal impedance is calculated, and a broadband impedance spectrum is constructed. Finally, the broadband impedance spectrum is mapped to the spatial domain to complete fault location. This method can significantly improve the location accuracy and robustness under complex operating conditions, greatly reduce engineering deployment costs, and adapt to the rapid fault location needs of distribution network cable networks of various structures.

Description

Technical Field

[0001] This application belongs to the field of power distribution network fault diagnosis technology, and specifically relates to a cable network fault location method based on characteristic mode impedance spectrum. Background Technology

[0002] Currently, commonly used cable fault location methods mainly include the traveling wave method and the impedance method. The traveling wave method calculates the fault distance by analyzing the propagation time of the transient traveling wave generated by the fault in the cable. However, this method requires extremely high sampling frequencies (usually above MHz), and in actual distribution networks, due to numerous line branches, unstable wave speeds, and severe noise interference, it is difficult to identify the traveling wave front, thus limiting the location accuracy. The impedance method (such as the traditional single-ended / double-ended impedance method) calculates the impedance by measuring the voltage and current at power frequency before and after the fault to locate it. However, it is easily affected by transition resistance, load current, and system operating mode, especially in high-resistance faults where the location error is relatively large.

[0003] In recent years, broadband impedance spectroscopy (BIS) technology has been introduced into the field of cable fault diagnosis. This method senses the cable condition by injecting a broadband excitation signal into the cable and analyzing its input impedance spectrum at the beginning. However, existing BIS-based methods mainly target single-phase or coaxial cables and do not fully consider the complex electromagnetic coupling effects between the conductors of each phase and the metal shielding layer of three-phase cables. When a single-phase ground fault occurs, traditional phase domain voltage and current signals are not sensitive to fault characteristics under high-impedance faults or complex distribution network structures, leading to difficulties in fault feature extraction and a sharp decrease in location accuracy. Existing technologies generally suffer from the following problems: excessively high sampling rate requirements, failure to consider multi-conductor coupling structures, poor noise interference resistance, large location errors under high-impedance faults, and insufficient robustness when data is missing. Summary of the Invention

[0004] This application provides a cable network fault location method based on characteristic mode impedance spectrum. By constructing a multi-conductor coupled transmission line model, introducing phase mode transformation to extract characteristic modes, and designing a broadband characteristic mode impedance spectrum, it maintains physical interpretability and location robustness even under low sampling rate and high data missing rate, in order to solve the problem of location failure under multiple constraints such as high impedance faults, low sampling rate and data missing.

[0005] To achieve the above objectives, this application provides a cable network fault location method based on characteristic mode impedance spectrum, comprising the following steps:

[0006] Step S1: Construct a multi-conductor transmission line model, obtain cable distribution parameters, and simultaneously acquire multiple electrical signals from the cable head end;

[0007] Step S2: Preprocess and decouple the acquired multi-channel electrical signals to extract the corresponding six modal signals;

[0008] Step S3: Construct a phase-mode transformation matrix based on the cable distribution parameters to convert the phase domain signal into a mode domain signal, and obtain the voltage σ mode uσ(t) and the current α mode iα(t);

[0009] Step S4: Construct a fault initiation criterion based on the voltage σ mode uσ(t) and the current α mode iα(t);

[0010] Step S5: Calculate the characteristic mode impedance and construct a broadband impedance spectrum to highlight the transient characteristics of the fault;

[0011] Step S6: Map the broadband impedance spectrum to the spatial domain to locate the fault point.

[0012] In one embodiment, the multiple electrical signals in step S1 are measured at the cable head end as the measurement point and the three-phase conductor voltages uA(t), uB(t), uC(t), three-phase conductor currents iA(t), iB(t), iC(t), and the voltages of each phase shielding layer to ground uAS(t), uBS(t), uCS(t) are collected synchronously at a sampling rate fs.

