CN116718868A - Cable defect positioning method based on sheath current signal frequency domain energy spectrum - Google Patents
Cable defect positioning method based on sheath current signal frequency domain energy spectrum Download PDFInfo
- Publication number
- CN116718868A CN116718868A CN202310603920.1A CN202310603920A CN116718868A CN 116718868 A CN116718868 A CN 116718868A CN 202310603920 A CN202310603920 A CN 202310603920A CN 116718868 A CN116718868 A CN 116718868A
- Authority
- CN
- China
- Prior art keywords
- signal
- cable
- formula
- reflection coefficient
- representing
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 230000007547 defect Effects 0.000 title claims abstract description 50
- 238000001228 spectrum Methods 0.000 title claims abstract description 21
- 238000000034 method Methods 0.000 title claims abstract description 20
- 230000014509 gene expression Effects 0.000 claims abstract description 33
- 238000000354 decomposition reaction Methods 0.000 claims abstract description 14
- 230000005540 biological transmission Effects 0.000 claims abstract description 6
- 238000009413 insulation Methods 0.000 claims description 13
- 230000002950 deficient Effects 0.000 claims description 9
- 230000003595 spectral effect Effects 0.000 claims description 7
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 claims description 3
- 230000002238 attenuated effect Effects 0.000 claims description 3
- 238000012216 screening Methods 0.000 claims description 3
- 230000007704 transition Effects 0.000 claims description 3
- 230000009466 transformation Effects 0.000 claims description 2
- 238000011156 evaluation Methods 0.000 abstract description 2
- 238000001028 reflection method Methods 0.000 description 7
- 230000000694 effects Effects 0.000 description 3
- 238000010586 diagram Methods 0.000 description 2
- 239000006185 dispersion Substances 0.000 description 2
- 238000012545 processing Methods 0.000 description 2
- 238000005311 autocorrelation function Methods 0.000 description 1
- 239000012141 concentrate Substances 0.000 description 1
- 230000001419 dependent effect Effects 0.000 description 1
- 238000002347 injection Methods 0.000 description 1
- 239000007924 injection Substances 0.000 description 1
- 230000004807 localization Effects 0.000 description 1
- 230000010355 oscillation Effects 0.000 description 1
- 230000000737 periodic effect Effects 0.000 description 1
- 230000035945 sensitivity Effects 0.000 description 1
- 230000001629 suppression Effects 0.000 description 1
- 238000010408 sweeping Methods 0.000 description 1
- 230000002194 synthesizing effect Effects 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/08—Locating faults in cables, transmission lines, or networks
- G01R31/081—Locating faults in cables, transmission lines, or networks according to type of conductors
- G01R31/083—Locating faults in cables, transmission lines, or networks according to type of conductors in cables, e.g. underground
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/08—Locating faults in cables, transmission lines, or networks
- G01R31/088—Aspects of digital computing
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
- Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
- Y04S10/00—Systems supporting electrical power generation, transmission or distribution
- Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
- Y04S10/52—Outage or fault management, e.g. fault detection or location
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Mathematical Physics (AREA)
- Theoretical Computer Science (AREA)
- Testing Relating To Insulation (AREA)
Abstract
The invention belongs to the technical field of power equipment state evaluation, and particularly relates to a cable defect positioning method based on a sheath current signal frequency domain energy spectrum. The invention comprises the following steps: step 1, establishing a distributed transmission line model based on a telegraph equation; step 2, decomposing the reflection coefficient amplitude signal by using empirical mode decomposition to obtain an eigenmode function signal; and step 3, positioning the cable defect position by utilizing the eigenmode function signals. The invention firstly derives the reflection coefficient expressions of three cable models, and decomposes the envelope of the reflection coefficient amplitude into an inherent mode function by utilizing empirical mode decomposition, so that the envelope of the signal is more sensitive to defects than a frequency domain spectrum. And then, according to the characteristic that the power spectrum of the stable random process is a deterministic function, carrying out power spectrum density analysis on the inherent mode function signal with limited power, thereby realizing cable defect positioning based on the power spectrum density.
