Cable hidden damage fault positioning method and device and computer program product

Abstract

The invention discloses a cable hidden damage fault positioning method and device and a computer program product, and the method comprises the steps: S1, obtaining the structural parameters of a detected cable, building a one-dimensional distribution parameter transmission line model according to the structural parameters, and dividing the whole cable into a plurality of normal sub-segments and defect sub-segments; s2, calculating a reflection coefficient spectrum of a cable head end reflection coefficient along with frequency change according to distribution parameter change caused by moisture intrusion; s3, performing spectrum analysis on the reflection coefficient spectrum by adopting windowing Fourier transform, inhibiting spectrum leakage and extracting a periodic component of the spectrum leakage; and S4, determining a defect position according to the extracted periodic component frequency in combination with the propagation speed of the electromagnetic wave in the cable. According to the method, the positioning precision of the hidden damage fault of the cable can be improved, the test frequency requirement is reduced, and the diagnosis robustness in different load environments is enhanced.

Description

Technical Field

[0001] This invention relates to the field of power cable condition assessment and fault diagnosis technology, specifically to a method, device, and computer program product for locating hidden cable faults. Background Technology

[0002] With the continuous advancement of new power system construction, sustained growth in power load, large-scale integration of new energy sources, and increasingly complex power network structures, higher demands are being placed on the safety and reliability of power transmission equipment. Cables are one of the most crucial components of power transmission and distribution systems, undertaking the task of stable transmission of large amounts of electrical energy, and their operating status directly affects the power supply quality and operational safety of the entire power system.

[0003] During long-term operation, cables are highly susceptible to various factors such as environmental changes, mechanical stress, and electrical aging, resulting in latent damage such as insulation degradation, sheath breakage, and moisture infiltration. These damages are characterized by their high degree of concealment, rapid evolution, and weak early warning signs, often making them difficult to detect and locate using traditional methods. Among these, latent cable damage is a major cause of cable failures. Once these latent damages develop into breakdown, short circuit, or grounding faults, they can not only cause regional power outages, severely impacting residents' lives and industrial production, but also potentially trigger serious safety accidents such as fires and explosions, threatening people's lives and property.

[0004] Traditional cable fault diagnosis relies on regular inspections and reactive repairs, which is not only inefficient and costly, but also makes it difficult to detect hidden problems in a timely manner. The complex cable network and laying environment also make fault location difficult, often requiring large-scale excavation for investigation, prolonging power outage time and increasing the maintenance burden. Summary of the Invention

[0005] The technical problem to be solved by the embodiments of the present invention is to provide a method, device and computer program product for locating hidden cable faults, so as to improve the positioning accuracy, reduce the testing frequency requirements and enhance the diagnostic robustness under different load environments.

[0006] To solve the above-mentioned technical problems, the present invention provides a method for locating hidden cable faults, comprising:

[0007] Step S1: Obtain the structural parameters of the cable under test, and establish a one-dimensional distributed parameter transmission line model accordingly, dividing the entire cable into several normal segments and defective segments.

[0008] Step S2: Based on the changes in distribution parameters caused by moisture intrusion, calculate the reflection coefficient spectrum of the cable head end as a function of frequency.

[0009] Step S3: Perform spectral analysis on the reflection coefficient spectrum using windowed Fourier transform to suppress spectral leakage and extract its periodic components;

[0010] Step S4: Determine the location of the defect based on the extracted periodic component frequency and the propagation speed of electromagnetic waves in the cable.

[0011] Preferably, the structural parameters include resistance, inductance, conductance, and capacitance per unit length of the cable.

[0012] Preferably, in step S1, establishing a one-dimensional distributed parameter transmission line model specifically includes:

[0013] Based on Kirchhoff's voltage and current laws, the differential form of the telegraph equations is derived, and the scattering parameters are solved to obtain the propagation constant and characteristic impedance.

[0014] Preferably, in step S2, calculating the reflection coefficient spectrum specifically includes:

[0015] The cable is segmented from the end to the beginning and iterated. The reflection coefficient of each interface is solved sequentially using the propagation constant and characteristic impedance of each segment. Finally, the curve of the reflection coefficient of the beginning as a function of frequency is obtained.

