A method for quantitatively evaluating cable positioning defects based on extended prony

Abstract

The application belongs to the technical field of cable diagnosis, and discloses a cable positioning defect quantitative evaluation method based on an extended Prony, which comprises the following steps: obtaining the head-end reflection coefficient of a cable to be measured; calculating a sample function and constructing an extended order matrix; calculating the effective rank of the extended order matrix and determining the least square estimation value of the first coefficient in the Prony method parameterization model; solving the characteristic polynomial of the Prony method parameterization model, obtaining the characteristic root of the characteristic polynomial, and calculating the approximate data; calculating the second coefficient by using the least square method according to the characteristic root of the characteristic polynomial and the approximate data; calculating and determining the defect position and the reflection coefficient amplitude of the corresponding reflection wave according to the characteristic root of the characteristic polynomial and the second coefficient; and quantitatively evaluating the defect severity based on the reflection coefficient amplitude at the defect position. The application can realize quantitative evaluation of the defect severity, thereby improving the effectiveness and accuracy of quantitative evaluation of cable defects with different severities.

Description

Technical Field

[0001] The present invention belongs to the technical field of cable diagnosis, and in particular relates to a cable positioning defect quantitative evaluation method based on extended Prony. Background Art

[0002] Cross-linked polyethylene (XLPE) cables are widely used in urban power grids due to their excellent electrical and mechanical properties. Over long-term operation, power cables can develop irreversible localized defects due to external factors such as extrusion, moisture, and corrosion. These defects can easily cause cable failures and impact the reliability of transmission and distribution lines. Quantitatively assessing the severity of cable defects is crucial. Specifically, if the defect is minor and has no impact on cable operation, maintenance of the defective section is unnecessary; only regular monitoring is required. However, if the defect is significant and has already impacted cable operation, immediate repair or replacement is necessary.

[0003] To address the problem of cable defect and fault location, time domain reflectometry (TDR) and frequency domain reflectometry (FDR), derived from the traveling wave method, are currently the main methods for non-destructive defect detection and have achieved certain results in the field of cable defect location. However, the frequency of the TDR incident wave is relatively low, resulting in its lack of sensitivity in detecting weak defects, and it is greatly affected by attenuation when propagating in the cable. Its positioning accuracy decreases when the cable under test is longer. Compared with TDR, FDR contains more high-frequency components, so it is more sensitive to defects and has a higher detection rate for weak defects. The existing technology proposes a method for locating and diagnosing local defects in cables based on broadband impedance spectroscopy, and studies the mechanism and extent of the influence of local defects in cables on the impedance spectrum, thereby achieving reliable positioning of local defects in cables and defect status assessment. In addition, a method for accurately locating local defects in power cables based on the reflection coefficient spectrum is proposed. This method uses the method of adding a Kaiser window to improve the recognition sensitivity and recognition accuracy of defects. A method for locating and diagnosing moisture in the intermediate joints of distribution cables using frequency domain reflection is also proposed, which eliminates the errors caused by spectrum leakage when locating the intermediate joints.

[0004] Although there have been many studies on FDR, they have only focused on the defect type issue and have not yet explored the issue of defect severity assessment. These methods can only make qualitative judgments on the polarity of the defect and cannot quantitatively calculate and evaluate the defect severity. Summary of the Invention

[0005] In view of the above problems in the prior art, the present application provides a cable positioning defect quantitative evaluation method based on an extended Prony, which realizes quantitative evaluation of cable defects.

[0006] To achieve the above-mentioned purposes, the present application adopts the technical solutions of:

[0007] A cable positioning defect quantitative evaluation method based on an extended Prony comprises the following steps:

[0008] Obtaining a head-end reflection coefficient of a cable to be measured;

[0009] Calculating a sample function according to the head-end reflection coefficient of the cable to be measured, and constructing an extended rank matrix;

[0010] Calculating an effective rank of the extended rank matrix by using singular value decomposition-least square method, and determining a least square estimation value of a first coefficient in a Prony parameterized model; the effective rank is the data amount of a reflection wave of the cable to be measured;

[0011] Solving a characteristic polynomial of the Prony parameterized model according to the least square estimation value of the first coefficient, obtaining characteristic roots of the characteristic polynomial, and calculating head-end reflection coefficient approximate data;

[0012] Calculating a second coefficient by using least square method according to the characteristic roots of the characteristic polynomial and the head-end reflection coefficient approximate data;

[0013] Calculating and determining a defect position and a reflection coefficient amplitude of a corresponding reflection wave according to the characteristic roots of the characteristic polynomial and the second coefficient;

[0014] Quantitatively evaluating a defect severity based on the reflection coefficient amplitude at the defect position.

[0015] Preferably, the sample function is calculated according to the head-end reflection coefficient of the cable to be measured, and specifically:

[0016]

[0017] wherein r(i,j) is a sample function of the i th mode and the j th mode, x(n-j) is an n-j th sampling point, x * (n-i) is a conjugate complex number of an n-i th sampling point, n is a sampling point serial number, p is a mode number, and N is a sampling point number.

