Wideband impedance spectrum cable fault location method based on terminal function compensation

Abstract

The application discloses a kind of wide frequency impedance spectrum cable fault location methods based on end function compensation, comprising: according to the equivalent model of micro-unit of healthy coaxial cable, the voltage current partial differential equation set of healthy coaxial cable is determined, and its general solution is calculated;According to general solution, the reflection coefficient of healthy coaxial cable load end is calculated, and according to the reflection coefficient and general solution, the impedance spectrum of healthy coaxial cable about frequency is calculated;The impedance spectrum about frequency of measured cable is measured, and difference comparison is carried out with the impedance spectrum of healthy coaxial cable, to determine whether the measured cable exists fault;According to phase spectrum, construct orthogonal integral function, introduce gauss filter to eliminate the interference of local big fault, and extract the extreme value and maximum value of function, form compensation function;Establish fault diagnosis function based on impedance phase spectrum, determine the local fault position and local soft fault type of measured cable, realize accurate positioning of different fault positions, and greatly improve the detection and positioning precision for traditional method.

Description

Technical Field

[0001] The present invention relates to the technical field of fault diagnosis of electrical engineering power equipment, and in particular to a broadband impedance spectrum cable fault location method based on terminal function compensation. Background Art

[0002] Common traditional fault types in power cables are categorized as low-resistance, high-resistance, open-circuit, and short-circuit. Open-circuit and short-circuit faults are relatively easy to detect using current engineering methods. Detection of low-resistance and high-resistance soft faults, which pose significant risks but do not significantly impact cable operation, involves both non-electrical and electrical parameter methods. Non-electrical parameter analysis primarily involves diagnosing the physical and chemical properties of the cable and is commonly used to assess the overall cable life. Examples include elongation at break (EAB), compression modulus testing, infrared spectroscopy, oxidation induction time / temperature analysis, and energy dispersive spectroscopy (EDX). Electrical parameter analysis, on the other hand, involves testing insulation resistance, dielectric constant, leakage current, and withstand voltage. These measurements only provide a limited assessment of the overall cable condition and cannot reveal localized defects or latent defects.

[0003] Currently, broadband impedance spectroscopy methods for detecting cable defects offer greater sensitivity to localized faults, such as cable aging. For example, the input impedance spectrum at the cable's headend is obtained and then integrated using the integral transformation method to obtain the fault location function. However, the measurement accuracy of this method depends on the impedance spectrum's measurement frequency or sweep bandwidth. While the upper limit of the impedance spectrum's measurement frequency should be as high as possible, excessively high test frequencies place high demands on the measurement equipment. Furthermore, impedance mismatches at the measurement fixture connections at high frequencies can significantly impact the test system. Furthermore, severe faults within multiple fault segments can cause the fault location point to shift, compromising location accuracy in the presence of multiple fault segments. Furthermore, location accuracy is limited by the sweep bandwidth. A larger sweep bandwidth generally results in more accurate location, which often requires a high-precision impedance analyzer or vector network analyzer. Low sweep bandwidths introduce significant ripples in the fault location, potentially leading to misjudgments.

[0004] Therefore, the analysis of local faults such as cable aging based on broadband impedance spectroscopy needs further research to improve the accuracy of fault detection and location. Summary of the Invention

[0005] The problem to be solved by the present invention is to provide a broadband impedance spectrum cable fault location method based on terminal function compensation, which can accurately determine the local soft fault type of the tested cable and realize the precise location of different fault locations, effectively improving the detection and positioning accuracy.

[0006] The present invention adopts the following technical solution: a broadband impedance spectrum cable fault location method based on terminal function compensation, comprising the following steps:

[0007] Step 1: Obtain the physical geometric parameters of the cable under test under the health standard, including: the radius r of the cable center conductor c , inner radius of cable shield r s , the total length L of the cable to be tested;

[0008] Step 2: Based on the coaxial transmission line distributed parameter model, the distributed parameters of the cable are modeled to obtain the distributed parameters of a healthy cable, including distributed resistance R, distributed inductance L, distributed capacitance C, and distributed conductance G. The admittance per unit length of each layer of the cable is calculated to obtain the total admittance of the N layers of insulating medium.