Description
Technical Field
The invention belongs to the technical field of power equipment state evaluation, and particularly relates to a cable defect positioning method based on a sheath current signal frequency domain energy spectrum.
Background
In recent years, power cables are increasingly applied to urban power transmission and distribution systems, and the number of faults caused by cable insulation defects is increased. The rapid localization of insulation defects helps to reduce the risk of short-circuit faults. At present, the insulation defect is positioned mainly by a traveling wave method, and according to the positioning principle, the method can be further divided into a time domain reflection method and a frequency domain reflection method. The time domain reflection method is mainly used for positioning by utilizing refraction and reflection of traveling waves in the time domain signals at the impedance mismatch position, and is mainly used for positioning open circuit or short circuit faults because the method is more dependent on reflection signals at the impedance mismatch position. On the basis of a time domain reflection method, different types of frequency reflection methods are used for processing signals, so that the injection signals have the characteristic that certain frequency domain ranges are easier to identify, the positioning sensitivity is higher, and in addition, the combination of time domain and frequency domain provides more signal characteristic information.
Disclosure of Invention
The invention aims at: the invention provides a cable defect positioning method based on a sheath current signal frequency domain energy spectrum, which is used for improving the precision of the existing frequency domain reflection method because reflected waves with different frequencies of various insulation defect points are overlapped in a time domain to form a dispersion effect and cause reflected wave distortion.
In order to achieve the aim of the invention, the technical scheme adopted by the invention is as follows:
a cable defect positioning method based on a sheath current signal frequency domain energy spectrum comprises the following steps:
step 1, establishing a distributed transmission line model based on a telegraph equation;
step 2, decomposing the reflection coefficient amplitude signal by using empirical mode decomposition to obtain an eigenmode function signal;
and step 3, positioning the cable defect position by utilizing the eigenmode function signals.
Further as a preferred technical scheme of the present invention, the step 1 specifically includes the following steps: the signal generating device is connected with the tested power cable through a coaxial signal cable, and the expression of the head-end voltage reflection signal is shown as the formula (1);
U 1 (ω)＝U 0 (ω)ρ 1 +U 0 (ω)(1-ρ 1 2 )ρ 2 e -2γl +U 0 (ω)(1-ρ 1 2 )(-ρ 1 )ρ 2 e -2γl +... (1)
wherein U is 1 Representing the reflected voltage signal at the head end of the power cable, U 0 The signal generator injects a voltage signal, ω=2pi f represents angular frequency, f represents frequency, γ represents propagation coefficient of the line, ρ 1 Representing the head-end reflection coefficient ρ 2 Representing the end reflection coefficient ρ 1 And ρ 2 The expression of (2) is as follows:
in the formula (2), Z 0 Representing the characteristic impedance of the power cable to be tested, R 0 Representing the characteristic impedance of the coaxial signal cable;
according to formula (1), the expression of the reflection coefficient is as shown in formula (3):
as can be seen from equation (3), the head-end reflection coefficient in a defect-free cable is an attenuated signal that does not vary with frequency;
the head-end reflected voltage signal expression of the cable containing the defective section will be as shown in formula (4):
in formula (4), ρ 3 ＝(Z d -Z 0 )/(Z d +Z 0 )，Z d Representing the characteristic impedance of the defective section, l 1 Representing the distance from the insulation defect point to the head end; the head-end reflection coefficient is shown as formula (5):
if the defect property of the tested cable is ground defect, namely insulation resistance is reduced, the ground point transition resistance is R g ，l 2 Representing the distance of the ground fault point from the head end, the head end reflected voltage signal expression of the cable will be as shown in formula (6):