[0018] Preferably, the extended rank matrix is constructed, and specifically:

[0019]

[0020] wherein R e is the extended rank matrix, r(p e ,pe ) is the pth e The mode and the pth e The sample function of the mode, p e is the rank of the expanded matrix.

[0021] Preferably, the least squares estimate of the first coefficient in the parameterized model is determined as follows:

[0022]

[0023] Among them, r(p,p) is the sample function of the p-th mode and the p-th mode, a p is the first coefficient of the pth mode, ε p is the cost function of the p-th mode.

[0024] Preferably, the characteristic polynomial of the Prony method parameterized model is solved according to the least squares estimate of the first coefficient, specifically:

[0025] 1+a1z -1 +a2z -2 +...+a p z -p =0

[0026] Among them, a1, a2, ..., a p is the least squares estimate of the first coefficient, z -1 ,z -2 ,...,z -p is the characteristic root of the characteristic polynomial, and p is the number of modes, that is, the number of reflected waves.

[0027] Preferably, the approximate data of the head-end reflection coefficient is calculated according to the first coefficient, specifically as follows:

[0028]

[0029] in, is the approximate value of the nth sampling point, a i is the first coefficient of the ith mode, is the approximate value of the ni-th sampling point, and p is the number of modes.

[0030] Preferably, the second coefficient is calculated using the least squares method, specifically:

[0031]

[0032] Among them, z p is the characteristic root of the characteristic polynomial, b p is the second coefficient of the pth mode, is the approximate value of the N-1th sampling point.

[0033] Preferably, the frequency of each reflected wave is calculated according to the characteristic root of the characteristic polynomial:

[0034] f i =arctan[Im(z i ) / Re(z i )] / (2π△t)

[0035] Among them, f i is the frequency of the i-th reflected wave, Im is the imaginary part function, Re is the real part function, △t is the sampling interval, z i is the characteristic root of the characteristic polynomial.

[0036] Then, the position of each reflected wave is determined according to its frequency:

[0037]

[0038] Among them, l i is the position of the i-th reflected wave, and v is the wave velocity.

[0039] Reflected waves may come from cable joints, cable defects and cable ends; therefore, the defect location can be determined based on the position of each reflected wave.

[0040] Preferably, the reflection coefficient amplitude of each reflected wave is calculated according to the second coefficient, specifically as follows:

[0041] A i =|b i |

[0042] Among them, A i is the amplitude of the reflection coefficient of the i-th reflected wave, b i is the second coefficient.

[0043] Thus, the reflection coefficient amplitude of the reflected wave at the defect location can be obtained, and the severity of the defect can be quantitatively evaluated based on the reflection coefficient amplitude at the defect location.

[0044] As an advantage, it also includes:

[0045] The phase and attenuation coefficient of each reflected wave are calculated according to the second coefficient and the characteristic root of the characteristic polynomial to obtain an estimated value of the head-end reflection coefficient.

[0046] Preferably, the phase and attenuation coefficient of the head-end reflection coefficient are calculated according to the second coefficient, specifically as follows:

[0047]

[0048] Among them, θ i is the phase of the i-th reflected wave, αi is the attenuation coefficient of the i-th reflected wave, Im is the imaginary part function, Re is the real part function, △t is the sampling interval, b i is the second coefficient, z i is the characteristic root of the characteristic polynomial.

[0049] Then, the estimated value of the head-end reflection coefficient is obtained according to the following formula:

[0050]

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] The present invention addresses the problem that the detected cable defects cannot be quantitatively evaluated in the current FDR process. By introducing a parameterized estimation method based on extended Prony, the measured cable reflection coefficient can be processed to finally obtain the required defect amplitude parameter, that is, the reflection coefficient of the defect. The severity of the defect can be evaluated based on the amplitude, thereby improving the effectiveness and accuracy of quantitative evaluation of cable defects of different severities. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 The figure is a flowchart of the quantitative evaluation method for cable location defects based on extended Prony;

[0054] Figure 2 Schematic diagram of the distributed parameter model of power cables;

[0055] Figure 3 Schematic diagram of the reflection coefficient model of a defective cable;

[0056] Figure 4 Schematic diagram of the original reflection coefficient spectrum and the fitted reflection coefficient spectrum when there is a single defect;

[0057] Figure 5 Schematic diagram of the original defect location spectrum and the fitted defect location spectrum;

[0058] Figure 6 Schematic diagram of the amplitude fitted at the defect;

[0059] Figure 7 Schematic diagram of the fitted amplitude when the defect gradually increases;

[0060] Figure 8 Schematic diagram of the original reflection coefficient spectrum and the fitted reflection coefficient spectrum when there are multiple defects;

[0061] Figure 9 Schematic diagram of the original defect location spectrum and the fitted defect location spectrum;

[0062] Figure 10Schematic diagram of the amplitude fitted at the defect when there are multiple defects;

[0063] Figure 11 This is a schematic diagram of the fitted amplitude when the first defect gradually increases;

[0064] Figure 12 This is a schematic diagram of the fitted amplitude when the second defect gradually increases;

[0065] Figure 13 Schematic diagram of the reflection coefficient spectrum after impedance matching and fitting;

[0066] Figure 14 Schematic diagram of the positioning spectrum after impedance matching and fitting;

[0067] Figure 15 This is a schematic diagram of the fitting amplitude at a single defect in the cable;

[0068] Figure 16 This is a schematic diagram of the fitting amplitude at multiple defects in the cable;

[0069] Figure 17 Schematic diagram of the amplitude fitted for different defects. DETAILED DESCRIPTION

[0070] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0071] like Figure 1 As shown, the embodiment of the present invention provides a cable positioning defect quantitative assessment method based on extended Prony, including the following steps S1 to S7:

[0072] S1. Obtain the reflection coefficient of the first end of the cable to be tested.