[0016] Preferably, in step S3, the window function used for the windowed Fourier transform is a second-order Hanning self-convolution window, and the window length N of the second-order Hanning self-convolution window satisfies the following relationship with the convolution order p:

[0017]

[0018] Among them, F floor To round down, M is the discrete length of a single Hanning window.

[0019] Preferably, in step S3, extracting the periodic component specifically includes:

[0020] The frequency of the real part of the reflection coefficient is obtained using a windowed Fourier transform interpolation algorithm. With phase and with Calculate the propagation distance d of each reflected wave. i :

[0021]

[0022] Where v is the propagation speed of electromagnetic waves in the cable.

[0023] Preferably, determining the defect location specifically includes: based on phase Determine the polarity of the reflection to distinguish between reflections from cable ends and reflections from defects.

[0024] Preferably, determining the defect location further includes: combining periodic components of different frequencies to perform multi-point fitting on the reflection point marked as the defect to obtain the hidden water tree damage area.

[0025] The present invention also provides a cable hidden damage fault location device, comprising:

[0026] One or more processors;

[0027] Memory;

[0028] One or more applications, wherein the one or more applications are stored in the memory and configured to be executed by the one or more processors, and the one or more applications are configured to perform the cable hidden damage fault location method.

[0029] The present invention also provides a computer program product, including computer instructions that instruct a computer device to perform an operation corresponding to the method.

[0030] The present invention offers the following advantages: By using segmented modeling driven by structural parameters, it transforms the weak disturbances of cable defects to distributed parameters into measurable differences in the reflection coefficient spectrum. Furthermore, it utilizes windowed Fourier transform to extract the periodic components of the spectrum with high fidelity, compressing the effective bandwidth and amplifying defect features, thus significantly improving the location resolution. Since closed-loop solutions require only single-end measurement at the beginning, no additional sensors or changes to the operating mode are needed on-site, greatly simplifying the test setup. The model and algorithm jointly suppress interference from load fluctuations, end impedance changes, and environmental noise, ensuring stable and repeatable defect location results under various operating conditions. This comprehensively improves the accuracy and efficiency of cable defect detection, making it suitable for various operating conditions such as urban power distribution networks, rail transit, and new energy power plants. It significantly enhances the reliability, real-time performance, and engineering applicability of distribution cable defect detection. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention 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 only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a flowchart illustrating a method for locating hidden cable faults according to an embodiment of the present invention.

[0033] Figure 2 This is a schematic diagram of the equivalent circuit of the cable distribution parameter network unit in an embodiment of the present invention.

[0034] Figure 3 This is a schematic diagram of a cable with a water tree defect in an embodiment of the present invention.

[0035] Figure 4 This is a schematic diagram of a cable with multiple water tree defects in an embodiment of the present invention.

[0036] Figure 5 This is the real part spectrum of the reflection coefficient at the intact cable end in an embodiment of the present invention.

[0037] Figure 6 This is a schematic diagram of the amplitude-frequency response curves of the 1st to 3rd order HSCW in an embodiment of the present invention. Detailed Implementation

[0038] The following description of the embodiments is taken with reference to the accompanying drawings, which illustrate specific embodiments in which the invention can be implemented.

[0039] Please refer to Figure 1 As shown, Embodiment 1 of the present invention provides a method for locating hidden cable faults, including:

[0040] Step S1: Obtain the structural parameters of the cable under test, and establish a one-dimensional distributed parameter transmission line model accordingly, dividing the entire cable into several normal segments and defective segments.

[0041] Step S2: Based on the changes in distribution parameters caused by moisture intrusion, calculate the reflection coefficient spectrum of the cable head end as a function of frequency.

[0042] Step S3: Perform spectral analysis on the reflection coefficient spectrum using windowed Fourier transform to suppress spectral leakage and extract its periodic components;

[0043] Step S4: Determine the location of the defect based on the extracted periodic component frequency and the propagation speed of electromagnetic waves in the cable.