in formula (6), ρ 4 ＝(R g -Z 0 )/(R g +Z 0 ) The reflection coefficient at the ground point is represented by the first-end reflection coefficient shown in the formula (7):
further as a preferred technical scheme of the present invention, the step 2 specifically includes the following steps:
step 2.1, find the local maximum set Γ of the signal Γ (ω) max And a local minimum set Γ min ；
Step 2.2 according to Γ max And Γ min Determining the upper envelope and the lower envelope of an original number set gamma (omega) by utilizing cubic spline interpolation;
step 2.3, find the local average value m (ω) according to the upper and lower envelopes of Γ (ω), and express the difference between the original signal and the local extremum as equation (8)
h 1 (ω)＝Γ(ω)-m(ω) (8)；
Step 2.4, substituting Γ (ω) for h 1 (ω) repeating steps 2.1 to 2.3 until the standard deviation of the two consecutive results satisfies the following constraint:
wherein omega max And omega min Represents the upper and lower angular frequencies of the signal, h k (ω) represents the kth continuous screening result, and h k (ω) is considered as a fundamental modulus component as shown in formula (10):
c 1 (ω)＝h k (ω) (10)
then, c is subtracted by Γ (ω) 1 (omega) obtaining a residual sequence r 1 (ω)：
r 1 (ω)＝Γ(ω)-c 1 (ω) (11)；
Step 2.5, r is calculated 1 (omega) as a new "original" signal, repeating the above step 2.4 until the nth c N (ω) or r N (omega) is less than a preset value, or r N (ω) becomes a monotonic function termination; empirical mode decomposition is complete and yields:
and (3) performing empirical mode decomposition on the original signal gamma (omega) to obtain N eigenvalue function components and residual signals, wherein the N eigenvalue function components and the residual signals respectively represent characteristic signals of different scales contained in the original signal.
Further as a preferred technical scheme of the present invention, the step 3 specifically includes the following steps:
the Kaiser self-convolution window KSCW is used, and the discrete expression is shown in the formula (13):
where N represents the index number of the sample, N represents the length of the window, β Ka Representing the adjustment coefficient, I 0 () The expression of the 0-order Bessel function representing the first class is shown as (14):
the p-th order KSCW is defined as the self-convolution of the parent Kaiser window, as shown in (15):
let the nth eigenmode function signal be a data set containing M samples, denoted X n ＝{x n (M) } m=1,..m, after removal of the mean, adding a window function, the expression of which is shown in (16):
calculating a sampleIs a self-convolution function of (1);
wherein K is more than or equal to 1 and less than or equal to M,is->Is a convolution of (1);
the power spectral density is obtained by fourier transformation:
finding out the main frequency contained in the eigenmode function signal according to the formula (18); the cable head-end reflection coefficient with the length of l is decomposed by Euler, and the expression is shown as (19):
Γ l (ω)＝ρ l e -2α(ω)l [cos(2β(ω)l)-jsin(2β(ω)l)] (19)
wherein ρ is l Representing the reflection coefficient at the end of the cable, the propagation coefficient γ (ω) =α (ω) +jβ (ω); for a cable containing defects, the real part expression of the reflection coefficient of the head end of the cable is as follows:
the defect position x is represented by formula (21):
compared with the prior art, the cable defect positioning method based on the sheath current signal frequency domain energy spectrum has the following technical effects: the method provided by the invention utilizes the characteristic that the amplitude envelope is sensitive to the defect characteristic frequency, and improves the accuracy of the defect positioning method based on the reflection coefficient.
Drawings
FIG. 1 is a schematic diagram of a signal generating device connected to a power cable to be tested through a coaxial signal cable in an embodiment of the present invention;
fig. 2 is a schematic diagram of a cable defect output positioning result in an embodiment of the invention.
Detailed Description
The invention is further explained in the following detailed description with reference to the drawings so that those skilled in the art can more fully understand the invention and can practice it, but the invention is explained below by way of example only and not by way of limitation.