[0073] In an optional embodiment of the present invention, according to the transmission line principle, when the length of the cable under test is much smaller than the wavelength of the test signal, the unit length of the cable can be represented by a distributed parameter model, and then a cable is constructed by cascading numerous distributed parameter models. The distributed parameter model is as follows: Figure 2 shown. Figure 2 Here, R0 (Ω / m), L0 (H / m), G0 (S / m), and C0 (F / m) represent the resistance, inductance, conductance, and capacitance of the cable per unit length dx, respectively.

[0074] Due to the skin effect and proximity effect, the parameters per unit length can be expressed as:

[0075]

[0076] Where μ0 is the magnetic permeability in a vacuum environment, ω is the angular frequency of the test, and its relationship with the test frequency can be expressed as ω = 2πf; r s 、r c Represent the radius of the shielding layer and the radius of the cable core, ρ c , ρ s They represent the resistivity of the cable core and the resistivity of the shielding layer respectively, and σ and ε are the conductivity and dielectric constant of the dielectric respectively.

[0077] The defect in the cable will directly cause the resistance value of the area to change, and the signal propagation constant will also be affected. Due to the changes in the above parameters, the cable will form an impedance discontinuity at the defect, causing the signal propagation characteristics to change. According to the traveling wave principle, when the signal propagates to the interface between the cable body and the impedance discontinuity, reflection will occur. The cable model with defects is established as follows: Figure 3 shown.

[0078] Assume that the total length of the cable under test is l, and there is a defective section in the cable at a distance of l1 from the head end. The length of the defective section is Δx, and the distance from the defective section to the end of the cable is l2. The propagation constant and characteristic impedance of the cable body are γ0 and Z0 respectively, while the propagation constant and impedance of the defective section are γ1 and Z1 respectively. L Assuming that ρ is the load impedance, according to the traveling wave reflection principle, the signal will be reflected at the end of the cable, the end of the defect segment, and the beginning of the defect. The reflection coefficients are ρ2, ρ1, and ρ0. The three reflection coefficients can be calculated by the following formula:

[0079]

[0080] At this time, the cable can be divided into three sections for calculation. The first section is from the beginning of the cable to the beginning of the defect, the second section is the defect section, and the third section is from the end of the defect to the end of the cable. Then, the reflection coefficient Γ2 and input impedance Z of the third section can be calculated. l2 for:

[0081]

[0082] Similarly, the reflection coefficient Γ1 and input impedance Z of the second segment can be obtained. Δx for:

[0083]

[0084] The reflection coefficient Γ0 of the first segment and the input impedance Z of the first segment l1 for:

[0085]

[0086] The calculation process reveals that the reflection coefficient and impedance at the cable's headend not only contain information about the impedance of the entire cable but also provide characteristics of local defects, effectively reflecting the cable's overall performance and location. Extracting the location information from the headend reflection coefficient and headend input impedance allows for defect location. Because the headend reflection coefficient and headend input impedance are essentially the same, this embodiment uses the headend reflection coefficient to locate defects.

[0087] The reflection coefficient at the head end of the cable carries the location information of the cable end and the cable defect, so it is only necessary to extract the location information to locate and measure the distance of the cable defect.

[0088] The head-end reflection coefficient can be written as:

[0089]

[0090] Among them, α0 and β0 are the cable attenuation constant and phase constant respectively, ρ i is the reflection coefficient of the i-th reflected wave, p is the number of reflections of the reflected wave, l i is the position of the i-th reflected wave.

[0091] According to Euler's formula, the above formula is expanded and calculated to obtain:

[0092]

[0093] Where f is the test frequency and v is the wave velocity.

[0094] Finally, by solving the real part of the above formula, we can get the reflection coefficient spectrum of the cable head end as shown below:

[0095]

[0096] It can be seen that the real part of the head-end reflection coefficient Real(Γ) consists of a constant term and an exponential term of attenuated oscillation. When the test frequency f is used as the independent variable, the attenuated oscillation term contains its frequency component f i , the frequency components can be written as:

[0097]

[0098] Among them, l i is the position of the i-th reflected wave, and v is the wave velocity.

[0099] The frequency component of the defect is determined by the time it takes for the signal to travel back and forth from the cable headend to the defect. Therefore, the defect can be accurately located by measuring the frequency component. When multiple defects are present, the different frequency components at each defect can be used to locate each defect individually.