[0009] Step 3: Based on the microelement equivalent model of a healthy cable, determine the voltage and current partial differential equations under the health standard of the cable to be tested, calculate the general solution, and obtain the phase spectrum of the input impedance spectrum of the healthy cable head end based on transmission line theory;

[0010] Step 4: Use an impedance analyzer to measure the cable under test, obtain the input phase spectrum of the cable under test, and compare it with the phase spectrum of the input impedance spectrum of the healthy cable to determine whether there is a fault section in the cable under test.

[0011] Step 5: Establish an orthogonal integral function H1(x), select an orthogonal basis in the orthogonal integral function system to integrate the phase spectrum, and introduce a Gaussian smoothing function to eliminate ripples. Based on the orthogonal integral function, the maximum peak value caused by the impedance mismatch caused by the line end break is used to form a compensation function for compensation, and the final fault diagnosis function H(x) is obtained, thereby obtaining the fault information of the cable to be tested.

[0012] Preferably, in step 2, the distributed resistance R, distributed inductance L, distributed capacitance C, and distributed conductance G are calculated according to the micro-element distributed parameter model of the coaxial transmission line in the following manner:

[0013] When current is freely conducted in a conductor, it will be affected by the skin effect. The skin depth δ of the conductor decreases with increasing frequency, satisfying the following relationship:

[0014]

[0015] Where μ is the magnetic permeability of the metal. For copper and aluminum metal conductors, their magnetic permeability is the same as the vacuum permeability μ0. σ is the electrical conductivity. ω is the angular frequency, that is, the frequency f of the electromagnetic wave is converted into angular frequency, ω = 2πf, and the unit is rad / s.

[0016] Due to the magnetic flux between the conductors, the leaving and returning currents are also attracted to each other, which is called the proximity effect. The resistance per unit length of the cable, R(ω), can be approximated as:

[0017]

[0018] Where r c and r s is the phase cable conductor radius and the inner radius of the cable shield; δ c and δ s are the skin effect coefficients of the core wire and the metal shield respectively; σ c and σ s is the conductivity of the conductor and shield.

[0019] The self-inductance per unit length of coaxial cable L in It can be approximated as:

[0020]

[0021] Where μ0 is the magnetic permeability of vacuum.

[0022] The external inductance is derived directly by considering the enclosed magnetic flux Φ between the center conductor and the shield in the surface s, caused by the current through the center conductor I (using Ampere's law for the transverse magnetic field):

[0023]

[0024] Where B t is the transverse magnetic flux density.

[0025] In composite insulated cables, semiconducting layers are usually present between the insulation material and the two conductors (phase conductor and metallic shield), but since these layers have little effect on the magnetic field, their effect on inductance is negligible.

[0026] The external inductance per unit length parameter can be described as:

[0027]

[0028] Therefore, the distributed inductance per unit length of coaxial cable is:

[0029]

[0030] The distributed capacitance and distributed conductance correspond to the imaginary and real parts of the distributed admittance respectively:

[0031] C(ω)=imag(Y / ω) (2-7)

[0032] G(ω)=real(Y) (2-8)

[0033] Where Y is the distributed admittance, which is a function of frequency and is expressed as: Y(ω)=G(ω)+jωC(ω)

[0034] The admittance per unit length of each layer of cable is calculated as follows:

[0035]

[0036] Where Y i is the dielectric admittance of the i-th layer, ε(ω) is the complex dielectric constant of the composite insulating material, r i With r i+1 are the inner and outer radii of the i-th layer of medium respectively, jω is the combination of the imaginary unit and angular frequency in the complex function, and is the independent variable of the frequency domain angle analysis.

[0037] The total admittance of N layers of insulating medium is:

[0038]

[0039] The complex dielectric constant ε(ω) is obtained by fitting the Cole-Cole formula:

[0040]

[0041] Where A, B and p are fitting parameters.

[0042] Preferably, in step 3, a transmission line equation is constructed, and a partial differential equation is established for the infinitesimal cable distribution parameters based on the cable distribution parameters obtained in step 2. The voltage and current expressions to be solved are obtained by Kirchhoff's law:

[0043]

[0044] Taking the derivative of both sides of the equation, we can get:

[0045]

[0046] Where, They represent the current and voltage at point x in the cable, and dx represents the infinitesimal distance.

[0047] Before solving the voltage wave and current wave, it is necessary to clarify the concepts of propagation coefficient γ and characteristic impedance Z0. Both are determined by the material properties of the transmission line itself and are expressed as follows:

[0048]

[0049] Characteristic impedance reflects the dielectric properties of the material. When the incident signal passes through the interface of heterogeneous materials during propagation, signal reflection will occur, resulting in different reflected signals and input impedance.