[0044] Specifically, in step S1, the cross-linked polyethylene cable under test is first regarded as a one-dimensional distributed parameter transmission line, and a distributed parameter network model is constructed. That is, by obtaining the basic structural parameters of the cable under test, a corresponding physical parameter library is established. Based on the distributed parameter model theory, the cable is regarded as a one-dimensional transmission line model composed of unit length resistance, inductance, conductance and capacitance.

[0045] To describe the impact of hidden defects on the electrical characteristics of cables, the entire cable is divided into multiple sub-segments. Normal segments retain their initial parameters, while defective segments are adjusted based on the increase in conductivity and changes in dielectric constant caused by moisture intrusion, water treeing, and other degradation factors. This segmented modeling method can accurately reflect the disturbance behavior of localized hidden defect areas on the cable's reflection characteristics, laying a mathematical foundation for subsequent fault location.

[0046] like Figure 2 As shown, the telegraph equations for distances x and x+dx from the cable start-up at time t are listed below based on Kirchhoff's current and voltage laws, respectively:

[0047]

[0048] Where v(x,t) is the instantaneous voltage of the cable at position x from the beginning and time t, i(x,t) is the instantaneous current of the cable at position x from the beginning and time t, R is the series resistance per unit length of the cable (Ω / m), L is the series inductance per unit length of the cable (H / m), G is the parallel conductance per unit length of the cable (S / m), C is the parallel capacitance per unit length of the cable (F / m), and dx is the differential length increment along the cable axis (m).

[0049] Solving formula (1), taking dx to be infinitesimal and letting limdx→0, we obtain the equivalent relationship expression between voltage and current in the transmission line:

[0050]

[0051] Step S2 involves calculating the cable reflection coefficient spectrum.

[0052] Taking the cable head as the reference point, solve the transmission line equation (1) to obtain the voltage vector U(x) and current vector I(x) at a distance x from the cable head:

[0053]

[0054] Among them, U i e γ(l-x) and U r e -γ(l-x) U represents the incident voltage wave and the reflected voltage wave, respectively. i U is the incident voltage. r denoted as the reflected voltage, l as the cable end position, γ as the propagation coefficient, and Z0 as the characteristic impedance.

[0055] Let x = l (cable end), and define the load reflection coefficient based on voltage and current:

[0056]

[0057] Among them, Z L This is the load impedance at the end of the cable.

[0058] According to the laws governing wave propagation on transmission lines, the reflection coefficient at any distance x from the beginning of the transmission line is:

[0059]

[0060] Specifically, taking x = 0, the reflection coefficient at the beginning of a healthy cable can be obtained as follows:

[0061] For example Figure 3As shown, if there is a water tree defect interval [la, lb] in the middle of the cable, the cable can be divided into three segments: normal segment A: (0, la), defective segment B: (la, lb), and normal segment C: (lb, l). Each segment has an independent propagation constant γ and characteristic impedance Z0, where the parameters of the defective segment are determined by the changes in distributed parameters caused by the defect. Calculated from right to left, starting from the normal segment C, the impedance at the end is Z0. L The derivation yields: Γ(l) b ),Z lb , will Z lb As the "load" of normal segment B, continue the calculation: Γ(la),Z la , will Z la As the "load" of normal segment A, the reflection coefficient Γ at the beginning of the defective cable is finally obtained. d (0).

[0062] like Figure 4 As shown, if there are n defective segments in the cable, each segment (normal / defective) can be treated as an independent transmission line. The above method is then applied iteratively from right to left to calculate the final reflection coefficient Γ at the beginning of the defective cable. d (0).

[0063] The head-end reflection coefficient of cables with varying degrees of water tree defects can be obtained by changing the corresponding distribution parameters. Electromagnetic signals propagate from the cable head-end towards the load end. When they reach the defect, refraction and reflection occur, ultimately reflected in the steady-state reflection coefficient. The model shows that the head-end reflection coefficient is a function containing effective information such as the number of defects, defect location, and defect severity.