[0013] In one embodiment, the preprocessing in step S2 is as follows: First, a system characteristic matrix YZ is constructed based on the parallel admittance matrix Y and the series impedance matrix Z of the cable. By solving the complex eigenvalues ​​of this matrix, a 6×6 order complex similarity transformation matrix is ​​obtained. ;

[0014] Secondly, to eliminate the phase uncertainty caused by complex number operations, a normalized real number processing algorithm is used for T. IC The transformation is performed as follows:

[0015] ①

[0016] In one embodiment, the mode decoupling is based on the voltage-current coupling relationship, and the voltage transformation matrix T is solved. V A complete phase mode transformation system is established, as shown below:

[0017] ;②

[0018] After modal decoupling, the six modal signals are denoted as follows: , , , , and As shown in formula ③;

[0019] ③

[0020] In one embodiment, the transformation algorithm for converting the phase domain signal to the modal domain signal in step S3 is as follows:

[0021] ⑤

[0022] Formula ⑤ includes the three-phase conductor voltages uA(t), uB(t), uC(t) of A, B, and C, the three-phase conductor currents iA(t), iB(t), iC(t), and the voltages of each phase shielding layer to ground uAS(t), uBS(t), uCS(t).

[0023] In one embodiment, step S4 involves calculating the effective value Uσ of the voltage σ mode uσ(t) and the effective value Iα of the current α mode iα(t) in real time, and dynamically comparing them with the reference thresholds Uσ_UBL and Iα_UBL under the maximum unbalanced load condition.

[0024] In one embodiment, the fault initiation criterion is defined as follows: when any of the following conditions are met, it is determined that a single-phase ground fault has occurred in the system, and the fault location process is initiated; if the following conditions are not met, S1 to S4 are continuously monitored and executed in a loop until the fault criterion is triggered.

[0025] ⑥

[0026] In formula ⑥, T is the duration of the signal; t0 is the moment of signal abrupt change. It is the voltage σ-mode value corresponding to the maximum single-phase load operating condition; It is the current mode value corresponding to the maximum single-phase load operating condition.

[0027] In one embodiment, the characteristic mode impedance Zα(t) in step S5 is defined as the ratio of the voltage α mode to the current α mode, as shown below:

[0028] ⑦

[0029] In one embodiment, when constructing the broadband impedance spectrum Zα(jω), a fast Fourier transform is performed on uα(t) and iα(t) within a short time window after the fault to obtain the broadband frequency domain representations Uα(jω) and Iα(jω), and then their ratio is taken to obtain Zα(jω), as shown below:

[0030] ⑧

[0031] In one embodiment, the method for mapping the broadband impedance spectrum to the spatial domain in step S6 is as follows:

[0032] S601. Calculate the actual propagation velocity v of the traveling wave in the cable based on the cable distribution parameters and the corrected relative permittivity ε′; wherein the formula for calculating the relative permittivity ε′ is as follows:

[0033] ; ⑨

[0034] In formula ⑨, R1 is the conductor radius; R2 is the shielding radius; a is the inner radius of the cable insulation; b is the outer radius of the cable insulation; and ε is the relative permittivity of the cable insulation.

[0035] The formula for calculating the actual propagation wave speed v is as follows:

[0036] ;⑩

[0037] In formula ⑤, c is the speed of light in a vacuum.

[0038] S602. Establish a mapping model from the frequency domain reflection signal to the spatial domain, perform inverse Fourier transform on the broadband impedance spectrum Zα(jω), and extract the reflection time Δt corresponding to the peak point in the time domain impulse response at the impedance discontinuity point;

[0039] S603. Based on the principles of double-ended ranging and single-ended reflection, and combining the wave velocity v and the reflection time Δt, calculate the distance xf from the fault point to the beginning; the calculation formula is as follows:

[0040] ⑥

[0041] A cable network fault location system based on characteristic modal impedance spectrum, comprising:

[0042] Multi-channel synchronous data acquisition unit: used to synchronously acquire voltage and current signals at the cable head end at a low sampling rate (≤10kHz);

[0043] Signal preprocessing and decoupling module: used to perform noise reduction and phase mode transformation on the acquired signals;

[0044] Fault initiation detection module: used for real-time monitoring and initiation of fault location based on voltage σ mode uσ(t) and current α mode iα(t);

[0045] Characteristic Mode Impedance Spectrum Calculation Module: Used to calculate characteristic mode impedances and generate their broadband impedance spectra;

[0046] Frequency-time-space mapping positioning module: used to convert broadband impedance spectrum into spatial domain distance and output the location of the fault point;

[0047] Result output and display unit: used to display fault distance and positioning error information.

[0048] Compared with the prior art, the beneficial effects of this application are:

[0049] 1. Significantly improved anti-interference capability: By extracting fault-sensitive characteristic mode components through mode decoupling technology to construct a broadband impedance spectrum, the identification of weak fault features submerged by noise is greatly enhanced, effectively improving the robustness of fault location under strong noise interference environment and ensuring the reliability of location under complex field conditions.

