CN116718868A - A cable defect location method based on the frequency domain energy spectrum of the sheath current signal - Google Patents

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

A cable defect location method based on the frequency domain energy spectrum of the sheath current signal

Technical field

The invention belongs to the technical field of power equipment status assessment, and specifically relates to a method for locating cable defects based on the frequency domain energy spectrum of sheath current signals.

Background technique

In recent years, power cables have been increasingly used in urban power transmission and distribution systems, and the number of faults caused by cable insulation defects has increased. Rapid localization of insulation defects helps reduce the risk of short-circuit failure. At present, the traveling wave method is mainly used to locate insulation defects. According to the positioning principle, it can be further divided into time domain reflection method and frequency domain reflection method. The time domain reflection method mainly uses the refraction and reflection of traveling waves in the time domain signal at the impedance mismatch position to locate. Since this method relies more on the reflection signal at the impedance mismatch position, this method is mainly used to locate open circuit or short circuit faults. Based on the time domain reflection method, different types of frequency reflection methods perform different types of processing on the signal itself, making the injected signal have characteristics that are easier to identify in certain frequency domain ranges, thereby making the positioning more sensitive. In addition, The combination of time and frequency domains will provide more signal characteristic information.

Contents of the invention

The purpose of the present invention is: since the reflected waves of different frequencies at various insulation defect points are superimposed in the time domain, forming a dispersion effect and causing the distortion of the reflected waves, the present invention proposes a method of locating cable defects based on the frequency domain energy spectrum of the sheath current signal. method to improve the accuracy of existing frequency domain reflectometry methods.

In order to achieve the above-mentioned object, the technical solutions adopted by the present invention are as follows:

A cable defect location method based on the frequency domain energy spectrum of the sheath current signal, including the following steps:

Step 1. Establish a distributed transmission line model based on the telegraph equation;

Step 2. Use empirical mode decomposition to decompose the reflection coefficient amplitude signal to obtain the eigenmode function signal;

Step 3. Use the intrinsic mode function signal to locate the cable defect location.

As a further preferred technical solution of the present invention, the step 1 specifically includes the following steps: the signal generating device is connected to the power cable under test through a coaxial signal cable, then the head-end voltage reflection signal expression is as shown in 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)

Among them, U ₁ represents the reflected voltage signal at the head end of the power cable, U ₀ represents the voltage signal injected by the signal generating device, ω = 2πf represents the angular frequency, f represents the frequency, γ represents the propagation coefficient of the line, ρ ₁ represents the head end reflection coefficient, ρ ₂ represents the end reflection coefficient, and the expressions of ρ ₁ and ρ ₂ are as shown in (2):

In formula (2), Z ₀ represents the characteristic impedance of the power cable under test, and R ₀ represents the characteristic impedance of the coaxial signal cable;

According to equation (1), the expression of the reflection coefficient is as shown in equation (3):

It can be seen from equation (3) that the head-end reflection coefficient in a defect-free cable is an attenuated signal that does not change with frequency;

The expression of the reflected voltage signal at the head end of the defective section cable will be as shown in Equation (4):

In formula (4), ρ ₃ =(Z _d -Z ₀ )/(Z _d +Z ₀ ), Z _d represents the characteristic impedance of the defect section, l ₁ represents the distance between the insulation defect point and the head end; its head end reflection The coefficient is shown in equation (5):

If the defect nature of the cable under test is a grounding defect, that is, a reduction in insulation resistance, the transition resistance of the grounding point is R _g , and l ₂ represents the distance between the grounding defect point and the head end, then the expression of the reflected voltage signal at the head end of the cable will be as follows: Equation (6) Shown:

In equation (6), ρ ₄ =(R _g -Z ₀ )/(R _g +Z ₀ ) represents the reflection coefficient of the ground point. At this time, its head end reflection coefficient is as shown in equation (7):

Further, as a preferred technical solution of the present invention, step 2 specifically includes the following steps:

Step 2.1. Find the local maximum set Γ _max and the local minimum set Γ _min of the signal Γ(ω);

Step 2.2. Use cubic spline interpolation to determine the upper and lower envelopes of the original number set Γ(ω) according to Γ _max and Γ _min ;

Step 2.3. Find the local average value m(ω) based on the upper and lower envelopes of Γ(ω), and express the difference between the original signal and the local extreme value as Equation (8)

h ₁ (ω)=Γ(ω)-m(ω) (8);

Step 2.4, replace Γ(ω) with h ₁ (ω) and repeat steps 2.1 to 2.3 until the standard deviation of two consecutive results satisfies the following constraints:

Among them, ω _max and ω _min represent the upper and lower limit angular frequencies of the signal, h _k (ω) represents the kth continuous screening result, and h _k (ω) is considered to be the basic mode component, as shown in Equation (10):

c ₁ (ω)＝h _k (ω) (10)

Then, subtract c ₁ (ω) from Γ(ω) to get the residual sequence r ₁ (ω):

r ₁ (ω)=Γ(ω)-c ₁ (ω) (11);

Step 2.5, use r ₁ (ω) as the new "original" signal, repeat the above step 2.4 until the Nth c _N (ω) or r _N (ω) is less than the preset value, or r _N (ω) becomes The monotonic function terminates; the empirical mode decomposition is completed and we get:

The original signal Γ(ω) is subjected to empirical mode decomposition to obtain N intrinsic mode function components and residual signals, which respectively represent the different scale characteristic signals contained in the original signal.

Further, as a preferred technical solution of the present invention, step 3 specifically includes the following steps:

The Kaiser self-convolution window KSCW is used, and its discrete expression is as shown in Equation (13):

Among them, n represents the index number of the sample, N represents the length of the window, β _Ka represents the adjustment coefficient, I ₀ () represents the first kind of 0th-order Bessel function, and its expression is as shown in (14):

The p-order KSCW is defined as the autoconvolution of the parent Kaiser window, as shown in (15):

Assume that the nth eigenmode function signal is _a data set containing M samples, _labeled as function, its expression is as shown in (16):

Calculate sample The autoconvolution function;

Among them, 1≤K≤M, Yes/> convolution;

The power spectral density is obtained by Fourier transform:

According to equation (18), find the main frequencies contained in the eigenmode function signal; through Euler decomposition, the reflection coefficient of the cable head end with length l is expressed as (19):

Γ _l (ω)＝ρ _l e ^-2α(ω)l [cos(2β(ω)l)-jsin(2β(ω)l)] (19)

Among them, ρ _l represents the reflection coefficient at the end of the cable, and the propagation coefficient γ (ω) = α (ω) + jβ (ω); for a cable containing defects, assuming that the defect position is x from the head end, the actual reflection coefficient of the head end The partial expression is:

The defect position x is expressed by equation (21):

The method of locating cable defects based on the frequency domain energy spectrum of the sheath current signal according to the present invention adopts the above technical solution and has the following technical effects compared with the existing technology: the method proposed by the present invention uses the amplitude envelope to determine the defect characteristics. The frequency-sensitive characteristic improves the accuracy of the defect location method based on reflection coefficient.

Description of the drawings

Figure 1 is a schematic diagram of the signal generating device connected to the power cable under test through a coaxial signal cable in an embodiment of the present invention;

Figure 2 is a schematic diagram of the output positioning results of cable defects in the embodiment of the present invention.

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings for further explanation, so that those skilled in the art can have a deeper understanding of the present invention and be able to implement it. However, the following reference examples are only used to explain the present invention and do not serve as the basis for the present invention. limitations.

A cable defect location method based on the frequency domain energy spectrum of the sheath current signal, including the following steps:

Step 1. Establish a distributed transmission line model based on the telegraph equation;

Step 2. Use empirical mode decomposition to decompose the reflection coefficient amplitude signal to obtain the eigenmode function signal;

Step 3. Use the intrinsic mode function signal to locate the cable defect location.