[0050] The propagation coefficient γ=α+jβ, where α is the attenuation coefficient, which is used to characterize the amplitude attenuation characteristics of the voltage wave and the current wave; β=2π / λ is the phase constant, which is used to characterize the phase change characteristics of the voltage wave and the current wave.

[0051] λ is the wavelength of the electromagnetic wave, which depends on its frequency and the properties of the transmission material:

[0052]

[0053] Where c is the speed of light 3×10 8 m / s, ε r and μ r are the relative permittivity and relative permeability.

[0054] Substituting equation (3-3) into (3-2), the solution of the second-order differential equation can be obtained as:

[0055]

[0056] Where, They represent the values ​​of voltage in the forward and reverse directions respectively. By solving the transmission line equation and combining the boundary conditions, the voltage and current at any point on the transmission line can be determined.

[0057] In transmission line theory analysis, the origin of the spatial coordinate system is often taken to be located at the load, with the positive direction pointing to the power supply end. If x is the distance from the load end, then formula (3-5) can be expressed at the load end (x = 0) as:

[0058]

[0059] If the load impedance is Z L ,because Substituting (3-6) we get:

[0060]

[0061] Where, Γ L is the reflection coefficient at the load end, which is the ratio of the reflected voltage to the forward voltage. If the load is open, the reflection coefficient is a real number 1.0. If the reflection coefficient is -1.0, Γ L Substituting (3-5) we get:

[0062]

[0063] Based on the above formula, the input impedance at a distance x from the load end is:

[0064]

[0065] Where Z xThe impedance of the cable line at a distance x from the load end is the ratio of the voltage to the current flowing through this point. It is a function of the cable distribution parameters and the load reflection coefficient, and has nothing to do with the applied voltage and current. If x is equal to the total length of the cable, l, then the input impedance expression of the cable head end is:

[0066]

[0067] The formula in (3-10) is the input impedance spectrum Z of the healthy cable at the head end. inH .

[0068] Preferably, in step 4, the Kelvin measurement bridge fixture is connected to the core wire and shielding layer of the cable to be tested, and the frequency impedance analyzer is swept to obtain the input impedance spectrum Z of the first end of the cable to be tested. inD , based on the input impedance spectrum Z of the healthy cable obtained in step 3 inH and the cable Z measured by the instrument inD To make a difference comparison, |Z inH -Z inD | is not zero, it means that there is a fault in the cable under test.

[0069] Preferably, the diagnostic function H(x) established in step 5 is a function of the distance variable x, and when a fault occurs at one point, different mutation peaks will appear.

[0070] First, obtain the input impedance phase spectrum of the faulty cable head end, which is more sensitive to fault information, and use the phase spectrum Z of the faulty cable as the phaseP Take (f) as an example:

[0071] Z phaseP (f,l)=rad_deg[angle(Z inD )] (3-11)

[0072] The measured impedance Z of the faulty cable inD Contains the real and imaginary parts, angle(Z inD )for:

[0073]

[0074] Where rad_deg() is the operation of converting radians to degrees, imag() is the operation of taking the imaginary part of a complex number, and real() is the operation of taking the real part of a complex number.

[0075] Furthermore, an orthogonal basis in the orthogonal function system is selected to integrate the phase spectrum, and a Gaussian smoothing function is introduced to eliminate ripples:

[0076]

[0077] Where β is the phase constant, df is the infinitesimal frequency variable;

[0078] Gaussian filter function G(x,σ):

[0079]

[0080] Define Δx as the compensation variable:

[0081]

[0082] Where σ is the Gaussian smoothing factor, L is the length of the transmission line, and the extreme value and maximum value of the extraction function are: is the inverse positioning function, i.e. the distance l under the maximum value of the fault state, is the positioning function, that is, the distance l under the first extreme point.

[0083] Then we get the final fault diagnosis function:

[0084]

[0085] Furthermore, the final fault diagnosis function graph with respect to x is plotted, and the fault point corresponding to the extreme point of the mutation peak is observed. The type of fault is further judged by the polarity of the mutation peak. Among them, "minimum-maximum" is an aging fault, and the extreme point corresponds to the starting and ending position of the fault. "Maximum-minimum" is a local defect fault, and the extreme point corresponds to the starting and ending position of the fault.