[0050] 2. Significantly enhanced adaptability to high-resistivity faults: The broadband impedance spectrum constructed based on characteristic modes is more sensitive to the changes in wave impedance caused by faults, effectively overcoming the adverse effects of transition resistance on the location results, greatly expanding the applicable scenarios for fault location, and solving the industry pain point of location failure under high-resistivity faults in traditional methods. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 This is a schematic diagram of the cross-sectional structure of the three-phase single-core cable used in this application;

[0053] Figure 2 A schematic diagram of the overall implementation process provided for this application;

[0054] Figure 3 The characteristic modal impedance spectra calculated under different fault conditions in this application are shown below;

[0055] Figure 4 This is a diagram showing the final fault location results obtained under different fault conditions in this application;

[0056] Figure 5 This is a model diagram of the 10kV distribution network cable fault simulation system built for this application;

[0057] Figure 6 This is a comparison of the localization results before and after denoising under strong noise interference (SNR=10dB).

[0058] Figure 7 This is a diagram showing the voltage and current signals and positioning results under severe operating conditions with 20% data loss. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions in the embodiments of this application are described clearly and completely below. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are also within the scope of protection of this application.

[0060] See Figures 1 to 7 This application provides a cable network fault location method based on characteristic mode impedance spectrum, comprising the following steps:

[0061] Step S1: Construct a multi-conductor transmission line model, obtain cable distribution parameters, and simultaneously acquire multiple electrical signals from the cable head end.

[0062] The multi-conductor transmission line model is based on the frequency of the three-phase single-core cable under test and relies on the distributed parameter model to obtain its series impedance matrix Z and parallel admittance matrix Y per unit length. This model fully characterizes the electromagnetic coupling effect between each phase conductor and the metal shielding layer.

[0063] It should be noted that the three-phase conductor voltages uA(t), uB(t), uC(t), three-phase conductor currents iA(t), iB(t), iC(t), and the voltages of each phase shield layer to ground uAS(t), uBS(t), uCS(t) are further synchronously acquired at a sampling rate of fs=3.2kHz to ensure complete capture of the transient process.

[0064] Step S2: Preprocess and decouple the acquired multi-channel electrical signals to extract the corresponding six modal signals.

[0065] The preprocessing is as follows: First, a system characteristic matrix YZ is constructed based on the parallel admittance matrix Y and series impedance matrix Z of the cable. By solving the complex eigenvalues ​​of this matrix, a 6×6 complex similarity transformation matrix is ​​obtained. ;

[0066] Secondly, to eliminate the phase uncertainty caused by complex number operations, a normalized real number processing algorithm is used for T. IC The transformation is performed as follows:

[0067] ①

[0068] The further modal decoupling calculation method is as follows: Based on the voltage-current coupling relationship derived from equation ②, solve for the voltage transformation matrix T. V This establishes a complete phase-mode transformation system. The six decoupled modal signals (taking voltage as an example) can be denoted as follows: , , , , and As shown in equation ③. Although theoretically there are also 6 modes of current, according to equation ④, except for the current α mode, the other mode signals cannot be calculated from the measured signals.

[0069] ;②

[0070] ;③

[0071] ④

[0072] Step S3: Construct a phase-mode transformation matrix based on the cable distribution parameters to convert the phase-domain signal into a mode-domain signal, and obtain the voltage σ-mode uσ(t)u σ (t) and current α mode iα(t)i α (t).

[0073] The transformation algorithm for converting phase domain signals to modal domain signals is shown below:

[0074] ⑤

[0075] Formula ⑤ includes the three-phase conductor voltages uA(t), uB(t), uC(t) of A, B, and C, the three-phase conductor currents iA(t), iB(t), iC(t), and the voltages of each phase shielding layer to ground uAS(t), uBS(t), uCS(t).

[0076] It should be noted that in this embodiment, the voltage σ mode uσ(t) and the current α mode iα(t) are selected to construct the broadband impedance spectrum. Alternatively, a combination of the voltage σ mode uσ(t) and the current σ mode, or other fault-sensitive characteristic mode pairs such as the voltage γ mode (e.g., the combination of voltage σ and current α), can be used to construct the characteristic mode impedance, which can also effectively amplify the fault characteristics and improve the robustness of fault location.

[0077] Step S4: Construct a fault initiation criterion based on the voltage σ mode uσ(t) and the current α mode iα(t).