[0100] S2. Calculate the sample function according to the reflection coefficient of the first end of the cable to be tested, and construct an extended order matrix.

[0101] In an optional embodiment of the present invention, the reflection coefficient at the head end of the cable is composed of a reflection coefficient term, an attenuation term including an attenuation coefficient α, and a phase term including a phase coefficient β. Its composition is similar to the parameter model of the Prony algorithm. The Prony algorithm is a time domain analysis method that is particularly suitable for analyzing dynamic signals, especially for the feature recognition of low-frequency oscillation signals. By processing the measured data, the Prony algorithm can be extended to effectively extract oscillation modal information. The parameterized model used by the extended Prony algorithm is a set of p exponential functions with arbitrary amplitude, phase, frequency, and attenuation coefficients, and its discrete time function form is:

[0102]

[0103] Among them, A i is the amplitude; θ i is the phase; α i is the attenuation coefficient; f i represents the oscillation frequency; Δt represents the sampling interval; and n represents the number of sampling points. Like the composition of the head-end reflection coefficient, it is composed of three terms: amplitude, attenuation coefficient, and phase. Both are linear combinations of attenuated sinusoidal components. The data is sampled at equal intervals, and the data of FDR is also sampled at equal intervals. Therefore, this embodiment introduces the extended Prony method into FDR, so that the frequency, attenuation coefficient, amplitude and phase of the given signal can be directly estimated, which is suitable for quantitative defect evaluation of FDR.

[0104] When using the Prony algorithm in this embodiment, the parameter model data needs to be close to the real data. Assume that the original signal x(n) is composed of a set of attenuated sinusoidal components and there are N original data. Using the principle of least square error, the cost function can be constructed:

[0105]

[0106] The Prony method considers the fitted value of the cost function as a homogeneous solution to a linear difference equation with constant coefficients. In order to obtain this difference equation, it is necessary to first determine its characteristic polynomial, which is as follows:

[0107]

[0108] The above formula means The difference equation that satisfies the recursion is as follows:

[0109]

[0110] Define the measured data x(n) and the approximate value of the head-end reflection coefficient The error between them is e(n), then:

[0111]

[0112] According to the above two formulas, we can get:

[0113]

[0114] The Prony method is to minimize the error between the measured data and the approximate data, so that the parameters of the established parameterized model are infinitely close to the real data. Finally, the severity of the defect is judged based on the specific estimate of the defect value formed by the model.

[0115] For the above formula, in order to make the sum of squares of errors is the smallest so that the parameters a1, a2, ..., a p Form the least squares estimate and define:

[0116]

[0117] The above formula can be transformed into:

[0118]

[0119] Solving for parameter a i , you need to make Minimum, then we can get the linear matrix equation:

[0120]

[0121] The above formula can be simplified as:

[0122] Xa=ε

[0123] The extended Prony method is used to process the above equation using linear least squares, in order to make the function:

[0124]

[0125] Taking the minimum, we can make Then we have:

[0126]

[0127] Where x * (ni) is the conjugate complex number of x(ni), then the corresponding minimum error energy is:

[0128]

[0129] In order to make εp Take the minimum and define the sample function:

[0130]

[0131] Among them, r(i,j) is the sample function of the i-th mode and the j-th mode, x(nj) is the nj-th sampling point, x * (ni) is the conjugate complex number of the ni-th sampling point, n is the sampling point number, p is the number of modes, and N is the number of sampling points.

[0132] Substitute the original data of the reflection coefficient of the cable under test obtained in step S1 into the above formula to calculate the sample function r(i, j), and construct the extended order matrix, specifically:

[0133]

[0134] Among them, R e is the extended order matrix, r(p e ,p e ) is the pth e The mode and the pth e The sample function of the mode, p e is the rank of the expanded matrix.

[0135] S3. Use the singular value decomposition-least squares method to calculate the effective rank of the expanded order matrix and determine the least squares estimate of the first coefficient in the Prony method parameterized model.

[0136] For the expanded order matrix constructed in step S2, construct the following Prony equation:

[0137]

[0138] Use singular value decomposition-least squares method to calculate the expanded order matrix R e The effective rank p (that is, the number of reflected waves) of the parameterized model is obtained, and the least squares estimate of the first coefficient a1, a2, ..., a p ; Among them, r(p,p) is the sample function of the p-th mode and the p-th mode, a p is the first coefficient of the pth mode, ε p is the cost function of the pth mode. For the specific process of singular value decomposition-least squares method, please refer to Zhu Lanxiang, Shan Zebiao, Shan Zetao, et al. EES-MIMO radar electromagnetic environment perception algorithm based on SVD-TLS[J]. Journal of Jilin University (Information Science Edition), 2015, 33(03): 246-250.

[0139] S4. Solve the characteristic polynomial of the Prony method parameterized model according to the least squares estimate of the first coefficient, obtain the characteristic roots of the characteristic polynomial, and calculate the approximate data of the head-end reflection coefficient.