[0086] The technical solution of the present invention further provides: an electronic device, comprising:

[0087] one or more processors;

[0088] a storage device having one or more programs stored thereon;

[0089] When the one or more programs are executed by the one or more processors, the one or more processors implement any of the above-mentioned broadband impedance spectrum cable fault location methods based on terminal function compensation.

[0090] The technical solution of the present invention also provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the program implements the steps of any of the above-mentioned methods for locating cable faults using broadband impedance spectrum based on terminal function compensation.

[0091] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0092] 1. The broadband impedance spectrum cable fault location method of the present invention uses the impedance phase spectrum to construct a fault location function and uses the terminal impedance mismatch to compensate for the location point in the location function. Compared with existing methods, it can more intuitively reflect the fault nature and fault degree of the fault point, while also compensating for certain positioning errors, making positioning more accurate.

[0093] 2. Compared with other methods that rely on a wider frequency sweep range to reduce positioning errors, the broadband impedance spectrum cable fault location method of the present invention uses a Gaussian smoothing function on the integration result to reduce the ripples in fault diagnosis through integral compensation. The curve remains smooth even in a narrow frequency sweep width, which will not cause misjudgment and greatly improve the accuracy of detection and positioning. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 This is a flowchart of the broadband impedance spectrum cable fault location method of the present invention;

[0095] Figure 2 These are the cross-section and physical geometric parameters of the cables measured in the present invention.

[0096] Figure 3 This is a diagram of the microelement distribution parameter model of the coaxial cable transmission line of the present invention;

[0097] Figure 4 This is a schematic diagram of the difference comparison between a healthy cable and an unknown cable in the present invention;

[0098] Figure 5 1 is a schematic diagram of the positioning effect of the traditional method in the embodiment;

[0099] Figure 6 3 is a schematic diagram comparing the positioning effects of the method proposed in the present invention and the traditional method in the embodiment. DETAILED DESCRIPTION

[0100] In order to make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions of the application are further elaborated in detail below with reference to the accompanying drawings. The described embodiments are only a part of the embodiments involved in the present invention. All non-innovative embodiments of other researchers in this field on this embodiment fall within the scope of protection of the present invention. At the same time, the step numbers in the embodiments of the present invention are only set for the convenience of explanation and description, and the order between the steps is not limited in any way. The execution order of each step in the embodiment can be adaptively adjusted according to the understanding of those skilled in the art.

[0101] In one embodiment of the present invention, a broadband impedance spectrum cable fault location method based on terminal function compensation is provided. Figure 1 The specific steps are as follows:

[0102] Step 1: Use a micrometer to measure the cross-sectional geometric parameters of the target cable for simulation research.

[0103] In this embodiment, taking a certain XLPE cable as an example, its corresponding parameters are as follows: Figure 2 As shown, the cable center conductor radius r c The inner radius of the cable shield is 3.5 mm. s The total length L of the cable to be tested is 100m.

[0104] Step 2: According to Figure 3 The infinitesimal distributed parameter model shown in the figure consists of four parts: distributed resistance R, distributed inductance L, distributed capacitance C, and distributed conductance G. The electrical connection diagram is shown in the figure. Figure 3 As shown, the respective calculation formulas are as follows:

[0105] Because current flows freely through a conductor, the current density near the surface is greater than that at the center. This phenomenon is known as the skin effect. This increases the inductance of the conductor in an AC circuit and reduces its conductivity.

[0106] The conductor skin depth δ decreases with increasing frequency, satisfying the following relationship:

[0107]

[0108] Among them, μ is the magnetic permeability of the metal. For copper and aluminum metal conductors, their magnetic permeability is the same as the vacuum permeability μ0. σ is the electrical conductivity. ω is the angular frequency, that is, the frequency f of the electromagnetic wave is converted into angular frequency, ω=2πf, and the unit is rad / s.

[0109] Due to the magnetic flux between the conductors, the outgoing and returning currents also attract each other, which is called the proximity effect. The current through the conductor is concentrated in the area determined by the skin depth. Therefore, due to the decrease in skin depth, the effective unit length resistance of the phase conductor and the metal screen will increase with increasing frequency. The resistance per unit length of the cable R can be approximated as:

[0110]

[0111] Where r c and r s is the phase cable conductor radius and the inner radius of the cable shield; δ c and δ s are the skin effect coefficients of the core wire and metal shield respectively; σ c and σ s is the conductivity of the conductor and shield.

[0112] The self-inductance per unit length of coaxial cable L in It can be approximated as:

[0113]

[0114] Where μ0 is the magnetic permeability of vacuum.

[0115] Furthermore, the external inductance can be derived directly by considering the enclosed magnetic flux Φ between the center conductor and the shield in the surface s, which is caused by the current through the center conductor I (using Ampere's law for the transverse magnetic field):

[0116]

[0117] Where B t is the transverse magnetic flux density.

[0118] In composite insulated cables, semiconducting layers are usually present between the insulation material and the two conductors (phase conductor and metal screen), but since these layers have little effect on the magnetic field, their effect on inductance is negligible.

[0119] The external inductance per unit length parameter can be described as:

[0120]

[0121] Therefore, the distributed inductance per unit length of coaxial cable is:

[0122]

[0123] Among them, the distributed capacitance and distributed conductance correspond to the imaginary part and real part of the distributed admittance respectively:

[0124] C(ω)=imag(Y / ω) (2-7)

[0125] G(ω)=real(Y) (2-8)

[0126] Where Y is the distributed admittance, which is a function of frequency and is expressed as: Y(ω)=G(ω)+jωC(ω).

[0127] The admittance per unit length of each layer of cable is calculated as follows:

[0128]

[0129] Where Y i is the dielectric admittance of the i-th layer, ε(ω) is the complex dielectric constant of the composite insulating material, r i With r i+1 are the inner and outer radii of the i-th layer of dielectric, respectively. The total admittance of N layers of insulating dielectric is:

[0130]

[0131] Where, the complex dielectric constant ε(ω) is obtained by fitting the Cole-Cole formula:

[0132]

[0133] Where A, B and p are fitting parameters.

[0134] In this embodiment, the fitting parameters of the cable at different aging degrees were obtained by consulting relevant literature. The specific parameters are shown in Table 1:

[0135] Table 1 Cable insulation aging fitting parameters

[0136]

[0137] Furthermore, in order to simulate local defect failures, the present embodiment defines a mathematical formula for cable distribution parameters under local damage:

[0138] Combined with the resistance formula under good condition, a shield layer damage coefficient K1 is added to the resistance of the corresponding shield layer. When local damage occurs, its value is greater than 1. At this time, the expression of distributed resistance is:

[0139]

[0140] When K1=1, it is the same as expression (2-2) for a normal healthy cable.

[0141] However, the distributed inductance at the damaged part includes the self-inductance of the core and shield, as well as their mutual inductance. The change in the shield's self-inductance is similar to resistance, and partial damage will cause its self-inductance to increase. After the shield is damaged, the magnetic field coupling between the core and shield becomes weaker, resulting in a decrease in mutual inductance. The distributed inductance at the damaged part is determined by the following formula:

[0142]

[0143] Where K2 is the mutual inductance damage coefficient. Its value is less than 1, which indicates that after the shielding layer is damaged, the magnetic field coupling between the core wire and the shielding layer is weakened, and the leakage magnetic flux increases.

[0144] When the insulation material at the damaged part is damaged, the shape of the insulation material will usually change. The overall distributed admittance of the damaged part is determined by the following formula:

[0145]

[0146] Where K3 is the insulation layer damage coefficient, which can be expressed as:

[0147]

[0148] Where, is the average effective thickness of the insulation structure. It can be seen that the damage coefficient is a value less than 1. The damage coefficients K1, K2 and K3 are directly related to the degree of local damage to the cable. The more serious the damage, the larger the damage coefficient K1, and the smaller K2 and K3.

[0149] Step 3: Based on the cable distribution parameters obtained in step 2, Figure 3 The partial differential equations are established based on the cable distribution parameters, and the voltage and current expressions are obtained from Kirchhoff's law:

[0150]

[0151] Taking the derivative of both sides of the equation, we can get:

[0152]

[0153] Before solving the voltage wave and current wave, it is necessary to clarify the concepts of propagation coefficient γ and characteristic impedance Z0. Both are determined by the material properties of the transmission line itself and are expressed as follows:

[0154]

[0155] Characteristic impedance reflects the dielectric properties of the material. When the incident signal passes through the interface of heterogeneous materials during propagation, signal reflection will occur, resulting in different reflected signals and input impedance.

[0156] The propagation coefficient γ = α + jβ, where α is the attenuation coefficient, which characterizes the amplitude attenuation characteristics of the voltage wave and the current wave; β = 2π / λ is the phase constant, which characterizes the phase change characteristics of the voltage wave and the current wave, where λ is the wavelength of the electromagnetic wave, which depends on its frequency and the properties of the transmission material.

[0157]

[0158] Where c is the speed of light 3×10 8 m / s, ε r and μ r are the relative permittivity and relative permeability.

[0159] Substituting equation (3-3) into equation (3-2), the solution of the second-order differential equation can be obtained as:

[0160]

[0161] By solving the transmission line equation and combining the boundary conditions, the voltage and current at any point on the transmission line can be determined. In transmission line theory analysis, the origin of the spatial coordinate system is often located at the load, with the positive direction pointing toward the power supply. If x is the distance from the load end, then formula (3-5) can be expressed at the load end (x = 0) as:

[0162]

[0163] If the load impedance is Z L ,because Substituting (3-6) into (3-6) yields:

[0164]

[0165] Where, Γ L is the reflection coefficient at the load end, which is the ratio of the reflected voltage to the forward voltage. If the load is open, the reflection coefficient is a real number 1.0. If the reflection coefficient is -1.0, Γ L Substituting (3-5) we get:

[0166]

[0167] Based on the above formula, the input impedance at a distance x from the load end is:

[0168]

[0169] Where Z x is the impedance of the cable line at a distance x from the load end. Its value is the ratio of the voltage and current flowing through this point. It is a function of the cable distribution parameters and the load reflection coefficient, and has nothing to do with the external voltage and current.

[0170] If x is equal to the total length of the cable l, then the input impedance expression of the cable head end is:

[0171]

[0172] The derivation of the input impedance calculation (3-10) at the beginning of the cable is based on differential analysis, which equates the line to distributed parameters. This allows the voltage and current at any point on the line to be calculated. This analysis method is not limited to medium and high frequency bands. At low frequencies, the propagation coefficient γ is very small, making γl→0. At this time, the cable input impedance is equal to the load impedance:

[0173]

[0174] When the frequency increases or the cable length becomes longer, the input impedance at the first end is increased by the exponential coefficient e -2γl Determined.

[0175] For cables, since their distributed parameters are frequency-dependent, the characteristic impedance Z0 and the propagation coefficient γ are both functions of frequency. Therefore, the impedance spectrum of the head end will also change with the change of the power supply frequency. The frequency variation curve of the head end impedance is called the broadband impedance spectrum of the cable. The broadband impedance spectrum can usually be divided into the impedance amplitude spectrum and the phase spectrum.

[0176] Step 4: Based on the input impedance spectrum Z of the healthy cable obtained in step 3 inH The fault cable Z measured by the instrument inD To make a difference comparison, such as Figure 4 As shown, there is a significant difference between the two, indicating that there is a fault.

[0177] Step 5: The diagnostic function H(x) established in this embodiment is a function of the distance variable x. When a fault occurs at one point, different mutation peaks will appear.

[0178] First, based on steps 2 and 3, the input impedance spectrum Z of a 100m long healthy cable head end is obtained. inH , assume that there is a fault section on the 100m cable as shown in Table 2 below.

[0179] Table 2 Fault model settings

[0180]

[0181] The diagnostic function image constructed by the traditional method is obtained through simulation. Figure 5 As shown in the figure, it can be seen that the positioning image of the traditional method has large ripples at the fault location, and except for the first fault point which is relatively accurate, the other fault points have offsets and errors.

[0182] Then, the diagnostic function method constructed in this embodiment is as follows:

[0183] Obtain the impedance phase spectrum that is more sensitive to fault information. In this embodiment, the phase spectrum Z of the faulty cable is used. phaseP Take (f) as an example:

[0184] Z phaseP (f,l)=rad_deg[angle(Z inD )] (3-20)

[0185] Furthermore, an orthogonal basis in the orthogonal function system is selected to integrate the phase spectrum, and a Gaussian smoothing function is introduced to eliminate ripples:

[0186]

[0187] Where, Gaussian filter function G(x,σ):

[0188]

[0189] Define Δx as the compensation variable:

[0190]

[0191] Wherein, angle is the phase angle of the impedance spectrum of the fault cable, rad_deg represents the conversion of radian to angle, and L is the length of the transmission line.