[0064] Step S3 involves spectral window function weighting, periodic component extraction, and propagation distance estimation. Details are as follows:

[0065] To address the issues of spectral leakage and scalloping loss in the traditional Discrete Fourier Transform (DFT) for cable reflection coefficient spectral analysis, this invention proposes an improved spectral analysis method based on Windowed Fourier Transform (WFT) to achieve highly sensitive identification and accurate location of local defects (such as water treeing, intermediate joint defects, etc.) in power distribution cables.

[0066] Based on transmission line theory, the periodicity and attenuation characteristics of the reflection coefficient spectrum at the cable head end are analyzed. The equivalent periodic component in the real part of the reflection coefficient is used to estimate the propagation distance of the reflected wave, thereby achieving accurate location of hidden damage in the cable.

[0067] When the cable end is open-circuited (i.e., Z) L When =∞), the first-end reflection coefficient spectrum Γ h (0) Expands to:

[0068] Γ h (0)=e -2γl =e -2(α+jβ)l =e -2αl (cos2βl)+hsin(2βl)) (6)

[0069] According to Euler's formula, the real part spectrum of the front reflection coefficient is as follows:

[0070]

[0071] Figure 5 The real part spectrum of the reflection coefficient at the beginning of a 50m intact cable is shown. The figure reveals that the reflection coefficient spectrum at the beginning of the cable exhibits significant attenuation and periodicity. Combining formula (7), the frequency at which the real part spectrum of the reflection coefficient at the beginning of the cable reaches its maximum value should satisfy the following relationship:

[0072]

[0073] As can be seen from formula (7), this attenuation characteristic is due to the factor e -2αl The attenuation rate is determined by both the cable length and the cable's distributed parameters. When the cable length is fixed, the attenuation of the reflection coefficient spectrum at the cable's head depends only on the attenuation coefficient α. At high frequencies, the attenuation coefficient α can be approximately solved by equation (9):

[0074]

[0075] The comparison of the reflection coefficient spectrum at the cable head end before and after the water tree defect reveals that the reflection coefficient spectrum at the head end has periodicity and attenuation. The water tree defect affects its periodicity and attenuation, causing the cable reflection coefficient at the resonant frequency to change drastically before and after the defect occurs.

[0076] As for periodic component extraction and propagation distance estimation, based on the window function optimization of cable local defect spectrum analysis, windowed Fourier transform (WFT) is used instead of ordinary DFT, and appropriate window functions are selected to suppress spectrum distortion, improve spectrum analysis accuracy, and thus improve the sensitivity of defect location.

[0077] Four window functions—Hamming window, Blackman window, four-term third-order Nuttall window, and second-order Nuttall self-convolution window—were selected to analyze their time-domain and frequency-domain performance (main lobe width, side lobe height, and side lobe attenuation rate). The time-frequency characteristics were compared under a uniform window length (N=64).

[0078] (1) Four-term third-order Nuttall window

[0079] The Nuttall window is a cosine combination window, and its time-domain expression is:

[0080]

[0081] In the formula: M and N are the number of terms in the window function and the window length, respectively; b m is the coefficient of the cosine combination term, m is the index of the cosine term; n is the index of the discrete-time sample point, n = 0, 1, ..., N-1.

[0082] (2) Nuttall self-convolution window function

[0083] A p-order Nuttall self-convolution window is constructed by convolving p identical Nuttall window functions.

[0084] (3) The discrete form of the Hanning window can be represented as:

[0085]

[0086] By comparing the performance of the four window functions, it can be seen that, under the same window length:

[0087] Sidelobe decay rate (leakage suppression capability): Four-term third-order Nuttall window > Blackman window > second-order Nuttall self-convolution window > Hamming window.

[0088] Sidelobe peak value (interference suppression capability): lowest with second-order Nuttall self-convolution window, highest with Hamming window.

[0089] In summary, the four-term third-order Nuttall window and the second-order Nuttall self-convolution window exhibit superior performance and are suitable for localization analysis.