[0078] Calculate the real-time voltage σ-mode effective value Uσ and the current α-mode effective value Iα, and dynamically compare them with the reference thresholds Uσ_UBL and Iα_UBL under the system's maximum unbalanced load condition. When any of the following conditions are met, determine that a single-phase ground fault has occurred in the system and initiate the fault location process:

[0079] ⑥

[0080] In formula ⑥, T is the duration of the signal; t0 is the moment of signal abrupt change. It is the voltage σ-mode value corresponding to the maximum single-phase load operating condition; It is the current mode value corresponding to the maximum single-phase load operating condition.

[0081] It should be noted that this embodiment uses an effective value comparison criterion based on modal components. Alternatively, wavelet transform, Hilbert-Huang transform (HHT) and other signal singularity detection algorithms can be used to monitor the instantaneous amplitude or instantaneous energy of uσ(t) or iα(t). When it exceeds the adaptively set dynamic threshold, the positioning is triggered.

[0082] Step S5: Calculate the characteristic mode impedance and construct a broadband impedance spectrum to highlight the transient characteristics of the fault.

[0083] The characteristic mode impedance Zα(t) is defined as the ratio of the voltage σ-mode uσ(t) to the current α-mode iα(t), used to amplify the transient characteristics of the fault, i.e., to highlight the transient characteristics of the fault. The formula is shown below:

[0084] ⑦

[0085] Furthermore, by performing a Fast Fourier Transform on uα(t) and iα(t) within a short time window (1-2 power frequency cycles) after the fault, the frequency domain expressions Uα(jω) and Iα(jω) in the broadband are obtained, and then a broadband impedance spectrum Zα(jω) is constructed. This broadband impedance spectrum exhibits a significant abrupt change or resonant peak at the characteristic frequency corresponding to the fault point. (See [reference]). Figure 3 As shown. The formula for calculating the broadband impedance spectrum Zα(jω) is as follows:

[0086] ⑧

[0087] Step S6: Map the broadband impedance spectrum to the spatial domain to locate the fault point.

[0088] The method for mapping the broadband impedance spectrum to the spatial domain is as follows:

[0089] S601. Calculate the actual propagation velocity v of the traveling wave in the cable based on the cable distribution parameters and the corrected relative permittivity ε′; wherein the formula for calculating the relative permittivity ε′ is as follows:

[0090] ; ⑨

[0091] In formula ⑨, R1 is the conductor radius; R2 is the shielding radius; a is the inner radius of the cable insulation; b is the outer radius of the cable insulation; and ε is the relative permittivity of the cable insulation.

[0092] The formula for calculating the actual propagation wave speed v is as follows:

[0093] ⑤

[0094] In formula ⑤, c is the speed of light in a vacuum.

[0095] It should be noted that the wave velocity in this implementation plan is calculated using theoretical formulas. As an alternative, a test signal of known frequency can be injected during normal cable operation, or historical fault data can be used to calibrate the actual traveling wave velocity of the cable line online or offline, thereby obtaining propagation parameters that are more consistent with the on-site working conditions and further improving positioning accuracy.

[0096] S602. Establish a mapping model from the frequency domain reflection signal to the spatial domain, perform an inverse Fourier transform on the broadband impedance spectrum Zα(jω), and extract the reflection time Δt corresponding to the peak point in the time domain impulse response and the impedance discontinuity point.

[0097] It should be noted that in this embodiment, the frequency domain and time domain are converted by inverse Fourier transform (FFT / IFFT). Alternatively, time-frequency analysis methods such as S-transform, Chirp-Z-transform, or wavelet packet transform can be used to convert the broadband impedance spectrum Zα(jω) to the time-frequency domain or spatial domain, thereby identifying the location of the fault point.

[0098] S603. Based on the principles of double-ended ranging and single-ended reflection, and combining the wave velocity v and the reflection time Δt, calculate the distance xf from the fault point to the beginning; the calculation formula is as follows:

[0099] ⑥

[0100] In this embodiment, the positioning result is as follows: Figure 4 As shown.