The present invention establishes a distributed transmission line model based on telegraph equations. The signal generating device is connected to the power cable under test through a coaxial signal cable. As shown in Figure 1, step 1 specifically includes the following steps: the signal generating device is connected to the power cable under test through a coaxial signal cable. If the measured power cable is connected, the expression of the head-end voltage reflection signal is as shown in Equation (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)

Among them, U ₁ represents the reflected voltage signal at the head end of the power cable, U ₀ represents the voltage signal injected by the signal generating device, ω = 2πf represents the angular frequency, f represents the frequency, γ represents the propagation coefficient of the line, ρ ₁ represents the head end reflection coefficient, ρ ₂ represents the end reflection coefficient, and the expressions of ρ ₁ and ρ ₂ are as shown in (2):

In formula (2), Z ₀ represents the characteristic impedance of the power cable under test, and R ₀ represents the characteristic impedance of the coaxial signal cable;

According to equation (1), the expression of the reflection coefficient is as shown in equation (3):

It can be seen from equation (3) that the head-end reflection coefficient in a defect-free cable is an attenuated signal that does not change with frequency. If the cable undergoes local aging and deterioration or changes in the physical structure, it will lead to changes in the impedance per unit length of the line. These local impedance changes are the insulation defects proposed by the present invention. In a cable with a defective section, the reflection coefficient of the cable in the defective section will also be different from that of the healthy cable section. The expression of the reflected voltage signal at the head end of the cable with a defective section will be as shown in Equation (4):

In formula (4), ρ ₃ =(Z _d -Z ₀ )/(Z _d +Z ₀ ), Z _d represents the characteristic impedance of the defect section, l ₁ represents the distance between the insulation defect point and the head end; its head end reflection The coefficient is shown in equation (5):

If the defect nature of the cable under test is a grounding defect, that is, a reduction in insulation resistance, the transition resistance of the grounding point is R _g , and l ₂ represents the distance between the grounding defect point and the head end, then the expression of the reflected voltage signal at the head end of the cable will be as follows: Equation (6) Shown:

In equation (6), ρ ₄ =(R _g -Z ₀ )/(R _g +Z ₀ ) represents the reflection coefficient of the ground point. At this time, its head end reflection coefficient is as shown in equation (7):

Due to the superposition of reflected waves at insulation defects. The mixed reflection signal causes periodic oscillation of the reflection factor, which affects the judgment of cable defects. The advantage of empirical mode decomposition is that it is adaptive to signals and is suitable for processing non-stationary signals. Step 2 specifically includes the following steps:

Step 2.1. Find the local maximum set Γ _max and the local minimum set Γ _min of the signal Γ(ω);

Step 2.2. Use cubic spline interpolation to determine the upper and lower envelopes of the original number set Γ(ω) according to Γ _max and Γ _min ;

Step 2.3. Find the local average value m(ω) based on the upper and lower envelopes of Γ(ω), and express the difference between the original signal and the local extreme value as Equation (8)

h ₁ (ω)=Γ(ω)-m(ω) (8);

Step 2.4, replace Γ(ω) with h ₁ (ω) and repeat steps 2.1 to 2.3 until the standard deviation of two consecutive results satisfies the following constraints:

Among them, ω _max and ω _min represent the upper and lower limit angular frequencies of the signal, h _k (ω) represents the kth continuous screening result, and h _k (ω) is considered to be the basic mode component, as shown in Equation (10):

c ₁ (ω)＝h _k (ω) (10)

Then, subtract c ₁ (ω) from Γ(ω) to get the residual sequence r ₁ (ω):

r ₁ (ω)=Γ(ω)-c ₁ (ω) (11);

Step 2.5, use r ₁ (ω) as the new "original" signal, repeat the above step 2.4 until the Nth c _N (ω) or r _N (ω) is less than the preset value, or r _N (ω) becomes The monotonic function terminates; the empirical mode decomposition is completed and we get:

The original signal Γ(ω) is subjected to empirical mode decomposition to obtain N intrinsic mode function components and residual signals, which respectively represent the different scale characteristic signals contained in the original signal.