A cable defect positioning method based on a sheath current signal frequency domain energy spectrum comprises the following steps:
step 1, establishing a distributed transmission line model based on a telegraph equation;
step 2, decomposing the reflection coefficient amplitude signal by using empirical mode decomposition to obtain an eigenmode function signal;
and step 3, positioning the cable defect position by utilizing the eigenmode function signals.
The invention establishes a distributed transmission line model based on telegraph equation, the signal generating device is connected with the tested power cable through the coaxial signal cable, as shown in figure 1, the step 1 specifically comprises the following steps: the signal generating device is connected with the tested power cable through a coaxial signal cable, and the expression of the head-end voltage reflection signal is shown as the formula (1);
U 1 (ω)＝U 0 (ω)ρ 1 +U 0 (ω)(1-ρ 1 2 )ρ 2 e -2γl +U 0 (ω)(1-ρ 1 2 )(-ρ 1 )ρ 2 e -2γl +... (1)
wherein U is 1 Representing the reflected voltage signal at the head end of the power cable, U 0 The signal generator injects a voltage signal, ω=2pi f represents angular frequency, f represents frequency, γ represents propagation coefficient of the line, ρ 1 Representing the head-end reflection coefficient ρ 2 Representing the end reflection coefficient ρ 1 And ρ 2 The expression of (2) is as follows:
in the formula (2), Z 0 Representing the characteristic impedance of the power cable to be tested, R 0 Representing the characteristic impedance of the coaxial signal cable;
according to formula (1), the expression of the reflection coefficient is as shown in formula (3):
from equation (3), the head-end reflection coefficient in a defect-free cable is an attenuated signal that does not vary with frequency. If the cable is locally aged and deteriorated or the physical structure is changed, the impedance of the unit length of the line is changed, and the local impedance changes are insulation defects proposed by the invention. In the cable containing the defective section, the reflection coefficient of the defective section cable will also be different from that of the healthy cable section, and the head-end reflection voltage signal expression of the cable containing the defective section will be as shown in the formula (4):
in formula (4), ρ 3 ＝(Z d -Z 0 )/(Z d +Z 0 )，Z d Representing the characteristic impedance of the defective section, l 1 Representing the distance from the insulation defect point to the head end; the head-end reflection coefficient is shown as formula (5):
if the defect property of the tested cable is ground defect, namely insulation resistance is reduced, the ground point transition resistance is R g ，l 2 Representing the distance of the ground fault point from the head end, the head end reflected voltage signal expression of the cable will be as shown in formula (6):
in formula (6), ρ 4 ＝(R g -Z 0 )/(R g +Z 0 ) The reflection coefficient at the ground point is represented by the first-end reflection coefficient shown in the formula (7):
the reflected waves at the insulation defect are superimposed on each other. The mixed reflected signal causes periodic oscillation of the reflection factor, which affects the judgment of cable defects. The empirical mode decomposition has the advantage of self-adapting to signals and is suitable for processing non-stationary signals. The step 2 specifically comprises the following steps:
step 2.1, find the local maximum set Γ of the signal Γ (ω) max And a local minimum set Γ min ；
Step 2.2 according to Γ max And Γ min Determining the upper envelope and the lower envelope of an original number set gamma (omega) by utilizing cubic spline interpolation;
step 2.3, find the local average value m (ω) according to the upper and lower envelopes of Γ (ω), and express the difference between the original signal and the local extremum as equation (8)
h 1 (ω)＝Γ(ω)-m(ω) (8)；
Step 2.4, substituting Γ (ω) for h 1 (ω) repeating steps 2.1 to 2.3 until the standard deviation of the two consecutive results satisfies the following constraint:
wherein omega max And omega min Represents the upper and lower angular frequencies of the signal, h k (ω) represents the kth continuous screening result, and h k (ω) is considered as a fundamental modulus component as shown in formula (10):
c 1 (ω)＝h k (ω) (10)
then, c is subtracted by Γ (ω) 1 (omega) obtaining a residual sequence r 1 (ω)：
r 1 (ω)＝Γ(ω)-c 1 (ω) (11)；
Step 2.5, r is calculated 1 (omega) as a new "original" signal, repeating the above step 2.4 until the nth c N (ω) or r N (omega) is less than a preset value, or r N (ω) becomes a monotonic function termination; empirical modeThe decomposition is completed and the following steps are obtained:
and (3) performing empirical mode decomposition on the original signal gamma (omega) to obtain N eigenvalue function components and residual signals, wherein the N eigenvalue function components and the residual signals respectively represent characteristic signals of different scales contained in the original signal.