[0090] Step S4 will construct a diagnostic function for defect identification.

[0091] To address the issues of spectral leakage and insufficient resolution in traditional DFT for cable defect detection, this invention employs a WFT algorithm optimized with Hanning window self-convolution (HSCW) to improve the accuracy and location precision of identifying local defects such as water trees in cables.

[0092] By constructing a multi-order HSCW window through the self-convolution of the Hanning window, the sidelobe attenuation capability is enhanced and the interference between periodic components is reduced. Choosing a second-order HSCW achieves an optimal balance between sidelobe performance and main lobe width, avoiding the complexity of selecting Kaiser window parameters.

[0093] The p-th order HSCW is obtained by self-convolving p Hanning windows:

[0094]

[0095] When constructing a p-order HSCW with a window length of N, the discrete length M of a single Hanning window is:

[0096]

[0097] In the formula, F floor This is for rounding down.

[0098] Figure 6 The amplitude-frequency response curves of 1st to 3rd order HSCWs with N=126 are shown. As the convolution order increases, the sidelobe level of the HSCW decreases while the sidelobe attenuation rate increases. This indicates that the HSCW can effectively suppress spectral leakage and reduce inter-spectral interference. Therefore, its application in reflection coefficient spectrum processing helps to accurately estimate the frequency and phase of each periodic component. When p is chosen too large, not only is the calculation complex, but the main lobe width becomes too large, making it unsuitable for identification in dense spectral conditions. Therefore, this embodiment of the invention uses a 2nd order HSCW to solve the problem of needing to determine parameters in the original Kaiser window. The frequency and phase of the periodic components in the real part of the reflection coefficient are extracted using the HSCW-FFT interpolation algorithm. Combined with the known cable length, the propagation distance of each reflected wave is estimated based on the frequency and phase, thereby locating the defect.

[0099] The frequencies and phases of each periodic component in the real part of the reflection coefficient were identified using the FFT interpolation algorithm of HSCW. and Can be used The propagation distance d of each reflected wave can be obtained directly. i for:

[0100]

[0101] Then based on phase Determine the polarity of the reflection to distinguish between reflections from cable ends and reflections from defects. For example, Or ±2π indicates that the reflection originates from the defect interface; This indicates that the reflection originates from the open interface at the end of the cable.

[0102] By combining periodic components of different frequencies, multi-point fitting is performed on the reflection points marked as defects to determine the defect region [la, lb].

[0103] Therefore, the present invention first performs periodic component analysis on the real part of the reflection coefficient in the FDR, and uses its frequency value and the corrected phase value to calculate the propagation distance of the reflected wave and determine its polarity, thereby realizing the location of cable moisture defects.

[0104] Corresponding to the cable hidden damage fault location method described in Embodiment 1 of the present invention, Embodiment 2 of the present invention also provides a cable hidden damage fault location device, comprising:

[0105] One or more processors;

[0106] Memory;

[0107] One or more applications, wherein the one or more applications are stored in the memory and configured to be executed by the one or more processors, and the one or more applications are configured to perform the cable hidden damage fault location method described in Embodiment 1 of the present invention.

[0108] Corresponding to the cable hidden damage fault location method described in Embodiment 1 of the present invention, Embodiment 3 of the present invention also provides a computer program product, including computer instructions, which instruct a computer device to perform the operation corresponding to the cable hidden damage fault location method described in Embodiment 1 of the present invention.

[0109] Preferably, the processor can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor, or the processor can be any conventional processor. The processor is the control center of the device, connecting various parts of the device through various interfaces and lines.

[0110] The memory mainly includes a program storage area and a data storage area. The program storage area can store the operating system, applications required for at least one function, etc., while the data storage area can store related data, etc. Furthermore, the memory can be a high-speed random access memory, or a non-volatile memory, such as a plug-in hard drive, a SmartMedia Card (SMC), a Secure Digital (SD) card, and a Flash Card, or other volatile solid-state storage devices.

[0111] It should be noted that the above-mentioned devices may include, but are not limited to, processors and memory, as will be understood by those skilled in the art.