Because the non-parametric estimate of the power spectral density of the intrinsic mode function signal based on FFT is a biased estimate. To reduce bias, a window function must be used to smooth the power spectral density. The present invention adopts the Kaiser self-convolution window (KSCW), which can mainly concentrate the signal energy in the frequency band on the main lobe and has good suppression performance on the side lobes. The discrete expression of the Caesar window is shown in Equation (13).

Step 3 specifically includes the following steps:

The Kaiser self-convolution window KSCW is used, and its discrete expression is as shown in Equation (13):

Among them, n represents the index number of the sample, N represents the length of the window, β _Ka represents the adjustment coefficient, I ₀ () represents the first kind of 0th-order Bessel function, and its expression is as shown in (14):

The p-order KSCW is defined as the autoconvolution of the parent Kaiser window, as shown in (15):

Assume that the nth eigenmode function signal is _a data set containing M samples, _labeled as function, its expression is as shown in (16):

Calculate sample The autoconvolution function;

Among them, 1≤K≤M, Yes/> The convolution of

According to equation (18), find the main frequencies contained in the eigenmode function signal; through Euler decomposition, the reflection coefficient of the cable head end with length l is expressed as (19):

Γ _l (ω)＝ρ _l e ^-2α(ω)l [cos(2β(ω)l)-jsin(2β(ω)l)] (19)

Among them, ρ _l represents the reflection coefficient at the end of the cable, and the propagation coefficient γ (ω) = α (ω) + jβ (ω); for a cable containing defects, assuming that the defect position is x from the head end, the actual reflection coefficient of the head end The partial expression is:

The defect position x is expressed by equation (21):

For specific implementation, the specific implementation steps are as follows:

1) Input: frequency sweep trigonometric function signal of the cable under test;

2) Use empirical mode decomposition to extract the intrinsic mode function signal and the remaining signals in the reflection coefficient;

3) Use the Euler equation to expand the eigenmode function signal into the form of formula (19);

4) Extract the real part of each eigenmode function signal;

5) According to formulas (16) to (18), synthesize the power spectral density of each eigenmode function signal;

6) Output: The location of the defect point of the tested cable.

During the specific implementation, 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

Set the defect point 500m away from the head end of the line, the defect length 1m, and the signal cable length 1m. During the test, set the cable line to open circuit. At this time, the load impedance is infinite, the end reflection coefficient is 1, and the sweep signal is 5kHz~10MHz. The final output positioning result is obtained as shown in Figure 2. The maximum point of output normalized fault energy is at 497m, which is the defect location result.

The present invention proposes a cable defect positioning method based on the frequency domain energy spectrum of the sheath current signal to improve the accuracy of the existing frequency domain reflection method. Due to the superposition of reflected waves of different frequencies at various insulation defect points in the time domain, a dispersion effect is formed, resulting in reflected wave distortion. First, the reflection coefficient expressions of three cable models are derived, and empirical mode decomposition is used to decompose the envelope of the reflection coefficient amplitude into intrinsic mode functions, thereby making the envelope of the signal more sensitive to defects than the frequency domain spectrum. Then, according to the property that the power spectrum of a stationary random process is a deterministic function, the power spectral density analysis of the inherent mode function signal with limited power is performed, so as to realize the cable defect location based on the power spectral density.

The specific embodiments described above further describe the purpose, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above are only specific embodiments of the present invention and are not intended to limit the present invention. Any equivalent changes and modifications made by those skilled in the art without departing from the concept and principles of the present invention shall fall within the scope of protection of the present invention.

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):