Because the non-parametric estimate of the FFT-based eigenmode function signal power spectral density is a biased estimate. To reduce the bias, a window function must be used to smooth the power spectral density. The invention adopts the Kaiser self-convolution window (KSCW), can mainly concentrate the signal energy in the frequency band on the main lobe, and has good suppression performance on the side lobe. The discrete expression of the Kaiser window is shown in formula (13).
The step 3 specifically comprises the following steps:
the Kaiser self-convolution window KSCW is used, and the discrete expression is shown in the formula (13):
where N represents the index number of the sample, N represents the length of the window, β Ka Representing the adjustment coefficient, I 0 () The expression of the 0-order Bessel function representing the first class is shown as (14):
the p-th order KSCW is defined as the self-convolution of the parent Kaiser window, as shown in (15):
let the nth eigenmode function signal be a data set containing M samples, denoted X n ＝{x n (M) }, m=1,..m, after removing the mean, adding a window functionThe number is represented by the expression (16):
calculating a sampleIs a self-convolution function of (1);
wherein K is more than or equal to 1 and less than or equal to M,is->Is a convolution of (1); since the autocorrelation function and the power spectral density are fourier transform pairs, the power spectral density can be obtained by fourier transform:
finding out the main frequency contained in the eigenmode function signal according to the formula (18); the cable head-end reflection coefficient with the length of l is decomposed by Euler, and the expression is shown as (19):
Γ l (ω)＝ρ l e -2α(ω)l [cos(2β(ω)l)-jsin(2β(ω)l)] (19)
wherein ρ is l Representing the reflection coefficient at the end of the cable, the propagation coefficient γ (ω) =α (ω) +jβ (ω); for a cable containing defects, the real part expression of the reflection coefficient of the head end of the cable is as follows:
the defect position x is represented by formula (21):
in specific implementation, the specific implementation steps are as follows:
1) Input: a sweep frequency trigonometric function signal of the cable to be tested;
2) Extracting an eigenmode function signal and other part signals in the reflection coefficient by using empirical mode decomposition;
3) Expanding the eigenmode function signal into a form of a formula (19) by using an Euler equation;
4) Extracting the real part of each eigenmode function signal;
5) Synthesizing the power spectral density of each eigenmode function signal according to formulas (16) - (18);
6) And (3) outputting: the location of the defective point of the cable being tested.
In practice, there is a section of cable with a length of 800m, and the structural parameters are shown in table 1:
TABLE 1 structural parameters of a typical high voltage cable line
The defect point is 500m away from the head end of the line, the defect length is 1m, the signal cable length is 1m, the cable line is set to be open circuit during testing, the load impedance is infinitely large, the reflection coefficient of the tail end is 1, and the frequency sweeping signal is 5 kHz-10 MHz. The final output positioning result is shown in fig. 2. And outputting a normalized fault energy maximum point at 497m, namely a defect positioning result.
The invention provides a cable defect positioning method based on a sheath current signal frequency domain energy spectrum, which is used for improving the precision of the existing frequency domain reflection method. Because reflected waves with different frequencies at various insulation defect points are overlapped in the time domain, a dispersion effect is formed, and the reflected waves are distorted. First, the reflection coefficient expressions of three cable models are derived, and the envelope of the reflection coefficient amplitude is decomposed into an inherent mode function by using empirical mode decomposition, so that the envelope of the signal is more sensitive to defects than the frequency domain spectrum. And then, according to the characteristic that the power spectrum of the stable random process is a deterministic function, carrying out power spectrum density analysis on the inherent mode function signal with limited power, thereby realizing cable defect positioning based on the power spectrum density.