[0192] In this embodiment, sigma is a Gaussian smoothing factor, and is taken as 0.3, is the positioning inverse function, i.e., the distance l under the maximum value of the fault state, and by analogy is the positioning function, i.e., the distance l under the first extreme point.

[0193] Further, the final fault diagnosis function is obtained as follows:

[0194]

[0195] Further, in this embodiment, the cable fault diagnosis function image obtained based on the method of the present application is shown in FIG. 6. Figure 6 As shown in FIG. 6, compared with the traditional method, the positioning of the method of the present application is more accurate, the ripple effect caused by the fault is weakened, the possibility of misjudgment is reduced, and the type of the fault can be determined by the polarity of the mutation peak. The "minimum-maximum" is an aging fault, and the extreme point corresponds to the start and end positions of the fault. The "maximum-minimum" is a local defect fault, and the extreme point corresponds to the start and end positions of the fault.

[0196] In the embodiments of the present application, an electronic device is also provided, which includes one or more processors, a storage device having one or more programs stored thereon, and when the one or more programs are executed by the one or more processors, the one or more processors implement the wideband impedance spectrum cable fault positioning method based on end function compensation described in any of the above embodiments.

[0197] In the embodiments of the present application, a computer readable storage medium having a computer program stored thereon is also provided, and when the program is executed by a processor, the steps in the wideband impedance spectrum cable fault positioning method based on end function compensation in any of the above embodiments are implemented.

[0198] The above description is only the preferred embodiments of the present application, and it should be noted that for those skilled in the art, without departing from the principles of the present application, a number of improvements and refinements can be made, and these improvements and refinements should also be considered as the protection scope of the present application.

Claims

1. A broadband impedance spectrum cable fault location method based on terminal function compensation, characterized in that: The steps include: Step 1: Obtain the physical geometric parameters of the cable under test under the health standard, including: the radius of the cable center conductor, the inner radius of the cable shield, and the total length of the cable under test; Step 2: Based on the coaxial transmission line distributed parameter model, the distributed parameters of the cable are modeled to obtain the distributed parameters of a healthy cable, including distributed resistance, distributed inductance, distributed capacitance, and distributed conductance; the admittance per unit length of each layer of the cable is calculated to obtain the total admittance of the N layers of insulating medium; Step 3: Based on the microelement equivalent model of the healthy cable, determine the voltage and current partial differential equations under the health standard of the cable to be tested, calculate the general solution, and obtain the input impedance spectrum of the healthy cable head end according to the transmission line theory; Step 4: Use an impedance analyzer to measure the cable under test, obtain the input impedance spectrum of the cable under test, and compare it with the input impedance spectrum of the healthy cable to determine whether there is a fault section in the cable under test. Step 5: Establish an orthogonal integral function, select an orthogonal basis in the orthogonal integral function system to integrate the phase spectrum, and introduce a Gaussian smoothing function to eliminate ripples. Based on the orthogonal integral function, use the maximum peak value caused by the impedance mismatch caused by the line end disconnection to form a compensation function for compensation, and obtain the final fault diagnosis function, thereby obtaining the fault information of the cable under test; In step 5, obtain the fault cable impedance phase spectrum , the method is as follows: ， Where, is the measured impedance spectrum of the faulty cable, including real and imaginary parts; rad_deg represents the conversion of radians to degrees, and angle is the phase angle of the impedance spectrum of the faulty cable; ， in, To take the imaginary part of a complex number, is the operation of taking the real part of a complex number; Establish the orthogonal integral function H1(x): ， Where, is the Gaussian filter function, is the phase constant, is the infinitesimal element of the frequency independent variable; The Gaussian filter function is calculated as follows: ， Where, is the Gaussian smoothing factor; The compensation function is formed by using the maximum peak value caused by the impedance mismatch caused by the line end disconnection, and the extreme value and the maximum value of the function are extracted to compensate the orthogonal integral function H1(x). Define is the compensation variable, calculated as follows: ， in, is the transmission line length, is the inverse positioning function, which represents the distance under the maximum value of the fault state , To locate the inverse function, it represents the distance under the first extreme point ; In step 5, the final fault diagnosis function H(x) is a function of the distance variable x, which is expressed as follows: ， Drawing about The diagnostic function graph is used to observe the fault point corresponding to the extreme value of the mutation peak and determine the fault type by the polarity of the mutation peak. "Minimum-maximum" indicates an aging fault, and "maximum-minimum" indicates a local defect fault. The extreme value points correspond to the starting and ending positions of the fault.