[0140] In an optional embodiment of the present invention, the characteristic polynomial of the Prony method parameterized model is specifically:

[0141] 1+a1z -1 +a2z -2 +...+a p z -p =0

[0142] Among them, a1, a2, ..., a p is the least squares estimate of the first coefficient, and p is the number of modes, that is, the number of reflected waves.

[0143] The characteristic polynomial of the Prony method parameterized model can be solved according to the least squares estimate of the first coefficient, and the characteristic root z of the characteristic polynomial can be obtained. i ,i=1,2,…,p。

[0144] Then, the data is approximated based on the reflection coefficient of the first end The difference equation that satisfies the recursion is:

[0145]

[0146] in, is the approximate value of the nth sampling point, a i is the first coefficient of the ith mode, is the approximate value of the ni-th sampling point, and p is the number of modes;

[0147] The approximate data of the head end reflection coefficient can be calculated in

[0148] S5. Calculate the second coefficient using the least squares method according to the characteristic roots of the characteristic polynomial and the approximate data of the head-end reflection coefficient.

[0149] In an optional embodiment of the present invention, the characteristic root z of the characteristic polynomial i It can be expressed in matrix form:

[0150]

[0151] Among them, z p is the characteristic root of the characteristic polynomial, b p is the second coefficient of the pth mode, is the approximate value of the N-1th sampling point.

[0152] According to the characteristic roots and approximate data of the characteristic polynomial, the second coefficient b can be calculated by the least squares method. i ,i=1,2,…,p。

[0153] S6. Determine the defect position and the reflection coefficient amplitude of the corresponding reflected wave based on the characteristic root and the second coefficient of the characteristic polynomial.

[0154] In an optional embodiment of the present invention, the frequency of each reflected wave is calculated according to the characteristic root of the characteristic polynomial:

[0155] f i =arctan[Im(z i ) / Re(z i )] / (2π△t)

[0156] Among them, f i is the frequency of the i-th reflected wave, Im is the imaginary part function, Re is the real part function, △t is the sampling interval, z i is the characteristic root of the characteristic polynomial.

[0157] Then, the position of each reflected wave is determined according to its frequency:

[0158]

[0159] Reflected waves may come from cable joints, cable defects and cable ends; therefore, the defect location can be determined based on the position of each reflected wave.

[0160] In an optional embodiment of the present invention, the reflection coefficient amplitude of each reflected wave is calculated according to the second coefficient, specifically as follows:

[0161] A i =|b i |

[0162] Among them, A i is the reflection coefficient amplitude of the i-th reflected wave, b i is the second coefficient.

[0163] S7. Quantitatively evaluate the severity of the defect based on the reflection coefficient amplitude at the defect location.

[0164] In an optional embodiment of the present invention, the amplitude A of the cable defect can be specifically calculated according to the extended Prony algorithm parameter model in step S6. i , and then the severity of the defect can be evaluated based on the specific numerical value of the amplitude.

[0165] In an optional embodiment of the present invention, this embodiment further includes:

[0166] S8. Calculate the phase and attenuation coefficient of each reflected wave according to the second coefficient and the characteristic root of the characteristic polynomial to obtain an estimated value of the head-end reflection coefficient.

[0167] The phase and attenuation coefficient of the head-end reflection coefficient are calculated based on the second coefficient and the characteristic root of the characteristic polynomial, specifically:

[0168]

[0169] Among them, θ i is the phase of the i-th reflected wave, α i is the attenuation coefficient of the i-th reflected wave, Im is the imaginary part function, Re is the real part function, △t is the sampling interval, b i is the second coefficient, z i is the characteristic root of the characteristic polynomial.

[0170] Substituting the calculated amplitude, phase, frequency and attenuation coefficient into the Prony method parameterized model can estimate the estimated value of the head-end reflection coefficient:

[0171]

[0172] The following is a simulation analysis of the above method proposed in this embodiment.

[0173] The simulated cable length is set to 500m, the test frequency is 150kHz-30MHz, and the number of sampling points is 3001. When a single defect is present, an intermediate joint defect is set 200m away from the head end, the joint length is 0.8m, and the capacitance change factor is 0.848. The cable head end reflection coefficient is obtained by testing. After processing the data according to the method steps of this embodiment, the real part of the original head end reflection coefficient spectrum and the real part of the head end reflection coefficient spectrum estimated by the parameter model can be obtained as shown in the following figure: Figure 4 shown.

[0174] Depend on Figure 4 It can be seen that both the original reflection coefficient spectrum and the reflection coefficient spectrum fitted by the parameter model show an exponential decay trend, consistent with the theoretical situation. The reflection coefficient spectrum fitted by the parameter model almost overlaps with the original reflection coefficient spectrum before 1500 sampling points, indicating that the fitted data and the actual data have a high degree of consistency in the low-frequency range. After 1500 sampling points, the fitted attenuation increases compared to the measured value, indicating that the fit rate of the fitted data and the actual data decreases in the high-frequency range, but its overall decay trend is the same as the original reflection coefficient spectrum.