While the foregoing is directed to embodiments of the present invention, other and further details of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.
Claims (4)
1. The cable defect positioning method based on the sheath current signal frequency domain energy spectrum is characterized by comprising the following steps of:
step 1, establishing a distributed transmission line model based on a telegraph equation;
step 2, decomposing the reflection coefficient amplitude signal by using empirical mode decomposition to obtain an eigenmode function signal;
and step 3, positioning the cable defect position by utilizing the eigenmode function signals.
2. The cable defect positioning method based on the sheath current signal frequency domain energy spectrum according to claim 1, wherein the step 1 specifically comprises the following steps: the signal generating device is connected with the tested power cable through a coaxial signal cable, and the expression of the head-end voltage reflection signal is shown as the formula (1);
U 1 (ω)＝U 0 (ω)ρ 1 +U 0 (ω)(1-ρ 1 2 )ρ 2 e -2γl +U 0 (ω)(1-ρ 1 2 )(-ρ 1 )ρ 2 e -2γl +...(1)
wherein U is 1 Representing the reflected voltage signal at the head end of the power cable, U 0 The signal generator injects a voltage signal, ω=2pi f represents angular frequency, f represents frequency, γ represents propagation coefficient of the line, ρ 1 Representing the head-end reflection coefficient ρ 2 Representing the end reflection coefficient ρ 1 And ρ 2 The expression of (2) is as follows:
in the formula (2), Z 0 Representing the characteristic impedance of the power cable to be tested, R 0 Representing the characteristic impedance of the coaxial signal cable;
according to formula (1), the expression of the reflection coefficient is as shown in formula (3):
as can be seen from equation (3), the head-end reflection coefficient in a defect-free cable is an attenuated signal that does not vary with frequency;
the head-end reflected voltage signal expression of the cable containing the defective section will be as shown in formula (4):
in formula (4), ρ 3 ＝(Z d -Z 0 )/(Z d +Z 0 )，Z d Representing the characteristic impedance of the defective section, l 1 Representing the distance from the insulation defect point to the head end; the head-end reflection coefficient is shown as formula (5):
if the defect property of the tested cable is ground defect, namely insulation resistance is reduced, the ground point transition resistance is R g ，l 2 Representing the distance of the ground fault point from the head end, the head end reflected voltage signal expression of the cable will be as shown in formula (6):
in formula (6), ρ 4 ＝(R g -Z 0 )/(R g +Z 0 ) The reflection coefficient at the ground point is represented by the first-end reflection coefficient shown in the formula (7):
3. the cable defect positioning method based on the sheath current signal frequency domain energy spectrum according to claim 1, wherein the step 2 specifically comprises the following steps:
step 2.1, find the local maximum set Γ of the signal Γ (ω) max And a local minimum set Γ min ；
Step 2.2 according to Γ max And Γ min Determining the upper envelope and the lower envelope of an original number set gamma (omega) by utilizing cubic spline interpolation;
step 2.3, find the local average value m (ω) according to the upper and lower envelopes of Γ (ω), and express the difference between the original signal and the local extremum as equation (8)
h 1 (ω)＝Γ(ω)-m(ω) (8)；
Step 2.4, substituting Γ (ω) for h 1 (ω) repeating steps 2.1 to 2.3 until the standard deviation of the two consecutive results satisfies the following constraint:
wherein omega max And omega min Represents the upper and lower angular frequencies of the signal, h k (ω) represents the kth continuous screening result, and h k (ω) is considered as a fundamental modulus component as shown in formula (10):
c 1 (ω)＝h k (ω) (10)
then, c is subtracted by Γ (ω) 1 (omega) obtaining a residual sequence r 1 (ω)：
r 1 (ω)＝Γ(ω)-c 1 (ω) (11)；
Step 2.5, r is calculated 1 (omega) as a new "original" signal, repeating the above step 2.4 until the nth c N (ω) or r N (omega) is less than a preset value, or r N (ω) becomes a monotonic function termination; empirical mode decomposition is complete and yields:
and (3) performing empirical mode decomposition on the original signal gamma (omega) to obtain N eigenvalue function components and residual signals, wherein the N eigenvalue function components and the residual signals respectively represent characteristic signals of different scales contained in the original signal.