2. The broadband impedance spectrum cable fault location method based on terminal function compensation according to claim 1 is characterized in that: In step 2, in the coaxial transmission line distributed parameter model, the distributed parameters of each section of the transmission line include: distributed resistance , distributed inductance , distributed conductivity and distributed capacitance , solve the distribution parameters of the healthy cable as follows: Step 2.

1. Calculate the resistance per unit length of the cable , which is approximately: ， Where, and is the phase cable conductor radius and the inner radius of the cable shield; and are the skin effect coefficients of the core wire and the metal shield respectively; and is the conductivity of the conductor and shield; Step 2.2: Calculate the self-inductance per unit length of the coaxial cable , which is approximately: ， Where, is the vacuum permeability; Step 2.3: Calculate the distributed inductance per unit length of the coaxial cable , the formula is: ， Where, is the external inductance per unit length parameter.

3. The broadband impedance spectrum cable fault location method based on terminal function compensation according to claim 2 is characterized in that: In step 2, the admittance per unit length of each layer of the cable is calculated: ， Where, is the admittance of the i-th layer medium, is the complex dielectric constant of the composite insulating material, and are the inner and outer radii of the i-th layer of medium respectively; The combination of imaginary unit and angular frequency in complex function is the independent variable of frequency domain angle analysis; Total admittance with N layers of insulating medium for: ， Where, 、 are the imaginary and real parts of the distributed admittance corresponding to the distributed capacitance and distributed conductance.

4. The broadband impedance spectrum cable fault location method based on terminal function compensation according to claim 3 is characterized in that: In step 3, based on the microelement equivalent model of the healthy cable, the voltage and current partial differential equations under the target cable health standard are determined, and the general solution is calculated as follows: Step 3.1: Based on Kirchhoff's law, construct the transmission line equation and obtain the voltage and current partial differential equations: ， Taking the derivative of both sides of the equation, we get: ， Where, 、 They represent the current and voltage at point x of the cable, respectively, and dx represents the infinitesimal distance; Step 3.2: Introduce propagation coefficient and characteristic impedance , we get the voltage and current expressions: ， Where, 、 Represent the values ​​of voltage in forward and reverse propagation respectively; by solving the transmission line equation and combining the boundary conditions, the voltage and current at any point of the transmission line are determined; Step 3.3: Based on the transmission line theory, take the origin of the space coordinate system at the load, with the positive direction pointing to the power supply end. If x is the distance from the load end, at x=0 at the load end, the voltage , current It is expressed as follows: ， Step 3.4, the load impedance is ,because , substituting into the formula in step 3.3, we get: ， Where, is the reflection coefficient at the load end, which is the ratio of the reflected voltage to the forward voltage; Step 3.5, Substituting the formula in step 3.2, we get: ， Step 3.6: The input impedance at a distance x from the load terminal is the ratio of the voltage to the current flowing through point x: ， Where, is the impedance of the cable line at a distance x from the load end, expressed as a function of the cable distribution parameters and the load reflection coefficient, and has nothing to do with the applied voltage and current; Step 3.7: When x is equal to the total length of the cable When the input impedance of the healthy cable head end is , which is expressed as follows: 。 5. The broadband impedance spectrum cable fault location method based on terminal function compensation according to claim 4 is characterized in that: In step 4, connect the Kelvin bridge fixture to the core wire and shield of the cable to be tested, and sweep the impedance analyzer to obtain the input impedance spectrum of the cable to be tested. , and subtract the impedance spectrum of the healthy cable head end obtained in step 3 to determine whether the impedance spectrum is consistent. If it is consistent, there is no fault in the cable under test; if it is inconsistent, there is a fault section in the cable under test.

6. An electronic device, characterized in that: include: one or more processors; a storage device having one or more programs stored thereon; When the one or more programs are executed by the one or more processors, the one or more processors implement the broadband impedance spectroscopy cable fault location method based on terminal function compensation as described in any one of claims 1 to 5.

7. A computer-readable storage medium, characterized in that A computer program is stored thereon, and when the program is executed by a processor, the steps of the broadband impedance spectrum cable fault location method based on terminal function compensation according to any one of claims 1 to 5 are implemented.

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