[0175] After that, the original reflection coefficient spectrum and the fitted reflection coefficient spectrum are Fourier transformed and the modulus value is taken to obtain the reflection coefficient spectrum that changes with the fundamental frequency; the frequency coordinate is converted into the cable distance coordinate to obtain the original defect location spectrum and the fitted defect location spectrum of the reflection coefficient that changes with the distance. Figure 5 As shown. Figure 5 , the positioning spectrum obtained by fitting the data is almost consistent with the original positioning spectrum, so it can be concluded that the proposed extended Prony method is effective for parameter fitting of single-defect cables.

[0176] Next, the severity of the cable defect can be judged based on the fitted amplitude parameters, and the fitted amplitude parameters of the defect can be obtained as follows: Figure 6 As shown. Figure 6 When the capacitance at the defect is reduced to 0.848 times that of the original capacitance, the normalized amplitude at the defect is 0.016. It can be seen that the amplitude of the original positioning spectrum is larger than the amplitude at the fitted defect. This is because the positioning spectrum is modulo-operated, and its peak value is the vector superposition of the amplitudes of adjacent frequency points at this location. Therefore, the amplitude in the positioning spectrum cannot be used to judge the severity of the defect. The fitted data only takes the amplitude of a single frequency point at the defect, eliminating the influence of other frequency points. Therefore, the amplitude at the defect can be used to judge the severity of the defect.

[0177] Next, we gradually increase the severity of the defect to verify the effectiveness of the method in this embodiment. Other conditions remain unchanged, and after changing the capacitance at the defect to 0.7 and 0.6 times of the body, we can get the amplitude change at the fitted defect point as follows: Figure 7 As shown. Figure 7 As the defect severity increases, the fitted amplitude at the defect also increases. The amplitudes corresponding to three defects of varying severity are 0.016, 0.032, and 0.042, respectively. This indicates that the proposed extended Prony method is effective for assessing cable defect severity. It fits amplitudes corresponding to the severity of the defect, and the greater the defect severity, the larger the fitted amplitude. This method can be used to monitor discovered cable defects over a long period of time, establishing regular inspections. If the amplitude at the defect increases, the defect can be repaired or replaced.

[0178] On the basis of the above single-defect cable, a defect with reduced capacitance (increased impedance) is set at 400m of the cable. Other conditions remain unchanged. The capacitances at the two defects are set to 0.848 times and 0.8 times of the main body respectively. The real part of the original head-end reflection coefficient spectrum and the real part of the head-end reflection coefficient spectrum estimated by the parameter model are obtained as follows: Figure 8 As shown. Figure 8 It can be found that the fitted reflection coefficient almost coincides with the true reflection coefficient, and compared with the case of a single defect, the fitted reflection coefficient spectrum in the case of multiple defects is more consistent with the original reflection coefficient spectrum, and a greater attenuation occurs after 2300 sampling points, that is, the frequency band of the fitted data and the true data in the case of multiple defects is wider.

[0179] After Fourier transforming the original reflection coefficient spectrum and the fitted reflection coefficient spectrum and taking the modulus value, the original defect location spectrum and the fitted defect location spectrum can be obtained as follows: Figure 9 As shown. Figure 9 The positioning spectrum obtained by fitting the data is almost consistent with the original positioning spectrum. Therefore, it can be concluded that the proposed extended Prony method is effective for parameter fitting of multi-defect cables.

[0180] Then, the severity of the cable defect is judged according to the fitted amplitude parameters, and the fitted amplitude parameters of the defect can be obtained as follows: Figure 10 As shown. Figure 10 The amplitudes fitted for the defects at 200m and 400m are 0.016 and 0.020, respectively. The defects at these two locations are 0.848 times and 0.8 times the bulk capacitance, respectively. The second defect is more serious, so the amplitude at the second location is higher than that at the first. It can be found that in the case of multiple defects, due to the influence of the attenuation coefficient, although the severity of the second defect is greater than that of the first, the amplitude of the second defect in the positioning spectrum is smaller than that of the first. Therefore, the severity of the defect cannot be judged by the amplitude in the positioning spectrum. The Prony method proposed in this embodiment eliminates the influence of the attenuation coefficient and frequency, and only uses the amplitude as the judgment factor for the severity of the defect. Therefore, the severity of the defect can be accurately judged.

[0181] Next, we gradually increase the severity of the defect to verify the effectiveness of the proposed method. The capacitance of the second defect remains unchanged, and the capacitance of the first defect is set to 0.7 and 0.6 times of the body respectively. The changes in the fitting amplitude at the defect point are observed. The results are as follows Figure 11 As shown. Figure 11 , when the first defect gradually increases, the corresponding defect amplitude also gradually increases. The amplitudes corresponding to the three defects of different degrees are 0.016, 0.031 and 0.042 respectively. The severity of the second defect does not change. When the first defect gradually increases, the amplitudes corresponding to the second defect are 0.020, 0.019 and 0.020 respectively, which are almost unchanged. At the same time, the first defect is set to 0.848 times the main body and the amplitude changes when the second defect is changed to 0.7 and 0.6 times the main body are observed. Figure 12 As shown. Figure 12 , when the second defect is 0.8, 0.7 and 0.6 times the size of the main body, the corresponding amplitudes are 0.020, 0.028 and 0.032; while the amplitudes of the first defect are 0.016, 0.016 and 0.017 respectively, which are almost unchanged. Figure 11 and 12 It can be found that when the severity of a single defect increases, it has almost no effect on the amplitudes of other defects. Therefore, the defect severity judgment method proposed in this embodiment is effective in the case of multiple defects.