4. The cable defect positioning method based on the sheath current signal frequency domain energy spectrum according to claim 1, wherein the step 3 specifically comprises the following steps:
the Kaiser self-convolution window KSCW is used, and the discrete expression is shown in the formula (13):
where N represents the index number of the sample, N represents the length of the window, β Ka Representing the adjustment coefficient, I 0 () The expression of the 0-order Bessel function representing the first class is shown as (14):
the p-th order KSCW is defined as the self-convolution of the parent Kaiser window, as shown in (15):
let the nth eigenmode function signal be a data set containing M samples, denoted X n ＝{x n (M) } m=1,..m, after removal of the mean, adding a window function, the expression of which is shown in (16):
calculating a sampleIs a self-convolution function of (1);
wherein K is more than or equal to 1 and less than or equal to M,is->Is a convolution of (1);
the power spectral density is obtained by fourier transformation:
finding out the main frequency contained in the eigenmode function signal according to the formula (18); the cable head-end reflection coefficient with the length of l is decomposed by Euler, and the expression is shown as (19):
Γ l (ω)＝ρ l e -2α(ω)l [cos(2β(ω)l)-jsin(2β(ω)l)] (19)
wherein ρ is l Representing the reflection coefficient at the end of the cable, the propagation coefficient γ (ω) =α (ω) +jβ (ω); for a cable containing defects, the real part expression of the reflection coefficient of the head end of the cable is as follows:
the defect position x is represented by formula (21):
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310603920.1A CN116718868A (en) | 2023-05-26 | 2023-05-26 | Cable defect positioning method based on sheath current signal frequency domain energy spectrum |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310603920.1A CN116718868A (en) | 2023-05-26 | 2023-05-26 | Cable defect positioning method based on sheath current signal frequency domain energy spectrum |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN116718868A true CN116718868A (en) | 2023-09-08 |
Family
ID=87868873
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310603920.1A Pending CN116718868A (en) | 2023-05-26 | 2023-05-26 | Cable defect positioning method based on sheath current signal frequency domain energy spectrum |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116718868A (en) |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20050156585A1 (en) * | 2004-01-15 | 2005-07-21 | Niedzwiecki Joshua D. | Reduced complexity transmission line and waveguide fault tester |
| CN104406510A (en) * | 2014-11-24 | 2015-03-11 | 江苏省电力公司镇江供电公司 | Cable length measurement method based on EE (empirical envelope) method |
| CN110320446A (en) * | 2019-07-18 | 2019-10-11 | 国网重庆市电力公司江北供电分公司 | Power cable defect location and diagnostic method based on return loss spectrometry |
| AU2020103078A4 (en) * | 2020-10-28 | 2020-12-24 | Sichuan University | High-sensitivity diagnostic method for local defects of power cable |
| CN114019309A (en) * | 2021-11-05 | 2022-02-08 | 国网四川省电力公司成都供电公司 | Cable defect positioning method based on frequency domain reflection technology |
| CN115825643A (en) * | 2022-11-09 | 2023-03-21 | 国网浙江省电力有限公司电力科学研究院 | Cable defect positioning method, equipment and medium |
-
2023
- 2023-05-26 CN CN202310603920.1A patent/CN116718868A/en active Pending
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20050156585A1 (en) * | 2004-01-15 | 2005-07-21 | Niedzwiecki Joshua D. | Reduced complexity transmission line and waveguide fault tester |
| CN104406510A (en) * | 2014-11-24 | 2015-03-11 | 江苏省电力公司镇江供电公司 | Cable length measurement method based on EE (empirical envelope) method |