[0112] As explained above, compared with existing technologies, the advantages of this invention are as follows: This invention uses segmented modeling driven by structural parameters to transform the weak disturbances of cable defects to distributed parameters into measurable differences in the reflection coefficient spectrum. Furthermore, it utilizes windowed Fourier transform to extract the periodic components of the spectrum with high fidelity, which both compresses the effective bandwidth and amplifies defect features, significantly improving the location resolution. Since closed-loop solutions can be obtained with only single-end measurement at the beginning, no additional sensors or changes in operating methods are required on-site, greatly simplifying the test setup. The model and algorithm jointly suppress interference from load fluctuations, end impedance changes, and environmental noise, ensuring stable and repeatable defect location results under different operating conditions. This comprehensively improves the accuracy and efficiency of cable defect detection, making it suitable for various operating conditions such as urban power distribution networks, rail transit, and new energy power plants, significantly enhancing the reliability, real-time performance, and engineering applicability of distribution cable defect detection.

[0113] The above description is merely a preferred embodiment of the present invention and should not be construed as limiting the scope of the invention. Therefore, any equivalent variations made in accordance with the claims of the present invention are still within the scope of the present invention.

Claims

1. A method for locating hidden cable faults, characterized in that, include: Step S1: Obtain the structural parameters of the cable under test, and establish a one-dimensional distributed parameter transmission line model accordingly, dividing the entire cable into several normal segments and defective segments. Step S2: Based on the changes in distribution parameters caused by moisture intrusion, calculate the reflection coefficient spectrum of the cable head end as a function of frequency. Step S3: Perform spectral analysis on the reflection coefficient spectrum using windowed Fourier transform to suppress spectral leakage and extract its periodic components; Step S4: Determine the location of the defect based on the extracted periodic component frequency and the propagation speed of electromagnetic waves in the cable.

2. The method according to claim 1, characterized in that, The structural parameters include the resistance, inductance, conductance, and capacitance per unit length of the cable.

3. The method according to claim 1, characterized in that, In step S1, establishing a one-dimensional distributed parameter transmission line model specifically includes: Based on Kirchhoff's voltage and current laws, the differential form of the telegraph equations is derived, and the scattering parameters are solved to obtain the propagation constant and characteristic impedance.

4. The method according to claim 3, characterized in that, In step S2, calculating the reflection coefficient spectrum specifically includes: The cable is segmented from the end to the beginning and iterated. The reflection coefficient of each interface is solved sequentially using the propagation constant and characteristic impedance of each segment. Finally, the curve of the reflection coefficient of the beginning as a function of frequency is obtained.

5. The method according to any one of claims 1-4, characterized in that, In step S3, the window function used for the windowed Fourier transform is a second-order Hanning self-convolution window, and the window length N of the second-order Hanning self-convolution window satisfies the following condition: Among them, F floor To round down, M is the discrete length of a single Hanning window.

6. The method according to claim 1, characterized in that, In step S3, extracting the periodic component specifically includes: The frequency of the real part of the reflection coefficient is obtained using a windowed Fourier transform interpolation algorithm. With phase and with Calculate the propagation distance d of each reflected wave. i : Where v is the propagation speed of electromagnetic waves in the cable.

7. The method according to claim 6, characterized in that, The determination of the defect location specifically includes: based on phase Determine the polarity of the reflection to distinguish between reflections from cable ends and reflections from defects.

8. The method according to claim 7, characterized in that, The determination of the defect location further includes: combining periodic components of different frequencies to perform multi-point fitting on the reflection points marked as defects to obtain the hidden water tree damage area.

9. A cable hidden damage fault location device, characterized in that, include: One or more processors; Memory; One or more applications, wherein the one or more applications are stored in the memory and configured to be executed by the one or more processors, the one or more applications being configured to perform the cable hidden damage fault location method as described in any one of claims 1 to 8.

10. A computer program product, characterized in that, Includes computer instructions that instruct a computer device to perform an operation corresponding to the method as described in any one of claims 1 to 8.

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