[0182] The method proposed in this embodiment is experimentally verified below.

[0183] In order to verify the effectiveness of the method proposed in this embodiment, a YJLV228.7 / 15-YJLV22 8.7 / 15-1×95 10kV XLPE power cable with a total length of 500m was first tested, and an intermediate joint was made at 250m. The test frequency band was 150kHz~10MHz, and the number of sampling points was 3001. The test results were eliminated at the head end, and then the defect quantitative evaluation study was performed on the matched positioning curve. After using the extended Prony method, the fitting reflection coefficient spectrum, fitting positioning spectrum and fitting defect amplitude of the 500m cable were obtained as shown in the following figure: Figures 13 to 15 shown.

[0184] The proposed method fits the reflection coefficient spectrum, location spectrum, and defect amplitude. The fitted data closely matches the original measured data. Since the amplitude of the defect location curve is the superposition of the fitted amplitudes at the frequency points near the defect, its amplitude is greater than the fitted amplitude. The normalized amplitude at the fitted defect is 0.049. Using a TH2816B LCR digital bridge to test the intermediate joint and the cable body at a frequency of 120kHz, the capacitances were found to be 211.881pF / m and 255.895pF / m, respectively. Substituting this into the calculation, the amplitude at this location is 0.047, which is not much different from the estimated amplitude. This verifies that the method is effective for actual cable testing, with an accuracy of 4%. In subsequent testing, the amplitude at the defect location can be used as the standard, with the 0.047 amplitude ±10% being considered the normal joint amplitude. Any amplitude outside this range is considered a defective joint.

[0185] To verify the effectiveness of the proposed method for multi-defect cables, a multi-defect cable in operation in Guangzhou was tested. This cable, a 1391m long YJLV22 8.7 / 15-YJLV22 8.7 / 15-1×95 10kV XLPE power cable, had intermediate connectors located 250m and 500m from the head end. The FDR test was conducted at a frequency of 0.15MHz to 5MHz, with 3001 test points.

[0186] Depend on Figure 16 As can be seen, the proposed method fits the amplitude of the defect in the 1391m cable. The normalized amplitude of the defect at 250m is 0.051, and the normalized amplitude of the defect at 500m is 0.039. The amplitude of the first joint is within the normal joint amplitude range mentioned above. However, considering signal attenuation, the amplitude of the second joint clearly exceeds the normal joint amplitude range, thus determining the second joint as a faulty joint. The test results show that the proposed method is also effective for testing cables with multiple defects.

[0187] In order to study the influence of different degrees of defects on the amplitude of FDR, the XLPE cable with the length of 787 m, YJLV228.7 / 15-YJLV228.7 / 15-1x9510 kV, is tested. The copper shielding layer is damaged at the position of 68 m in the cable. The damage degree of the shielding layer is set to three degrees, i.e., no damage, 10 cm damage, and 20 cm damage of the shielding layer. The test results are fitted in amplitude and the head-end elimination is performed. Then, the matched positioning curve is used for quantitative evaluation of the defects. The fitted defect amplitude of the 787 m cable is shown in Figure 17 When the damage length of the shielding layer is 10 cm, the fitted amplitude at the defect is 0.027, and when the damage length of the shielding layer is 20 cm, the fitted amplitude at the defect is 0.033. With the increase of the defect severity, the fitted amplitude at the defect also increases. Therefore, it is concluded that the method is effective for judging the severity of the defect. In the process of cable defect monitoring, the fitting method can be used for long-time observation of the defect. According to the fitted amplitude, it is determined whether the defect severity is increased and whether the subsequent maintenance is needed.

[0188] In summary, in view of the problem that the detected cable defects cannot be quantitatively evaluated in the FDR process, the estimation method based on the parameterized model is introduced. The extended Prony method in the parameterized model is introduced into the cable defect detection. The measured cable reflection coefficient is processed by using the method. Finally, the amplitude parameter of the defect, i.e., the reflection coefficient at the defect, is obtained. According to the amplitude, the severity of the defect is evaluated. Then, the simulation cable with single defect and multiple defects is tested. The test results prove the effectiveness of the extended Prony method for fitting the amplitude at the defect. Finally, the 10 kV cables with the lengths of 500 m, 1391 m, and 787 m are tested. In view of the phenomenon that the test line and the cable head-end impedance are not matched in the actual test, the head-end impedance matching algorithm is introduced to reduce the influence of the head-end mismatch on the defect evaluation. The test results of the 500 m and 1391 m cables prove the effectiveness of the proposed method for single defect and multiple defects in long-distance cables. The test results of the 787 m land cable realize the testing of defects with different severity. The amplitudes at the defects with different severity are successfully fitted. It is proved that the method is effective for testing defects with different severity.