| CN110320446A (en) * | 2019-07-18 | 2019-10-11 | 国网重庆市电力公司江北供电分公司 | Power cable defect location and diagnostic method based on return loss spectrometry |
| AU2020103078A4 (en) * | 2020-10-28 | 2020-12-24 | Sichuan University | High-sensitivity diagnostic method for local defects of power cable |
| CN114019309A (en) * | 2021-11-05 | 2022-02-08 | 国网四川省电力公司成都供电公司 | Cable defect positioning method based on frequency domain reflection technology |
| CN115825643A (en) * | 2022-11-09 | 2023-03-21 | 国网浙江省电力有限公司电力科学研究院 | Cable defect positioning method, equipment and medium |
Non-Patent Citations (3)
| Title |
|---|
| YANAN ZHANG, ET AL: "An Application of the Frequency-domain Experience Mode Decomposition to Enhance Deconvolution Results", 《ADME 2013》, pages 2120 - 2123 * |
| ZHIRONG TANG ET AL: "A Frequency-Domain Location Method for Defects in Cables Based on Power Spectral Density", 《IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT》, vol. 71, pages 9005110 - 1 * |
| 容健纲;: "关于冲击测量分压器的分析和校验(三)", 高电压技术, no. 02, pages 42 - 52 * |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Jamehbozorg et al. | A decision tree-based method for fault classification in double-circuit transmission lines | |
| US7940056B2 (en) | Time-domain reflectometry | |
| CN112697887B (en) | Ultrasonic detection defect qualitative identification method based on neural network | |
| CN111679159A (en) | Method for judging impedance change type in frequency domain reflection method | |
| CN113702754A (en) | Distribution cable defect positioning algorithm adopting windowed Fourier transform | |
| US20150066408A1 (en) | Time frame measuring method with calibration in the frequency range | |
| CN109541405B (en) | Power cable partial discharge positioning method | |
| Huai et al. | Single-ended line fault location method for multi-terminal HVDC system based on optimized variational mode decomposition | |
| CN112782539A (en) | Cable insulation defect detection method and system | |
| CN104406509A (en) | HHT (Hilbert Huang transform))-based electric cable length measuring method | |
| Tang et al. | A frequency-domain location method for defects in cables based on power spectral density | |
| CN115097261A (en) | Cable local defect positioning and identifying method based on frequency domain reflection | |
| CN112213560A (en) | High-precision power grid broadband signal measuring method based on Z-ADALINE | |
| CN114936347A (en) | Fault traveling wave detection method based on variable modal decomposition and wavelet modulus maximum | |
| CN114966320A (en) | New single-ended fault traveling wave distance measurement algorithm based on deep learning | |
| CN113642417B (en) | Denoising method for partial discharge signal of insulated overhead conductor based on improved wavelet algorithm | |
| Liang et al. | Partial discharge location of power cables based on an improved single-terminal method | |
| CN113589109A (en) | Time domain waveform recovery method based on cable frequency domain reflection | |
| CN116718868A (en) | Cable defect positioning method based on sheath current signal frequency domain energy spectrum | |
| CN117310374A (en) | Distance measurement method for submarine cable faults | |
| CN116540016A (en) | Cable defect diagnosis method based on reflection coefficient discrete sequence | |
| CN112964965A (en) | Cable fault type identification system based on frequency response | |
| CN111523231A (en) | Subsynchronous oscillation analysis method based on EEMD and Prony method | |
| CN115932470A (en) | Cable defect time-frequency analysis method, system and medium based on improved Wigner distribution | |
| CN103971012B (en) | Lamb wave signal denoising method based on John Saris model and fractional differentiation |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |