Single fault point distance measurement method based on reflection coefficient spectrum period

Abstract

The invention discloses a single fault point distance measurement method based on a reflection coefficient spectrum period, and relates to the technical field of fault detection, and the method comprises the specific steps: 1, constructing a model, and building an incidence relation; 2, determining the frequency range and bandwidth of frequency sweeping; 3, collecting data and constructing a smooth interpolation curve; 4, detecting feature points to obtain a phase coefficient value; 5, calculating a period and solving a fault distance; according to the method, the improved reflection coefficient spectrum model integrated with the cable basic parameters is constructed, the correlation between the period and the fault distance is established, interference of a traditional method is avoided, the near-area fault distance measurement problem is solved, and accuracy and adaptability are improved; and meanwhile, data is processed by adopting segmented cubic spline interpolation, fuzzy feature points are eliminated, redundancy check of three cycle calculation modes is designed, the anti-interference capability is enhanced, the fault distance is stably output in signal attenuation and noise interference scenes, and the reliability and consistency of a distance measurement result are guaranteed.

Description

Technical Field

[0001] This invention relates to the field of fault detection technology, specifically a single fault point ranging method based on the periodicity of the reflection coefficient spectrum. Background Technology

[0002] In fields such as power transmission, communication networks, rail transportation, and industrial control, cables serve as the core carriers of signal and energy transmission, and their operational stability directly determines the overall reliability of the system. With power grid upgrades, communication bandwidth expansion, and the advancement of industrial automation, cable laying lengths are constantly increasing, and cables often operate under complex conditions, leading to frequent single-point fault problems such as insulation aging, mechanical damage, and joint failures. If such faults cannot be quickly located, they can cause power outages, communication paralysis, or industrial production shutdowns, resulting in significant economic losses. Currently, spectral domain reflection methods, due to their advantages in frequency characteristic analysis, are gradually replacing traditional time-domain reflection methods as a research hotspot in cable fault location. The core idea is to correlate fault distance through the characteristics of the reflection coefficient spectrum. However, traditional spectral domain methods lack sufficient integration of basic cable parameters and have not yet formed a stable ranging benchmark, making it difficult to meet the precise ranging requirements in complex scenarios.

[0003] Traditional cable fault location technology suffers from several key drawbacks: First, the traditional reflection coefficient spectrum model does not fully couple the cable characteristic impedance, the load impedance at the fault point, and the signal attenuation coefficient. This makes the period of the real part curve of the reflection coefficient spectrum susceptible to parameter fluctuations. For example, when the load impedance changes or the signal attenuation intensifies during long-distance transmission, the period stability drops sharply, directly causing the ranging reference to shift, with errors exceeding 10%. Second, the ranging shielding distance is not defined. In the case of near-field faults, due to unreasonable design of the sweep frequency range and bandwidth, the reflected signal is directly covered by the reflected signal at the head end, making it impossible to effectively capture the reflection characteristics of the fault point, leading to near-field ranging failure. Third, discrete sampling data often uses linear interpolation, which cannot eliminate sampling noise and data fluctuations. Key feature points such as zero-crossing points and peak points are difficult to identify, and the period calculation relies on only a single feature point, resulting in weak anti-interference capabilities. In scenarios with electromagnetic noise or signal attenuation, the period calculation error increases significantly, leading to low reliability in engineering applications. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a single-fault-point ranging method based on the period of the reflection coefficient spectrum. This method constructs an improved reflection coefficient spectrum model that incorporates basic parameters such as cable characteristic impedance and fault-point load impedance to obtain a real part curve of the first-end reflection coefficient spectrum with a constant period and establishes its correlation with the fault distance. This method defines the ranging shielding distance, solves the problem of near-zone fault ranging, and uses piecewise cubic spline interpolation to process the data to improve anti-interference capability.

[0005] To solve the above-mentioned technical problems, this invention provides the following technical solution: a single-fault point ranging method based on the periodicity of the reflection coefficient spectrum, the specific steps of which are as follows:

[0006] Step 1: Model building and relationship establishment: Obtain the basic parameters of the cable, including characteristic impedance, load impedance at the fault point, signal attenuation coefficient, and phase coefficient; Based on the basic parameters, build an improved cable head-end reflection coefficient spectrum model, obtain the real part curve of the head-end reflection coefficient spectrum with constant period from the model, and establish the relationship between the period of the real part curve of the head-end reflection coefficient spectrum and the cable fault distance.

[0007] Step 2, determine the sweep frequency range and bandwidth: define the ranging shielding distance, derive the sweep frequency phase coefficient bandwidth based on the correlation between the period and the fault distance established in Step 1; convert the sweep frequency phase coefficient to the corresponding sweep frequency through the conversion relationship between the sweep frequency phase coefficient and the sweep frequency, and determine the sweep frequency range and sweep frequency bandwidth.

[0008] Step 3, Data Acquisition and Construction of Smooth Interpolation Curve: According to the frequency sweep range determined in Step 2, collect discrete sampling data of the real part of the reflection coefficient spectrum at the cable head end; process the discrete sampling data using the piecewise cubic spline interpolation method, construct a piecewise cubic spline interpolation function, and obtain a smooth interpolation curve from the interpolation function;

[0009] Step 4, feature point detection to obtain phase coefficient values: perform feature point detection on the smooth interpolation curve obtained in Step 3 to obtain the phase coefficient values ​​corresponding to the zero-crossing points and peak points of the interpolation curve.

[0010] Step 5, calculate the period and solve the fault distance: Based on the phase coefficient values ​​of the zero-crossing point and peak point obtained in Step 4, calculate the period of the real part curve of the first end reflection coefficient spectrum; combined with the correlation between the period and the fault distance established in Step 1, solve for the fault distance of a single fault point in the cable.

[0011] Furthermore, in step one, the improved formula for calculating the complex function model of the cable head-end reflection coefficient spectrum is as follows: in, Z represents the complex function of the reflection coefficient spectrum at the cable tip; Z0 represents the characteristic impedance of the cable; Z L Indicates the load impedance at the cable fault point; l F α represents the cable fault distance; β represents the signal attenuation coefficient in the cable; j represents the imaginary unit; e represents the natural constant; cos represents the cosine function; sin represents the sine function.

[0012] Furthermore, in step one, the formula for calculating the real part curve of the reflection coefficient spectrum at the cable head end with a constant period is: in, Z represents the real part of the complex function of the reflection coefficient spectrum at the cable tip; Z0 represents the characteristic impedance of the cable; Z L Indicates the load impedance at the cable fault point; l F α represents the cable fault distance; β represents the signal attenuation coefficient in the cable; e represents the natural constant; and cos represents the cosine function.

[0013] Furthermore, in step one, the formula for calculating the relationship between the period of the real part curve of the first-end reflection coefficient spectrum and the cable fault distance is as follows: Among them, l F π represents the distance to the cable fault; T represents the period of the real part curve of the reflection coefficient spectrum at the beginning of the cable.

[0014] Furthermore, in step three, the formula for calculating the quantization relationship between the sweep bandwidth and the ranging blocking distance is as follows: Frequency sweep phase coefficient starting point And it satisfies cos(2β1l) s ) = 0, where Δβ represents the bandwidth of the sweep phase coefficient; β1 represents the starting point of the sweep phase coefficient; β2 represents the ending point of the sweep phase coefficient; l s π represents the distance of the distance measurement and the obstruction distance; cos represents the cosine function.

[0015] Furthermore, in step two, the formula for calculating the conversion relationship between the sweep phase coefficient and the sweep frequency is as follows: The formula for calculating the sweep frequency parameter is: Sweep start frequency. Sweep termination frequency The sweep bandwidth Δf = f2 - f1; where β represents the sweep phase coefficient; f represents the sweep frequency; v represents the signal propagation speed in the cable; π represents pi; f1 represents the sweep start frequency; β1 represents the start point of the sweep phase coefficient; f2 represents the sweep end frequency; β2 represents the sweep phase coefficient end point; and Δf represents the sweep bandwidth.

[0016] Furthermore, in step three, the formula for calculating the piecewise cubic spline interpolation function is: S(x) = a i (xx i ) 3 +b i (xx i ) 2 +c i (xx i )+d i Where S(x) represents the piecewise cubic spline interpolation function; x represents the phase coefficient variable; x i a represents the phase coefficient of the i-th sampling point; i b i c i di These represent the interpolation function in the interval [x], respectively. i ,x i The undetermined coefficients are within [+1]; i is the sampling point index, taking values ​​of 0, 1, ..., n; n represents the number of sampling points minus one; x i +1 represents the phase coefficient of the (i+1)th sampling point.

[0017] Furthermore, in step three, the piecewise cubic spline interpolation method satisfies the following constraint: interpolation condition S(x i )=y i And S(x) i+1 )=y i+1 Continuity conditions and and Natural boundary conditions S″(x0)=0 and S″(x n ) = 0, where S(x) represents the piecewise cubic spline interpolation function; x i y represents the phase coefficient of the i-th sampling point; i x represents the real part of the reflection coefficient spectrum at the i-th sampling point; i+1 y represents the phase coefficient of the (i+1)th sampling point; i+1 This represents the real part of the reflection coefficient spectrum at the (i+1)th sampling point; i is the sampling point index, which takes the value 0, 1, ..., n; n represents the number of sampling points minus one. x represents i+1 The phase coefficient value on the left; x represents i+1 The phase coefficient values ​​on the right; S′(x) represents the first derivative of the piecewise cubic spline interpolation function; S″(x) represents the second derivative of the piecewise cubic spline interpolation function; x0 represents the phase coefficient of the first sampling point; x n This represents the phase coefficient of the last sample point.

[0018] Furthermore, in step four, the phase coefficient values ​​corresponding to the zero-crossing points and peak points of the interpolation curve are obtained as follows: the phase coefficient value corresponding to the zero-crossing point is obtained by solving the equation S(x) = 0, and the phase coefficient value corresponding to the peak point is obtained by solving the equation S′(x) = 0 and verifying that S″(x) < 0, where S(x) represents the piecewise cubic spline interpolation function; x represents the phase coefficient variable; S′(x) represents the first derivative of the piecewise cubic spline interpolation function; and S″(x) represents the second derivative of the piecewise cubic spline interpolation function.

[0019] Furthermore, in step five, the period calculation method for the real part curve of the first-end reflection coefficient spectrum and the fault distance solution are as follows: There are three methods for calculating the period, the first of which is: T = x z(i+1) -x ziMethod two is: T = 2(x) pi -x zi Method three is: T = x p(i+1) -x pi The fault distance is calculated by substituting the period T into the equation. Solve for x, where T represents the period of the real part curve of the front reflection coefficient spectrum; zi x represents the phase coefficient value corresponding to the i-th zero crossing point; z(i+1) This represents the phase coefficient value corresponding to the (i+1)th zero crossing; i is the zero crossing index; x pi x represents the phase coefficient value corresponding to the i-th peak point; p(i+1) This represents the phase coefficient value corresponding to the (i+1)th peak point; l F This represents the distance to a cable fault; π represents pi.

[0020] Compared with existing technologies, this single-fault-point ranging method based on the periodicity of the reflection coefficient spectrum has the following advantages:

[0021] I. This invention constructs an improved cable head-end reflection coefficient spectrum model, incorporating fundamental parameters such as cable characteristic impedance and fault point load impedance, to obtain a periodically constant real part curve of the head-end reflection coefficient spectrum. This establishes its correlation with fault distance, avoiding interference from signal attenuation and load changes inherent in traditional methods. Simultaneously, it defines the ranging obstruction distance to derive the sweep frequency phase coefficient bandwidth and frequency range, solving the problem of near-field fault ranging obstruction. This adapts to different cable characteristics and scenarios, significantly improving the accuracy and scenario adaptability of single-fault point ranging.

[0022] Second, this invention uses piecewise cubic spline interpolation to process discrete sampled data and constructs a smooth curve under multiple constraints, eliminating the feature point ambiguity caused by data fluctuations. It also designs three periodic calculation methods to form redundant verification, avoiding the influence of single feature point detection errors and exhibiting strong anti-interference capabilities. It can stably output fault distance in scenarios with signal attenuation and noise interference, reducing engineering application errors and ensuring the reliability and consistency of single-fault point distance measurement results for cables.

[0023] Other advantages, objectives and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination or study, or may be learned from the practice of the invention. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0025] Figure 1 This is a flowchart of a single-fault-point ranging method based on the periodicity of the reflection coefficient spectrum;

[0026] Figure 2 This is a framework diagram of a single-fault-point ranging method based on the periodicity of the reflection coefficient spectrum. Detailed Implementation

[0027] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0028] Example 1: Low-voltage cable fault location in residential communities

[0029] Step 1: Building the model and establishing relationships

[0030] In a 10kV / 0.4kV power distribution system of a residential community, a buried low-voltage cable supplies power to buildings 3-5. A single fault in this cable caused a power outage for some residents in the area, requiring the measurement of the fault distance using the method of this invention. Technicians first obtained the basic parameters of the low-voltage cable by consulting the cable's manufacturer's data and using portable testing instruments in the field, including the cable's characteristic impedance, the load impedance at the fault point, the signal attenuation coefficient in the cable, and the phase coefficient.

[0031] Based on the aforementioned basic parameters, and following the improved complex function model calculation formula for the cable head-end reflection coefficient spectrum in the document, a complex function model for the reflection coefficient spectrum of this low-voltage cable is constructed. The improved complex function model calculation formula for the cable head-end reflection coefficient spectrum is as follows: in, Z represents the complex function of the reflection coefficient spectrum at the cable tip; Z0 represents the characteristic impedance of the cable; Z L Indicates the load impedance at the cable fault point; l FLet represent the cable fault distance; α represent the signal attenuation coefficient in the cable; β represent the signal phase coefficient; j represent the imaginary unit; e represent the natural constant; cos represents the cosine function; and sin represents the sine function. By extracting the real part of this complex function model, and based on the calculation formula for the real part curve of the cable head-end reflection coefficient spectrum with a constant period, the real part curve of the cable head-end reflection coefficient spectrum with a constant period is obtained. The calculation formula for the real part curve of the cable head-end reflection coefficient spectrum with a constant period is: in, Z represents the real part of the complex function of the reflection coefficient spectrum at the cable tip; Z0 represents the characteristic impedance of the cable; Z L Indicates the load impedance at the cable fault point; l F The following parameters represent the cable fault distance: α represents the signal attenuation coefficient in the cable; β represents the signal phase coefficient; e represents the natural constant; and cos represents the cosine function. Finally, referring to the correlation formula between the period of the real part curve of the first-end reflection coefficient spectrum and the cable fault distance in the reference document, the correlation between the period of the real part curve of the first-end reflection coefficient spectrum and its fault distance is established, laying the foundation for subsequent distance measurement. The correlation calculation formula is as follows: Among them, l F π represents the distance to the cable fault; T represents the period of the real part curve of the reflection coefficient spectrum at the beginning of the cable.

[0032] Step 2: Determine the sweep frequency range and bandwidth

[0033] Considering that the low-voltage cables in this community are buried under the community road and close to the building foundations, there is a problem that the near-distance fault signals are easily interfered with by the buildings. Based on the cable laying path avoiding the area of ​​the building foundations and the requirement that the error in fault diagnosis should be controlled within 1 meter, the technicians defined an appropriate distance measurement shielding distance to avoid the near-distance interference signals affecting the distance measurement results.

[0034] Based on the correlation between the cycle and the fault distance established in Step 1, and combined with the quantization relationship between the sweep frequency phase coefficient bandwidth and the ranging obstruction distance in the document, the required sweep frequency phase coefficient bandwidth for this ranging is derived. Simultaneously, the starting and ending points of the sweep frequency phase coefficient are determined. The formula for calculating the quantization relationship between the sweep frequency bandwidth and the ranging obstruction distance is as follows: Frequency sweep phase coefficient starting point And it satisfies cos(2β1l) s ) = 0, where Δβ represents the bandwidth of the sweep phase coefficient; β1 represents the starting point of the sweep phase coefficient; β2 represents the ending point of the sweep phase coefficient; l s π represents the distance of the distance measurement and the obstruction distance; cos represents the cosine function.

[0035] Subsequently, using the conversion relationship between the sweep phase coefficient and the sweep frequency in the document, the derived sweep phase coefficient starting point was converted into the sweep start frequency, and the sweep phase coefficient ending point was converted into the sweep stop frequency. Then, the sweep bandwidth was calculated using the difference between the sweep stop frequency and the sweep start frequency. Finally, the sweep frequency range and sweep bandwidth for this low-voltage cable fault location were determined. The formula for calculating the conversion relationship between the sweep phase coefficient and the sweep frequency is as follows: The formula for calculating the sweep frequency parameter is: Sweep start frequency. Sweep termination frequency The sweep bandwidth Δf = f2 - f1; where β represents the sweep phase coefficient; f represents the sweep frequency; v represents the signal propagation speed in the cable; π represents pi; f1 represents the sweep start frequency; β1 represents the start point of the sweep phase coefficient; f2 represents the sweep end frequency; β2 represents the sweep phase coefficient end point; and Δf represents the sweep bandwidth.

[0036] Step 3: Data Acquisition and Construction of Smooth Interpolation Curves

[0037] According to the frequency range determined in step two, the technicians connect the signal generator to the cable head end and collect discrete sampling data of the real part of the reflection coefficient spectrum of the low-voltage cable head end through the data acquisition card. During the acquisition process, it is ensured that the sampling interval is uniform and covers the entire frequency range of the sweep frequency to fully reflect the variation law of the real part of the reflection coefficient spectrum.

[0038] After data collection, the discrete sampled data was processed using the piecewise cubic spline interpolation method described in the document. During processing, the constraints of this method were strictly followed, including: interpolation conditions ensuring the interpolation function passes through all sampling points; continuity conditions ensuring the function value, first derivative, and second derivative of the interpolation function are continuous at the junctions of sampling points; and natural boundary conditions ensuring the second derivative of the interpolation function is zero at the first and last sampling points. A piecewise cubic spline interpolation function was constructed, and its calculation formula is: S(x) = a i (xx i ) 3 +b i (xx i ) 2 +c i (xx i )+d i Where S(x) represents the piecewise cubic spline interpolation function; x represents the phase coefficient variable; x i a represents the phase coefficient of the i-th sampling point; i b i c i d i These represent the interpolation function in the interval [x], respectively. i,x i The undetermined coefficients are within [+1]; i is the sampling point index, taking values ​​of 0, 1, ..., n; n represents the number of sampling points minus one; x i +1 represents the phase coefficient of the (i+1)th sampling point; the constraint condition satisfied by the piecewise cubic spline interpolation method is: interpolation condition S(x i )=y i And S(x) i+1 )=y i+1 , and and And S″(x) n ) = 0, where S(x) represents the piecewise cubic spline interpolation function; x i y represents the phase coefficient of the i-th sampling point; i x represents the real part of the reflection coefficient spectrum at the i-th sampling point; i+1 y represents the phase coefficient of the (i+1)th sampling point; i+1 This represents the real part of the reflection coefficient spectrum at the (i+1)th sampling point; i is the sampling point index, which takes the value 0, 1, ..., n; n represents the number of sampling points minus one. x represents i+1 The phase coefficient value on the left; x represents i+1 The phase coefficient values ​​on the right; S′(x) represents the first derivative of the piecewise cubic spline interpolation function; S″(x) represents the second derivative of the piecewise cubic spline interpolation function; x0 represents the phase coefficient of the first sampling point; x n This represents the phase coefficient of the last sampling point. This interpolation function is used to interpolate the discrete data, generating a smooth interpolation curve that eliminates random fluctuations in the discrete data, providing a clear and continuous signal curve for subsequent feature point detection.

[0039] Step 4: Feature point detection to obtain phase coefficient values

[0040] Technicians used signal feature analysis software to detect feature points on the smooth interpolation curve obtained in step three, focusing on obtaining the phase coefficient values ​​corresponding to the zero-crossing points and peak points of the interpolation curve.

[0041] When detecting zero-crossing points, the software uses a built-in algorithm to solve the equation for the piecewise cubic spline interpolation function to equal zero, following the method for calculating the phase coefficient values ​​corresponding to zero-crossing points in the documentation. This yields the phase coefficient values ​​for all zero-crossing points, and the sequence number and corresponding phase coefficient of each zero-crossing point are recorded. When detecting peak points, the software first solves the equation for the first derivative of the piecewise cubic spline interpolation function to equal zero, yielding the phase coefficients corresponding to multiple possible extreme points. Then, the second derivative is verified for these extreme points, i.e., it is determined whether the second derivative of the piecewise cubic spline interpolation function at each extreme point is less than zero. Extreme points that meet this condition are identified as peak points, and the phase coefficient values ​​for all peak points are obtained. The sequence number and corresponding phase coefficient of each peak point are recorded.

[0042] Step 5: Calculate the cycle and solve the fault distance

[0043] Based on the phase coefficient values ​​of the zero-crossing points and peak points recorded in step four, the technicians calculated the period of the real part curve of the first-end reflection coefficient spectrum using three period calculation methods given in the document: The first method is to select two adjacent zero-crossing points, subtract the phase coefficient value of the previous zero-crossing point from the phase coefficient value of the latter zero-crossing point to obtain the period, i.e., the period is calculated by using adjacent zero-crossing points; the second method is to select a zero-crossing point and an adjacent peak point, subtract the phase coefficient value of the zero-crossing point from the phase coefficient value of the peak point, and then multiply by 2 to obtain the period, i.e., the period is calculated by using a zero-crossing point and an adjacent peak point; the third method is to select two adjacent peak points, subtract the phase coefficient value of the previous peak point from the phase coefficient value of the latter peak point to obtain the period, i.e., the period is calculated by using adjacent peak points.

[0044] The period values ​​calculated using the three methods were compared and verified. After removing outliers, the average value was taken as the final period value. Subsequently, this final period value was substituted into the formula relating the period of the real part curve of the first-end reflection coefficient spectrum established in step one to the cable fault distance to solve for the fault distance. Finally, the accurate fault distance of a single fault point of the low-voltage cable in the community was obtained. Subsequent excavation verified that the error was only 0.8 meters. Based on this, technicians quickly located the fault point and completed the repair, restoring power to the residents.

[0045] Example 2: Fault Location Measurement of Medium-Voltage Cables in Industrial Parks

[0046] Step 1: Building the model and establishing relationships

[0047] In an industrial park, a 10kV medium-voltage cable supplies power to industrial equipment in factories such as machinery plants and chemical plants. A single fault in this cable caused production stoppages at three companies within the park, necessitating urgent measurement of the fault distance to shorten repair time. Technicians first retrieved basic parameters such as characteristic impedance and phase coefficient from the cable's manufacturing records. Then, through on-site fault detection, they estimated the load impedance at the fault point using the high-voltage signal injection method and obtained the attenuation coefficient through signal attenuation testing along the cable route, thus collecting complete basic parameters for the medium-voltage cable.

[0048] Based on these fundamental parameters, and according to the improved complex function model calculation formula for the cable head-end reflection coefficient spectrum in the document, a complex function model of the cable head-end reflection coefficient spectrum is constructed. By separating the real part of the complex function model and combining it with the calculation formula for the real part curve of the cable head-end reflection coefficient spectrum with a constant period, a real part curve of the cable head-end reflection coefficient spectrum with a constant period is generated. Finally, according to the correlation formula between the period of the real part curve of the cable head-end reflection coefficient spectrum and the cable fault distance in the document, the correlation between the period of the real part curve of the medium-voltage cable reflection coefficient spectrum and the fault distance is established.

[0049] Step 2: Determine the sweep frequency range and bandwidth

[0050] The medium-voltage cable laying path in this industrial park is complex. Some sections are laid parallel to gas pipelines and communication optical cables within the park, which can easily cause signal interference. Furthermore, the fault point may be located far from the maintenance station, requiring the ranging range to cover the entire cable length of approximately 2km. Based on the total cable length and the distribution of interference sources, technicians avoided interference from the parallel sections of the gas pipelines and communication optical cables, defining a reasonable ranging shielding distance to ensure that fault signals at medium to long distances could be effectively captured.

[0051] Based on the correlation between the cycle and fault distance established in Step 1, and referring to the quantification relationship between the sweep frequency phase coefficient bandwidth and the ranging shielding distance in the reference document, the sweep frequency phase coefficient bandwidth is derived, and the start and end points of the sweep frequency phase coefficient are determined. Subsequently, using the conversion relationship between the sweep frequency phase coefficient and the sweep frequency frequency, the start and end points of the sweep frequency phase coefficient are converted into the sweep start frequency and sweep end frequency, respectively, and the sweep frequency bandwidth is calculated. Finally, the sweep frequency range and sweep frequency bandwidth suitable for fault ranging of this medium-voltage cable are determined.

[0052] Step 3: Data Acquisition and Construction of Smooth Interpolation Curves

[0053] Technicians used specialized signal acquisition equipment for medium-voltage cables, connecting the equipment to the test terminals at the cable's head end according to the frequency sweep range determined in step two. They then activated the signal acquisition function to collect discrete sampling data of the real part of the reflection coefficient spectrum at the cable's head end. During the acquisition process, considering the significant signal attenuation of medium-voltage cables, the sampling time was appropriately increased to ensure that discrete data of long-distance fault signals could still be effectively acquired.

[0054] After data acquisition, the discrete sampled data was processed using the piecewise cubic spline interpolation method described in the document. During processing, the constraints of this method were strictly met, including interpolation conditions ensuring complete fitting of the sampled points, continuity conditions ensuring smooth curve transitions, and natural boundary conditions eliminating abrupt changes at the beginning and end. A piecewise cubic spline interpolation function was then constructed. This interpolation function was used to interpolate the discrete data, generating smooth interpolation curves that compensate for the fluctuations in discrete data from long-distance medium-voltage cable signals, providing a reliable curve basis for feature point detection.

[0055] Step 4: Feature point detection to obtain phase coefficient values

[0056] Using a professional medium-voltage cable signal analysis system, feature point detection is performed on the smooth interpolation curve obtained in step three to obtain the phase coefficient values ​​of the zero-crossing point and the peak point.

[0057] When detecting zero-crossing points, the system solves the equation for the piecewise cubic spline interpolation function to be equal to zero using a built-in algorithm, automatically identifying and recording the phase coefficient values ​​and corresponding numbers of all zero-crossing points. When detecting peak points, the system first solves the equation for the piecewise cubic spline interpolation function to be equal to zero, filters out the phase coefficients of all extreme points, and then calculates the second derivative of the piecewise cubic spline interpolation function for each extreme point. Extreme points with a second derivative less than zero are marked as peak points, and their phase coefficient values ​​and corresponding numbers are recorded to ensure the accuracy of peak point identification.

[0058] Step 5: Calculate the cycle and solve the fault distance

[0059] Based on the zero-crossing and peak point phase coefficient values ​​recorded in step four, technicians use the system software to call three period calculation methods from the document: one is to calculate the period by the difference in phase coefficients between adjacent zero-crossing points, the second is to calculate the period by twice the difference in phase coefficients between the zero-crossing point and the adjacent peak point, and the third is to calculate the period by the difference in phase coefficients between adjacent peak points.

[0060] The software statistically analyzes the period values ​​obtained from the three methods, removes abnormal period values ​​caused by interference, and outputs the average period value. This average period value is then substituted into the correlation formula between the period of the real part curve of the first-end reflection coefficient spectrum established in step one and the cable fault distance, automatically calculating the fault distance of the medium-voltage cable. Based on this distance, technicians excavate and inspect the corresponding location along the cable, accurately locating the fault point and quickly completing the repair. Power supply to businesses in the industrial park was restored in just 2 hours, significantly reducing production downtime losses.

[0061] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A single fault point ranging method based on the period of the reflection coefficient spectrum, characterized in that, The specific steps of the method are: Step one, model construction and correlation relationship establishment: obtain cable basic parameters of characteristic impedance, fault point load impedance, signal attenuation coefficient and phase coefficient; based on the basic parameters, construct an improved cable head-end reflection coefficient spectrum model, obtain a periodic constant head-end reflection coefficient spectrum real part curve from the model, and establish a correlation relationship between the period of the head-end reflection coefficient spectrum real part curve and the cable fault distance; Step two, determine the sweep frequency range and bandwidth: define the ranging masking distance, based on the correlation relationship between the period and the fault distance established in step one, deduce the sweep phase coefficient bandwidth; convert the sweep phase coefficient to the corresponding sweep frequency by the conversion relationship between the sweep phase coefficient and the sweep frequency, determine the sweep frequency range and the sweep bandwidth; Step three, data acquisition and smooth interpolation curve construction: according to the sweep frequency range determined in step two, acquire discrete sampling data of the real part of the cable head-end reflection coefficient spectrum; process the discrete sampling data by using the piecewise cubic spline interpolation method to construct a piecewise cubic spline interpolation function, and obtain a smooth interpolation curve from the interpolation function; Step four, feature point detection to obtain phase coefficient values: perform feature point detection on the smooth interpolation curve obtained in step three to obtain phase coefficient values corresponding to the zero-crossing points and peak points of the interpolation curve respectively; Step five, period calculation and fault distance solving: calculate the period of the head-end reflection coefficient spectrum real part curve according to the phase coefficient values of the zero-crossing points and peak points obtained in step four; combine the correlation relationship between the period and the fault distance established in step one to solve the fault distance of the cable single fault point.

2. The single fault point ranging method based on the period of reflection coefficient spectrum according to claim 1, characterized in that, The improved cable head end reflection coefficient spectrum complex function model calculation formula in the step one is: Wherein, represents the cable head end reflection coefficient spectrum complex function; Z0 represents the cable characteristic impedance; Z L represents the cable fault point load impedance; l F represents the cable fault distance; α represents the signal attenuation coefficient in the cable; β represents the signal phase coefficient; j represents the imaginary unit; e represents the natural constant; cos represents the cosine function; and sin represents the sine function.

3. The single fault point ranging method based on the period of reflection coefficient spectrum according to claim 1, characterized in that, The real part curve calculation formula of the cable head end reflection coefficient spectrum in step one is: Wherein, represents the real part of the cable head end reflection coefficient spectrum complex function; Z0 represents the cable characteristic impedance; Z L represents the cable fault point load impedance; l F represents the cable fault distance; α represents the signal attenuation coefficient in the cable; β represents the signal phase coefficient; e represents the natural constant; and cos represents the cosine function.

4. The method of claim 1, wherein, The formula for calculating the correlation between the period of the real part curve of the head-end reflection coefficient spectrum and the cable fault distance in step one is: Wherein, l F represents the cable fault distance; π represents the circular constant; T represents the period of the real part curve of the head-end reflection coefficient spectrum.

5. The method of claim 1, wherein, In the step three, the quantization relationship calculation formula between the sweep frequency bandwidth and the ranging shadow distance is as follows: Sweep frequency phase coefficient starting point And satisfies cos(2β1l s )=0, wherein, Δβ represents the sweep frequency phase coefficient bandwidth; β1 represents the sweep frequency phase coefficient starting point; β2 represents the sweep frequency phase coefficient terminal point; l s represents the ranging shadow distance; π represents the circular constant; and cos represents the cosine function.

6. The reflection coefficient spectrum period based single fault point ranging method according to claim 1, characterized in that, The conversion relationship calculation formula of the sweep frequency phase coefficient and the sweep frequency in the second step is: The calculation formula of the sweep frequency parameter is: sweep start frequency sweep end frequency sweep bandwidth Δf=f2-f1; wherein, β represents the sweep phase coefficient; f represents the sweep frequency; v represents the signal propagation speed in the cable; π represents the circular constant; f1 represents the sweep start frequency; β1 represents the sweep phase coefficient start point; f2 represents the sweep end frequency; β2 represents the sweep phase coefficient end point; and Δf represents the sweep bandwidth.

7. The reflection coefficient spectrum period based single fault point ranging method according to claim 1, characterized in that, In the step three, the calculation formula of the piecewise cubic spline interpolation function is: S(x) = a i (x-x i ) 3 +b i (x-x i ) 2 +c i (x-x i )+d i , wherein, S(x) represents the piecewise cubic spline interpolation function; x represents the phase coefficient variable; x i represents the phase coefficient of the i-th sampling point; a i , b i , c i , d i respectively represent the undetermined coefficients of the interpolation function in the interval [x i , x i +1]; i is the sampling point serial number, taking values of 0, 1, …, n; n represents the sampling point quantity minus one; x i +1 represents the phase coefficient of the i+1-th sampling point.

8. The method of claim 1, wherein, The constraint condition satisfied by the piecewise cubic spline interpolation method in step three is: interpolation condition S(x i ) = y i and S(x i+1 ) = y i+1 , continuity condition and and natural boundary condition S″(x0) = 0 and S″(x n ) = 0, wherein S(x) represents the piecewise cubic spline interpolation function; x i represents the phase coefficient of the i-th sampling point; y i represents the real part value of the reflection coefficient spectrum of the i-th sampling point; x i+1 represents the phase coefficient of the i+1-th sampling point; y i+1 represents the real part value of the reflection coefficient spectrum of the i+1-th sampling point; i is the sampling point serial number, and takes values of 0, 1, …, n; n represents the sampling point quantity minus one; represents the phase coefficient value on the left side of x i+1 ; represents the phase coefficient value on the right side of x i+1 ; S'(x) represents the first derivative of the piecewise cubic spline interpolation function; S″(x) represents the second derivative of the piecewise cubic spline interpolation function; x0 represents the phase coefficient of the first sampling point; x n represents the phase coefficient of the last sampling point.

9. The reflection coefficient spectrum period based single fault point ranging method according to claim 1, characterized in that, In step four, the solving method of the phase coefficient values corresponding to the zero-crossing points and peak points of the interpolation curve is as follows: the phase coefficient value corresponding to the zero-crossing point is obtained by solving the equation S(x) = 0, and the phase coefficient value corresponding to the peak point is obtained by solving the equation S'(x) = 0 and verifying S''(x) < 0, wherein S(x) represents the piecewise cubic spline interpolation function, x represents the phase coefficient variable, S'(x) represents the first derivative of the piecewise cubic spline interpolation function, and S''(x) represents the second derivative of the piecewise cubic spline interpolation function.

10. The method of claim 1, wherein, In the step five, the period calculation method of the real part curve of the head-end reflection coefficient spectrum and the fault distance solving are as follows: the period calculation method includes three kinds, the first kind is: T=x z(i+1) -x zi ; the second kind is: T=2(x pi -x zi ); and the third kind is: T=x p(i+1) -x pi ; the fault distance is solved by substituting the calculated period T into , wherein T represents the period of the real part curve of the head-end reflection coefficient spectrum; x zi represents the phase coefficient value corresponding to the i-th zero-crossing point;x z(i+1) represents the phase coefficient value corresponding to the i+1-th zero-crossing point;i is the zero-crossing point serial number;x pi represents the phase coefficient value corresponding to the i-th peak point;x p(i+1) represents the phase coefficient value corresponding to the i+1-th peak point;l F represents the cable fault distance; represents the circular constant.

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