[0189] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0190] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0191] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0192] Specific embodiments are used in the present invention to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core ideas. At the same time, for those skilled in the art, according to the ideas of the present invention, there may be changes in the specific implementation methods and application scopes. In summary, the contents of this specification should not be understood as limiting the present invention.

[0193] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A quantitative evaluation method for cable positioning defects based on extended Prony, characterized in that: The following steps are involved: Obtain the reflection coefficient of the first end of the cable under test; Calculate the sample function according to the reflection coefficient of the first end of the cable to be tested and construct an extended order matrix; The effective rank of the expanded matrix is ​​calculated using the singular value decomposition-least squares method, and the least squares estimate of the first coefficient in the Prony method parameterized model is determined; the effective rank is the amount of data of the reflected wave of the cable to be tested; Solve the characteristic polynomial of the Prony method parameterized model based on the least squares estimate of the first coefficient, obtain the characteristic roots of the characteristic polynomial, and calculate the approximate data of the head-end reflection coefficient; The second coefficient is calculated using the least square method according to the characteristic roots of the characteristic polynomial and the approximate data of the head-end reflection coefficient; Determine the defect position and the reflection coefficient amplitude of the corresponding reflected wave according to the characteristic root and the second coefficient of the characteristic polynomial; The severity of the defect is quantitatively assessed based on the reflection coefficient amplitude at the defect location.

2. The cable positioning defect quantitative assessment method based on extended Prony according to claim 1 is characterized in that: Calculate the sample function based on the reflection coefficient of the first end of the cable to be tested, specifically: Among them, r(i,j) is the sample function of the i-th mode and the j-th mode, x(nj) is the nj-th sampling point, x * (ni) is the conjugate complex number of the ni-th sampling point, n is the sampling point number, p is the number of modes, and N is the number of sampling points.

3. The cable positioning defect quantitative assessment method based on extended Prony according to claim 2 is characterized in that: Construct an extended order matrix, specifically: Among them, R e is the extended order matrix, r(p e ,p e ) is the pth e The mode and the pth e The sample function of the mode, p e is the rank of the expanded matrix.

4. The cable positioning defect quantitative assessment method based on extended Prony according to claim 3 is characterized in that: Determine the least squares estimate of the first coefficient in the parameterized model, specifically: Among them, r(p,p) is the sample function of the p-th mode and the p-th mode, a p is the first coefficient of the pth mode, ε p is the cost function of the p-th mode.

5. The cable positioning defect quantitative assessment method based on extended Prony according to claim 4 is characterized in that: Solve the characteristic polynomial of the Prony method parameterized model based on the least squares estimate of the first coefficient and obtain the characteristic root z of the characteristic polynomial i ,i=1,2,…,p; specifically: 1+a1z -1 +a2z -2 +...+a p z -p =0 Among them, a1, a2, ..., a p is the least squares estimate of the first coefficient, and p is the number of modes, that is, the number of reflected waves.

6. The cable positioning defect quantitative assessment method based on extended Prony according to claim 5 is characterized in that: The approximate data of the head-end reflection coefficient is calculated based on the first coefficient, specifically: in, is the approximate value of the nth sampling point, a i is the first coefficient of the ith mode, is the approximate value of the ni-th sampling point, and p is the number of modes.

7. The cable positioning defect quantitative assessment method based on extended Prony according to claim 6 is characterized in that: The second coefficient is calculated using the least squares method, specifically: Among them, z p is the characteristic root of the characteristic polynomial, b p is the second coefficient of the pth mode, is the approximate value of the N-1th sampling point.

8. The cable positioning defect quantitative assessment method based on extended Prony according to claim 7 is characterized in that: Calculate the frequency of each reflected wave according to the characteristic roots of the characteristic polynomial: f i =arctan[Im(z i ) / Re(z i )] / (2π△t) Among them, f i is the frequency of the i-th reflected wave, Im is the imaginary part function, Re is the real part function, △t is the sampling interval, z i is the characteristic root of the characteristic polynomial; Then, the position of each reflected wave is determined according to its frequency: Determine the defect location based on the position of each reflected wave; The reflection coefficient amplitude of each reflected wave is calculated based on the second coefficient, specifically: A i =|b i | Among them, A i is the amplitude of the reflection coefficient of the i-th reflected wave, b i is the second coefficient.

9. The cable positioning defect quantitative assessment method based on extended Prony according to claim 7, characterized in that: Also includes: The phase and attenuation coefficient of each reflected wave are calculated according to the second coefficient and the characteristic root of the characteristic polynomial to obtain an estimated value of the head-end reflection coefficient.

10. The cable positioning defect quantitative assessment method based on extended Prony according to claim 9, characterized in that: The phase and attenuation coefficient of the head-end reflection coefficient are calculated based on the second coefficient, specifically: Among them, θ i is the phase of the i-th reflected wave, α i is the attenuation coefficient of the i-th reflected wave, Im is the imaginary part function, Re is the real part function, △t is the sampling interval, b i is the second coefficient, z i is the characteristic root of the characteristic polynomial; Then, the estimated value of the head-end reflection coefficient is obtained according to the following formula:

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