[0101] A cable network fault location system based on characteristic modal impedance spectrum, comprising:

[0102] Multi-channel synchronous data acquisition unit: used to synchronously acquire voltage and current signals at the cable head end at a low sampling rate;

[0103] Signal preprocessing and decoupling module: used to perform noise reduction and phase mode transformation on the acquired signals;

[0104] Fault initiation detection module: used for real-time monitoring and initiation of fault location based on voltage σ mode uσ(t) and current α mode iα(t);

[0105] Characteristic Mode Impedance Spectrum Calculation Module: Used to calculate characteristic mode impedances and generate their broadband impedance spectra;

[0106] Frequency-time-space mapping positioning module: used to convert broadband impedance spectrum into spatial domain distance and output the location of the fault point;

[0107] Result output and display unit: used to display fault distance and positioning error information.

[0108] The above system and methods have achieved the following significant results in practical applications:

[0109] (1) Strong noise robustness: This scheme extracts the fault-sensitive voltage σ mode uσ(t) and current α mode iα(t) components through modal decoupling technology, and constructs a broadband impedance spectrum Zα(jω), which greatly enhances the weak fault characteristics that are submerged by noise. Simulation shows that in extreme noise environments with a signal-to-noise ratio (SNR) as low as 10dB, the positioning error of this method can still be controlled within 3% of the total cable length, which is far better than the existing methods (see Table 1, maximum error 26m, comparison method 38m).

[0110] Table 1 Comparison of different methods

[0111] (2) Excellent high-resistance fault location capability: The broadband impedance spectrum Zα(jω) is extremely sensitive to the change in wave impedance caused by the fault. Even for high-resistance grounding faults with a transition resistance as high as 5000Ω, the present invention can still achieve accurate location with a location error of no more than 19m (see Table 2). This breaks through the bottleneck of traditional methods failing under high-resistance faults.

[0112]

[0113] Table 2 Typical Fault Verification Results

[0114] (3) Low requirements for sampling rate and data integrity: This invention can achieve high-precision positioning at a low sampling rate of 3.2kHz, significantly reducing the requirements for hardware costs. Furthermore, even under harsh conditions where voltage or current signal data loss is as high as 20%, this method can still control the positioning error within 23m (see Table 3), demonstrating excellent robustness and engineering applicability. Optionally,

[0115] Table 3. Localization results under missing data conditions

[0116] (4) Accurate physical model and strong universality: Based on the multi-conductor transmission line theory, this invention accurately establishes the electromagnetic coupling model of a three-phase cable and realizes the "phase-mode" conversion through mode decoupling, which fundamentally ensures the accuracy of the model. Simulation verification shows that under complex working conditions such as asymmetrical load and line parameter fluctuations (such as ±20% variation), the maximum positioning error is still less than 0.25% of the total cable length (see Table 4), which has extremely strong scenario adaptability.

[0117]

[0118] Table 4 Fault location results under different line parameters

[0119] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A cable network fault location method based on characteristic mode impedance spectrum, characterized in that: Includes the following steps: Step S1: Construct a multi-conductor transmission line model, obtain cable distribution parameters, and simultaneously acquire multiple electrical signals from the cable head end; Step S2: Preprocess and decouple the acquired multi-channel electrical signals to extract the corresponding six modal signals; Step S3: Construct a phase-mode transformation matrix based on the cable distribution parameters to convert the phase domain signal into a mode domain signal, and obtain the voltage σ mode uσ(t) and the current α mode iα(t); Step S4: Construct a fault initiation criterion based on the voltage σ mode uσ(t) and the current α mode iα(t); Step S5: Calculate the characteristic mode impedance and construct a broadband impedance spectrum to highlight the transient characteristics of the fault; Step S6: Map the broadband impedance spectrum to the spatial domain to locate the fault point.

2. The cable network fault location method based on characteristic mode impedance spectrum according to claim 1, characterized in that: In step S1, the multiple electrical signals are measured at the cable end as the measurement point and the sampling rate fs are used to synchronously acquire the three-phase conductor voltages uA(t), uB(t), uC(t), the three-phase conductor currents iA(t), iB(t), iC(t), and the voltages of each phase shielding layer to ground uAS(t), uBS(t), uCS(t).

3. The cable network fault location method based on characteristic mode impedance spectrum according to claim 1, characterized in that: The preprocessing described in step S2 is as follows: First, a system characteristic matrix YZ is constructed based on the parallel admittance matrix Y and the series impedance matrix Z of the cable. By solving the complex eigenvalues ​​of this matrix, a 6×6 order complex similarity transformation matrix is ​​obtained. ; Secondly, to eliminate the phase uncertainty caused by complex number operations, a normalized real number processing algorithm is used for T. IC Perform the transformation as follows: ①。 4. The cable network fault location method based on characteristic mode impedance spectrum according to claim 3, characterized in that: The modal decoupling is based on the voltage-current coupling relationship, solving for the voltage transformation matrix T. V A complete phase mode transformation system is established, as shown below: ；② After voltage mode decoupling, the six modal signals are denoted as follows: , , , , and As shown in formula ③; the same applies after current mode decoupling; ③。 5. The cable network fault location method based on characteristic mode impedance spectrum according to claim 1, characterized in that: The transformation algorithm for converting the phase domain signal to the modal domain signal in step S3 is as follows: ；⑤ Formula ⑤ includes the three-phase conductor voltages uA(t), uB(t), uC(t) of A, B, and C, the three-phase conductor currents iA(t), iB(t), iC(t), and the voltages of each phase shielding layer to ground uAS(t), uBS(t), uCS(t).

6. The cable network fault location method based on characteristic mode impedance spectrum according to claim 1, characterized in that: Step S4 calculates the effective value Uσ of voltage σ mode uσ(t) and the effective value Iα of current α mode iα(t) in real time, and dynamically compares them with the reference thresholds Uσ_UBL and Iα_UBL under the maximum unbalanced load condition.

7. The cable network fault location method based on characteristic mode impedance spectrum according to claim 5, characterized in that: The fault initiation criterion is defined as follows: when any of the following conditions are met, the system is determined to have a single-phase ground fault, and the fault location process is initiated; if the following conditions are not met, the system will continue to monitor and execute S1 to S4 in a loop until the fault criterion is triggered. ；⑥ In formula ⑥, T is the signal duration; t0 is the moment when the signal changes abruptly; It is the voltage σ-mode value corresponding to the maximum single-phase load operating condition; It is the current mode value corresponding to the maximum single-phase load operating condition.

8. The cable network fault location method based on characteristic mode impedance spectrum according to claim 1, characterized in that: The characteristic mode impedance Zα(t) mentioned in step S5 is defined as the ratio of the voltage α mode to the current α mode, as shown below: ； ⑦ When constructing the broadband impedance spectrum Zα(jω), a fast Fourier transform is performed on uα(t) and iα(t) within a short time window after the fault to obtain the broadband frequency domain expressions Uα(jω) and Iα(jω), and then their ratio is taken to obtain Zα(jω), as shown below: ⑧。 9. The cable network fault location method based on characteristic mode impedance spectrum according to claim 1, characterized in that: The method for mapping the broadband impedance spectrum to the spatial domain in step S6 is as follows: S601. Calculate the actual propagation velocity v of the traveling wave in the cable based on the cable distribution parameters and the corrected relative permittivity ε′; wherein the formula for calculating the relative permittivity ε′ is as follows: ；⑨ In formula ⑨, R1 is the conductor radius; R2 is the shielding radius; a is the inner radius of the cable insulation; b is the outer radius of the cable insulation; and ε is the relative permittivity of the cable insulation. The formula for calculating the actual propagation wave speed v is as follows: ；⑩ In formula ⑤, c is the speed of light in a vacuum; S602. Establish a mapping model from the frequency domain reflection signal to the spatial domain, perform inverse Fourier transform on the broadband impedance spectrum Zα(jω), and extract the reflection time Δt corresponding to the peak point in the time domain impulse response at the impedance discontinuity point; S603. Based on the principles of double-ended ranging and single-ended reflection, and combining the wave velocity v and the reflection time Δt, calculate the distance xf from the fault point to the beginning; the calculation formula is as follows: ⑥。 10. A cable network fault location system based on characteristic mode impedance spectrum, based on the cable network fault location method based on characteristic mode impedance spectrum as described in claims 1 to 9, characterized in that, include: Multi-channel synchronous data acquisition unit: used to synchronously acquire voltage and current signals at the cable head end at a low sampling rate; Signal preprocessing and decoupling module: used to perform noise reduction and phase mode transformation on the acquired signals; Fault initiation detection module: used for real-time monitoring and initiation of fault location based on voltage σ mode uσ(t) and current α mode iα(t); Characteristic Mode Impedance Spectrum Calculation Module: Used to calculate characteristic mode impedances and generate their broadband impedance spectra; Frequency-time-space mapping positioning module: used to convert broadband impedance spectrum into spatial domain distance and output the location of the fault point; Result output and display unit: used to display fault distance and positioning error information.

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